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Hoeeee: Pte bebmisie tenes viateie)eopeg atopy Py ps 6 . hey me PY ete r Vehafe Prerey Trebetelesistoarieinghy eg tot site fer PPPs tmefmtng. 4 fi Vte8 Veh fetoicgey hebejar, faletepate eb Me tehepe pe yys ee bebepiany Ve bets pe pete edo hodng Vet het sy. 44 tm Veto e SN PP pete pete Veh i Rbefoyand: “ 1OHM/ Taw GEOPHYSICAL EXPLORATION PRENTICE-HALL GEOLOGY SERIES Epitep by Norman E.A. HINDs GEOPHYSICAL ExpLoraTion, by C. A. Heiland SEDIMENTATION, by Gustavus E. Anderson STRENGTH AND STRUCTURE OF THE HEARTH, by Reginald Aldworth Daly GEOPHYSICAL EXPLORATION By C. A. HEILAND, Sc.D. Professor of Geophysics Colorado School of Mines New York PRENTICE-HALL, INC. 1946 CopyRiGcHtT, 1940, By PRENTICE-HALL, INC. 70 Firta AVENUE, NEw YorREK ALL RIGHTS RESERVED. NO PART OF THIS BOOK MAY BE REPRODUCED IN ANY FORM, BY MIMEOGRAPH OR ANY OTHER MEANS, WITHOUT PERMISSION IN WRITING FROM THE PUBLISHERS. First Printing, sas sen October, 1940 Second Printing. ..0. 9: October, 1946 PRINTED IN THE UNITED 8TATES OF AMERICA PREFACE "Luts Book is intended as a comprehensive survey of the entire field of geophysical exploration. The author has endeavored to present the subject in broad perspective, emphasizing the relations, differences, com- mon features, and, above all, the fundamentals of geophysical methods. The material is divided into two parts of six chapters each. The first part, written in elementary language, addresses those desiring an insight into the working principles and geological applications of geophysical methods. It is intended for individuals in executive and geologic advisory capacity and for persons not directly concerned with field or laboratory operations. The second and major portion is written for the technical student of geophysics. It presents the subject from an engineering point of view, striving at a balanced discussion of theory, field technique, laboratory procedure, and geological interpretations. The author has aimed at a presentation that will enable the geophysicist to get an insight into the geologist’s reasoning in selecting geophysical methods and in interpreting geophysical data, and that will acquaint the geologist with the mathematic. cal and physical approach to instrument and interpretation problems. Certain compromises were unavoidable if a volume of practical size was to be arrived at. It is not possible to cover the ground in such detail as a specialist, working with a particular method, may deem advisable. Geophysical exploration changes rapidly; processes once in the limelight have been discarded; others, seemingly forgotten, have been revived. In this book the fundamental or methodical significance of a given method is its chief criterion for inclusion. This has been followed even at the risk of describing “‘older’’ methods. Field, office, and laboratory procedures are so changeable and so subject to personal preferences that the discussion of such procedures is confined to a few examples illustrative of method but not of detail. Since there is a limit to the number of geophysical surveys that can be illustrated, a choice was made on the basis of distinctness of response to subsurface conditions, and not on the basis of survey date. The necessity for elementary treatment has occasioned a certain breadth in the mathematical discussions, possibly at the expense of rigor and elegance. In many cases formulas are given without derivation. The Vi; vi PREFACE description of procedures and instruments used in geophysical science is limited to those having a direct bearing on geophysical exploration. A chapter on the history of geophysical exploration was abandoned in favor of a few historical references. The material is arranged in methodical rather than historical order. A table of symbols precedes each major chapter dealing with methods that represent a geophysical entity. This applies to gravitational, mag- netic, seismic, and electrical methods (Chapters 7 through 10). In these chapters the discussion follows a uniform plan. First is an outline of fundamentals, followed by a description of rock properties and rock-testing methods. Instruments and instrument theory, as well as corrections and interfering factors, are reviewed next. The treatment is concluded in each case with a derivation of the fundamental interpretation equations and a description of surveys made on known geologic conditions. Various individuals and organizations have assisted in the preparation of this book. Specific acknowledgment is made on the following page. C. A. HEILAND ACKNOWLEDGMENTS Ir 1s 4 PLEASURE to acknowledge the assistance of a number of individuals and organizations. Professor Perry Byerly reviewed the entire manu- script; Doctor M. M. Slotnick and Mr. H. Guyod read several chapters and made valuable suggestions. Dr. R. F. Aldredge contributed diagrams on curved-ray interpretation; Mr. Charles Erdmann supplied values of rock resistivities for Colorado, Wyoming, and Montana; and Mr. Dart Wantland supervised compilations of densities, and magnetic and elastic rock properties by students of the Colorado School of Mines. Permission to use material from their publications was granted by the American Institute of Mining-and Metallurgical Engineers, the Akademische Ver- lagsgesellschaft, the American Petroleum Institute, the American Asso- ciation of Petroleum Geologists, the Society of Exploration Geophysicists, and a number of other institutions and publishing houses. Specific reference to source for such illustrations will be found in footnote references in the text. A number of illustrations are reproduced by courtesy of the following companies and institutions: American Askania Corporation Cambridge Instrument Company Colorado School of Mines Geo. E. Failing Supply Company Heiland Research Corporation Harvey Radio Laboratories, Inc. James G. Biddle Company Seismos Company Texas Body and Trailer Company U. S. Bureau of Mines U. S. Bureau of Standards U. 8. Coast and Geodetic Survey U.S. Geological Survey Messrs. M. P. Capp and A. N. McDowell made most of the line drawings, and Miss Johanna Lyon assisted in the preparation and indexing of the manuscript. CxA. HH: eae CONTENTS PART I CHAPTER PAGH AMRUNTRODUCTION iets stars, Shibe co MA Ses ahs cle doen MeN Ren aoe RIDIN AS caer 3 I. Significance of Geophysical Exploration.......................... 3 II. Geophysics as a Tool for Determining Geologic Structure; Excep- tions-\indirect) Mineral Location. o\g).s05 00% qc yon te 2 ae 4 III. Major Fields of Geophysical Exploration...... COR CMG Ryo aa aa 5 2. METHODS OF GEOPHYSICAL HXPLORATION.................--.. 7 Ja) OPE RCEL TCE) tga eet Hea, SUID RR ch GR A EN fe Ae MORE 7 MeO ravityvaNiet nods: fen. a ent uimen SPM Ny Ane RMN Rha el 9 ee NagnieticoVethoased ce ic he ys tans RC cpremen estan inaier ait 16 PV SCISIICIVICEHOGS co sec ae CeO ee Pinto Shima ty HAMDEN: 19 WenilecEriCAalMNIGEHOGS se le tee Sie ete are tN MN MCCUE Lar 25 WalenGeophysrcaleWellwhesting: = 2.0 in. Sue rN mnt NE ease LNs 2 | 33 VII. Miscellaneous Geophysical Methods.....:........5............... 35 3. MEASUREMENT PROCEDURES IN GEOPHYSICAL EXPLORATION..... 38 I. Significance and Measurement of Physical Quantities Involved.... 38 II. Arrangement of Observation Points with Relation to Geologic Objects. 3s) HG AE RD, GRE RG MCENROE. 41 4. GEOPHYSICAL METHODS IN OIL EXPLORATION...............--- 43 5. GEOPHYSICAL METHODS IN MINING..............-..+-0-0++055 . 49 AemNetaly Nitin 2th. Se ees di GaN ltaarih oe? iat Soe Hesen tEBA a 49 Ee Mining. of, Nonmetallits: <4 gous 2h ease hae as oan Pane Say 52 A. Coal, Including Anthracite and Lignite....................... 53 Sar Str ete A a acre a ime oA elles Mike Lela Li a SERRA at 53 CRISTEA EAR VE a NN Cm eR a Sea TAN YA Ai ER 54 D. Nitrates “Phosphates, Potash..06 jo deceee) oie ees 2 dal 54 EeBuildingvandykoad Materials.) uj f ums tat a eto el iets 54 EWA TAS UVEB ECON cteaat teddy hale! Cencetir. a suhd N e ei MPa re 55 G. Materials for Various Industrial Uses.......................-.- 55 Hi. ‘Gems: and) Precious Stones ei: of. = 5 be orci peeves aieteetos = Sie scr4s 56 6. APPLICATIONS OF GEOPHYSICS IN ENGINEERING................ 57 ie Geological Applications. Hen eg ae alealt 57 AER OUNG AON Problema sinc ccge ed ites sits ited cel aia se aueta 57 B. Location of Construction Materials....................200-06- 60 CUUILOCACLON Gl WALOT ec career a MIU 2 ata SPNaat ny Stiga 60 II. Nongeological Applications....... Pisa siege Me UNS EMMA IO ae Bi 62 A. Dynamic Vibration Tests of Structures.....................-.. 62 SEPA GAURINE 8 PhO tuo ie Mab ili cs Me clel Sees nivale til 62 ix CONTENTS x CHAPTER PAGH 6. APPLICATIONS OF GEOPHYSICS IN ENGINEERING (Cont.) Gy Corrosion Surveys cee ick Jc oscaed ee Oe 63 DP: }Pipe and Metal’ location”... J... 028. 2-20-.oe eee 63 E. Sound Ranging and Other Acoustic Detection Methods........ 63 F. GastDetection cee ha 2 Pa ae i 64 GThermal Detection: :...2. 305.2 ges kee eee 64 PART II 7. GRAVITATIONAL METHODS... 5 .)6 50. cee > 2 ee Sea 67 I’ Introduction.6-13 ee ee en a 67 Il: Rock: Densities: 2. xc cs soe cd aise hole on ae 70 A. Determination of Rock Densities......................2+20-05- 70 B. Factors Affecting Formation Densities.......................- i2 C. Tabulations of Mineral and Rock Densities.................-. 77 III. Gravitational Constant; Gravity Compensator; Gravity Multi- DUCA COR 05 ages Mes gia hc Rn Pe acon 85 IV. Principles of Gravitation as Applied in Gravity Measurements...... 88 V. Pendulum and Gravimeter Methods......................--20-+ 97 A. Theory of the Pendulum on Fixed and Moving Support........ 97 B. Observation and Recording Methods; Pendulum Apparatus.... 103 C. Time-Determination and Time-Signal-Transmission Methods... 113 D. Instrument Corrections in Pendulum Observations............ 116 BE (Gravimeterss 65.) ss dee eat aw 0 st ee eee 123 F. Corrections on Observed Gravity Values....................-. 135 G. Theory of Subsurface Effects; Methods of Interpretation...... 143 H. Results of Pendulum and Gravimeter Surveys................. 157 VI. Time Variations of the Gravitational Field....................... 162 A. Planetary (Lunar) Variations. .(..........4-..-- 4: - ose ee eee 163 B. Secular (Geologic) Variations.........:...........4.)2 52 165 C. Changes in Water Level (Tides and the Like)................. 165 D. Artificial Mass Displacements (Mining Operations) and the Tike a oes ha a Nc BR 167 VII. Determination of the Deflections of the Vertical.................. 167 VIII: ‘Torsion-Balance Methods...'0) 202s. eee 170 A. Quantities Measured; Space Geometry of Equipotential Surfaceseis.c05.0. s7 09 ace’ « Daa oe. ee ee 170 Bs Theory of ‘Torsion Balances). 9-05.00 6) eee eee 175 C. Instrument Types, Instrument Constants..................... 192 D. Corrections}. jcc.c.teocte foes: one we ee 210 E. Graphical Representation of Torsion Balance Data............ 244 F. Theory of Subsurface Effects, Interpretation Methods......... 250 G. Discussion of Torsion Balance Results.................-....-- 270 8. MAGNETICMETHOD 000000. 2 Ws ee oe eee 293 T. Introduction oi 0y ccc Sie eis ao ae eee ae en ae 293 Il: Magnetic = Rock-Properties: 0-5. 1-5 a0) ee ee eee 297 Ac Dhimmi tions. bose ake Cry NCS Ae nas en eee rer 297 B. Methods of Determining Rock Magnetization................. 299 C. Numerical Data on Magnetic Properties of Minerals and Rocks.. 309 D. Factors Affecting Rock Magnetization.......................4 314 CONTENTS x1 CHAPTER PAGE 8. Macnetic MetuHop (Cont.) hie Mneneticy nstrumentaeeery i.e a Nena OE I 318 Ae Construction Principles. aii hunhin yee bmi ON Te 318 iB. y Prospecting Magnetometerss 2.4.0) eg ote tbt als folate ove as 321 C. Instruments for Regional Magnetic Surveys................... 355 beeObservatory, Instruments) 0.0... 6. oo.) saa ee ees 366 VIREO OTRECEIONS eh sete Veto moe Once cic 5. BR hi Oe 366 Aca Memperat ures. sits mene ec ns. oe, EEN el oT 366 Bus Magnetics ariatiOns)..0. ee ee ee oes eee Maree canoe dic 367 @uePlanetary.VariatiOm.4ya) cae rec oo eT ene Se 372 D. Base Change............. Bena 28) Sh, ANN RR i ane a! 372 E. Influence of Iron and Steel Objects........................... 373 Pee herrainpAnomaliestiy ten s)he eee RE Roe 375 Gey Normally biel awd iver ota ith Pairs e hk) aa ee Sa ik Se: 377 V. Magnetic Fields of Subsurface Bodies (Interpretation Theory).... 377 A. Graphical Representation of Results.......................... 377 B. Qualitative and Quantitative Analysis........................ 380 CxePolerand line Mheory ss is 6 ah ks Gig 381 Derinduetion-“Mbearys tases et kere ee ky oe 389 E. Interpretation Theory Based on Both Permanent and Induced Magnetization tite: 615 lito: Bek ye MOPARS RR MON Yer 400 F. Model Experiments in Magnetic Interpretation................ 402 G. Underground, Aerial, and Platform Surveys................... 404 WilsMagnetio Surveysinn ces) sc Pia eer Me smelted fede te 408 AS Magnetic Surveys ini Mining? .0)2)/e ose Wm eo 409 B. Magnetic Surveys in Oil Exploration.......................... 422 C. Magnetic Surveys in Civil and Military Engineering........... 433 CRE IS RTG™ Ve THODES «4.5015 Mil a wine a eee ae eAcame ces oats 4 SS 437 EN CROCUCEI ONS co.) vid theca ace en a es Ry Sa ORG OR ARCO, 437 II. Physical Rock Properties in Seismic Exploration; Selected Topics IIT. IV. on the Theory of Elastic Deformations and Wave Propagation... 441 Generals: 2. s2c:- tiene or eee pe RA IRE kine Bass Fon 441 B. Elements of Theory of Elastic Deformation and Wave Propa- (ELOY | aesear m ae ES RIE E, ec tae Covrnk Akh, rc an ea 442 C. Laboratory and Field Methods for the Determination of Elastic Modulivand) Wave: Velocities.....2) tian Mileetn es. ices. 452 D. Factors Affecting Elastic Properties of Rocks................. 474 E. Physical Rock Properties Related to Seismic Intensity........ 477 Methods of Seismic i’rospecting..................0000 cece eee ues 483 A. Technique of Shooting; Shot Instant Transmission; Review of SeismicH Methods. smacks nit eh rs PRIN Med oe 483 Be eban-Shooting Method: =).0.02) Yen ee ie ads 499 CrpRetraction. Methodsir 450s...) ee ee nee eonibetoe ae. ne! 504 iDeRetections Methods lei). 25 ee seis ahleem ew MR A os 549 Elementary Theory and Description of Seismographs............. 579 ABAGIAaRIneAtIOnU Nei taht alc.) Bek Va, oe aioe REL 579 Ba elementary seheorymen neni) ak kd weil (kk a i 8 Bee) 580 Cy. ThemMechanical/Seismopraph Mie) iis. Usk A leas k 591 D. The Electromagnetic Séismograph........................2.055 592 E. Review of Prospecting Seismographs.......................-.. 607 xii CONTENTS CHAPTER PAGE 9. Seismic Metuops (Cont.) F. Photographic Recording; Time Marking....................... 614 G. ‘Calibration. of Seismographs.. 0.4000. ee ieee cee 615 10°: HERECPRICAL METHODS. ic %)0 cco selec, cin dle Ghetedsereeicee hee eae 619 1, Introduction. (22 uk so lace ee cee age oe 619 A. Fundamentals: yQ" 27 ue ey ea a) er 619 B. Classification of Plectrical Methods.............0:4./:....2808 624 II. Electrical Propertiesjof Rocks. \...0." in 542 8 ee 628 A. ElectrochemicaliProperties: (2. 4.05 «asain ee eee 628 B. Metallic and Electrolytic Current Conduction................. 632 GC» Dielectric, Current Conduction. & 3.4..4-1. 9. 24050 eae 640 D. The Effects of Magnetic Permeability......................... 642 I). Methods for the Determination of Rock Resistivity............. 642 F. Methods for the Determination of Dielectric Constants........ 649 G. Resistivities and Dielectric Constants of Minerals, Ores, Rocks, and: Formations i: s.é-aeks iiatees aindehl nk a) oe ihe eee 656 LIL JSelf-Potential Method)... 2448.04: dea ee Re 667 Ai 'General. sits Meee, cae’ ee ae DS Ee 667 B. Equipment; Electrodes; Surveying Procedure.................. 669 C: ‘Interpretation... Beye ee, he ee 671 De }Gorrectione'ss «cei oie eels wielded each ct ge eld teen ee 675 We! Results...) puointek | hed er cae a Re 4 nls er 675 IV. Equipotential-Line and Potential-Profile Methods....... ......... 681 A. ‘Conditions in Stationary Mieldsaqj. 4. 4-0 aise eee ee 681 B. Conditions for A.C: Bields4ct ve. «72.4 oe a 685 C., ‘Field Procedure;.Equipment. 4/42 4.0) >be cue eee 692 iD) siniterpretationie: 22.0 a ix $) Sud Aas aes oh pe 697 E. ‘Discussion of Results: 05. ..4 14.04 ,.000-0: Ae 703 Vi Resistivity: Methods: 0 .).s Gos6 0 sen. een ns 707 ps \is © 729 12) of: Me ero Se oe PORE TN RT TTA ee EE LIA REET A of 56 So 5 3 « 707 Bi Electrode Arrangements: (24. 2.42.2 1 aa ee 709 C.. Potential Functions for Layered Media:-:.... .1.9904-.ee eee Wel PD Procedures.quipment....... hae Bee fe ee eee 723 E. Interpretationin 2 Wha.cer sock eon pee se ee ae 127 F. Results Obtained by Resistivity Surveying.................... (aa G. Blettrical: Logging. oa 0Wb Vee ae bre eee 744 V1.: Potential-Drop=Ratio Methods!) a) s295. 2205.4 ee ee ee 744 A Generali: 4 i)ai:3h 23, sens ee Eh 744 Be PHeOry is | ens ek eels «ed Re i ere i a 745 Ce EquipmentsProcedureize. 14:4: on ee eee eee t52 D.. Results... 0.42), als eS VII. Electrical Transient (“‘Eltran’”’) Methods) *<. 4.22.2. es) eee 757 VIIT:, Electromagnetic: Methods:.3.0. 45. 25) See ee 763 A. Electromagnetic Methods with Galvanic Power Supply........ 764 B. Electromagnetic Methods with Inductive Power Supply....... 773 IX. Radio, Methods: )t)5.4 pasos Oks as ee 809 A General oii Ue oS RE Ae ey Mi I a 809 B. Transmission Measurements: sive once ty ae ere 812 C. Field-Strength Measurements. .....0...0..0...00...00.....00.. Bee oy 15) CONTENTS xiil CHAPTER PAGH 10. EvecrricaAL Mrtruops (Cont.) Nem hreasurevand: Lipeshindersieens yr aah ok em as de 818 A. Treasure and Pipe Finders with Separate Excitation........... 818 Ben (Self-Contained) Treasure Winders .2 5... 8). 819 Mes HOPEYSICAL, WELE CESTING.(20)os sci ( eee aee os en by we ea es 825 mMlectriesl AsomoIne jc eel eee edt ty teaming Me 825 A. Determination of Resistance or Impedance of Formations..... 825 B. Determination of Spontaneous Potentials (Porosities)......... 831 C. Determination of Resistance of Drilling Mud.................. 8384 DriMeasurement of Dip andistrike sy 0.40544 yee ean ae 834 Fea Determinationiot Casing Depth, 2). 42f2. a. loot sesh eee 835 HASDISCUSSIONVOL. NeSUItS: .,.5.ch nue cee eee aie aie, e ep een ene 835 iieewemperature Measurements... 9.050208. ose Zoe ee ea 837 AEA DALATUS: EnOCeGUTE:.” 3} / Jails at Ne ees) Pee lc ar nae 840 Bathe Umyersal Geothermal Gradient, 8 0 4ees a 845 @ydhermal Properties: Of ROCKS +10) 400s) een omed la) GUNN 847 D. Heat Generating Processes; Causes of Transient Temperatures. 853 E. Effect of Surface Relief and Surface Temperature............. 860 HUM Sersmre Measirements )... 0.50.02 ose a) Ot ee ct ln 862 We Miscellaneous Measurementsin*Wells.:..2.0:.3. 2:8... tc. 3 863 Ae Determinationcol Radioactivity .osoeia seen. a a8hl |. nen 863 Bay vagnetie Measurements... .:, ). Rese te hehe a TN 865 @aeNcoustic: Measurements uc ae A eo eg ea 866 1). Fluid-Level Measurements by Sound Reflection............... 867 I). High-Frequency Measurements in Open Holes................. 867 [fret (GUE Des yc 0) 1 ag RR RCE APs ie ee a TOU eR 868 Gralhotoeleetric Measurements tap. dae pci. boo ol ae oe ee 869 ier srde-Wall- sampler Bulletswar. sere tent lee kes coke eters cee 869 12. MiscELLANEOUS GEOPHYSICAL METHODS...................... 870 Wektadioactivity Measurements ene oem oe Pei il 870 che CHEF 0 2h RMR SOAR SOS NY EIGN 7 a ae Re a 870 BoyRadioaativity of Rocks.) ven, wie eee dle a anise 873 C. Instruments and Procedure in Radioactivity Exploration...... 878 D. Results and Interpretation of Radioactivity Measurements.... 883 Me ity droearvon.(soi! and Gas) Amnalysishusaneulcc cacodasees tek 885 A. Macroscopic and Microscopic Methods........................ 886 B. Significant Hydrocarbons; Occurrence...................2..... 888 | CiaGas-Detection I Methods:aiii-—eee emetic Grimes Ohst GN ll: 892 DU SOU YAUTA SI Siue ceed yk h a e024 Man pe Menta rac in TKE 7) w te ei 898 E. Interpretation and Results of Gas and Soil Analysis........... 902 III. Vibration Recording, Dynamic Testing, and Strain Gauging...... 910 A. Vibration Recording (Free Vibrations)..:...................-- 912 aeD Hamar HRes time sit ) ib) MUN Summa onus 173 9) ign Bie eee oa op 914 CO TAT Greauigi nig ie wey i's oe tec UR RANT reat ake AN ON Sah 928 RVPAC OLISHIC VIEL OOS) iis nbc: Sita iis Ae uence yn et) nels Sal oR 934 AGH Atmosphere Acoustic Methodsy.) 0... ade se he nies 935 Be Marine AcouspicoMiethods: ni vara eet ca! 943 C. Geoacoustic Methods.............. Gi el SG, aD Pie ets aR op caeRE eTA 956 ES PDPODSG DS ANd “HRB tag sn). Saito HUM PR Bae Gal od Oba MU a aga ER pe RE ALN 965 PART I I INTRODUCTION I. SIGNIFICANCE OF GEOPHYSICAL EXPLORATION GEOPHYSICAL EXPLORATION may be defined as prospecting for mineral deposits and geologic structure by surface measurement of physical quantities. Geophysical exploration does not rely on magic or on any other super- natural procedure. It makes use of phenomena which can be interpreted fully through the fundamental laws of physics, measured, and verified by anyone as long as suitable instruments are used. A psychological reaction of the individual does not enter. Therein lies the difference between geophysical exploration and the ‘‘divining rod’”’ whose scientific merits have never been established. There may be persons who can “sense” the presence of subsurface geologic anomalies; however, if they are so distinguished, they should have no need to surround their ability with a veil of mysterious devices. Experience has shown that the divin- ing rod, contrary to geophysical instruments, will rarely give identical in- dications at the same place or for different operators. Geophysical exploration may be considered an application of the prin- ciples of geophysics to geological exploration. Derived from the Greek # yn and % gto.s, the word geophysics means “physics” or ‘‘nature’”’ of the earth. It deals with the composition and physical phenomena of the earth and its liquid and gaseous envelopes; it embraces the study of terrestrial magnetism, atmospheric electricity, and gravity; and it includes seismology, voleanology, oceanography, meteorology, and related sciences. The foundation to the development of most geophysical exploration methods was laid by geophysical science. In the past century systematic efforts were begun in all parts of the world to study earth’s phenomena, such as gravity, magnetism, earthquakes, and volcanism. Such studies were expected to give information in regard to the constitution of the earth’s interior. Magnetic and gravitational surveys were organized by government and state agencies, and observatories for recording meteoro- logic, oceanographic, and earthquake phenomena were established. Practically every geophysical exploration method has been developed 3 4 INTRODUCTION [CHap. 1 from corresponding procedures in geophysical science. While the objects of these earlier studies were the broad regional features, present geophysical methods aim at the location of local geologic structures and mineral de- posits. This development resulted from a substantial increase in accuracy and reliability of field methods. It has been coincident with the advances made in physics generally and in electricity in particular and received its impetus from the need for raw materials during and after the World War. Geophysical exploration may be called the application of the principles of geophysical sczence to (commercial) problems of smaller geoiogic scale. Experience has demonstrated that most subsurface structures and mineral deposits can be located, provided that detectable differences in physical properties exist. The main properties exhibited by the more common rocks and formations are: density, magnetism, elasticity, and electrical conductinty. “This entails four major geophysical methods: gravitational, magnetic, seismic, and electrical. II. GEOPHYSICS AS A TOOL FOR DETERMINING GEOLOGIC STRUCTURE; EXCEPTIONS; INDIRECT MINERAL LOCATION The first objective of geophysical exploration is the location of geologic structures; as a rule, information regarding the occurrence of specific minerals is obtained only in an indirect manner. The geophysicist measures, at the earth’s surface, anomalies in physical forces which must be interpreted in terms of subsurface geology. In many cases he has to be content with a general statement that a given area is structurally high or low (as in oil exploration), or that a zone of good or poor conductivity exists (as in mining). In some instances, how- ever, an appreciation of the geologic possibilities and a background of experience obtained by working in similar areas makes it possible to in- terpret surface anomalies more specifically. Assume, for example, that an iron ore deposit has been traced by magnetic instruments. When surveying adjacent properties, one would, therefore, be justified in attribut- ing large magnetic anomalies to the same ore. In a different area, how- ever, large magnetic anomalies may result from entirely different geologic bodies, such as intrusions of igneous rocks or contact-metamorphic zones. Other definite geophysical indications are: gravity minima on salt domes, magnetic highs on basement uplifts, seismic refraction travel-time curves typical of salt domes, electrical indications characteristic of sulfide ore bodies, and so on. In such cases interpretation of findings in terms of definite mineral deposits has been very successful. On the other hand, a geophysicist unacquainted with geologic possibilities may carry interpre- Cuap. 1] INTRODUCTION 9) tative analogies too far into unknown territory. Failures resulting from such procedure are forceful reminders that geophysics does not locate specific deposits, but furnishes only a physical indication which must be interpreted conservatively in geologic terms. In this connection a word may be said about the present status and future possibilities of methods for direct location of oil, gold, or water. At present there is no established direct means for finding oil; it is located indirectly by mapping geologic structures which, from experience, are ex- pected to be favorable for the accumulation of oil. Gold in placer chan- nels may be located indirectly by tracing magnetic black sand concentra- tions, provided that the geologic association of gold with black sand has been established. Water is difficult to locate; the indications require careful interpretation in the light of the electrical characteristics and dis- position of near-surface beds. On the other hand, recent developments along the line of direct methods indicate definite possibilities. The best chances for direct oil location are in the fields of electrical prospecting and soil and gas analysis. Electrical induction methods show promise of suc- cess in locating placer gold concentrations and water. As indicated above, the greater number of applications of geophysical methods are of an indirect nature. If a mineral, rock, or formation does not have any distinguishing physical properties, another mineral or geologic body may be utilized which has such properties and bears a known rela- tion to the ineffective body. The location of oil by the mapping of struc- tures which provide a trap for oil (anticlines, salt domes, faults, and buried hills), and the location of ore bodies by determining associated structure are examples of indirect procedure. III. MAJOR FIELDS OF GEOPHYSICAL EXPLORATION Since geophysical exploration is the determination of subsurface geologic structure by means of surface physical measurements, it is applicable in industrial fields where a knowledge of geologic conditions is essential. It is understood that such applications are advisable only where structures and ore bodies are not exposed, as most geophysical measurements are more expensive than surface geological surveying. At present the greatest use of geophysical prospecting is made in oil exploration. In this country relatively few oil areas exist where geologic structure is exposed at the surface; in the majority of cases, the deeper formations are concealed by (frequently unconformable) younger strata. This is particularly true for the entire Gulf coast, the Midcontinent, the Great Plains, Western Canada, and a part of California. The Gulf coast has seen the most extensive geophysical activity because conditions exist- 6 INTRODUCTION [CHaP. 1] ing there are virtually ideal for geophysical exploration. At present seismic and gravitational methods for mapping oil structures dominate the field; electrical well-logging is widely used for the purpose of correlat- ing formations by their resistivity and for identification of oil sands. It has been estimated that the oil industry spends between 15 and 20 million dollars annually for geophysical field work and laboratory research. Compared with the oil industry, the mining industry has made relatively little use of geophysical exploration although there have been more pub- lished accounts of mining surveys. Various reasons account for this lack of geophysical activity. (1) The small size of the average ore body makes it impossible to cover systematically township after township, as in oil surveying. (2) Large industrial groups capable of financing extensive re- search and exploration programs are few. (3) In mining areas geology is frequently known from outcrops, so that a determination of subsurface structure so important in oil exploration is less necessary. (4) Structural relations and dispositions of ore bodies are usually complex, making inter- pretation of geophysical data more difficult. (5) Many geophysical methods are adversely affected by the rugged topography prevalent in mining districts. (6) Seismic methods, at present most prominent in oil exploration, have found little application in mining because dynamo- and contact-metamorphic agencies have obliterated original differences in elas- ticity between formations. (7) Transportation in mining regions is diffi- cult and inadequate. In spite of these handicaps, the application of geophysics in mining is often more fascinating to the geophysicist than in oil because of the greater variation in method and procedure. Not only may structural investigations be made, but the ore itself may produce indications; further, associations of the sought but ineffective mineral with noncommercial but physically effective minerals may be utilized. Generally speaking, the planning and execution of a geophysical survey in mining and oil are quite different; further details are presented in Chapter 5. } A third major field for geophysical work is that of engineering, encom- passing civil engineering, engineering geology, and allied fields such as military, structural, gas, and pipe-line engineering, and the like. Geophys- ics is being applied to problems involved in dam-site and tunnel investiga- tions, determination of foundation conditions in highway and railroad construction, location of construction materials for highway and railroad work, water location, detection of corrosion and leakage in gas and water pipes, investigation of building and road vibrations, and so on. Military engineering has utilized geophysics in similar ways; Chapter 6 covers these topics in more detail. Z METHODS OF GEOPHYSICAL EXPLORATION I. CLASSIFICATION GropuysicaL methods may be broadly classified under two headings: major and minor (see Tables 1 and 2). There are four major geophysical methods: gravitational, magnetic, seismic, and electrical. In the gravitational methods, measurements are made of anomalies in gravity attraction produced by differences in densities of formations and structures. In the magnetic method, measurements are made of anomalies in the earth’s magnetic field due to geologic bodies of different degrees of para- or dia-magnetism. In either case, the reactions of geologic bodies are permanent, spontaneous, and unchangeable; the operator cannot con- trol the depth from which they are received.! In the other two major methods, energy is applied to the ground for the purpose of producing a measurable reaction of geologic bodies. This gives the possibility of spacing transmission and reception points in such a manner that the depth range can be controlled. In the sezsmic method, energy is supplied by dynamite explosions, and the travel times (time interval between firing of the shot and reception of elastic impulses) of refracted and reflected waves are measured. In one group of the electrical methods energy is applied galvanically, and the distribution of the potential or the electromagnetic field resulting from conductive bodies is measured. These are known as potential and electromagnetic (electromagnetic-galvanic) methods. In another group, known as electromagnetic-inductive methods, the primary energy is ap- plied inductively to the ground and the distortions of the electromagnetic field are determined. 1 If only one geologic body is present, this limitation may be overcome by varying the position of the receiving units in a horizontal direction away from the axis of the geologic body. Thereby, a variation of the anomaly with distance is introduced and, for one geologic body at least, enough equations may be established so that direct depth determinations may_ be made. Horizontal changes of distance may be supplemented by vertical changes in distance, with observations from scaffolds and aircraft. In practice, these methods are of limited value when a plurality of geologic bodies exists. 7 uolysiyoueg JO yYdaqj jo JoIyUOD SPP BuiziB19uq 07 woryossay jorqyuop yydeq ON uoTyOy snosuezuodG 87[NBJ ‘SeSpll poting ‘seinjoniys dip-MoT swue[qoid ABM -YsIy *Y UOlyspuNo}] ‘sq[Ney fsoin4 -oniys “049 [BUI[DIyUB ‘SewWOp 4IBG SeIpoqg 910 epyyns fainjoniys “oye ‘[eUIp[OIyUe {szNeT saIpog e10 epyyng IO ‘Sue [IAI “TIO SurarUr “TIO muolyIBBeYy “gq OTWIstag “AT UOTPIBIJOY “VW AZ19u9 Areuwtid Jo uorywsorypdds aayonpuy -d SuUlUIy JUIsSO] “O09Ta ‘sursjqoid Avmysiy ‘Setpoq 210 opyyns ‘seinjons4s IO ‘10}8M pUNOIs ‘soz1s Wep uO yydep yooipeq ‘suoryipuod [ein -onij3s pus oIydeiZy4eI3s [elauery saIpoqg a10 spying [to *Zua [LATO ‘Zulalyay SUrUI sia08|d pos /S8aJ0 epyns ‘oosse pus ‘aqyy0Y1 -14d ‘910 UOII {syne} ‘suOIsNIzUrI ‘Sedpli paring ‘seinjonijs [BUI[OIyUy spudl} [einjoni4s Jofew ‘sadpil paling ‘sewop 4[%9 SUOISNIZUL /S}[NBJ SsauIOp 4/[eS ‘Saspli poring ‘sainqond}s [BUI[IyUy IOULNOD aNV NOLLDY NOILVOIIddY 0190104) Surarur ‘TIO “SBOUl Play oIjousewoIyII[q *Z O1yel doip-"40q (9) APATSISOY (9) 719 -o1d [etyueqjod “godinby (”) AZ19ua ABU -1d jo uo1}8o1/d -de a1unaypy *g poinsvour preg A,puooes jo uoryNqr44 -SIp [81}U9}0g “T [styuejod-jjog “Vy [89joeTH “ITT orjouseyl “T] I9JIUIIABIN) “O umnjnpueg “g Le) gouB[eq UOISIO], “VY [BUOI}BYIABID “T aig aqoHnLaW SGOHLYW TVOISAHdOHD YOLVI WNOT AHL 4O AUVIINOAS I Gav Cuap. 2] METHODS OF GEOPHYSICAL EXPLORATION 9 Some of the minor geophysical exploration or detection methods make use of the elastic properties of the surface soil (dynamic soii testing) and of the water and atmospheric air (acoustic detection). Other methods involve the detection of thermal effects (geothermal well testing), the detec- tion of gases, and the mapping of radioactive radiations (see Table 2). TABLE 2 SUMMARY OF MINOR GEOPHYSICAL METHODS METHODS FIELD APPLICATION Mining, civil Mine safety; pipe leak detection engineering Acoustic Military Sapper, submarine, airplane de- engineering tection; sound ranging Utilizing Navigation Echo depth sounding; iceberg elastic location properties a Dynamic Structural; civil | Earthquake & vibration-damage vibration engineering tests of buildings, ground, & road tests beds Strain Mining, Mine safety gauging Civil engineering| Tests of structures Geothermal | Oil exploration Structural correlation of wells; Utilizing cementation problems thermal — effects Thermal Military Airplane location detection Navigation Iceberg location Oil Location of oil (?) : Mining Mine safety Gas detection Military Poisonous gases Civil engineering} Gas leaks Radi as Mining Radioactive ores adioactivity measurements Oil Well logging In the following sections, a summary of both major and minor geo- physical methods is presented, with special reference to general principles involved, instruments used, corrections applied, and interpretation pro- cedure. II. GRAVITY METHODS General. Variations in the gravitational field may be mapped by the pendulum, gravimeter, and torsion balance. The pendulum and gravim- eter measure relative gravity, whereas with the torsion balance, the 10 METHODS OF GEOPHYSICAL EXPLORATION [CHap. 2 variations of gravity forces per unit horizontal distance, also known as “gradients” of gravity are determined. Since the gravitational effects of geologic bodies are proportional to the contrast in density between them and their surroundings, gravity methods are particularly suitable for the location of structures in stratified formations. As there is generally an increase of density with depth, the uplift of deeper formations will result in placing formations of greater density in the same horizontal level as lighter and younger formations. Pendulum methods. It is well known that a pendulum may be used to determine not only time but gravity as well. Gravity pendulums are kept as constant as possible in length so that variations in period indicate changes in gravity only. To obtain the necessary accuracy, the pendulum period must be determined to within 1/10,000,000 of a second. By using an inverted pendulum (Lejay- Holweck type, see Fig. 2-1), the sensitivity of the period to gravity variations may be increased 1000 to 2000 times. The most common method for securing the necessary accuracy in pendulum observations is the ‘‘coincidence”’ or beat method whereby the gravity pendulum is compared with a chronometer or another pendulum of nearly equal period. If the interval between successive coincidences of the Fic.'2'1, Lejay-Hol- 0WO time pieces is measured with an accuracy of 1 weck pendulum (sche- millisecond, gravity is determined with an accuracy matic). P, Pin; Q, of 1 milligal.2 Comparisons of field pendulums quartz rod; E, elinvar : ; : pane a) dinpieaent with the reference time piece are usually made A, arresting device. by electrical wire or radio transmission. Correc- tions are applied on observed periods for the “rate” of the comparison time piece, air temperature and density, pendu- lum amplitude and flexure of the support. Gravimeters. Pendulum, or “dynamic’’ methods of measuring gravity have been superseded recently by ‘‘static” or “gravimeter’”’ methods in which gravity is compared with an elastic spring force. Mechanically simplest are the Threlfall and Pollock instrument (in which a thin hori- zontal quartz bar is suspended from a horizontal torsion wire), the Hartley gravimeter (containing a horizontal, hinged beam suspended from two helical springs), the Lindblad-Malmquist and the Askania gravimeters in which the masses are suspended directly from a spring or springs, with 2 “Gal” (after Galileo), acceleration unit of 1 centimeter per second squared. Cuap. 2] METHODS OF GEOPHYSICAL EXPLORATION 11 arrangements for electrical or similar means of magnifying the displace- ment. An increase in mechanical sensitivity may be attained by providing “astatizing’”’ mechanisms which involve the application of a labilizing force nearly equal and opposite to the elastic restoring force. Examples are the Ising gravimeter, in which a vertical quartz rod is suspended in in- verted position from a taut horizontal quartz fiber, gravimeters using bifilar and trifilar suspensions, the Truman-Humble gravimeters and the Thyssen gravimeter (Figs. 2-2 and 2-3), astatized by a rigidly attached inverted pendulum. Corrections on gravity values observed with pendulums and gravimeters. The following corrections must be applied on relative gravity values: (1) a correction for normal variations of gravity (planetary effect); (2) ter- rain correction; (3) free-air and Bouguer (elevation) correction. The planetary correction is due to the variation of gravity with latitude. The effect of terrain is calculated from elevations along radial lines and concentric circles around the station. Elevation is allowed for by a reduction to sea level (free- air correction) to which the influence of the rocks between station and sea level is added (Bouguer reduction). Interpretation of gravity anomalies. Gravity anomalies may be represented by contours (iso- gams) or profiles in connection with geologic sec- ea tions. Their interpretation is largely qualitative Eig: 2-2.) Gravimeter, Bar? : ; owered to ground through and is given in terms of structural highs and lows floor of passenger car or presence or absence of heavier or lighter bodies (Thyssen). (see Fig. 2-3). If some information is available about the subsurface section and di- mensions and nature of geologic bodies to be expected, more quantitative interpretation methods may be applied by calculating their attraction and by varying the assumptions regarding dimensions, shape, differences in density, and depth until a reasonable agreement between field curves and theoretical curves is obtained. This method of interpretation is of a trial and error nature and generally referred to as indirect interpretation. The Eotvés torsion balance. Contrarily to the beam in an ordinary balance, the beam in a ¢orsion balance revolves in a horizontal plane and is deflected from a position corresponding to the torsionless condition of the suspension wire by the unbalance of horizontal forces acting on it. For the sake of illustration, two types of torsion balance beams may be distinguished. In the beam of the first type (see Fig. 2-4a) two masses are at the ends of the beam and at the same level. The beam is deflected by forces resulting from horizontal differences of the horizontal compo- 12 METHODS OF GEOPHYSICAL EXPLORATION [CHap. 2 nents of gravity. These forees are frequently referred to as “horizontal directing forces” or “‘curvature values” since they are related to the curva- ture of the equipotential surfaces of gravity. If a spherical equipotential surface be so placed that its apex coincides with the beam center, the Actus cael / Lines of equal gravity anomaly Fia. 2-3. Gravimeter on traverse across anticline (schematic). horizontal components of the gravity forces (which at all points are at right angles to the equipotential surface) all point to the axis of rotation and no deflection of the beam takes place. When this surface is curved in a different manner, the horizontal components no longer point in a radial direction; they tend to turn the beam into the direction of minimum CuapP. 2] METHODS OF GEOPHYSICAL EXPLORATION 13 curvature of the equipotential surfaces (see Fig. 2-5). Hence, the de- flection is proportional to the deviation of the equipotential surface from the spherical shape and the deviation of the beam from the direction of minimum curvature. In the second type of beam the two weights are attached to its ends at different levels (Fig. 2-4b). In addition to the above “horizontal direct- (a) (b) (c) (d) Fig. 2-4. Eétvés torsion balance. (a) Beam of the first kind; (6) beam of the second kind; (c) tilt beam; (d) Askania double tilt-beam balance (American Askania Corp.). ing forces,” this beam is affected by the difference in direction of the gravity forces on the upper and lower weights, which increases with the convergence of the equipotential surfaces passing through the weights, that is, with the rate of change, or “gradient,” of gravity (see Fig. 2-6). The torsion balance is so sensitive that one may detect convergences of equipotential surfaces of the order of 1/100,000 of an arc-second, which corresponds to a horizontal variation of gravity of 10~-° gals*/cm. * See footnote on p. 10. 14 METHODS OF GEOPHYSICAL EXPLORATION [CHap. 2 In practice, only a beam of the second type is used. The gradients and curvature values may be resolved into their north and east components. Hence the torsion balance beam is affected by four unknown quantities, to which is added a fifth, the zero or torsionless position of the beam. As the deflection of the beam depends on its azimuth, the action of gravity forces on it may be changed by rotating the entire instrument in a dif- ferent direction. ‘To determine the five unknown quantities, five azimuths are therefore required. To shorten the observation time (20 to 30 minutes in each position), two beams are mounted side by side in antiparallel arrangement. The second beam adds its torsionless position as sixth unknown, so that three positions separated by angles of 120° are required to determine all quanti- ties. In present practice, double mit beam instruments of the second Fqupeiett) ty WOotvds type are used exclusively, arranged either for visual observa- tion of the beam deflection or with full automatic recording mecha- nism. Most recent torsion balances carry beams suspended at an an- gle of 45° (see Fig. 2-4c and d). Calculation of gradients and curva- tures proceeds in accordance with formulas or nomographs based on the fundamental theory of the in- strument. air rey oat i Corrections on torsion balance of first kind eetactae aad eharaetedicd results. Torsion balance results by cylindrical equipotential surface. must be provided with a number of corrections. Most important is the terrain correction, which is obtained from elevations measured around the instrument in a number of radial directions and along suitably selected concentric circles. In rugged terrain, topographic corrections may become involved and inaccurate, which limits the usefulness of the torsion balance to fairly level country. A second (planetary) correction results from the variation of gravity with latitude. Finally, it is often desirable to correct for regional geologic structure. In torsion balance measurements under- ground, allowance must be made for mass deficiencies due to tunnels, drifts, and so on. Interpretation. In plan view, gradients are represented as arrows point- Horizontal Ca of Gravity — — Cuap. 2] METHODS OF GEOPHYSICAL EXPLORATION 15 ing in the direction of maximum change of gravity (see Fig. 2-6); curva- ture values are plotted as straight lines through the station, the length of the line being in proportion to the deviation of the equipotential surface from spherical. Torsion balance results may also be plotted in the form of curves along profiles at right angles to the strike (see Fig. 2-6). Rela- tive gravity may be calculated from gradients, and points of equal relative gravity may be connected by ‘“‘isogams.”’ Torsion balance interpretation may be qualitative or quantitative. In the former, gradients are given preference over curvature values. The < e Swe SSS Fic. 2-6. Convergence of equipotential surfaces of gravity caused by subsurface fault and reaction of torsion balance beam of the second kind. largest gradients occur above such portions of subsurface geologic features as are characterized by the greatest horizontal variation of density, for example, on flanks of anticlines, synclines, edges of salt domes, igneous intrusions, buried escarpments, and faults. Quantitative interpretation is usually of an indirect nature; geologically plausible assumptions are made about subsurface mass dispositions; their gravity anomalies are calculated and compared with the field findings. Discrepancies between the two are reduced step by step by modifying the assumptions regarding depth, shape, and density of the subsurface bodies. 16 METHODS OF GEOPHYSICAL EXPLORATION [Cuap. 2 III. MAGNETIC METHODS General. In common with gravitational methods, magnetic prospect- ing utilizes a natural and spontaneous field of force, with fields of geologic bodies superimposed upon a normal terrestrial field. Coulomb’s law, which controls the attraction of magnetic bodies, is identical in form with Newton’s law; integral effects of all bodies within range are observed and depth control is lacking. One important difference is that the gravita- tional fields of geologic bodies do not depend on the earth’s gravitational field, whereas magnetic bodies frequently owe their magnetization to the magnetic field of the earth. For this reason, magnetic anomalies are often subject to change with latitude. Moreover, rocks may have mag- netism of their own whose direction may or may not coincide with that induced by the terrestrial magnetic field. An important factor in the interpretation of magnetic methods is that rock magnetism, contrary to rock density, is of a bipolar nature. In gravity methods, total field vector and the horizontal gradients of the vector or of its horizontal components, are observed. In magnetic prospecting, measurements of the total vector are the exception rather than the rule; it is usually resolved into its horizontal and vertical com- ponents. Experience has shown that the vertical component exhibits the clearest relation between magnetic anomalies and disposition of geoldgic bodies, at least in northern and intermediate magnetic latitudes. There- fore, measurements of the magnetic vertical intensity are preferred and are supplemented occasionally by horizontal intensity observations for greater completeness in the evaluation of the anomalies. Magnetic fields are generally expressed in gauss;* in magnetic explora- tion it is more convenient to use 1/100,000 part of this unit, called the gamma (y). The accuracy requirements in magnetic prospecting are less than in gravity work; hence, it is a comparatively easy matter to design instruments suitable for magnetic exploration. The magnetic anomalies of geologic bodies are dependent on their mag- netic “susceptibility” and “remanent” magnetism, properties which vary much more widely than their densities. Rocks and formations fall into two natural groups: igneous rocks and iron ores are strongly magnetic, whereas sedimentary rocks are generally weak in magnetization. The magnetic characteristics of rocks are affected by numerous factors such as: magnetite content, grain size, lightning, heat, contact metamorphism, mechanical stresses, disintegration and concentration, and also by struc- tural forces which may alter the disposition of magnetic formations in the course of geologic periods. 4 Simplest definition is lines per square centimeter (in air). See also footnote on p. 295. Cuap. 2] METHODS OF GEOPHYSICAL EXPLORATION 17 Magnetic instruments. Most widely used in magnetic prospecting are the Schmidt magnetometers. In the Schmidt vertical intensity magnetom- eter (see Figs. 2-7 and 2-8), a magnetic system is suspended on a knife- edge at right angles to the magnetic meridian; its center of gravity is so arranged that the system is approximately horizontal in the area under test. Deflections from this position are measured with a telescope and scale arrangement, expressed in scale divisions, and are then multiplied by a scale value to give relative vertical intensities. In the Schmidt horizontal magnetometer, a magnetic system is suspended in the mag- netic meridian and its center of gravity is so adjusted that the system stands approxi- mately vertical in the area under survey and is deflected by the horizontal force. The methods of taking the readings and applying corrections are the same as for the verti- cal magnetometers, except that for large anomalies of vertical intensity a correction for vertical intensity variations is required. In the Hotchkiss superdip, a magnetized needle is suspended on a horizontal pivot and provided with a counter arm so that both the position and the sensitivity of the needle may be controlled. The system may be used at right angles to the direction of the inclination so that it will then measure variations in total intensity. The instruments described above furnish the high degree of accuracy required in oil exploration. In mining exploration, how- ever, simpler devices are often quite satis- f ff if” factory. The earliest instrument of this kind | American Askania Corp. is the Swedish mining compass in which a _—-*F!¢- 2-7. Schmidt-Askania A : = magnetometer. magnetic needle is suspended on a jewel and a stirrup so that it can rotate about a horizontal and vertical axis. Another early instrument is the dial compass which is a combination of a compass and sun dial. Extensive use has been made of the dipneedle, which is a magnetic needle capable of rotation about a horizontal axis and is essen- tially a vertical-intensity instrument. Corrections. The following corrections are required in magnetic ex- ploration: (1) correction for temperature of instrument, arising from the fact that the magnets used for comparison with the earth’s magnetic field lose their strength with an increase in temperature; (2) a “base” correction 18 METHODS OF GEOPHYSICAL EXPLORATION [CHap. 2 which allows for errors of closure when checking back to a base station; (3) a correction for daily variation which may be determined by visual observa- tion or recording of a second magnetometer; (4) a planetary correction, which eliminates the normal variations of the earth’s magnetic field with latitude. Magnetic Vertical Intensity Anomaly aaa, Lines of equal Vert Infens, Anomaly Lescatle, [87 TN Fic. 2-8. Vertical magnetometer on traverse across buried granite ridge. Fences, bridges, pipe lines, tanks, derricks, well casings, and the like, are a serious handicap to magnetic exploration and must be kept at sufficient distance, as it is difficult to correct for them. Interpretation. Magnetic results are generally represented in the form of lines of equal magnetic anomaly (“‘isanomalic” lines‘) or in the form 5 The name ‘‘isogams’’ as applied to magnetic lines is a misnomer. Cuap. 2] METHODS OF GEOPHYSICAL EXPLORATION 19 of curves for profiles at right angles to the assumed strike (see Fig. 2-8). Interpretation of magnetic anomalies is usually qualitative. Depth de- terminations are the exception rather than the rule, because magnetic anomalies may be due not only to variations in the relief of a magnetic formation but also to changes in magnetization; moreover, the ratio of induced and remanent magnetization is frequently subject to unpredict- able variations. In the interpretation of magnetic data in oil exploration, magnetic anomalies ranging from fifty to several hundred gammas may be assumed to result from variations in topography and composition of igneous or metamorphic basement rocks or from igneous intrusions. Anomalies of lesser magnitude are usually due to variations in the mag- netization and structural arrangement of sedimentary rocks. Magnetic anomalies observed in mine exploration are of large magnitude and result in most cases from igneous rocks or magnetic ore bodies. In quantitative interpretation magnetic effects of assumed bodies are calculated, compared with the field curves, and assumptions changed until a geologically reasonable agreement is obtained. Direct methods of in- terpretation ‘are applicable when the magnetic anomaly is simple and arises from one geologic body only; in that case, approximate calculations of depth may be made directly from the anomaly curves by assuming that the magnetic bodies are equivalent to single poles, magnetic doublets, single magnetized lines, and line doublets. The pole and line theories make no assumptions regarding the origin of the magnetic poles and may, therefore, be applied irrespective of whether geologic bodies are normally or abnormally polarized. On the other hand, where the magnetization is sufficiently homogeneous and the remanent magnetization small, the magnetic anomalies may be attributed to induc- tion in the earth’s magnetic field. In that case the so-called ‘induction theory’ is applied. This theory relates the magnetic effects to the strength and direction of the earth’s magnetic field and therefore to the magnetic latitude in which geologic bodies occur. Considerable help may be derived in the interpretation of magnetic anomalies from the use of model experiments. In underground magnetic exploration it is necessary to measure both horizontal and vertical intensi- ties, since magnetized bodies may occur not only below but also above the plane of observation. Depths of magnetized bodies may be determined by observations on scaffolds, in balloons, and in airplanes. IV. SEISMIC METHODS General. Seismic methods are in the category of “indirect”? geophysi- cal methods, in which the reactions of geologic bodies to physical fields are measured. Since the depth of penetration of such fields depends upon the spacing of transmission and receiving points, variations of physical 20 METHODS OF GEOPHYSICAL EXPLORATION [CHap. 2 properties with depth may be measured by noting how certain physical quantities change in horizontal direction. Seismic methods are therefore well adapted to depth determination of horizontal formation boundaries. In seismic exploration a charge of dynamite is fired at or near the surface and the elastic impulses are picked up by vibration detectors, likewise at the surface. ‘The time which elapses between generation and reception of the elastic impulses (‘‘travel time’’) is measured by recording also the in- stant of the explosion and time marks (usually at 1/100 sec. interval). The simplest form of seismic exploration is the “fan shooting” method, which has for its objective the determination of the nature of the media occurring between the shot point and a number of detectors set up in a circle around it. A second important seismic method is the “refraction method,” in which travel times of first arrivals are observed along a profile. The variation of this travel time with distance or the ‘travel time curve” makes it possible to determine true velocities and depths of the refracting formations. A third, and now the most important, method of seismic prospecting is the ‘‘reflection method,’ in which the time re- quired for an elastic impulse to travel to and from a reflecting bed is measured. From the travel times it is possible to make a direct calcula- tion of the depths of the reflecting sufaces but not an evaluation of the elastic wave speeds within the reflecting formations. Seismic equipment. Seismic equipment falls into two groups, that used at the shot point and that used at the receiving points. For the genera- tion of elastic impulses, dynamite is employed, although weights dropped from scaffolds or towers and unbalanced flywheel machines have been applied to generate nonperiodic and periodic impulses (see Chapter 12). The dynamite is set off by special electric blasting caps, and the break in the firing circuit is transmitted by wire or radio to the recording truck. Seismic shot holes are drilled by special rotaries, spudders, or centrifugal pumps. In reflection work a special detector is set up at the shot hole for transmitting the time elapsed between the firing of the shot and the arrival of the wave at the surface. The equipment at the receiving points consists of as many vibration detectors as there are receiving points (6 or 12), connected to as many amplifiers and a recording camera in a specially designed truck. The function of this equipment is to detect, amplify, and record the ground vibrations on rapidly moving photographic paper (see Figs. 2-9, 2-10, and 2-11). The detectors, also referred to as ‘‘geophones,” phones, or pickups, record the vertical component of the vibration and are constructed like microphones. ‘Inductive’ detectors are built like moving coil dynamic microphones, “reluctance” detectors like phonograph pickups and ‘‘capaci- tive’’ detectors like condenser microphones and “‘piezo-electric”’ detectors CuaP. 2] METHODS OF GEOPHYSICAL EXPLORATION 21 like crystal microphones. At present the inductive and reluctance types predominate. The amplifiers have usually three to four stages, are either straight transformer or resistance-impedance coupled, and include auto- matic volume control and amplitude expanding circuits to offset the de- crease of (reflection) amplitude with depth. Recording units are coil galvanometers, bifilar oscillographs, or unifilar string galvanometers. Fan shooting. In this method receivers are grouped at equal distances along the circumference of a circle, at the center of which the shot is fired. This gives the arrangement the appearance of a fan. An area is covered with a series of overlapping fans for the purpose of determining the char- Heiland Research Corp. Fig. 2-9. Representative seismic recording channel. From left to right: detector; three-stage self-contained amplifier; six-element camera with six electromagnetically damped galvanometers and timing mechanism. acter of a medium intervening between shot point and receiving points. A salt dome or other high speed medium will appear as a reduction of the normal travel time for the particular distance and area, or as a time “lead.”’ By plotting these leads for each fan line a salt dome, anticline, or the like can be outlined rapidly. Usually, fan-shooting indications are detailed by other geophysical methods. In mining, the method has been applied to the location of gold placer channels which appear as time lags instead of leads. Refraction methods. In refraction shooting, travel times (of first im- pulses) are determined and plotted as functions of the distance of recep- tors arranged in a profile. If the medium between source and reception 22 METHODS OF GEOPHYSICAL EXPLORATION [CHaP. 2 points is homogeneous in horizontal and vertical direction, the arrival times will be proportional to distance, and therefore the travel time curve will be a straight line, its slope giving the velocity in the medium. If the ground is horizontally stratified and if a high speed medium occurs beneath a low speed medium, only the first part of the travel time curve will give the speed in the upper medium. From a certain distance on, waves that have taken a “detour” through the lower high-speed medium will overtake and therefore arrive ahead of the wave through the upper medium (see ae ie es en A lone BVReeee chs ; | ua te =| halbi le oath Distance Fic. 2-10. Wave path, schematic record, and travel-time curve in single-layer refrac- tion problem. Fig. 2-10). The simultaneous arrival of the two waves will be indicated by a break in the travel time curve; the slope of the second part of the travel time curve will correspond to the velocity in the lower medium. From these two velocities and the abscissa of the break in the travel time curve, the depth of the interface may be calculated. If more than one interface exists, depths are calculated from the cor- responding breaks and velocities. In the case of dipping beds the slopes of the travel time curve no longer give a true but only an apparent velocity. Compared with the horizontal bed, an up-dip profile shows a greater ap- Crap. 2] METHODS OF GEOPHYSICAL EXPLORATION 23 parent velocity in the second part of the travel time curve, and the inter- cept moves toward the shot point. If the profile is down dip, the apparent velocity is less than the true velocity, and the intercept moves away from the shot point. Dip and depth may be obtained from 2 profiles (perpen- dicular to strike), one up and the other down the dip. To determine strike and dip, it is necessary to shoot two up- and down-dip profiles at right angles to each other. Interpretation of refraction data may be simplified where considerable velocity contrasts exist, so that the rays may be assumed to be perpendicular to the interfaces. This leads to simplified field technique, widely used in mining exploration and weathered- layer reflection correction, known as “method of differences.” It in- volves forward and reverse shooting of a refraction profile with one re- ceptor set out at the end of the forward profile away from the rest of the units. This location serves as the shot point for the reverse profile with the other receptors in the same location. In most refraction problems interpretation is based on the assumption of straight wave paths, that is, uniform velocity within each medium. In areas with great thicknesses of unconsolidated formations, a continuous depth-increase of velocity occurs and manifests itself in a curved travel time diagram. In that case special interpretation methods are used. Reflection methods. Reflection impulses, or “echoes,” always appear in a seismic record after the first arrivals. Since there is no way of dif- ferentiating between a later refraction impulse and a reflection in a single record a multiplicity of receivers is used in a number of shot distances. In a six- or twelve-receiver record, reflection impulses stand out by their almost simultaneous arrival (see Fig. 2-11). Important factors controlling the appearance of reflections in a seismogram are the placement (depth) of the charge and the distance between the shot point and receiver locations. Depths are calculated from reflection records by timing the reflections for a mean receptor distance, and multiplying the time by one-half of the average velocity. This is true for nearly vertical incidence. For greater distances a “‘spread correction” is applied. Although reflection rays are curved, it is usually satisfactory to calculate depths on the basis of straight ray propagation. If beds are dipping, at least two profiles must be shot up and down dip. For the determination of dip and strike, two profiles at an arbitrary angle with each other, shot up and down dip, are required. Relative depth determination may be made by plotting travel time only. For absolute depth determinations the average velocity must be known. It may be determined by recording reflections from known depths, by shooting in wells, or by surveying a long reflection profile at bd 24 METHODS OF GEOPHYSICAL EXPLORATION [CHap. 2 the surface. If squares of travel times are plotted against squares of distances, the square of the average velocity follows from the slope of rr 2 - é rit — ames = Se -2=—— REFRACTION WAVES — oe = Spear eT = eee SS SECOND REFLECTING BED = mae Taw See Se a EE ae ees Se Ge Ge Ee GR ee SS Heiland Research Corp. Fic. 2-11. Wave paths, record, and arrangement of seismic reflection party. such curve. Because of the delay affecting primarily the return ray in the low-velocity surface zone, a ‘weathered layer’ correction must be applied. Data for this correction are obtained by the refraction procedure Cuap. 2] METHODS OF GEOPHYSICAL EXPLORATION 25 described above. Elevations are considered by a topographic correction to shot datum; by reducing to a regional datum, variations in the geology of surface beds may be allowed for. Sometimes it is necessary to make corrections for horizontal velocity variations. In practice, reflection technique is applied as correlation shooting, con- tinuous profiling, or dip shooting. Correlation shooting consists of placing individual reflection locations from one-half to one mile apart and cor- relating reflection depths through that distance. In continuous profiling, there is an overlap of reflection profiles, whereas in dip shooting, profiles are shot in opposite directions. It may be necessary to use dip shooting on horizontal, but discontinuous beds to avoid errors due to miscorrelation. The reflection method is at present the most accurate method of determin- ing depths of formations in oil exploration. V. ELECTRICAL METHODS General. Mineral deposits and geologic structures may be mapped by their reaction to electrical and electromagnetic fields. These are produced by either direct or alternating current, except where ore bodies spontane- ously furnish their own electrical field (self-potential methods). Elec- trical energy may be supplied to the ground by contact or by induction. The field of the electrical currents so produced may likewise be surveyed by contact or by induction. In respect to surveying procedure and the field measured, three main groups of electrical methods may be distin- guished: (1) self-potential, (2) surface-potential, and (3) electromagnetic methods. Frequently the first two groups are combined into one group of potential methods; the electromagnetic methods are usually subdivided into galvanic-electromagnetic and inductive-electromagnetic in respect to the manner in which the primary field is applied. Four frequency bands may be used in connection with alternating cur- rent electrical prospecting: (1) low frequencies of from 5 to about 100 cycles; (2) the audio-frequency range of from 200 to 1000 cycles; (3) high frequencies of from 10 to 80 kilocycles; and (4) radio frequency of from 100 kilocycles to several megacycles. The low-frequency range is applied in most potential methods; the audio-frequency range is used in some po- tential and most electromagnetic methods; the high-frequency range in the high-frequency electromagnetic methods; and radio frequency in the radio methods of electromagnetic prospecting. The application of high and radio frequencies is limited owing to their lack of depth penetration; of greatest importance are the audio frequencies and the low frequencies. In a number of respects, electrical methods are similar to seismic methods; comparable to the refraction methods are the resistivity and the potential- 26 METHODS OF GEOPHYSICAL EXPLORATION [Cuap. 2 drop-ratio methods; inductive methods as applied to the mapping of horizontal beds are comparable to reflection methods but lack their re- solving power. In electrical prospecting, three kinds of current conduction are sig- nificant: (1) electronic conduction in solids (metallic minerals and ores); (2) electrolytic conduction (by ions); (3) dielectric conduction (by dis- placement current). Conductivity of rock minerals plays a part only in metallic ores; in most igneous and sedimentary formations ‘‘mineral’’ con- ductivities are insignificant. Their conductivity is a function of the pore volume and of the conductivity and amount of the water filling the pores. For all practical purposes it is sufficient to assume that sodium chloride is the only substance in solution. Self-potential method. The self-potential method is the only electrical method in which a natural field is observed; its causes are spontaneous electrochemical phenomena. These phenomena occur on ore bodies and on metallic minerals and placers; they are produced by corrosion of pipe lines and on formation boundaries in wells by differences in the conduc- tivity of drilling fluid and formation waters. Ore bodies whose ends are composed of materials of different solution pressure and are in contact with solutions of different ion concentration, act as wet cells and produce an electrical field which can be detected by surveying equipotential lines or potential profiles. To prevent interference from electrode potentials set up by contact of metallic stakes with moist ground, nonpolarizable electrodes are used. These consist of porous pots filled with copper sulphate into which a cop- per rod is immersed. For the mapping of equipotential lines, a high-resist- ance milliammeter is connected to two nonpolarizable electrodes. One is kept stationary and the other is moved until the current vanishes. At that point the electrodes are on an equipotential line. Potential profiles are run by measuring potential differences between successive electrode locations (see Fig. 2-12). Interpretation of self- potential surveys is qualitative; the negative potential center may be taken with sufficient accuracy to be the highest location of an ore body. Approximate depth determinations can be made by observing the dis- tance from the point of maximum potential to the half-value point in the potential curve. Interpretative advantages are often gained by plotting the results in the form of current-density curves which are obtained from the potential curve by graphical differentiation. Equipotential-line and potential-profile methods. When a source of electrical energy is grounded at two points, an electrical field is produced. Distortions of this field result from the presence of bodies of different conductivity; good conductors will attract the lines of flux, and vice versa. Cuap. 2] METHODS OF GEOPHYSICAL EXPLORATION 27 As it is difficult to survey these lines of flux, lines of equal potential, that is, lines along which no current flows, are mapped instead. In practice power is supplied to two grounded electrodes from an alternating current generator. Two types of primary electrodes may be used: (1) point elec- Spontaneous Potential! an he, a4 ~~ “| Fia. 2-12. Self-potential mapping (schematic). trodes, so laid out that their base line is in the direction of strike, (2) line electrodes laid out at right angles to the strike. Equipotential lines are surveyed with one fixed and one moving probe which are connected to an audio amplifier with head phones. Greater detail is obtainable by the 28 METHODS OF GEOPHYSICAL EXPLORATION [CHap. 2 use of so-called ‘‘compensators,’’ which measure the voltage between the search electrodes in terms of generator voltage and phase, or split it up into one component which is in phase and another which is 90° out of phase with the generator voltage. Interpretation of equipotential-line methods is largely empirical and makes use of the displacement of the lines from their normal position. More quantitative interpretation is possible by comparing the field results with laboratory experiments made on small scale models. Because of the fact that in stratified ground the conductivity is generally better in the direction of the bedding planes than at right angles thereto, it is possible to use equipotential-line methods for structural and stratigraphic investigations. Since an equipotential line near one electrode will be elliptical instead of circular, the direction of the major axis indicates the direction of strike. Resistivity methods. Equipotential-line methods, while useful for the mapping of vertical or steeply dipping geologic bodies, are not suited to the investigation of horizontally stratified ground. Conversely, resistivity methods are applicable to depth determinations of horizontal strata and the mapping of dipping formations. In resistivity procedures not only the potential difference between two points but also the current in the primary circuit is observed. The ratio of potential difference and current, multiplied by a factor depending on electrode spacing, gives the resistivity of the ground. True resistivities are observed in homogeneous ground only; the presence of horizontal or vertical boundaries in the range of the instrument gives what is known as “‘apparent”’ resistivity. The arrangement in most frequent use is the four-terminal Wenner-Gish-Rooney method (see Fig. 2-13). Resistivity methods may be applied in two ways: (1) with constant electrode separa- tion (that is, constant depth penetration), called resistivity ‘‘mapping’’; (2) with fixed center point and progressively increasing electrode separa- tion, called resistivity “sounding,’’ whereby the apparent resistivity is observed as a function of electrode separation and therefore of depth. A modification of the resistivity mapping method is used in electrical logging. Interpretation of resistivity data may be qualitative and quantitative. The qualitative method uses the appearance of the curves and is applied primarily in resistivity mapping, a drop in apparent resistivity indicating the approach of bodies of better conductivity, and vice versa. In resistiv- ity sounding, the horizontal variation of apparent resistivity is interpreted in terms of the equivalent vertical variation of resistivity; however, the curves do not have sharp breaks at formation boundaries. Structural correlations are sometimes possible by comparing curves through a series of locations. When only one or two formation boundaries are effective, direct depth determinations are possible by comparing the field data with CHAP. 2] METHODS OF GEOPHYSICAL EXPLORATION 29 “type’’ curves calculated for given conductivity ratios and for various possible depths. Potential-drop-ratio methods. The essential feature of the resistivity methods previously discussed is a determination of the potential difference between two points at the surface and a measurement of the current in the external circuit. In potential-drop-ratio methods current measure- ments in the external circuit are not made and the potential drops in two successive ground intervals (represented by three stakes arranged in a Apoarert Potential- Drop- Resistivity hatio Curve Normal Katia Fig. 2-13. Resistivity and potential-drop-ratio mapping (schematic). straight line, radiating from one of the power electrodes) are compared. The potential-drop-ratio method is best suited for the location of vertical formation boundaries (faults, dikes, veins, and the like). The arrange- ment used for the comparison of the potentials is a modified A.C. Wheat- stone bridge; the two external stakes are connected to two resistors (with condensers in series or parallel) whose center tap connects through the indicating instrument to the center stake. When this arrangement is moved across a vertical formation boundary, a potential-drop ratio greater than one is obtained when proceeding from a medium of lower resistivity _ toward a medium of greater resistivity, and vice versa (see Fig. 2-13). 30 METHODS OF GEOPHYSICAL EXPLORATION [CHap. 2 Other potential methods. Surface potential measurements may be made not only with continuous direct or alternating current but also by the use of transients, such procedure being known as “Eltran.’”’ The electrode arrangement is similar to the resistivity method. In the pri- mary circuit, impulses are applied to the ground and the time change of the potential between two stakes (usually placed outside the two current stakes) is measured with an amplifier and cathode-ray oscillograph. Fic. 2-14. Semiabsolute and relative electromagnetic prospecting methods (schematic). Electromagnetic-galvanic methods. Electromagnetic methods of elec- trical prospecting differ from potential methods in that the electromagnetic field of ground currents and not their surface potential (electrical field) is measured. They fall into two major groups: (1) electromagnetic- “galvanic”? methods in which the primary energy is supplied by contact as in the potential methods; (2) electromagnetic-“‘inductive’’ methods in which the ground is energized by inductive coupling (with insulated loops). To supply electrical energy to the ground by contact, line electrodes or point electrodes are used. Line electrodes are laid out at right angles to the strike, point electrodes parallel with the strike. Cuap, 2] METHODS OF GEOPHYSICAL EXPLORATION 31 Numerous methods are available for measuring the electromagnetic field. The simplest procedures involve a determination of direction only or of the absolute values of the horizontal and vertical components by using a vacuum-tube voltmeter in the output circuit of an amplifier connected to a reception frame. A determination of the in-phase and quadrature com- ponents of the field is possible by the use of the compensators previously described (see Fig. 2-14). These are connected by a pair of leads to the source of the primary power and thus determine the electromagnetic field in terms of the current and phase of the primary circuit. Finally, the ratios of field intensities and their phase differences at successive points may be measured by dual coil arrangements and “ratiometer’” bridges (see Fig. 2-14). Interpretation of results obtained with the electromagnetic-galvanic method is both qualitative and quantitative. In approximation, lines of equal direction of the field vector (in horizontal projection) may be as- sumed to represent flux lines which are attracted by bodies of good conductivity, and vice versa. If the current is concentrated in a good conductor and flows along its strike, then the horizontal component will have a maximum above the current concentration. The vertical com- ponent will be zero at a location immediately above the concentration and will have a maximum and minimum, respectively, on either side of the concentration, their distance being equal to twice the depth. ‘Indications are also obtained from induction currents concentrated along the edges of a subsurface body. Therefore, in the case of an ore body of some width, the horizontal intensity will show not merely a maximum over the center but a maximum and minimum, respectively, over the edges. This, strictly speaking, comes under the heading of electromagnetic- inductive methods described in the next paragraph. Electromagnetic-inductive methods. In inductive procedures power is supplied to the ground by insulated loops which will cause induction cur- rents to flow in subsurface conductive bodies. An advantage of inductive methods is the ease with which power may be transferred into the ground when the surface formations are poor conductors. Since currents induced in the subsurface conductors are dependent on frequency, interpretative advantages may be gained by regulating the frequency. However, there are limitations to this procedure. Too low frequencies will reduce the strength of the induced currents, while too high frequencies lack depth penetration and cause interference from near-surface noncom- mercial conductors and from topography. Frequencies usually applied in mining, range from 250 to 1000 cycles; in structural exploration the range is from 25 to 200 cycles. The other extreme is represented by the high-frequency methods using several tens of kilocycles which have been 32 METHODS OF GEOPHYSICAL EXPLORATION [CHaP. 2 practically abandoned on account of the limitations mentioned. In induc- tive methods a horizontal or vertical loop may be employed. The former afford the most effective coupling with horizontal subsurface conductors and are used in the form of long cables and rectangular or circular loops. Theoreticaily verticai loops would be more suitable for steeply dipping bodies, but they are difficult to handle. For the measurement of the electromagnetic field, the same procedures are used as described before in connection with the electromagnetic-galvanic methods. Interpretation methods in electromagnetic-inductive exploration depend to some extent on the purpose of the survey and the general shape and disposition of the subsurface conductor. In wide and steeply dipping conductive bodies the electromagnetic field is due primarily to currents — flowing along the edges. Hence, the horizontal component will show a maximum and minimum, respectively, over the edges; a minimum in the vertical component will occur over the center. Depth calculations of the equivalent current concentrations are based on the relations discussed before in connection with electromagnetic-gaivanic methods. Inductive methods, using separate measurements of the in-phase and out-of-phase components, have great interpretative advantages. The in-phase component is largely due to the field-supplying loop, while the out-of-phase components resuit from the induced subsurface current con- centrations. In horizontally stratified ground, interpretation is usualiy based on the out-of-phase components. If a very good conductor occurs in horizontal position, the surface anomaly is largely due to the refiection of the primary cable on the conductor, with a phase change of 180°. Depth determinations of this conductor are, therefore, possible by locating the ‘Image’ of the primary cable from the trend of the horizontal intensity curve. Attempts have also been made to determine resistivities of sub- surface formations and their variation with depth by using a horizontal circular loop of gradually increased radius. The quadrature component in this case depends on resistivity and frequency, depth penetration being controlled by the radius of the loop. As in most other electrical meth- ods, interpretation of results obtained with inductive methods is aided greatly by model experiments. Radio methods. Since radio methods employ frequencies still higher than the high-frequency—inductive methods, they are subject to the same limitations. In one group of radio methods the effect of subsurface con- ductors on the emission characteristics of a transmitter is observed. In a second group a receiving arrangement is employed in addition to the transmitter, and the variation of field intensity with location is measured. This will give some idea of the absorption, interference, and reflection that the waves may have undergone along their path from the trans- Crap. 2] METHODS OF GEOPHYSICAL EXPLORATION 33 mitter to the receiver. In the catagory of radio methods belong the so- called ‘‘treasure finders.’”’ These are portable instruments for the location of shallow metallic objects, pipe lines, and the like. VI. GEOPHYSICAL WELL TESTING Geophysical well-testing methods may be divided into four groups: (1) electrical testing methods, known as ‘“‘electrical logging’’; (2) temper- ature measurements; (3) seismic measurements; and (4) miscellaneous measurements of radioactivity, rock magnetism, opacity of drilling fluid, and so on. Electrical logging methods. Electrical logging methods fall into two groups: (a) methods calling for the application of an electrical field, which furnish the resistivities of the formations traversed; and (b) methods in which spontaneous electrical potentials are observed. The latter will give data regarding the porosity of formations. Numerous arrangements have been proposed for the determination of resistivities in wells. The system most widely used is the Schlumberger procedure. Three elec- trodes are lowered into the well and the fourth is the casing at the surface (see Fig. 2-15). Current is supplied to the casing and the lowest electrode, and the potential difference between the two other electrodes is recorded. The resistivities thus obtained are not true formation resistivities but apparent resistivities which are functions of the electrode spacing and of the absolute resistivities involved. Electrical logging makes possible the correlation of formations by their resistivity parameters, and the loca- tion of water- and oil-bearing strata. In some wells it has been found that the resistivities are a true indication of the productivity of oil sands. In the second group of electrical coring methods spontaneous potentials are observed. These are of two types: (1) electrofiltration potentials (caused by movement of fluids through porous formations), and (2) con- centration potentials (caused by difference in ion concentration of drilling fluid and formation water). Spontaneous potential records are valuable in connection with resistivity logs. A high resistivity may mean a lime- stone or an oil sand, but high porosity will eliminate the limestone from the picture. Temperature measurements. It is generally known that there is an increase in temperature with depth of penetration into the earth’s crust. However, this temperature variation with depth is not uniform; it depends not only on the local geologic and stratigraphic conditions but also on the prc. nce or absence of heat developed by physical and chemical actions of the formation fluids. As the heat conductivity of beds is greater in the bedding planes than at right angles thereto, uplifts of sedimentary beds and salt domes will generally result in a rise of well temperatures. 34 METHODS OF GEOPHYSICAL EXPLORATION [CHap. 2 Chemical and physical processes responsible for changes of the normal temperature gradient are: the transformation of anhydrite to gypsum; the oxidation of sulfides; the influx of water, oil, and gas into the hole; and the heat developed by the setting of cement behind the well casing. Recording Potentiometer Grounded Current Terminal " \ Electrical Logs Fia. 2-15. Electrical logging arrangement (schematic). It is clear, therefore, that temperature measurements in wells will furnish valuable information in connection with the location of oil, gas, and water- bearing strata, cementation problems, and so on. Correlation of tem- perature curves obtained in a series of wells will give valuable clues to geologic structure. Cuap. 2] METHODS OF GEOPHYSICAL EXPLORATION 35 Seismic measurements. Seismic measurements in wells are made for two purposes: (a) to supplement surface refraction data, and (b) to obtain average velocity data for reflection shooting. In both applications a vibration detector is lowered into the well to the depth desired and shots are fired at the surface. In wells drilled into or near the edge of salt domes, it is thus possible to obtain valuable information in regard to presence of overhang and the behavior of strata along the flanks. In order to make absolute depth determinations in reflection shooting, it is desirable to know the velocity of seismic waves at right angles to the bedding, which is likewise determined by firing several shots at or near the well at the surface, with a detector lowered to various depths. Miscellaneous measurements. The radioactivity of strata traversed by the well may be determined by lowering a small ionization chamber to the desired depth. Magnetic well investigations are generally confined to determinations of core orientation. Acoustic measurements are made in deep wells for the location of gas and water flows. Gas detectors, when used in connection with shallow holes, permit of locating leaks in gas mains. VII. MISCELLANEOUS GEOPHYSICAL METHODS Radioactivity methods. Application of radioactivity methods rests on the fact that zones of shattering in the earth’s crust, such as faults and fissures, will allow passage and accumulation of radioactive disintegration products. Owing to the limited penetration power of radioactive gases and radiations, the depth range of these methods is limited. It does not appear to be necessary for the channels of radioactive products to remain open. If they have become mineralized, it is nevertheless possible to locate them by increased activity; hence, there is a possibility of locating sulfide and other veins by measurement of radioactivity. Some shallow oil deposits emit radioactive radiations because oil is an absorbent of radon. It goes without saying that radium ore, such as pitchblende and the other uranium compounds, may be located by radioactivity measurements. Radioactivity methods fall into two groups: in the first the relative content of radon in the surface soil is determined; in the second the penetrating radiation of radioactive disintegration products is measured. Hydrocarbon (soil and gas) analysis. Oil seepages and gas emanations have served for decades as indications of oil deposits. These macroscopic examination methods have been supplemented recently by microscopic procedures for determining small amounts of hydrocarbon in the soil air and in the soil itself. The air from shallow holes is pumped into a gas 36 METHODS OF GEOPHYSICAL EXPLORATION [(Cuap. 2 detector which may be of the hot filament type or which may indicate the amount of carbon dioxide liberated on combustion of the hydro- carbons contained in the air. These detectors do not differentiate be- tween methane and the heavier hydrocarbons. In soil analysis methods, on the other hand, the soil samples are degassed and the gases passed through an analytical apparatus, where their constituents are separated by low-temperature distillation and combustion into methane, ethane, and the heavier hydrocarbons. Soil samples may also be extracted by suitable solvents, and their content in socalled pseudohydrocarbons (soil waxes, and the like) may be determined. Several of the known oil fields have been found to be characterized by a corona or halo pattern of the significant heavy hydrocarbons. The pseudohydrocarbons and methane appear to follow a similar, though less regular, trend, methane being possibly least significant, since its distribution may be affected by near- surface decomposition processes. Dynamic ground tests, strain gauging, vibration tests. Building sites may be tested by setting them into forced vibration and measuring their amplitudes at any desired points by vibration recorders as functions of frequency, thereby determining their natural frequency and damping. Experience appears to indicate that the former frequently coincide with their predominant response frequency to earthquake vibrations. Hence, any structure to be built on such ground should be so designed that reso- nance between structure and ground is avoided. Strain gauging is a comparatively new field of geophysics. Its purpose is the measurement of small displacements between adjacent portions of ground in underground openings such as tunnels, mine shafts, and the like. Continuous recording of strains in subsurface openings and of their fluctuations with time makes it possible to predict roof and wall failures and to guard against them. The purpose of vibration tests is to determine the magnitude and char- acteristics of vibrations set up in buildings by traffic, mine operations, blasting, and so on, by one or more vibration recorders set up at various distances from the source of the disturbance or in various stories of the building. Results of such tests have played no unimportant part in settling disputes arising from damage claims in connection with industrial operations. Acoustic methods. Acoustie methods are concerned with the trans- mission and reception of audible sounds in the air, in water, and in the ground. Their purpose is communication, position finding, sound rang- ing, direction finding, echo sounding, and, indirectly, the collection of data for noise prevention. For communication or signaling, transmitters of suitable frequency and directional characteristic are required, depending Crap. 2] METHODS OF GEOPHYSICAL EXPLORATION 37 on the medium. Position finding is the procedure of determining one’s location by distance measurements from two acoustic sources of known coordinates or, as in radio-acoustic position finding, from one source transmitting a simultaneous radio and acoustic impulse. Conversely, sound ranging is the location of a source of unknown position by acoustic triangulation, that is, by recording sound impulses on receivers of known positions. By direction finding is meant the determination of the direc- tion of sound by a rotatable base with two receivers (binaural hearing) or with multiple receivers equipped with electrical delay networks to balance their phase differences (compensators). Echo sounding is identi- cal in principle with reflection shooting described on page 24, except that because of the homogeneous character of the medium of propagation (usually water) the devices may be so made as to indicate or record depth directly. Noise prevention extends into the fields of architecture, building construction, industrial activity, vehicle traffic, and sound insulation of military conveyances. Military and peacetime applications of acoustic methods are numerous and are covered in Chapters 6 and 12 in greater detail. 3 MEASUREMENT PROCEDURES IN GEOPHYS- ICAL EXPLORATION I, SIGNIFICANCE AND MEASUREMENT OF PHYSICAL QUANTITIES INVOLVED In GEOPHYSICAL EXPLORATION geologic bodies are located by surface observation of their physical fields. What type of physical field is selected as being the most characteristic of a subsurface body depends entirely upon what rock property is most characteristic of tnat body. The choice of which field parameter is used, in turn, is determined by four factors: (1) distinctiveness of response; (2) ease and rapidity of field determination; (3) accuracy; and (4) freedom from interference (of surface or subsurface origin). Notwithstanding the widely varying nature of physical fields observed, there is a definite similarity in the parameters measured by various meth- ods. Broadly interpreted, geophysical methods fall into two groups: (1) methods in which the propagation of a field with time (and location) is observed; (2) methods in which the characteristics of stationary and quasi- stationary fields are measured. Virtually all seismic and certain electrical methods fall in the first group. Related in principle are those methods in which the variation of a field with time is observed. In this group fall the majority of the “recording”? methods, such as the observation of time variations in gravity; of magnetic variations, of fluctuations in electric currents produced by corrosion of pipes, and so forth. There are some methods in which quantities related to time—for example, phase shift and frequency—are measured (A.C. potential and electromagnetic method and dynamic soil testing method); however, as they operate with quasi-sta- tionary fields they are discussed in the following group. Most geophysical exploration is concerned with stationary and quasi- stationary fields, such as in the gravitational, magnetic, self-potential, and other electrical prospecting methods. It is here that similarities in the selection of a suitable field parameter and method of observation may be most readily observed. In these methods we- usually work with fields 38 Cuap. 3] MEASUREMENT PROCEDURES 39 which have a potential and are characterized by four parameters: (1) the potential itself; (2) the potential gradient, or field intensity; (3) the direc- tion of the field; and (4) the field gradient and its direction (second deriva- tives of the potential). Derivatives of the potential higher than the second are rarely, if ever, measured in geophysical exploration. Interpretative experience indicates that the distinctiveness and therefore the resolving power of a method increases with the order of the potential derivative. However, accuracy requirements and the field difficulties also increase. Measurements of absolute potentials are rarely undertaken. They probably would accomplish no useful purpose in gravitational and mag- netic exploration. Potential measurements in electrical prospecting actually involve a determination of potential difference, potential gradient or electrical field strength. The first derivative of a potential is measured in most methods em- ploying stationary or quasi-stationary fields. In gravitational exploration, the first derivative of the gravity potential with respect to the vertical— that is, gravity—is determined in a number of ways, particularly by pendulums and gravimeters. The horizontal derivative (horizontal gravity component), is not measured directly, although there is no reason why instruments for this purpose could not be developed and perform a useful function. In magnetic exploration, the derivatives of the magnetic potential in almost any desired direction can and have been measured. Instruments have been developed for the determination of the total inten- sity and its vertical and horizontal components. However, the vertical component has been found to be of the greatest diagnostic value. In electrical prospecting, potential difference and therefore electrical field strength is determined in the self-potential, the potential profile, and the resistivity methods. Intensities of electromagnetic fields are observed in the electromagnetic, the inductive, and the high-frequency methods of electrical prospecting (although these fields do not derive from a potential). As far as technique is concerned, simple conditions prevail when merely the direction of a field is observed. This is done in magnetic exploration by measuring declination and inclination and in electrical prospecting by tracing equipotential lines and by observing the minimum-signal position of a reception coil. However, direction observations are less readily interpreted than intensity measurements; hence, the latter are usually given preference. Measurements of second derivatives of a field potential play an impor- 1 This component may be obtained indirectly from torsion balance observations by graphical integration of curves representing the horizontal variation of curvature values. 40 MEASUREMENT PROCEDURES {[CHap. 3 tant part because of their greater resolving power. In practice this advantage is sometimes offset by increased difficulties in technique. The best-known example of this method is the torsion balance. Observations of second derivatives have been made in magnetic exploration by an adaptation of the earth inductor. In electrical prospecting it has been found advantageous to measure the ratio of fields in successive intervals rather than to measure their gradients. This advantage is due to the ease with which ‘‘ratio” bridges can be designed. Examples are the potential- drop-ratio method and the determination of the ratio of electromagnetic fields with dual coil arrangements. As stated at the outset, preference is given to field parameters which can be measured with the greatest accuracy as well as ease and rapidity; hence, the tendency to measure physical fields relatively and not abso- lutely whenever possible. The terms “absolute” and “relative” are somewhat difficult to define in geophysical exploration, since most quanti- ties, which by their nature can be determined absolutely, may with greater ease be observed relatively by reference to a fixed point or base station. Absolute procedures include measurements of direction (magnetic inclination and declination, equipotential lines, dip and strike of induction coils), time and distance (seismic refraction and reflection measurements), and electric voltage (as in electrical potential methods). Semiabsolute procedures are those which measure a physical parameter by comparison with another which is assumed to remain constant for a reasonable interval of time. Examples are: relative gravity measure- ments, made with the assumption that the pendulum length remains constant; magnetometer measurements, made by comparing the vertical intensity with the presumably constant gravity; the gravimeter, whose reliable functioning depends on the constancy of the elastic comparison force; and many others. Relative procedures involve physical measurements by actual con- nection of the detecting unit with a similar unit located at a reference station or an adjacent ground interval. Examples are: the transmission of the oscillation of a reference gravity pendulum from a base station to a field station; the magnetic earth-inductor gradiometer; the potential- drop-ratio method; the comparison of electromagnetic fields with the amplitude and phase of the current in the generator circuit by compen- sator arrangements; and two-coil ratiometer bridges for a comparison of electromagnetic fields with respect to amplitude and phase at successive points. It is seen that by such procedures time variations of comparison parameters are virtually eliminated. CuHap. 3] MEASUREMENT PROCEDURES 41 Il. ARRANGEMENT OF OBSERVATION POINTS WITH RELATION TO GEOLOGIC OBJECTS In geophysical exploration, the objects of detection are geologic struc- tures or mineral deposits, and the detecting units are usually spread out along the earth’s surface. This is done (1) to determine the variation of TABLE 3 PROCEDURES OF MEASUREMENT IN GEOPHYSICAL EXPLORATION OBJECT Stationary. Moving. Measurement of variation of physical quantities with time. DETECTOR Stationary; hori- zontal position va- ried, or multiple detectors used. Stationary; verti- cal position varied. Moving; vertical and horizcntal po- sition varied. Stationary; posi- tion not varied. Stationary or moving. Stationary; record- ing. MEASUREMENT Gravitational, magnetic, seismic, electric surveying on land, in shallow water, and underground; radioactivity measurement, water- and gas-pipe leak detection, and corrosion surveying; model experiments in laboratory. Scaffold or underground observations, well shooting at different levels; electrical and geothermal well surveying; vibration tests of structures at different stories. Gravity and magnetic surveys on ships, floats, submarines; magnetic surveys in ve- hicles and aircraft; resistivity surveys from ships and floats; other electric surveys by aircraft; echo sounding from ships. Determination of physical properties of rocks on outcrops or samples in laboratory; vibration tests on structures. Acoustic and thermal submarine and air- plane detection; iceberg location. Recording of magnetic variations, of corro- sion voltage fluctuations, and of traffic vibrations, sound ranging; strain gauging. the physical quantities measured between points and to obtain a clue to the presence or absence of a geologic body; and (2) to determine the depth of a formation if it remains in horizontal position throughout the length of a profile. The first operation falls under the heading of geophysical map- ping; the second is known as geophysical sounding. By far the greater portion of all geophysical work is done by means of surveying processes on land, in shallow water, underground, or on small-scale laboratory models 42 MEASUREMENT PROCEDURES [(Cuap. 3 with miniature detecting units. As depth to geologic bodies is com- mercially a most desirable quantity, wells are used whenever possible. Examples are: seismic determination of average velocities; measurement of resistivity, temperature, and radioactivity in wells; and observations at different levels of mines. Although attempts have been made to survey from moving supports (automobiles, ships, floats, submarines, and planes) little has been accomplished along this line, since measurements on moving supports introduce a reduction in accuracy. The present trend in geo- physics is more toward accuracy than speed. The use of moving objects and moving detectors plays a part in the military and oceanographic fields of geophysics. Stationary detectors for determining variations in physical effects of stationary objects are used in the recording of magnetic variations, corrosion voltages, traffic vibrations, strain gauging, sound ranging, and in small-scale laboratory investigations where model ore bodies may be used and detectors remain stationary. Table 3 gives a summary of these procedures. 4 GEOPHYSICAL METHODS IN OIL EXPLORATION "Tue FoLLowING CHAPTER is intended to assist the operator in the selection of the correct geophysical method when prospective oil territory is to be surveyed. It contains a discussion of (1) the general possibilities of geophysical methods, with chief reference to new areas where the expected type structure is unknown; (2) the choice of methods for specific types of structures; and (3) other nongeological considerations in the selection of methods. If nothing whatever is known about the geology of an area, the most expedient procedure is to make a magnetic reconnaissance survey with widely spaced stations. This may be expected to indicate the topography of areas of the basement rocks, provided they are uniformly magnetized. After promising high areas have been located, the magnetic discoveries should be followed up (preferably by seismic-reflection methods) to deter- mine whether the basement uplifts are accompanied by structure in the overlying sediments. In certain areas magnetic anomalies may also be caused by magnetic sediments. Cases have been known where salt domes have furnished magnetic indications, and where anticlines and faults could be traced by virtue of the presence of magnetic beds in the stratigraphic sections. If the basement rocks are not uniformly magnetized, a magnetic high may simply mean an area of greater magnetization or an area occupied by more magnetic rocks. In some instances it has been found that the magnetization was the reverse of that normally expected and that magnetic highs indicated structural lows. Where magnetic anomalies have no structural significance, it is necessary to use other reconnaissance methods—for instance, the gravitational method. A survey made with pendulums or gravimeters can generally be depended upon to depict fairly accurately the major structural trends. In a few instances it has been found that gravity highs do not reflect geologic structure in the oil-bearing strata. In such cases the work has to be conducted by methods, such as seismic refraction or reflection, which rely only on the structure in the sedimentaries. 43 44 GEOPHYSICAL METHODS IN OIL EXPLORATION (Crap. 4 The refraction method has definite possibilities in virgin areas as a means of stratigraphic analysis of a section. As a means of finding salt domes, its use has decreased considerably on the Gulf coast in favor of gravity and reflection-seismic work. Some oil companies still retain the use of the refraction method for work preceding or accompanying reflection work if the section to be followed out does not exceed 6000 feet in depth. Beyond the distances required for such depth penetration (about seven miles) difficulties in transportation, handling of dynamite, and therefore operation costs generally increase out of proportion to the results achieved and detail of information obtained. For detail, the reflection method is unquestionably the most widely used geophysical technique; it works best on low-dip structures but encounters difficulties with beds of complex faulting, folding, and steep dip. Com- pared with many other geophysical methods, it has the advantage of giving positive depth information. Because of the fact that several reflecting beds may be mapped in one area, this method gives data in regard to lateral variations of the thicknesses of formations and permits the oO ing of unconformities. As aptly expressed by Barton,’ “Geophysical orientation in regard to an area is as necessary to the geophysicist as geological orientation is to the geologist.”’ The geologist must acquire a knowledge of the general stra- tigraphy and regional structure of an area and musi learn the relation of particular features to the regional geology before he can begin to evaluate the significance of local structure in respect to its potential productivity. Likewise, the geophysicist should first investigate the general magnetic, gravitational, seismic, and electric characteristics of an area from a regional point of view before he can begin to evaluate the local significance of geophysical anomalies. Moreover, the regional geological features must be correlated with the regional geophysical features. It often takes considerable time until certain magnetic and gravity anomalies, seismic velocities, reflection travel times, and electrical logging indications can be definitely tied up with specific formations or groups of formations. The geophysicist frequently must wait for the driller before he.can compiete his correlations. The task of choosing methods for reconnaissance and for detail which will give the most reliable information at least expense is facilitated if it is definitely known what type of geologic structure will be encountered in a given area, and if geophysical measurements have been made on a known field. When geophysical methods were first introduced in oil prospecting, practically every method was first tried on known structure. In exploring 1A. E. Dunston, et al., The Science of Petroleum, Oxford University Press (1938). Cuap. 4] GEOPHYSICAL METHODS IN OIL EXPLORATION 45 a new territory it is still advisable to start with, and work away from, known conditions. If the type structure to be encountered in a given area is known, a selection of the most advantageous method is much facilitated. In Fig. 4-1 a schematic representation of reconnaissance and Magnetic Gravimeter heflection Seismic Refraction Seisruc Reflection Seismc TANT. 2\(0 \ Torsion Galante (2) Magnetic 3 Refraction Seisimt 7 (3)\ 2 | Resistivity, Inductive (2)\ Gas Survey Gravimerer Torsion Galance Refraction Sersact ()\ Reflection Seismic 2 | kesistivity, Inductive / 2 OF Cll ~ Giriclire Magnetic Gravimeler Torsion Galance 2 | Reflection Seismic Location Magnetic Torsion Balance / 2 | Reflection Seismic i SSS 1 | Magnetic (2) ens a E = 2 | Resistivity (2) 1 | Soil & Gas Analysis (2) From Jurtace shiva ¥ 4 2 | Resistivity (Y Fic. 4-1. Geophysical methods in oil exploration. Electrical Co oring detail methods for definite geologic conditions is given. Oil structures are divided into the better-known types of tectonic, volcanic, salt, and buried- ridge structures, with schematic illustration of the geologic forms. It is seen that for the tectonic-type structure the magnetic method is first choice 46 GEOPHYSICAL METHODS IN OIL EXPLORATION [CHap. 4 for reconnaissance, provided it is expected that basement rocks are some- what conformable to the structure in the sedimentaries, or provided some of the sedimentary beds are magnetic themselves. Second and third choices, respectively, in structure exploration are reflection-seismic and gravity methods. For detailed surveys, reflection work is first choice, torsion balance and gravimeter second. The reflection method has had the most brilliant success in Oklahoma for mapping the Viola and Hunton (Ordovician) limestone topography and has been applied in most other petroliferous areas in the United States and abroad. There are comparatively few prospective oil territories that cannot be worked with reflection methods. For general structural reconnaissance, gravimeter surveys to locate re- gional structural trends have been and are being conducted on a large scale along the coastal belt of the Gulf and in the northern parts of Texas and in the mid-continent. The torsion,balance has successfully located or detailed general structure-type fields in Texas, Oklahoma, California, New Mexico and other states. For the fault-type of structure, magnetic methods are probably not recommendable for first place in reconnaissance surveying. Even if basement rocks are expected to be somewhat con- formable to the oil-bearing series, they usually are too far away to furnish satisfactory information regarding faults—that is, faults of such throw as to be of importance in oil work. However, there are some faults which give a magnetic expression without apparent association with igneous rocks—the indication being directly above the fault plane. In the absence of a definite explanation for this phenomenon, magnetic methods should be relegated to second place for reconnaissance, while first place probably would be given to reflection and possibly torsion-balance methods, for both reconnaissance and detail. Applications of these two methods to the location of faults have been numerous in oil areas of this country and abroad. In cases where oil occurrence is associated with volcanic intrusions or dikes, the magnetometer is first choice for reconnaissance and detail, and the torsion balance is second. Examples are the intrusions at Monroe and Richland, Louisiana; and Jackson, Mississippi; and the intrusive dikes in the Tampico region of Mexico. There has been so much work done with geophysical methods in the salt-dome areas of the Gulf coast that the choice of methods in salt dome exploration is very definite, although the order of preference has undergone some changes during the past ten years. For domes down to 5000 to 6000 feet, refraction-seismic work was first choice, but the torsion balance and gravimeter are now more in favor, particularly for the deep domes and for detailing their crests. Reflection-seismic methods are best adapted for Cuap. 4] GEOPHYSICAL METHODS IN OIL EXPLORATION 47 detailing formations above and on the flanks of domes. The same applies to the salt dome or salt anticline regions of Tehuantepec in Mexico, the northern and north central regions of Germany, Rumania, and other areas of similar geologic structure. For the buried-ridge type of oil structure, magnetic methods are still first choice for reconnaissance surveying. However, as pointed out before, care must be exercised in the interpretation of the results. The magnetic method has been quite successful in general reconnaissance of the Amarillo buried mountains, the Nemaha granite ridgé in Kansas and its extension into Oklahoma and Texas, and similar buried-ridge type structures. Pendulum, gravimeter, and reflection-seismic methods are second choice in reconnaissance for this type. For detail, torsion balance ranks first, reflection-seismic methods second. Extensive torsion-balance, pendulum, and gravimeter work has been done in the buried-ridge areas mentioned above in connection with magnetic surveys. Very little has been accom- plished by geophysical methods in location of oil pools controlled by porosity variations and not by structure, that is, the lensing type of deposit. Magnetic work has been reported to be somewhat successful; resistivity methods also appear to be applicable. As far as the direct location of oil is concerned, it has not been demon- strated beyond all doubt that this is possible by use of the methods avail- able at present. Indications by the “Eltran’’ method appear in some cases to be related to shallow stratigraphic conditions above deeper oil accumulations. Eltran anomalies frequently coincide with hydrocarbon halos revealed by soil analysis methods. To what extent these methods can be depended upon to furnish reliable oil indications in completely new areas remains to be seen. The only place where indications can be obtained from the oil itself is underground, that is, by using the electrical logging method in wells. In fact, the resistivities recorded have in some cases been correlated with the productivity of formations. The advantages of electrical logging are: (1) the increase in drilling speed as mechanical coring is eliminated or re- duced to a minimum; (2) correlation of formations which may not have distinct petrographic or paleontological characteristics; (3) the possibility of locating water horizons; (4) continuity of the records; and (5) the ease with which electrical logging may be combined with other procedures, giving important physical data in a drill hole—such as measurement of temperature, side-wall sampling by bullets, and the like. In geophysical oil exploration it is often impossible to select the most suitable method, since other factors—cost, time, terrain, permits, and secrecy—in addition to the geologic factors, must be considered. Cost is of principal importance. It determines whether the work can be done 48 GEOPHYSICAL METHODS IN OIL EXPLORATION [CHap. 4 at all, in view of the available appropriation and anticipated returns, and, if so, which method will be the most economical. Frequently the con- sideration of cost may lead to the adoption of geological surveying or shallow drilling, where applicable, to replace or at least reduce the geo- physical work. Time may be another factor in view of competitive activities or expirations of leases and options, and it may readily lead to the selection of a faster but more expensive, in place of a slower and less expensive, method. Certain terrain conditions, such as swamps and water, will often eliminate some of the methods, for example, torsion balance, gravimeter and magnetometer, from consideration. Fortunately the most important reconnaissance and detail methods—seismic refraction and reflection—can be operated on both land and water. Rugged topog- raphy precludes the application of torsion balances, but seismic reflection work is still possible unless conditions are extreme. Adverse surface geo- logic conditions will handicap many methods, such as heterogeneous glacial beds in torsion balance work, igneous and metamorphic rocks in magnetic exploration, and high-speed surface formations in refraction and reflection shooting. Some types of surveys, for example, those with gravimeters and magnetometers, may be made along public roads without permits, while others requiring the most favorable terrain setups, as torsion balance and some reflection work, will necessitate going on private land. Remark- ably free from this restriction is the refraction method, inasmuch as plots of ground for which permits are not obtained may be placed between shot and detector location. In respect to secrecy, operation of gravimeters or magnetometers is much more favorable than is torsion-balance or seismic exploration. Finally, restrictions in regard to the use of dynamite or patented processes may be decisive factors in the selection of a method. Specific applications of geophysical methods to oil exploration problems will be found in Chapter 7 on pages 157-162, 272-286; in Chapter 8 on pages 422-433; in Chapter 9 on pages 499-501 and in Figs. 9-46, 9-74, 9-85, 9-92, 9-93; in Chapters 10, 11, and 12 on pages 706, 735-739, 752, 835-837, 856, 863-865, 869, 898-901, and in Figs. 10-122 and 10-123. The role of geophysics in oil exploration is reflected in a statement by De Golyer who says: “With good, not average, practice the cost of oil finding in the early twenties was 20 to 25 cents per barrel. Today on volume operation, the cost of oil finding for good practice is 10 to 12 cents per barrel.” It is estimated that geophysics has been responsible for the discovery of over 5 billion barrels of crude oil to 1939.° 2B. De Golyer, Mining and Metallurgy, 20(391), 335 (1939). 3G. Egloff, Colo. School of Mines Mag., 29(6), 277 (1939). 5 GEOPHYSICAL METHODS IN MINING Sxxecrine the correct geophysical method in mining is not so simple as in oil exploration because of the greater complexity and geologic variety of ore deposits. The choice is often facilitated by the fact that the type of ore body to be located is already known. Conditions prevailing in most mining areas (see page 6) eliminate the possibility of gravitational! and seismic methods, so that the choice is likely to be magnetic or electrical exploration. Which of these is preferable depends much on the type of ore and its origin. In the genetic classification of Fig. 5-1 mineral deposits are arranged largely in accordance with the scheme suggested by Lindgren. Geological and geophysical “type” locations, schematics of the zeologic form, and suggestions as to choice of direct and structural geophysical methods are given for six groups: (I) magmatic differentiation deposits, which are formea by crystallization within magmas and occur, therefore, mostly in intrusive igneous rocks; (II) heterogenetic solution deposits, formed by infiltration of solutions from without, usually derived from adjacent ig- neous formations; (III) autogenetic solution deposits, originating from chemical concentration of rock substance; (IV) sedimentation deposits, such as salt, coal, and limestone; (V) dynamo-metamorphic deposits, formed by concentration and chemical transformation of rock substance in conse- quence of diastrophic forces; and (VI) mechanical concentration deposits in gravels, conglomerates, and the like. Metal mining is concerned primarily with groups I-III and V-VI. Nonmetallic minerals are derived largely from deposits in group IV. I. METAL MINING Surprisingly enough the greatest number of geophysical methods are applicable to location of mechanical concentration (placer) deposits. They may be worked by magnetic methods where a definite relation between gold concentration and black-sand content can be established. For determination of depth to bedrock, resistivity and refraction-seismic 49 50 GEOPHYSICAL METHODS IN MINING [Cuar. 5 methods may be used. Extensive magnetic surveys have been conducted on gold deposits of similar type in the Witwatersrand fields of South Africa, where the suboutcrop of the gold series could be traced by virtue Type Locality Seophysical Deposit (Geophysical Geologic Form Method or Geelogrcal) pve lL. Magmatic Differentiation Deposits Diamonds ) Platinum S Chromite) Arkansas Urals Quebec lotrusives Kiruna, Urals, Magnetite lalirads Sulphide Nickel ores, Ores Sudbury HW Heteragenetic Solution Deposits Confact-mefamorphic: S Magnetile; Specl Hem. | New Mer, Sarony ~ Lead, Linc New Mer, SI Copper New Mex, Arizona Gold - Silver-Sulphides|) Calif. Nevada. Lead- Silver; Baryle Canada Tungsten, Fluorite Cole, /Minols Siderite, Molybdenite | N.Mex. Quarlz & Pegmatife vetos| Appol Chad brazil Fig. 5-la. Genetic classification of mineral deposits and applications of geophysical methods. of its association with magnetic shales. Reflection-seismic and electrical methods likewise hold promise in this area for structural investigations. Much geophysical work has been done on the type of mineral deposits classified above in group II (heterogenetic solution deposits). An example Cuap. 5] GEOPHYSICAL METHODS IN MINING ol is the application of magnetic methods to the mapping of contact-meta- morphic iron ores. For the location of contact-metamorphic sulfides, elec- trical methods have been employed. Magnetic exploration may be of Type Locality Geophysical Deposit (Geophysical Geologic Form Method or Geological) Ml. Autogenetic Solution Deposits Residual weathering & sec. depos: Lisonite, Hematite, Manganese, Gauxile Vanedium, Ureniura 35 Limestone, Cement rocks Organic: Coal Lignite Magnetite Kursk, Adrrond- acks, MY, Ms. Pyrrkotite Ducklown Platinum) Placers Witwarersrand (Possibly in Group 4) Fic. 5-1b. Genetic classification of mineral deposits and applications of geophysical methods (concluded). assistance for structural investigations (mapping of intrusives, contact zones, and the like). Electrical methods have good possibilities in the direct or indirect loca- tion of deposits falling in the category of hot-water concentrations. Ex- 52 GEOPHYSICAL METHODS IN MINING [CHap. 5 amples are: lead sulfides, iron and copper pyrites, cobalt ores associated with other sulfides, and gold-bearing quartz veins. It is often possible to trace the ore-bearing faults or fissures in which mineralized waters are circulating. This method has been applied on tungsten deposits in Colo- rado and fluorite deposits in Illinois. Magnetic prospecting will frequently furnish valuable structural information in such cases. In the Tri-State district referred to under group II, various methods were tried but no satisfactory way of locating the ore itself was found. Torsion balance measurements appeared to be capable of tracing chert zones associated with the ore and magnetic observations were used to outline highs in the underlying porphyry to which the major ore accumulations appeared to be related. The principal reason for the failure to locate the Tri-State ores directly is that zine sulfide, unlike other sulfides, is a nonconductor of electricity. Magmatic-differentiation deposits have been worked principally with magnetic and electrical methods. In part, these applications have been of an indirect nature, such as the location of diamond-bearing intrusions in Arkansas and of platinum ores in intrusive rocks in the Urals by magnetic methods. Chromite has been worked indirectly by its association with igneous rocks and with magnetite. Magnetite deposits of the magmatic- differentiation type have been surveyed primarily with the magnetometer, though torsion-balance and electrical methods have been applied occa- sionally. Much work has been done on nickel sulfide ores in the Sudbury district with electrical and magnetic methods. Magnetite deposits of the dynamo-metamorphic type (group V) have been surveyed primarily with magnetic and gravity methods (Kursk). Magnetic exploration likewise has had some success in the location of sedimentary ores, such as iron (hematite) and manganese. A moderate amount of geophysical work has been done on deposits re- sulting from concentration of rock substance (group III). Examples are: magnetic surveys of bauxite deposits, radioactive measurements on ura- nium and vanadium ores, and electrical prospecting for sulfide veins in intrusive rocks. Considerable attention has been given to the possibilities of geophysics in locating copper deposits in the lava flows of the Lake Superior region, but only the magnetic method was found to be successful for determining structural relations of the flows by tracing suboutcrops, faults, and the like. II. MINING OF NONMETALLIGS Nonmetallic mining is chiefly concerned with mineral deposits formed by chemical precipitation and mechanical sedimentation in surface waters (group IV, Fig. 5-1). In discussing the applications of geophysics in this Cuap. 5] GEOPHYSICAL METHODS IN MINING 53 field, a classification somewhat different from that customary in economic geology will be adopted. Petroleum, natural gas, asphalt, and related bitumina will be excluded, and the remainder will be classed as follows: (a) coal, (b) sulfur, (c) salt, (d) nitrates, phosphates, potash, (¢) building and road materials, (f) abrasives, (g) materials for various industrial uses, (h) gems and precious stones. A. Coat, INcLUDING ANTHRACITE AND LIGNITE In this group only anthracite and possibly lignite offer possibilities of direct geophysical location; virtually all other types of coal are amenable to indirect prospecting only. Anthracite may be located directly by self- potential measurements or resistivity or other electrical methods. Some anthracitic coals are conductive while some other varieties act as insu- lators.” In stratigraphic and structural investigations of coal deposits, various methods are applicable. For general reconnaissance, the magnetic method may be useful if the carboniferous strata are conformable with basement topography. For the mapping of regional Paleozoic structure, extensive pendulum surveys were undertaken at one time in northern Germany. For detail, electrical resistivity methods have been used. Examples are the Carboniferous syncline of Villanueva de Minas and Villanueva del Rio in Spain and the Saar coal basin. Both refraction and reflection-seismic methods can render valuable service in the determination of the structure of Carboniferous areas, as demonstrated in Spain, in Silesia, and in West- phalia. Under favorable conditions structural studies of the Carbonif- erous have been made by means of the torsion balance and the gravimeter. Various geophysical methods have been tried on lignite deposits. The success of electrical methods appears to depend greatly on the local stra- tigraphy and the water content of the lignite. Seismic-refraction methods have possibilities for determining the thickness of lignite beds. However, structural and stratigraphic investigations may be expected to be more successful as exemplified by Schlumberger’s electrical surveys in the de- partment of Landes, France, and by Edge-Laby’s and Seblatnigg’s torsion balance work on faults associated with lignite deposits in Australia and Germany respectively. B. SuLFuR Geophysics has been applied on a large scale to the indirect location of sulfur deposits found in the cap rocks of salt domes on the Gulf coast. 1¥For details and bibliography see C. A. H., ‘‘Geophysics in the Non-Metallic Field,’’ A.I.M.E. Geophysical Prospecting, 546-576 (1934). o4 GEOPHYSICAL METHODS IN MINING [Cuap. 5 Methods ordinarily used for the location of salt domes are applicable, especially gravimetric and seismic methods. C. SALT Salt is obtained commercially from salt brines, salt beds, or salt domes. The literature on the location of salt brines is meager and deals only with the type occurring in salt mines. As far as salt domes are concerned, the geophysical problem is the same as in oil exploration (see Chapter 4); for depth determinations of salt beds, seismic and electrical resistivity methods have been used. D. Nirrates, PHOSPHATES, POTASH It is doubtful whether any commercial geophysical work has been done on these deposits (owing to the abundant supply of nitrate in Chile, and of phosphate in the western United States). Since the commercially impor- tant potassium minerals occur with salt, the geophysical methods discussed in the preceding paragraph have found frequent application in the indirect location of potash deposits. Sifieriz’ second report? contains numerous examples for depth determination of salt beds in Spain. Underground, it appears possible to differentiate between potash beds of different age by measurement of their penetrating radiation. EE. BuitpING AND Roap MATERIALS Applications of geophysical methods in this branch of the nonmetallic field overlap with those in engineering and include cement. materials, gravel, sand and clay, and building and road stone. Cement materials possess a number of physical characteristics (for example: high elastic wave speed and density of gypsum, anhydrite, and limestone; electrical resistivity of lime, chalk, and the like) which indicate the best possibilities for electrical and seismic methods. Electrical, seismic, and (in case of crystalline bedrock) magnetic methods are suitable for the location of gravel, sand, and clay. Further details are given in Chapter 6 under the heading of engineering applications. A few geophysical surveys have been made for the location of building or road materials. Electrical exploration appears to hold the greatest possibilities, since resistivities of formations depend on their degree of alteration and moisture content. Magnetic methods are often applicable, since rocks preferable from the standpoint of roadbuilding (igneous rocks) 2 J. G. Sifieriz, ‘‘La interpretacion geologica de las mediciones geoficicas applica- das a la prospeccion,’”’ Inst. Geol. y Minero Espana Mem. (1933). Cuap. 5] GEOPHYSICAL METHODS IN MINING a5) are more magnetic than are sedimentary rocks, and basic (and more mag- netic) igneous rocks are preferred to acidic rocks in regard to toughness and abrasive resistance. Seismic methods have good possibilities for the location of road materials as well as for determining their composition, alteration, and general nature. F. ABRASIVES Where deposits are of sufficient size, as in the cases of diatomaceous earth, quartz sand and sandstone, the application of seismic refraction and electrical resistivity is indicated. G. MaTERIALS FOR VARIOUS INDUSTRIAL USES 1. Fluorspar. As this mineral is usually found in fissure and fracture zones, indirect structural prospecting, or locating of such zones by resis- tivity or electromagnetic methods is suitable. 2. Talc and soapstone. One instance is known in the literature where tale formations could be located by an electromagnetic method, since they reacted as poor conductors in contrast with adjacent graphite deposits. 3. Lithographic stone. See road and building materials. 4. Sand (used as construction material, abrasive, for glass manufac- ture, molding, filtering, furnace lining, and so on). Provided an applica- tion of geophysics is at all economical compared with surface-geological methods, electrical-resistivity method will be most suitable for the delinea- tion of sand lenses. 5. Monacite sands. In addition to resistivity and refraction surveys usable for the location of channels (see Chapter 6), radioactivity methods may be «r, tied to sands of high thorium content. 6. Serpentine. Magnetic methods are best suited for reconnaissance, to be supplemented by electrical and possibly seismic measurements for detail. 7. Barite. Its high density makes the torsion balance or gravimeter applicable, provided that topography is suitable. Barite, being a poor conductor, may be located in more conductive rocks by surface-potential methods. When barite occurs with conductive minerals such as pyrite, almost any electrical method could be suited. 8. Graphite. This mineral may be readily located by most electrical methods. It produces strong self-potentials, usually of positive sign. 9. Magnesite, feldspar, asbestos, mica. The geologic occurrence of these minerals suggests that any application of geophysical methods (probably magnetic or electrical) would have to be of an indirect nature. 56 GEOPHYSICAL METHODS IN MINING [CHap. 5 H. Gems AND PREcious STONES A direct location of gems by geophysical methods is out of the question. In some instances a survey of the formation in which they occur may be of assistance. Examples are the peridotite plugs in Arkansas and the blue- ground pipes in South Africa. Where diamonds occur in sands and gravels of stream and beach deposits, methods discussed under the heading of engineering applications of geophysics may be useful for locating and tracing lenses or channels. Specific applications of geophysical methods in mining are discussed in Chapter 7 on pages 162, 286-292; in Chapter 8 on pages 409-422; in Chap- ter 9 on pages 501-502 and Figs. 9-41, 9-49, 9-75; and in Chapter 10 on pages 675-681, 703-706, 739-741, 755-757, 771-773, and 802-805. 6 APPLICATIONS OF GEOPHYSICS IN ENGINEERING A ppiications of geophysical methods in engineering are of fairly recent date. Although many engineering problems may be attacked by geo- physics, developments have been slow for various reasons: (1) information on the possibilities of geophysics has not been readily available to engineers; (2) few engineering projects compare in commercial scope with oil and mining projects; (3) in near-surface engineering problems geophysical exploration has to complete with surface geology and drilling. It is unfor- tunately true that numerous engineering projects are still undertaken without consulting a geologist. With an increased appreciation of the advantage of geological advice, an increase in the number of applications of geophysics to engineering problems will undoubtedly follow. Engineering applications of geophysics may be divided into two classes: (1) geological, and (2) nongeological. I. GEOLOGICAL APPLICATIONS These are concerned with: (a) foundation problems; (b) location of construction materials, and (c) water location. A. FouNDATION PROBLEMS As shown in Table 4, special problems in this category are: determina- tion of depth to bedrock, of type of rock encountered in dam, aqueduct, canal, tunnel, shaft, harbor, bridge, railway, highway, tramway, subway, _ and other construction projects. Similar problems in the field of military engineering are tests of foundations for military roads, railroads, shelters, forts, and other underground mining operations. They are best attacked by seismic-refraction and electrical-resistivity and potential-drop-ratio methods. ‘The seismic-refraction method is aided by the considerable velocity contrast existing between overburden and bedrock. Similar con- ditions prevail in electric potential surveys, since the resistivity of the 57 NOLL -OULEC IVWUaHL aL x x x x ‘wag ‘sex “IO ‘10978 aN ad sainyoni3g 4 x x eyeIIUOD ‘Ta01g ‘19q TV¥UOLONULe -wiy, ‘Aiuossyy ‘saspiug x x x Aeeng seme ty NOILVLYUOdSNVU ‘Kemprey ‘Away siyy L esvulvig puB ‘UOT}ESILU] x x x x x x ‘adviamag ‘Ajddng 10984 SINS s10qie x x x pus ‘sisAIy ‘sjouuny, | OlINvVaaAy aNv ‘syyeyg ‘speusy ‘syonpoen NOILVGNQOJ -by ‘sweq ‘syiomyyreq 2189 ,1, o1pey F UuOIPIBIJOY esuodsay |euoqdosy| oroorg | oviouteyy | “Sr Sou.e weeny Bae 81070030 eeree JO |T819WE}0d Z) -ON0TA CE) “gar | orumstag g | orumsieg Z +—dOHLa 40 GOIOHD OD | eoaner een Teg Te lenuoree g| OMPULZ | Sunde | oxoIGF aengt | aneumey 1] oe, leNueved Tperueiodt g@OVAVG NOLL SLOEraO OEE “Vaal, panics exmauag UTIVIGW | yazy M TVIUALV poet ae oma | asvnp |ONVNOL| Nors padi ao |PNTCNOAD | -Nog +—IVOISAHY HO IVOISKHAOMH ‘WAIGOUT Tar], sv5 -nuavg | @8C | -O880D | paar ao | NOMVIOT |worzyoor, | INV Of ‘ontoayy| TX20S NOLLVOO'] BISECT NIVUIG ONIYHUNIONG AUVLITIN AGNV TIAIO NI SGOHLAW TVOISAHd ANV TVOISAHAOUD py GIav ye ONIUHANIONY TIAIO 58 u01}09}9q [ewseyy, ‘Sursuey punog IVINay WOT}BIOT Siaqaoy ‘Zuripunog oyoq ‘u01j00}9q «= 9ulIBUIqng ‘SUI[BUBIC oulIBUIqng ANIUVIN DIVJIBVAA [BOTWIYD x x x ‘soAIso[dxy paring Sjsog Sul -uaysIT ‘duIsuey punog | |] fv anv x osevurviq ‘Ajddng 10384 SUONBVOAIOT PP me x ‘Sulu, Areqyy ‘spvos “Tey ‘speoy AreqI ITV 59 ONIYGANIONG AUVLITIY 60 APPLICATIONS OF GEOPHYSICS IN ENGINEERING § [Cuap. 6 overburden is usually lower than the resistivity of the more consolidated bedrock. Both seismic velocities and electrical conductivities furnish valuable information on the type of rock encountered in dam, tunnel, or similar sites. Additional information may be obtained by dynamic vibra- tion tests which will give the natural frequency of a building site as well as the elastic moduli and bearing strengths of overburden and bedrock. B. LocaTIon OF CONSTRUCTION MATERIALS This application of geophysics is important in (1) foundation and hy- draulic engineering in connection with the construction of dams, canals, tunnels, bridges, and the like; (2) sanitary engineering; (3) transportation engineering: (railway, highway, tramway, and subway construction); (4) structural engineering; and (5) military engineering. FElectrical-resistivity, potential-drop-ratio and seismic-refraction methods are applicable; details were given previously in the section on nonmetallics in Chapter 5. C. LocaTION OF WATER The location of water plays an important part in sanitary engineering in connection with water supply, sewage disposal, irrigation, and drainage problems. In transportation engineering, determination of water levels and water-bearing fissures is essential for subway and tunnel construction. The same applies to military engineering. Prospecting for water is one of the most difficult tasks in geophysical exploration. It requires exceptional geologic ability on the part of the geophysicist. In the ideal case, the geophysicist should be able to (1) locate the water, (2) determine its salinity, and (8) estimate yields. At the present status of technique, he can rarely hope to predict yields, and he can make only approximate calculations of salinity when working away from wells of known water composition. Hence, the geophysicist’s task is narrowed down primarily to the location of water itself. Underground waters may be divided as follows’ in decreasing order of geophysical importance: (1) ground water proper, which includes waters derived from precipitation and “‘connate’”’ water; (2) fissure water; (3) cavern water; (4) spring water; and (5) water issuing from leaks in water pipes. Applications of geophysics to waters in the first group are con- trolled largely by the geometric disposition of the reservoir. The following types are of importance: (a) horizontal (or stratigraphic) boundaries; (b) lateral confinement by vertical boundaries such as faults, dikes, or fracture zones; and (c) erosional boundaries of impervious rocks. 1 See tabulation in C. F. Tolman, Ground Water, p. 265, McGraw-Hill (1937) and in Trans. Am. Geophys. Union (1937), Hydrology section, p. 575. Cuap. 6] APPLICATIONS OF GEOPHYSICS IN ENGINEERING 61 There are three general possibilities for the geophysical location of water: (1) direct, (2) structural, and (8) stratigraphic location. 1. Direct location. Water occurring in the form of thermal, saline, or radioactive springs may be located by temperature, electrical, or radio- activity measurements, or by its noise in escaping from pipe leaks. Brine accumulations in salt mines may be found by electrical-resistivity, induc- tive, or radio-transmission observations. Water occurring in caves and fissures is on the borderline between direct and stratigraphic location, as it is often difficult to decide whether the indication comes from the water as such or from an impregnated medium. Water filling large cavities in limestones or dolomites may be located directly by resistivity measure- ments or, if it is sufficiently conductive, by inductive or radio methods. Water which occupies fissures is often heavily mineralized and may thus be detected by inductive, resistivity, radioactivity, or radio measurements. Direct application of geophysics to the location of the ground-water table is limited to such special problems as the determination of the vertical moisture gradient by hygrometric observations in different depths and the calculation of the rate of motion of a ground-water stream in wells by salting the water and measuring the rate of motion of the surface potential peak due to the lateral motion of the salt-water front. 2. Structural water location involves the attempt to find locations favor- able for its occurrence. It entails the mapping of certain formations which may or may not be aquifers and which may occur in synclines, troughs, or areas of general depression. Hence, virtually all major geophysical methods are applicable, depending upon whether differences in density, magnetism, elasticity, or conductivity occur on a stratigraphic or erosional boundary. For instance, water-bearing gravel channels and valley fills may be mapped by torsion-balance, seismic, or resistivity methods. The magnetometer may be applied for tracing channels in igneous or meta- morphic rocks. Ifa reservoir is confined laterally by faults, gravitational, seismic, resistivity, or magnetic methods are applicable (if igneous dikes cut through the water-bearing strata). Key beds in large artesian basins have been surveyed by reflection-seismic methods. - In the location of fissure water the function of structural geophysical work is the mapping of fissures or faults. Gravitational, magnetic, seismic, or electrical methods apply, depending upon whether strata with differ- ences in density, magnetic, elastic, or electric properties have been placed in juxtaposition by the faults. 3. Stratigraphic water location has for its objective a determination of the condition and depth of the aquifer itself. The choice of geophysical methods is here much more limited. Seismic methods are applicable under favorable circumstances as the elastic wave velocity is greater in moist than in dry, unconsolidated formations. More important and inex- 62 APPLICATIONS OF GEOPHYSICS IN ENGINEERING § [Cuap. 6 pensive are electrical methods. Their application rests on the fact that water in the pores of a rock changes its conductivity to such an extent that the conductivity of the mineral substance is virtually without effect. Hence, the following factors are effective: (1) porosity, (2) percentage of pores filled, and (8) electrolytic conductivity of the water. The latter depends very much on the degree of stagnation in a rock and complicates the geophysical picture, as the groundwater may be either a good or a poor conductor. Very pure waters are more difficult to locate than waters of fair conductivity. The former requires sensitive electrical- potential methods, while waters of high salinity, particularly connate waters, may also be found by inductive-electrical procedures. It is further impossible to recognize water by a spectfic value of rock conductivity. The change brought about by the presence of water is not great enough to produce outstanding values; therefore, it would be diffi- cult to select an arbitrary location in virgin territory and to determine the presence and depth of water from the geophysical response. However, where the presence of an aquifer has been established by wells, it is possible to correlate conductivities with water-bearing formations, their depth, type, and thickness, and to follow this type of indication into unknown territory until a complete change in character occurs. With resistivity methods, frequently a “typical” ground-water curve is obtained, which is discussed in greater detail in Chapter 10. II. NONGEOLOGICAL APPLICATIONS Though not directly geophysical but closely related to geophysics, since they involve-similar techniques, these applications include: (a) dy- namic vibration tests of structures, (b) strain gauging, (c) corrosion surveys, (d) pipe and metal location, (e) sound ranging and other acoustic detection methods, (f) gas detection, and (g) thermal detection. A. Dynamic VIBRATION TESTS OF STRUCTURES These tests involve a determination of natural frequency and damping characteristics of completed structures and of models of proposed struc- tures to determine their seismic resistance to earthquakes and artificial vibrations by the free and forced vibration methods. Details are given in Chapter 12. B. StraIn GAUGING The purpose of these measurements is to determine the variations of elastic strains with time in structures and underground workings so that Cuap. 6] APPLICATIONS OF GEOPHYSICS IN ENGINEERING 63 zones of weakness may be found and failures predicted. In connection with subsidence investigations, mine workings have been thus tested to predict wall or roof failure; shafts and tunnels have been examined in areas of active faults and earthquakes; strain gauges have been installed in important structures, such as Boulder Dam; and like methods have been used on models of dams and other structures. C. Corrosion SURVEYS The purpose of these surveys is to follow the process of corrosion, chiefly on buried pipes, and to determine progress made by preventive measures, such as cathodic protrction and coating. Two procedures of geophysical exploration are applicable: (1) self-potential surveys and recordings, and (2) resistivity measurements. By self-potential measurements along a pipe, the areas of ingress and egress of current and therefore the zones of greatest destruction of pipe material may be located. Recording fiuctua- tions of spontancous potentials issuing from buried pipes, gives information about occurrence and time variations of vagabondary currents producing corrosion. Resistivity measurements serve to find areas of high ground conductivity in which, according to experience, corrosion is greatest. D. Pier anp Metau LOCATION Occasionally it is necessary to locate pipes of which the record has been lost. If the lost pipe is part of a network accessible elsewhere, it may be energized by contact and located by following the electromagnetic field surrounding it. Isolated pipes can be found by so-called ‘‘treasure finders,” consisting of combined radio transmitters and receivers, described in more detail in Chapter 10. Magnetic prospecting can be applied in favorable cases. Methods for the location of buried ammunition and other war machinery, and procedures for the detection of metal and weapons on workers and visitors of mints and penal institutions belong in the same category and require the same or similar procedures. I. Sounp RANGING AND OTHER AcousTIC DETECTION METHODS As outlined at the end of Chapter 2, (page 37), acoustic detection methods are used for communication, direction finding and noise analysis, position finding, sound ranging, and echo sounding. Applications of these methods in the fields of civil and military engineering are numerous. Acoustic means of communication, particularly at supersonic frequencies, are widely used between surface vessels and submarines, and between submarines and shore stations. Radio-acoustic position finding is a valu- 64 APPLICATIONS OF GEOPHYSICS IN ENGINEERING [CuHap. 6 able aid in navigation. Sound ranging is used in both the army and the navy for locating enemy guns and for determining the range of their own artillery. Direction finding and noise analysis applies in the detection of airplanes, submarines, and enemy sappers, and the location of pipe leaks in sanitary and pipe-line engineering. Echo sounding methods are cur- rently applied in the merchant marine and the navy for measuring the depth to sea bottom. Occasionally they have been applied in the location of icebergs and in finding the depth to fish shoals. An electrical reflection method based on frequency modulation of ultrashort waves has made possible the airplane terrain-clearance indicator. F. Gas DETECTION Gas detection methods are applied in chemical warfare, in pipe-line engineering, and in mine safety work. Detectors have been constructed for both combustible and toxic gases and are used to find leaks in buried gas pipe lines, gases in manholes, mine openings, and the like. G. THERMAL DETECTION Thermal-detection methods involve the location of objects by their heat radiation. During the war it was found that planes could be detected by the heat issuing from their exhaust pipes; icebergs have been located at appreciable distances by such detection methods. PART II 7 GRAVITATIONAL METHODS I. INTRODUCTION GRaVITATIONAL EXPLORATION falls in the category of “direct” geo- physical procedures by which physical forces are measured at the earth’s surface without application of an artificial extraneous field: The field of gravitation is present everywhere and at all times; it is due to the funda- mental property of all matter to have mass. Since all masses, regardless of size, exert an attraction upon one another, any method designed to measure the gravitational field will invariably determine the influence of all masses within range and, therefore, lack the depth control possessed by the seismic and the electrical methods. Consequently, direct methods of interpretation (that is, determinations of the depths, dimensions, and physical properties of geologic bodies from surface indications) are rare and applicable only where essentially one single mass produces the gravi- tational anomaly. The application of gravitational exploration methods is dependent on the existence of differences in density between geologic bodies and their surroundings. Because of the vertical differentiation of the earth’s crust in regard to density (due to the general increase of density with depth and the effect of structural movements which have uplifted deeper and denscr portions and have placed them in the same level as younger and lighter formations) there occur changes of density in horizontal direction which are essential for the successful application of gravitational methods. For the interpretation of gravity data, it is fortunate that densities remain constant for considerable distances in formations which had their origin in large depositional basins. Although gravitational exploration is concerned with one field of force only, a number of characteristic parameters exist which lend themselves readily to accurate observation. The magnitude of the gravity vector is determined by measuring the oscillation period of a pendulum or the deflection of a mass suspended from a spring (gravimeter). It is not feasible to measure the absolute direction of the gravity vector in space. 67 68 GRAVITATIONAL METHODS SYMBOLS USED IN CHAPTER 7 [CHaP. 7 BScvwrFer FE YHe AOSTA ~ 2 XR 'D Q io bh -aNice 8 ae. distance, equatorial radius distance, breadth (spring) constant, polar radius deflection, distance, thickness distance frequency gravity height, elevation, distance dip gravitational constant - length, thickness mass scale reading, coincidence inter- val pressure quotient radius, distance distance time volume width coordinate coordinate coordinate jar moments of inertia \terrain correction coefficients depth Young’s modulus Eétvés unit force couple per radian height, elevation integral sectional moment of inertia moment of inertia distance, length m oO & 2 & 5 4 mo sw K coefficient coefficient coefficient coefficient coefficient focal length humidity coefficient number coefficient coefficient coefficient coefficient coefficient coefficient coefficient coefficient coefficient; weight astatization buoyancy constant, curvature value, capacity couple, moment voltage flexure gravity gradient horizontal force terrain correction Cnap. 7] GRAVITATIONAL METHODS 69 SYMBOLS USED IN CHAPTER 7 NNWMwMWSTAHBWaROWOSE bP oR DR Oe! ocean « SUSE 82) GE 6 MO ato ea avr ee Se mass restoring force coefficient porosity pyknometer weight radius, distance chronometer rate period potential potential potential horizontal force horizontal force vertical force azimuth, amplitude angle angle density difference scale value elevation restoring force angle angle labilizing force angle micron (10-4 em) scale interval angle 3.1416 radius, distance water content sensitivity torsion coefficient deflection angle, latitude, phase angle parallax angle angular velocity, angular fre- quency yo. a 2 < Yo coefficient coefficient coefficient coefficient differential curvature section, surface, area static magnification weight coefficient coefficient normal gravity torsion balance deflection elasticity temperature rigidity modulus sum 70 GRAVITATIONAL METHODS [Cuap. 7 However, differences in its direction between locations may be determined (‘deflections of the vertical’). The Eétvés torsion balance is used for measuring the rate of change, or gradients, of gravity and of its horizontal components in horizontal direction. In more common terminology, this measures (1) the north gradient of gravity, (2) the east gradient of gravity, (3) the difference in the maximum and minimum curvatures, and (4) the direction of minimum curvature of an equipotential surface of gravity. For the measurement of the vertical gradient, various instruments have been suggested but they have not come into practical use. There are no methods in present use to measure the potential of gravity; the pendulum and gravity meters measure its first derivative and the torsion balance its second derivatives. Instruments employed in pendulum exploration rather closely resemble those developed for scientific purposes. The development of a geologically useful gravimeter, attempted repeatedly since the turn of the century, is largely the result of the efforts of commercial geophysicists. On the other hand, the torsion balance, long known to physical science, has been adopted by exploration geophysicists in the form developed by Eétvés, with com- paratively minor changes. The pendulum and gravimeter have been used predominantly in oil exploration to outline large regional geologic features, to determine base- ment-rock topography, and to locate buried ridges. Owing to its greater accuracy and rapidity, the gravimeter is being used for more local problems of oil geology, for example, location of domes, anticlines, salt domes and general structure. Attempts have also been made to use the gravimeter in mining, primarily for large near-surface ore bodies, to supplement data secured by other geophysical methods. The torsion balance has been used predominantly in oil exploration for the determination of general geologic structure, mapping of basement topography, and location of buried ridges, anticlines, domes, terraces, faults, volcanic dikes, intrusions, and salt domes. In mining exploration, the following problems have been attacked by the torsion balance: location of iron, copper, and lead ore bodies, faults, dikes, veins, meteors, lignite and barite deposits, and salt domes (exploration for sulfur and potash). Indirectly the torsion balance has been of use in mining in the determina- tion of the thickness of the overburden, mapping of buried channels, and the like. II. ROCK DENSITIES A. DETERMINATION OF Rock DENSITIES A direct determination of formation densities in situ is possible from gravitational measurements if the dimensions and depth of a geclogic Cuap. 7] GRAVITATIONAL METHODS 71 body are known from drilling or from other geophysical surveys, or these measurements may be made from a gravimeter traverse across a known topographic feature not associated with structure.” The prevalent pro- cedure is to secure representative samples from outcrops, well cuttings, or *underground workings, and to test them in the laboratory. Methods of rock-density determination do not differ much from standard physical methods of measuring densities of solids. Difficulties arise only with specimens from unconsolidated formations or with samples of large pore volumes or permeabilities. 1. Measurement of weight and volume is widely used for determining densities of surface strata in connection with torsion balance terrain correc- tions and is practically the only method available for this purpose. A comparatively large quantity of the sample is placed in a cylinder ranging in volume from 1000 to 2000 cc, taking precautions not to alter its pore volume. Cylinder and sample are weighed, and the weight of the empty cylinder is deducted. If mass of the sample is m grams and its volume is v cc, the density 6 = m/v. If a great number of determinations have ‘to be made, it is of advantage to use a portable balance with horizontal arm graduated in density units, since the volume of the sample may be kept constant. If the rock sample is solid and of irregular shape, its volume is determined from the amount of water it displaces in a calibrated glass cylinder; for water-soluble samples, alcohol, machine oil, kerosene, toluol, or a saturated solution of the same substance is substituted. Air bubbles must be removed with a brush, by shaking the vessel, boiling the water, or by using an air pump. 2. The pyknometer is a small glass flask of precisely determined volume with a ground-in glass stopper extending into a fine capillary to provide an overflow for excessive liquid. It is useful for measuring densities of small specimens only. Determination of three weights is necessary: (1) of the specimen (m); (2) of the pyknometer filled with water (Q); (3) of the pyknometer with specimen (Q’). Then the density of the sample: 6 = m/(Q + m — Q’). | 3. Weighing in air and water is a very common method of density deter- mination. If the weight of a specimen in air is m and under water it is m’, the buoyancy B = m — m’, and the density 6 = m/B. An ordinary balance may be adapted to this test by first balancing the sample on the balance in air and then suspending it in water with a fine wire or in a small pan. Allowance for the weight of this pan under water is made by a corresponding adjustment of the balance. Specimens soluble in water are weighed in some other liquid (see paragraph No. 1); the result is multiplied by the specific gravity of the liquid used. Powdered minerals 1 This applies only to near-surface formations. See L. L. Nettleton, Geophysics, 4(3), 176-183 (1938). 72 GRAVITATIONAL METHODS [CHaP. 7 and rocks are inclosed in a thin glass tube. Porous specimens are coated thinly with wax, shellac, or paraffin. Clays should be weighed in machine oil of high viscosity. To reduce interference due to surface irregularities, fairly large samples should be used, since the surface is proportional to the second power of the dimensions and the volume is proportional to the third power. A number of balances have been designed for the determination of the density of rocks by the buoyancy method. Typical examples are the Schwarz and Jolly balance. The former (see Fig. 7-1a) is designed in the fashion of a letter scale and may be used for light and heavy samples, two ranges being provided by two lever arms and two graduations. In the Jolly balance (Fig. 7-16) the two pans are suspended from a coil spring whose extension is read on a scale. If the speci- Fic. 7-la. Schwarz bal- Me 38 Placed in the upper pan and the index ance for determining spe- lowered h scale divisions, and is then placed in the area Cueus Keil- lower pan corresponding to a reading of A’ ac divisions, the density 6 = h/(h — h’). 4. The flotation method is used for the determination of densities of very small mineral specimens. A specimen is first floated in a liquid of greater density which is then diluted until the specimen neither comes to the surface nor goes to the bot- tom. At that moment the density of the liquid as determined by a hydrometer is equal to the density of the specimen. Examples for heavy solutions are: bromo- Fic. 7-16. Jolly balance. form (CHBrs), 6 = 2.9; mercury-potas- sium-iodide (Thoulet’s solution, 2Hgl-- 2KI.3H.O), 6 = 3.2; barium-mercury-iodide (HgI,:2Bal), 6 = 3.59; and thalliumformiate, 6 = 4.76 at 90°C. B. Factors AFFECTING FORMATION DENSITIES In an evaluation of the applicability of gravitational methods to a given geologic problem, and in the calculation of the effects of geologic bodies of definite properties, it is necessary to make reasonable assumptions in regard thereto or to extrapolate from tabulated values when samples for the desired depth or locality are not available. In order to arrive at correct values, an evaluation of the influence of changes in chemical compo- Cuap. 7] GRAVITATIONAL METHODS 73 sition, depth of crystallization, porosity, depth of burial, moisture, and so on, is desirable. 1. Densities of igneous rocks generally increase with a decrease in SiO content. For instance, the average density of granite is about 2.65, that of gabbro, 3.00; the density of quartz porphyry is 2.63, that of diabase, 2.95; the density of rhyolite is 2.50, that of basalt, 2.90. Holocrystalline igneous rocks solidified at greater depth generally have a higher density than effusive igneous rocks of the same chemical composition. Hence, the igneous rocks older than Tertiary are heavier than Tertiary and younger igneous rocks, as is seen from the tabulations in paragraph 2 following. The density of igneous rocks decreases with an increase in the amount of amorphous material. Igneous magmas solidified as volcanic glasses are generally lighter than magmas with more crystalline matter. For instance, the average density of basalt is 2.90; that of basaltic glass, 2.81; the density of rhyolite is 2.50, but that of rhyolite glass is 2.26. 2. Mean densities of ore bodies as a function of mineral composition. Although the density of most commercial minerals is high, its influence upon the mean density of an ore body is not always so great as may be expected because of irregular distribution or lack of concentration through- out the ore body. Table 5, which gives average quantities of commercial ore per 100 tons of mined material, illustrates the small contribution to the mean density of an ore body which may be expected from even the heavy minerals. TABLE 5 AVERAGE QUANTITIES OF COMMERCIAL ORE PER 100 TONS OF MINED MATERIAL JSC iS 2 Nee ei aa 25-45 tons COppere Ge. ec a-. 1-2} tons Manganese................ 10-25 ‘‘ PL ieperwiyin: Wahone | Sess 3 0.5-1 ae Wr OMe i a2): Svlaidisis So's 10-25 ‘‘ ING CK SL aioe So 2ahs wena s 0.75-2.5 My MAI Cre Meese Pi ly dcr. sO=Lo) use MerGunyics..). Yor. denis a2 Oke * 1LG yt le a tiyeth beet i ail emme, 5-12.“ Silver fo ee 0.020-0.075 ‘‘ Golden ooh. eee 0.0008-0.0015 ‘‘ Source: F. Beyschlag, P. Krusch, and J. H. L. Vogt, Die Lagerstaetten der nutzbaren Mineralien und Gesteine, Vol. 1, p. 216 (1914). On the other hand, an association with (usually noncommercial) minerals may increase the mean density of an ore body; for example, if silver or zinc is associated with lead; copper and gold with pyrite; nickel with pyrrhotite, and so on. If the quantities of minerals present are well enough known, it is a simple matter to compute mean densities. For an ore body containing 75 per cent quartz and 25 per cent galena, the re- sultant density is 0.75 X 2.6 + 0.25 X 7.5, or 3.82. The tests in Table 6 were run on ore samples containing quartz as gangue and containing 74 GRAVITATIONAL METHODS [Cuar. 7 varying percentages of iron, copper, and zinc-sulfide ore whose mean density was 4.71.” In some ores the densities are directly dependent on the iron, lead, or copper content; the mean density may then be computed from chemical analyses, as borne out by the correlation of analyses and densities in Table 7.° 3. Densities of sedimentary formations change with porosity, mozsture, and depth of burial. The porosity of a rock is given by the ratio of volume weight and density. If 64 is the dry volume weight (“‘bulk density’), and 5 the density of the substance (“mineral density”), the porosity P = 1 — 6/6. The density of the sample (powdered, if necessary) may be determined in a pyknometer and the volume weight by the method de- TABLE 6 SAMPLE No. Per CENT ORE DENSITY ty) TE CO SR BES ee ie, 18.0 Balu DR a7 Valea hc euie tee pee aete pa Tne ed 5 Am 24.0 3.32 NRA TERC CEE ERENCE red nbn TE URE de 36.4 4.09 OAR EUAN seaport RMR) hin: 2p tok 43.9 4.48 TABLE 7 SampLte No Inon Content Density SaAmPur No. Iron ConTENT DENSITY | et arte on oe 14.33% 2.88 (ge Seat Hees ie Me 43.95% 3.78 PAE AS EISLER 24.45 3.20 EES AEN Aa 47.50 3.92 BS Aen Oe eer 31.10 3.37 Brahe ted eek apes 49.25 4.01 Bee: Eaten seek Ne 31.15 3.37 Qe ahr ane eras 62.35 4.73 Se eee eke 36.25 3.56 LO ses eee 63.95 4.83 TABLE 8 Igneous rocks (except pumistone) and metamorphics................... 1%- 3% Dynamo-metamorphosed sediments................... cece eee e eens 1 -10 Consolidated sediments: .o. .3). ce)5506 25. AG ee ee a ee eee 10 -30 Unconsolidated sediments, mostly postcretaceous (except diatomaceous earth and’ peat) 5.65 oy. ccs 5 As eee nels ee tee 5 anc eee 25 ~60 scribed under paragraph A-1. Porosity of rocks depends on the degree of consolidation in the course of their geologic history as well as on weather- ing when exposed at the surface. Igneous rocks have smaller porosities than sedimentary rocks. Table 8 gives a tabulation of average values for unweathered rocks. In the last group, shales and clays show the greatest variation. Imme- diately after deposition, muds may have porosities as high as 70 to 90 per cent, silts from 50 to 70 per cent, sands from 30 to 40 per cent. Moisture affects their bulk density considerably. Hedberg has deter- mined porosities and densities of clays and sands from many localities.” 2 After H. Reich, Handbuch der Experimentalphysik, Vol. XXV, pt. 3, p. 16 (1930). 3 Ibid. 4H..D. Hedberg, ‘‘The effect of gravitational compaction on the structure of sedimentary rocks,’’? A.A.P.G. Bull., 10(11), 1035-1072 (1926). Cnap. 7] GRAVITATIONAL METHODS 75 Weathering may produce appreciable changes in porosities and densities of surface formations, which may have to be allowed for in torsion-balance terrain corrections when they occur near the instrument. Densities of formations undergo considerable change when their condi- tion is disturbed artificially. Consideration of this effect is important in leveling torsion balance stations in hilly country. The volume weight of soil or clay may be reduced as much as 50 per cent, as shown in Table 9.° TABLE 9 Buie Dsgnsity or Rock Rock in Situ Fill ELS Yy ae se Me a oral te chs) 4) welt g al apaaiele aan cua 2.992 1.712 GrANiter sete bis oars Cu MP ee aad 2.720 1.552 Sandstone: sce cetasn «cle Meo ek Let eee 2.416 1.376 In the course of their geologic history, sediments are submerged to greater depth and subjected to gravitational pressure and diastrophic forces which bring about an expulsion of excess water, a dehydration of colloids, and a deformation and granulation of soft grains. This results in an apparent increase of density with geologic age. The effect of gravi- tational pressure on density and porosity may be determined for moderate pressure from experiments on sands, clays, and muds. Hedberg® calcu- lated the variation of shale porosity to be expected with variations in overburden thickness. A number of other attempts have been made’ to express changes in density with depth by a simple formula. However, it is doubtful whether such relations, based on observations in one area, are universally applicable for geophysical purposes, since the variable effects of diastrophism cannot be separated from those resulting from — gravitational compaction. For instance, Hedberg’s recent density-depth curves® (see Fig. 7-2) indicate a much smaller increase of density with depth than do the curves published earlier for the mid-continent. Hedberg concludes that it is best to use different expressions for the ranges 0 to 800, 800 to 6000, and 6000 to 10,000 feet,® but for practical convenience he gives the following approximation formula for the entire range (except the first 200 to 300 pounds): P (porosity) = 40.22.0.9998? where p (the exponent) is pressure in pounds per square inch. 5 After A. C. Lane, Geol. Soc. Amer. Bull., 33, 353-370 (1922). 8 Loc. cit. 7W. W. Rubey, Amer. Assoc. Petrol. Geol. Bull., 11, 621-638, 1333-1336 (1927) ; U.S. Geol. Survey. Prof. Paper, 166A, 1-54 (1930). L. F. Athy, Amer. Assoc. Petrol. Geol. Bull., 14, 1-24 (1980), zbid., Sidney Power Mem. Vol., 811-823 (1934). 8H. D. Hedberg, Am. J. Sci. $1(184), 241-287 (April, 1936), with very complete bibliography on the subject. ® Depth in feet and pressure in pounds per square inch are almost equal nu- merically. 76 GRAVITATIONAL METHODS [CHaP. 7 The pores of rocks are usually not filled with air alone, but also with water, oil, and/or gas, of which, for geophysical purposes, water is the most important. It is difficult to estimate the percentage of pores filled; 50 per cent is probably a good average. Water content ranges from 20 to 60 per cent in moderate climates and is less in arid, greater in humid Porosity Density Depth of Overburden in Feet Fig. 7-2. Relation of shale porosity and density to depth, Venezuela (after Hedberg). TABLE 10 Wet VOLUME Rock DENSITY 6 WBIGHT dg TENCOUBITOCKS 4A; oh..5ciereeenc ie aes takers Meee 2.80 2.80 Clase oN yt Mae ne, RRR eu ati ens MERE NL WE 2.69 2.51 Sandstones ih.) 86s) sis. See ote tae 2.67 2.35 IIMIESF ONES i yinejarcthiss\nive hee eae oe eee 2.76 2-64 TABLE 11 : Dry VoLUME Wet VoLUuME Rock . WEIGHT WEIGHT GRATES ieee Sass Sed ee ae fs ee, 2.58 2.60 TD OVEN IGG ig sca eee aS oe eRe See. ee 2.89 2.90 A BTV STr Rea ea 95 Te DAN NER CRS a as Sate 0h 2.87 2.88 Serpentine: osi070 ts. At sa Uae. RMON Oa 2 2.71 TiAl ScHistt as apd tise) chess Ses ae cet ee 2.65 2.67 Shaley car Foe Ae ks Mok cae aa re Ee Qaeo P(E Sandstonere tance Mek otter are de er ree Ree DAG 2530 Permian and Triassic sandstone, av.............. £2200 2.27 Hocenevsandstones. +h. soca 0) tae eins ee eee 1.86 2.18 1.91 2.20 Porousdimest 2.012 2h, ashe nk ce Mea See eee climates. The wet volume weight (natural density) 6, may be computed from the mineral density 6, the pore volume P, and the water content of the pores a: de o ; = 5-7 (6-{%). Since bg = 6(1 Pye P o Oe °¢ + i600 ° 100° Cuap. 7] GRAVITATIONAL METHODS 77 Table 10 illustrates the effect on density produced by a water content of 50 per cent in the more important types of rocks.’ Table 11 shows the difference between dry and wet volume weight (bulk density and natural density) based on actual determinations." C. TasBuLaTIONsS oF MINERAL AND Rock DENSITIES Tables 12 through 18, based on the work of many investigators, largely Reich,” show density values for (1) minerals, and (2) rocks and formations. They are divided into groups of metallic minerals, nonmetallic minerals, combustible minerals, rock-forming minerals, intrusive and extrusive ig- neous rocks, volcanic glasses, metamorphics, and sedimentary rocks. TABLE 12 DENSITIES OF METALLIC MINERALS MATERIAL Locality INVESTIGATOR Density (6) REMARKS Gold Fuchs Brauns 15.6-19.4 Silver be es 10.5 Bismuth ‘§ os 9.7 Copper i ie 8.7 Sylvanite ; He tf 8.2 Cinnabar os os 8.1 Uraninite Reich 8.0-9.7 Galena Dana 7.4-7.6 Argentite Fuchs Brauns 7.2 Wolframite Reich 7.1-7.5 Nagyagite Fuchs Brauns 6.8-7.0 Cassiterite gs a 6.8 Wulfenite a as 6.8 Vanadinite ss £6 6.9 Antimony es by 6.7 Bismuthinite s¢ se 6.5 Calomel s6 s 6.5 Anglesite rs ne 6.4 Smaltite 6.4-6.6 Phosgenite i ne 6.2 Polybasite a a 6.1 Arsenopyrite Reich 6.0-6.2 Crocoite Fuchs Brauns 6.0 Cobaltite Dana 5.8-6.2 Pyrargyrite Fuchs Brauns 5.8 Cuprite i BG 5.7-6.0 Hornsilver as ss 5.6 Proustite fs es 5.6 Valentinite a fe 6.0 Psilomelane Reich 5.5-6.0 10 After J. Barrell, Journal of Geology, 22, 214 (1914). After H. Reich, op. cit., p. 13. 12 Ibid. 78 GRAVITATIONAL METHODS TaBLe 12—Concluded DENSITIES OF METALLIC MINERALS [Cuap. 7 MATERIAL LocauiTy INVESTIGATOR Chalcocite Dana Millerite Fuchs Brauns Senarmontite ss f6 Magnetite ae cf Franklinite | a8 S Bornite te “ Pyrolusite ‘ rs Hematite Reich Pyrite ay Tetrahedrite Fuchs Brauns Molybdenite Dana Markasite Reich Molybdenite Fuchs Brauns Stibnite Dana Antimonite Reich Pyrrhotite Fuchs Brauns Chromite fs “ Manganite He of Enargite He We IImenite Reich Smithsonite Dana Rutile Reich ; Chalcopyrite Fuchs Brauns Malachite pe ae Psilomelane fs ay Zincblende Reich Azurite Fuchs Brauns Spinel ef a Atacamite He “ Covellite He a Siderite Reich Realgar Fuchs Brauns Orpiment sf Fy Sphalerite Dana Limonite Reich Titanite Reich Hypersthene Fuchs Brauns Pharmacosiderite ts He Cobaltbloom He eh Annabergite ts ne Cryolite Ps of Glauberite s se Vivianite tf es Thenardite Le G Kieserite He a Brucite if a Chrysocolla a ss Gaylussite pa 3 Thermonatrite He sr Sassoline Density (5) | REMARKS 5.5-5.8 5.3 on i OO Tey en Coe ae onwo = bo rez oo cans He GU iNeaicue Oona = re aon co © PRG orc Ore ENG a Sat cs tN woe TOF wo wo a) Te) ih bo rt) lee tr WM @ co cot “Teo co Moo Oo wo 0 CODER AMNN. E oscar aie (eres owe ww Qo ap Ft bo | IPOONNNYNNwW Dr NWwNNwWwwwo WWOHOOUMSS ceone robo [Jw] wih oO ree LP Cuar. 7] GRAVITATIONAL METHODS 79 TABLE 13 DENSITIES OF NONMETALLIC MINERALS MATERIAL Locairy INVESTIGATOR Density (4) REMARES Barite Reich 4.34.7 Corundum “ 3.9-4.0 Fluorite < 3.1-3.2 Magnesite “hs 2.9-3.1 Anhydrjte Beienrode salt Tuchel 2.9-3.0 dome, Germany Kaolinite Ross & Kerr 2.59 Kaolin 2.5-2.6 Bauxite Fuchs Brauns | 2.3-2.4 Phosphate Reich 2.2-3.2 Kaolinite ae 2.2-2.6 Gypsum Beienrode salt Tuchel 2.2 dome, Germany Gypsum Reich 2.2-2.4 Salt Gulf coast Barton 2.16-2.22} Average Impure salt Malagash, Nova Miller 2.16-2.21 Scotia Salt. “s cs 2.14-2.24 Rock salt Reich 2.1-2.2 Older rock salt Beienrode salt Tuchel 2.1 dome, Germany Younger rock salt es os 2.1 Kainite Fuchs Brauns Ze Graphite Reich 2.1-2.3 Graphite Fuchs Brauns | 1.9-2.3 Sulfur - ist ts 1.9-2.1 Sylvite Reich 1.9-2.0 Carnallite Fuchs Brauns 1.6 Av. values Carnallite Tuchel 1.6-1.7 | German salt Potassium salt de-| Beienrode salt ns 1.6 domes posit dome, Germany TABLE 14 DENSITIES OF COMBUSTIBLE MINERALS AND MISCELLANEOUS MATERIALS MATERIAL LocaLity INVESTIGATOR Density (6) REMARKS Saltpeter Fuchs Brauns 2.0 Borax ss 1.5-1.7 Brick Reich 1.5 Anthracite ts 1.34-1.46 Coal of 1.26-1.33 Lignite Germany Seblatnigg ike ?4 Lignite Reich 1.10-1.25 Asphalt ie 1.1 -1.2 Peat * 1.05 Ozokerite Fuchs Brauns 0.94-0 .97 Ice Ambronn 0.88-0.92 Wood Reich 0.7 -1.0 Petroleum i 0.6 -0.9 Snow Ambronn 0.125 80 GRAVITATIONAL METHODS TABLE 15 [Cuap. 7 DENSITIES OF ROCK-FORMING AND OTHER MINERALS MATERIAL LocaLity Zircon Garnet Topaz Diamond Olivine Epidote Zoisite Augite Apatite Andalusite Tourmaline Pyroxene & amphibole Hornblende Dolomite Mica Beryl Chlorite Calcite Tale Nephelite Flint Quartz Feldspars Oligoclase Albite Feldspar Orthoclase Serpentine Leucite Kansas INVESTIGATOR DENSITY (6) REMARKS Fuchs Brauns Reich Fuchs Brauns 6c 6c Dana Reich 6é Fuchs Brauns Reich “ec iz% cc George Reich Dana Reich TABLE 16 DENSITIES OF IGNEOUS ROCKS bo on eee bo Sietewie [eelcn sale (tents | bd bh by CAPS eo Cp Cele bv Nonnwnntwrv APRARAANNA SGoWaNwDy on @& 00 CO NI Se rs lor) ou MATERIAL LocaLity INVESTIGATOR Density (6) RE- MARKS 1. Intrusive Rocks Augite-diorite Hornblende-gabbro Pyroxenite Gabbro Olivine-gabbro Nephelite-basalt Igneous rocks Peridotite Diorite Norite Essexite Quartz-diorite Syenite Reich Swynnerton,| McLintock and Scotland Phemister Barrell Reich bc NNdNd ww bw @eomwowm so ce eae Ie aa Www www S& © 00 CO SeSwHS Cuap. 7] GRAVITATIONAL METHODS 81 TaBLB 16—Concluded DENSITIES OF IGNEOUS ROCKS MATERIAL LocaLity INVESTIGATOR Doansity (6) Saale Anorthosite Reich 2.64-2.94 Granite se 2.56-2.74 Nephelite-syenite HY 2.53-2.70 2. Extrusive Rocks (a) Older than Tertiary Diabase Reich 2.73-3.12 Melaphyre ee 2.63-2.95 Porphyrite US 2.62-2.93 Porphyry a 2.60-2.89 Quartzporphyrite a 2.55-2.73 Quartzporphyry ne 2.55-2.73 (b) Younger than Tertiary Picrite Reich 2.73-3.35 Basalt es 2.74-3.21 Andesite fs 2.44-2.80 Dacite pe 2.35-2.79 Trachyte rf 2.44-2.76 Phonolite “ 2.45-2.71 Rhyolite a 2.35-2.65 3. Volcanic Glasses Basaltic glass Reich 2.75-2.91 Andesite- and porphyrite glass te 2.50-2.66 Vitrophyre rf 2.36-2.53 Obsidian Es 2.21-2.42 Rhyolite glass Z .2..20-2 .28 TABLE 17 DENSITIES OF METAMORPHIC ROCKS MATERIAL LocaLity INVESTIGATOR | Density (65) REMARES Eclogite Reich 3.20-3 . 54 Jadeite y 3.27-3 .36 Pre-Cambrian Hazeldean, Ont. Miller 3.0 Amphibolite Reich 2.91-3 .04 Serpentine He 2.80-3.10 Pre-Cambrian Leitrim, Ont. Miller 2.8 Chloritic slate Reich 2.75-2.98 Slate Hedberg 2.7 -2.85 Haelleflinta Reich 2.70-2.86 Phyllite he 2.68-2.80 Siliceous lime 8 2.67-3.11 Quartzitic slate a 2.63-2.91 Marble ss 2.63-2.87 Gneiss af 2.59-3.0 Granulite Hh 2.57-2.73 Schists 2.39-2.87 Graywacke es 2.6 -2.7 * 82 GRAVITATIONAL METHODS [Cuap. 7 TABLE 18 DENSITIES OF SEDIMENTARY ROCKS MATERIAL Locality INVESTIGATOR Density (6) REMARES Soil, Clay, and Various Formations Clay, potash-bear- Ross & Kerr 2.46 ing Marl, Lower Tri- | Scotland McLintock 2.4 Keuper Marl assic Phemister Jurassic forma- Tuchel 2.3-2.5 tions Marl, Lower Tri- ue 2.3-2.5 assic Clay, Basal Penn- | Fulton, Mo. Hedberg 2.37 White flint sylvanian F clay Clay, grey Malagash, N.S. | Miller 2.15 Overburden Kassel, Germany| Seblatnigg 2.1 Soil, stamped wet Reich 2.1-2.2 Tertiary forma- Tuchel 2.0-2.4 tions Sediments Gulf coast Barton 1.9-2.05 | From surface to 500 ft. Sediments af BS 2.20 From 2000- 4000 ft. Sediments ff ee ne 2.25 From 4000- 8000 ft. Sediments et - a 2.30 From 8000- 12,000 ft. (average values at these depths) Drift Leitrim, Ont. Miller 1.8 0-70 ft. Clays & sands Glasgow, Scot- | McLintock 1.72 land Phemister Loam, sandy wet Reich 1.7-2.2 Soil, stamped dry “s 1.6-1.9 Clay, Mio-Plio- | Crossley, N. J. | Hedberg 1.66 cene Alluvium, recent | Missouri River, * 1.54 Air dried St. Charles Co., Mo. Soil Reich 1.5-2.0 Clay, Cretaceous | Richland Co., | Hedberg 1.51 Mittendorf 8. C. white clay Loess, Pleistocene | Collinsville, Ill. bh 1.43 Clay, Miocene Yorktown, N. J. - 1.30 Yellow Allo- way clay, depth 4’ Cuap. 7] GRAVITATIONAL METHODS 83 TaBLE 18—Continued DENSITIES OF SEDIMENTARY ROCKS MATERIAL LocaLity INVESTIGATOR Density (6) REMARKS Soil, loose dry Reich 183 Top soil, wet ne 1.2-1.7 Top soil, dry os 1.1-1.2 Sands, Sandstones, and Conglomerates Carboniferous Glasgow, Scot- | McLintock & 2.38 sandstone & land Phemister ironstone Black River, Chazy| Hazeldean, Ont. | Miller 2.7 sandstone Sandstones ‘ Barrell 2.67 Sandstone McLean Co., Ky.| Russel 2.64 Sandstone Reich 2.59-2.72 Potsdam = sand- | Leitrim, Ont. Miller 2.5 stone Gravels & sand, Reich 2.5 compacted Conglomerate Malagash, N.S. | Miller 2.35-2.38 Sandstone, Tri- | Germany Seblatnigg 2.35 assic Sandstone Malagash, N. S. |Miller 2.32-2.67 Variegated sand- Tuchel 2.3 stone Sandstone, Tri- | Beienrode _ salt Hh 2.25 assic dome, Germany Sandstone Malagash, N.S. | Miller 2.25-2.45 Quartz sand, wet Reich 2.2-2.3 Conglomerates He 2.1-2.7 Coarse gravel, dry fe 2.0-2.2 Woodbine sand Brankstone, 1.95 Gealy & Smith Gravel, wet Reich 1.9-2.1 Sand, wet i 1.7-1.9 Sand, dry ee 1.4-1.7 Shales Shale, Permian Salina, Kan. Hedberg 2.39 Wellington shale Shale, Pennsyl- | Fulton, Mo. ee 2.29 Cherokee vanian shale (weath- ered) Shale, Pennsyl- | Independence, a 2.31 Chanute vanian Kan. shale Shale, Pennsyl- | Bonner Springs, a 2.28 Weston shale vanian Kan. 84 GRAVITATIONAL METHODS [Cuar. 7 TasiLE 18—Concluded DENSITIES OF SEDIMENTARY ROCKS MATERIAL Loca.ity INVESTIGATOR Density (6) REMARKS Shale, Black, Com-| Falun, Kan. Hedberg 2.12 From Mentor manchean beds Shale, Upper Cre- | Hamilton Co., 1.98 Graneros taceous Kan. shale Shale, Devonian | Hannibal, Mo. BY 2132 Hamilton shale Shale, black Irvine Field, Ky. ry 2.57 Shale, red Malagash, N.S. | Miller 2.56 Shale, red Malagash, N.S. | Miller 2.50 Chazy shale & | Leitrim, Ont. a 2.5 | At 200 ft. sandstone Shale Brankstone, 2.36. | Gealy & Smith Shales Reich 2.3-2.6 Shales, yellow Malagash, N.S. | Miller 2.17-2.30 Shales Venezuela Hedberg 2.0-2.45 | Increasing | with over- | | : burden Shales, Tertiary | Beienrode salt | Tuchel 1.9 dome, Germany Limestones and Dolomites Anhydrite Beienrode — salt | Tuchel | 2.9 dome, Germany Dolomite | Leitrim, Ont. Miller 2.8 Dolomite, Beck- | Hazeldean, Ont. | ‘“‘ 2.8 mantown Limestones | Barrell 2.76 Limestone | Leitrim, Ont. Miller Dt At 588 ft. Limestones | Reich | 2.68-2.84 Limestones | Kansas George 2.67 Cap rock Gulf coast Barton 2.6 Average Shales & limestone} Leitrim, Ont. Miller 2.6 At 158 ft. Gypsum & anhy- | Beienrode — salt | Tuchel 2.6 drite dome, Germany Shell limestone : 2.4-2.6 Limestone Brankstone, 2.07 Gealy & Smith Chalk Reich 1.8-2.6 Cuar. 7] GRAVITATIONAL METHODS 895 III. GRAVITATIONAL CONSTANT; GRAVITY COMPENSATOR; GRAVITY MULTIPLICATOR The mutual attraction of all masses is governed by Newton’s law of gravitation which states that the attraction of two masses m, and mz is proportional to their product and inversely proportional to the square of the distance between them, k-my: me Mie F r , (7-1) where F' and k are measured in dynes if m is in grams and r in centimeters. When m = m, = r = 1, F = k; hence, k (called the gravitational constant) is the force of attraction between two equal masses of 1 g. each at a distance of lem. Its dimension in the C.G.S. system is gr -cm’. sec; although it is exceedingly small (about one 15 billionth part of gravity), it may be determined accurately from the force exerted by large masses upon small masses at a known distance. The Cavendish torsion balance is generally used in making these measurements. The @ force may be determined statically (by meas- uring deflections) or dynamically, that is, by (¢) observing the period of oscillation of the Fie. 7-3a. Arrangements balance beam under the influence of known ce cee an ee masses. Fig. 7-3a shows arrangements of de- tional constant (after Heyl). flecting masses M in reference to the deflected beam of the length 2/1, carrying two small masses m at its ends. The angle of deflection, y, is measured at great distances from the balance with telescope and scale. Sometimes the dou- ble deflection is observed by revolving the masses M about a horizontal axis to the other side of the small masses. For the single deflection, the gravitational constant follows from (b) 2 [ee MES 7-2 2Mml’ Kee) where 7 is the torsional coefficient of the wire, and r the distance between M and m. A correction is applied since, for very small distances, the mass of M may not be assumed to be concentrated in its center of gravity.” 13 P. R. Heyl, ‘‘A Redetermination of the Newtonian constant of Gravitation,” Proc. Natl. Acad. Sci., 18(8), (Aug., 1927). 86 GRAVITATIONAL METHODS [Cuap. 7 In the dynamic method the period of oscillation of the beam is determined with an arrangement shown in Fig. 7-3a and 7-3b. The large masses are used first in the extension of the beam and second with their axis at right angles to the beam. Heyl,” using masses of 66 kg each for the deflectors, a beam 20 cm long with platinum balls of 54 g each, and a scale distance of 3 m, obtained a difference in the two periods of oscillation in the two defiector positions of about 330 seconds. The transits of the beam were o> pene lea METER Os AER haha iy Sma see aE Saimiri ChE To eri Hele anh eee DRI "Fig. 7-3b. Torsion-balance arrangement for the determination of the gravitational constant (after Heyl). recorded on a chronograph, with second signals from a Riefler clock. Heyl reduced the mean error of measurement to +0.002-10° C.G.S., and obtained for k the value of k = 6.664-10°° C.G.S. which is considered the most accurate value now available. 14 Loc. cit. Cuap. 7] GRAVITATIONAL METHODS 87 It has been proved by a number of experiments that the gravitational constant does not change with the chemical or physical nature of the masses used. By the measurement of the gravitational constant, not only is the proportionality factor in Newton’s law determined, but an experiment of greater physical significance is made. Since gravity is the earth’s attraction upon a mass of 1 g, and since, from Newton’s law, Mrz = (gR’,)/k, (g is gravity, Mg the mass of the earth, and R,, its mean radius) it is seen that determination of the gravitational constant is equiva- lent to weighing the earth. As the earth’s volume can be calculated, its mean density, 5m, may be obtained from the gravitational constant: 8 gs OO 4r k Rowe? where gis = 980.616 cm-sec’, and Rn = 6.371-108 cm. This relation yields 5.53 for the mean density of the earth. (7-3) Fig. 7-4. Edétvés gravity compensator (adapted from Jung). To increase the effect of gravitating masses upon the torsion balance, Eétvés” designed the gravity compensator and the gravity multiplicator. The instruments incorporate a regular torsion balance of the first type (curvature variometer), provided with four sector-shaped deflectors whose position may be changed by rotation about a horizontal axis (see Fig. 7-4). In vertical position the attraction of the deflectors is a minimum; when arranged in horizontal direction, it is a maximum. If the balance beam is in the center of the case, the attraction of the deflectors is zero because of their symmetrical disposition; however, if a small deflection, ¢, is pro- duced by an outside mass whose attraction is to be measured, the de- flectors become effective since they are now unsymmetrically disposed 1R. v. Edtvés, ‘Untersuchungen ueber Gravitation und Erdmagnetismus,”’ Ann. d. Phys. und Chem., 59, 392 (1896). 88 GRAVITATIONAL METHODS [Crap. 7 with respect to the beam. If D is the couple produced by an outside mass (or by the “curvature” effect of the gravitational field), and G-¢ is the couple produced by the gravity compensator, then re = D + Gog. It is seen that 7, the torsional coefficient of the wire, is reduced to 7 — G = 7’ by the action of the deflectors and that the balance becomes more sensitive. The “apparent” torsion coefficient is given by ; kKM (FNS r (1 + 3 cos 2y), (7-4) where K is the moment of inertia of the balance beam, M the deflector mass, 7 the distance from the beam and y the deflector angle from hori- zontal. The difference between the extreme values of 7 (when y is 90° and 0°) is 6kKM/r*. With the arrangement used by Hétvés (very thin wires, 7 = 0.15, M = 40 kg, r = 10 cm, and K = 20,000 C.G:S.) it is possible even to overcompensate external gravity forces. The gravity compensator is applicable in gravitational model experiments not only with a curvature variometer but with a gradient variometer as well. The gravity multiplicator is essentially a gravity compensator for “dynamic” measurements. The deflector positions are changed in syn- chronism with the beam oscillations and thereby the beam amplitude is gradually increased. IV. PRINCIPLES OF GRAVITATION AS APPLIED IN GRAVITY MEASUREMENTS As in all geophysical problems involving fields of force, the analysis of the gravitational field makes extensive use of two parameters, the field vector and the potential. The gravity field vector has the peculiarity that its three space components are very unequal; the horizontal compo- nents are small and the vertical component is almost equal to the total vector. The force of gravity, that is, the pressure which 1g mass exerts . on its base, is measured in units of g-cm.sec -, or dynes, and is numerically but not physically equal to the acceleration of gravity measured in units of em.sec *, or “Gals.” Convenient practical units are the milligal, or 10 ° Gal, and the microgal, or 10 °Gal. Gravity varies from 9.78 m-sec ~ at the equator to 9.83 m-sec” at the pole. Gravity anomalies rarely exceed 100 milligals. The potential of the gravity field is frequently employed in its analysis since, contrarily to the vector, it is a scalar quantity. Its first negative derivatives with respect to the coordinates represent the components of gravity. The gravity potential at the earth’s surface may be defined as 16 Named after Gaiileo. Cuap. 7] GRAVITATIONAL METHODS 89 the work performed by a mass of 1 g in falling from space upon the earth. Since the gravity force g, in accordance with Newton’s law, is g = k(M/R’) (M = earth’s mass, R = earth’s radius), and since work is the product of force and distance, the attraction potential V = kM/R = 6.25.10" ergs. The gravity potential may also be defined as potential energy of the unit mass. Since the potential energy of a body of the weight m-g at an elevation h is m-h g and since, at the earth’s surface, g = kM/R’,h = R, and V = kM/R, the potential energy is m-V. Ac- tually the system to which this potential is referred is not stationary but rotates with the earth; hence, the potential of the centrifugal force, or V’ = 14°(2’ + y’), must be added to the attraction potential. The total potential at the earth’s surface is usually designated by the letter U = V + V’;w is the angular velocity of the earth’s rotation, or 27/86,164sec -. For any point outside a heavy mass, the potential function with all its derivatives of arbitrary order is finite and continuous and controlled by Laplace’s equation: P} 2 2 aU A aU ap aU 2 mt a ae a (7-5) Points of equal value of U may be connected by ‘‘equipotential”’ (“‘level,”’ or ‘‘niveau’’) surfaces. The potential gradient in this surface is zero, and no force component exists. Any equipotential surface is always at right angles to the force. The value of gravity can change arbitrarily on a niveau surface; hence, a niveau surface is not a surface of equal gravity. The ocean surface is an equipotential surface of gravity, since the surface of a liquid adjusts itself at right angles to the direction of gravity. The - distance of successive equipotential planes is arbitrary and depends on their difference of potential. The difference in potential of two surfaces 1 cm apart is 980 ergs; conversely, the distance corresponding to unit (1 erg) potential difference is 1/980 cm. The interval h between successive planes is a constant and is inversely proportional to gravity, or C = g-h, where h is the interval and g gravity. Fundamentally, the aim of gravitational methods is to measure ‘‘anoma- lies” in the gravitational field of the earth. Since it is not possible!™ to compensate the normal field by the technique of measurement (as shown in Chapter 8, a compensation of the normal terrestrial field is possible in magnetic instruments), its value must be computed for each point of observation and must be deducted from the observed gravity. The theorem of Clairaut makes it possible to caiculate the normal distribution of gravity from the mass and figure and the centrifugal force at the surface 16a This applies to the total vector and its vertical component. Horizontal gravity components may be compensated (as in the gravity compensator, see p. 87). 90 GRAVITATIONAL METHODS [Cuap. 7 of the earth, and to express this distribution as a simple function of lon- gitude and latitude. The coefficients of the final equation may be deter- mined from gravity measurements in different latitudes and longitudes, leading to an empirical formula for the variation of the normal value of gravity distribution at the surface. The only assumptions made in its derivation are that the surface of the earth is a niveau surface, and that the earth consists of concentric and coaxial shells on which arbitrary changes of density may occur. Stokes and Poincaré showed later that the theorem of Clairaut follows alone from the assumption that the earth’s surface is a niveau surface and that it is not necessary to assume a distribution of density in concentric shells. Referring to Fig. 7-5, consider!® the potential at the point P’ with the coordinates 21, yi, Z1, due to a mass element dm with the coordinates z, y, Zz | Fic. 7-5. Relation of outside point to mass element in spherical body. andz. The distance of P’ and of dm from the origin is 7; and r, respectively, the angle between them being y. If the distance between P’ and dim is e, then V = k(dm/e). Further, e=V(m — 2)? + (wm — y)? + (a — 2)73 _ thi + YY + 221, cos 7 = 1 TiN x — y" + 2 and 1® See also A. Prey, Einfuehrung in die Geophysik, p. 60 (1922). Cuap. 7] GRAVITATIONAL METHODS 91 Thus, ee (r? + r? — 2rr; cos y) 4, (7-6a) which may be written so that by series expansion and considering only terms up to the second order: : cos” 7) | (7-6b) Substituting the value given above for cos y, the potential by multiplica- tion with k { dm becomes: v=" fam +3 fs ie +o [vam +3 a fe dik + ea was Fy aie p= 2 [1+ 00842 +5 ( gt a | (0 -—y = 28) dm + BE fey — 2° — 2°) dm +2 fae — a2 —y)dm+ 2h fo dm a ae re cnet ral Ape Ty (7-2) The integrals have to be extended over the mass of the whole earth. If we assume the latter to be concentrated in the center of gravity and make it the zero point of the system of coordinates, [ am = M, [ cam = [ yam = | 2am = 0; [ zyam = [ yeam = [ exam = 0. The integrals involving the squares of the coordinates are not zero. Assuming that the earth is a three-axial ellipsoid of rotation with three 92 GRAVITATIONAL METHODS [Cuar. 7 moments of inertia, A, B, and C, about the three principal axes, l; , lz , and ls, = | tam ; att C= | Gam ; when 1; = Vy+te: aan) ey ; 2/2 7: hence, Are / (y? + 2°)dm; Be i (27+ 2°)dm; Ce / (2? + y*)dm. (7-8) oe these values in (7-7), 2 mah My Bi eto- 2a) + Bic + a - 2B) + (A + B — 20). ry If we drop subscripts, the location of any surface point may be written in geocentric coordinates: z=rcosycos\ and « =7 cos o-4(1 + cos 2d); ; 2 2 2 y=rcos¢gsindX and y =r cos ¢-3(1 — cos 2a); : a pieeeOen 4 Zina and 2 — 7 sin @: Hence, after combining terms containing ¢ and A, V -™ 43 (c- APB — asin’ ¢) +S cos" y cos 2\(B — A) r (7-9a) This is the potential of the attraction only. The potential of the centrif- ugal force must be added to it. Its three components are C, = tw; C, = y-w; C, = 0, when w is the ‘angular velocity. Thus, the resultant centrifugal force is w/z? + y? and its potential is V’ = 5 + 7). In polar coordinates, V’ = : -y cos’ ¢. Then the total gravity potential, Vests = Upis -™ sh (o-4 FBV 3 sinty) + = cos’ ¢ cos 2\(B — A) aS cos: (7-9b) This expression may be further simplified by confining the derivation to a two-axial ellipsoid, that is, by neglecting the deviation of the equator Cuap. 7] GRAVITATIONAL METHODS 93 from circular shape and by assuming that the two equatorial moments of inertia are equal. Thus, if A = B, the final expression for the total potential is 2.2 Of my - iB (C — A)(1 — 3sin’y) + pune f cos’ ». (7-9c) r on 2 From this expression, the gravity may be obtained with sufficient ap- proximation, by differentiation with respect to r: _ dU _ kM or kM or Sas E -} 7 7? (C — A)(1 — 3sin’g) — =i cos *e|. (7-10a) The second and third terms in the first of the above equations are of the second order and are small. Therefore, another simplification may be made by letting r = a, that is, by replacing the radius of the earth with the equatorial radius, a. For reasons which will be evident from what is to follow, it is convenient to express g in terms of U. Eq. (7-9b) may be written: We kM my an ai (C — A) 2Mr2 — (1 — 3 sin’ ¢) ob Be = cos” o|. By substituting a for r in the brackets, ty eal peytGs 4) A) r a® Ma (ie arsine Qh ae ae ir °° *o| Using the abbreviated notation 0 for (C — A)(1 — 3 sin’ ¢)/2a°M and p for wa’ cos’ ¢/2kM, g =" [lL +30 - 2p] and (7-10b) b= eS [1+o0+p]. The r may be eliminated from the last two equations so that U? 1+ 30 — 2p 9~ eM (1-0 +p)* 94 GRAVITATIONAL METHODS [CHaAP. 7 The division gives g = U* (1 + 0 — 4p)/kM or in the Se notation (fe C-—A Qu” g= le + Oat (1 — 3sin’ ¢) — ae cos -c05"¢ |. (7-10c) Substituting 1 — sin’ @ for cos’ y, and using the abbreviations s, = (C — A)/2a°M andt = 20a" /kKM y 2 q= U oH ss — a in? Ot — 3 kM a f " t aM for which Jo = = “(1 +s — t)(1 +sin’ g(t — 3s))] approximately. The neglected term, sin’ ¢ (4st — 3s’ — t’), is very small, since all terms in the brackets involve the square of the earth’s mass in the denominator. Asg=V/rand V = kM/r,1/r= V/kM; thus, g = V’/kM. Therefore, the term before the bracket in eq. (7-10c) is the gravity at the equator (since a was previously substituted for r) or rather the portion of gravity due to attraction only. Since the term (s — t) expresses the effect of inertia and centrifugal force upon the attraction, V’/kM -(1 + s — t) represents the total equatorial gravity, g.. Substituting gafor V’ (1 + s — t)/kM, and b’ for ( t— 3s), we obtain a simple form for the gravity at any point at the surface, thus: Je = ga(l + b’ sin” ¢) (7-11) This equation represents gravity as a function of latitude. It will also be convenient to express the earth’s radius, r, as a function of latitude. From (7-106) kM = a ii +o+ pl. Recalling the significance of the abbreviated notations 0, p, s, and t, 0 may be expressed in terms of s, and p in terms of t: 0 = s(1 — 3 sin’ ¢) and p = (t/4)-cos’y. Thus, for r we have: kM r= iy [1 + 8 Basin e + 5-cos" e|. Again substituting (1 — sin’ ¢) for cos’ ¢: r= Ml ts+ f— sin’ (35+ )| CuapP. 7] GRAVITATIONAL METHODS 95 which may be written with the approximations used before: or eee | cee Since V is kM/r (the attraction potential), the total (attraction and centrifugal) potential at the equator would be u=v(i+s+f)=™ (tse), 4 a 4 Hence, aiskM (1 + s + t/4)/U, so that To = a(1 — a’ sin’ ¢) (7-12) where a’ is t/4 + 3s. Resubstituting the values of the coefficients a’ and b’, t —3(C — A) wa® ea Sal Mc ee and 3(C. — 1 Adi 2ana, U = —_— — = b’ =t — 3s 20? Mf + kM Their sum is paliatieesanus Dit abe once Sie ated aeeNa or, substituting ¢’ for wa°/kM, a’ +b’ = 3’ (7-13) This equation represents Clairaut’s theorem. 'To determine the physical significance of the three coefficients, a’, b’, and c’, use eq. (7-12) thus: r = a(1 — a’sin’g). If ¢ is 90°, then r is the polar radius, or the minor axis, of the earth ellipsoid, which may be denoted by c. Hence, c = a (1 — a’), or ao y (7-14a) The coefficient a’ is the ratio of the difference of the polar and equatorial radii, divided by the equatorial radius. It is called the flattening (com- pression). In eq. (7-11), which expresses the variation of gravity with 96 GRAVITATIONAL METHODS [Cuap. 7 latitude, the gravity at the pole becomes g. = ga(1 + b’), if ¢ = 90°. Therefore, the coefficient p= &&_% (7-14) Ga represents the ratio between the difference of polar and equatorial gravity and equatorial gravity, or the gravitational flattening. Finally, the coefficient 2.3 2 2 2 Ae _@wa@ _wa Ai KM ~ kM/a U/a 9a (inkeel indicates the ratio of the centrifugal force at the equator to the gravity at the equator. Therefore, the theorem of Clairaut may be stated as follows: geometric + gravitational fiattening = : x i atotichanahte Toren Since this relation involves only suriace quantities, the figure of the earth may be computed from a known surface distribution of gravity. From a number of carefully selected stations, gravity as a function of latitude, and thus the coefficient b’, may be determined. The coefficient c’ is computed from the known velocity of revolution of the earth. Thus, by applying Clairaut’s theorem, the fiattening may be ealculated. With a more rigorous derivation involving spherical harmonies of higher order in (7-6b) and all moments of inertia in (7-8), Clairaut’s theorem may be stated in more extended form. If the variation of gravity with longitude, in addition to its change with latitude, is considered, g = g(1 + b’sin’ g + b’’ cos’ y-cos 2A +----). — (7-15a) By a careful analysis of the distribution of gravity and by eliminating stations with large topographic effects and local anomalies, Berroth has computed the following values for the coefficients in (7-15a): g = 978.046 [1 + 0.005296 sin? » 44.4 + 0.0000116 cos’ ¢ cos 2(\ + 10°) — 0.000007 sin? 2g] (7-15) from which follows the flattening as a function of longitude (from Green- wich): a’ = 0.003358 + 0.000012 cos 2(\ + 10°). The major axis of the elliptical equator is 10° west of Greenwich. The flattening in this meridian is 1/296.7, and at right angles thereto it is 1/298.9. The mean flattening is 1/297.8. The difference of the equatorial radii is only 150 + 58 meters. Hence, the equator is practically a circle and is considered as such in ail Cuap. 7] GRAVITATIONAL METHODS 97 problems in gravitational exploration involving caiculations of normal gravity, normal gravity gradient, and so on. Likewise, for many problems in geodesy and geophysical science it is desirable to use the same reference surface (namely, an ellipsoid of revo- lution) for both normal gravity and geodetic measurements. For this reason the International Association of Geodesy adopied at the Stockholm meeting of the International Geodetic and Geophysical Union in 1930 a formula not including a longitude term, based on an ellipsoid of revolution with a flattening of 1/297: g = 978,049 (1 + 0.0052884 sin” ¢ — 0.0000059 sin’ 29). (7-15c) This international gravity formula is now used in all gravity reductions by the U. S. Coast and Geodetic Survey.” V. PENDULUM AND GRAVIMETER METHODS A. THEORY OF THE PENDULUM ON FIXED AND MOoOvING Support 1. Penduium on fixed support. A mathematical pendulum consists of a particle of mass suspended from a point by means of a massless, flexible, inextensible cord. In Fig. 7-6 let m be the mass, I the length of the cord, and @ the angle of deflection from its rest position. In the state of motion the inertia force m-1-d’0/dt’ balances the restoring force —m-g-sin 6 for sustained amplitudes; the weight component m-g-cos 6 and the centrifugal force m-1-(d6/dt)” are compensated by the tension of the suspension cord and need not be considered. Hence, GOk wig? ere an ate 7 sin 6=0. (7-16a) An exact evaluation of this expression leads to an elliptical integral. For small amplitudes, sin 6 = 6 and d’6 ae wA =0 (7-16b) where w = +/g/l is the natural angular frequency or the number of oscilla- tions in 27 sec, so that with f as frequency and T' as period, w = 2z2f = 27/T. For finite amplitudes, equation (7-16b) does not apply. A solution of (7-16a) is possible by decreasing the order of the differential equation and considering the energy of motion, assuming again that no energy is con- ¢ 17 Personal communication, courtesy of Admiral L.O. Colbert, Director, U. S. Coast and Geodetic Survey. 98 GRAVITATIONAL METHODS [CHaP. 7 sumed by friction or damping. The energy for the maximum amplitude, a, is m-g-l(1 — cos a),” and is equal to the sum of the potential energy, m-g-1(1 — cos 6), and the kinetic energy, 4m.-1’- (d6/dt)’, for the position 6. Hence, aye dé dt = So SSS (7-16c) 2w? 4/cos 6 — cosa The period 7’, is twice the time required\for the pendulum to swing from 6 = ato 6 = —a. By substitution of 1 — 2 sin’ 6/2 for cos @ and 1 — 2sin’ a/2 for cos a, a dé =1 | ati Pa MAD (7-16d) We Iie 4/ si a5 sin’ 5 By introducing the auxiliary angle y, so that sin \ 6/2 = sin y sin a/2 and NY 2 sin 5 cos y dy da = —_—_______—,, \/ 1— sin? 5 sin? y mg 2 uid Fic. 7-6. Mathematical T,=— Si : (7-16e) pendulum. oO] - W/ ] =‘ sin? 5 sin? y Te The elliptic integral has the form areal panier) LURC LS - V/1 — psin? y’ 2 whose solution, (see B. O. Pierce, Table of Integrals, No. 524) is [1+ (3) #+ (Ga) + Gar) + | so that the period the period 2m. 1 - 2a 9 - 4 fe sti at 5 + eg sm a. .). (7 16f) If the period for small amplitudes is T, , ee 1 - 2 9 - 4a Aa Ta=7,(1+ tin 5 + eq sin f+), (7-169) 18 Partly after L. Page, Theoretical Physics, Van Nostrand (1928). Cnap. 7] GRAVITATIONAL METHODS 99 in which for most practical applications it is sufficient to use the angle for its sine so that the ‘amplitude reduction formula” is 2 T. = T, +54 ss). (7-16h) For the physical pendulum of the mass M and the moment of inertia K, d’6 K. aes — Mgs sin 6 where s is the distance of the center of gravity from the axis of rotation (see Fig. 7-7). By comparison with equation (7-16a) it is seen that a phys- ical pendulum, in which K/Ms =1= reduced pendu- lum length, is isochronous with a mathematical pen- dulum; its period T = 24r~/ K/Mgs. The reversible pendulum (Fig. 7-8) is a physical pendulum with two knife edges so placed that the period of oscillation about either axis is the same. Their distance is then equal to the length of the equivalent mathematical pendulum. It is for this reason that the reversible pendulum has been and is still being used for the precise determination of abso- lute gravity. The distance between knife edges may be measured by means of a vertical comparator. Determination of absolute gravity by means of the reversible pendulum is a difficult procedure and requires a number of corrections: (1) for the flexure of the support, (2) for the effect of the surrounding air, (3) for the elastic tension and bending of the pendulum, (4) for changes in temperature, and (5) for the rate of the comparison chronometer. Inverted or near-astatic pendulums have the advantage of smaller mass, greater periods, and greater sensitivity in period to variations in gravity. The best-known representative is the Lejay-Holweck pendulum.” If an ordinary pendulum is suspended from a spring instead of from a massless thread as in Fig. 7—9a, the restoring force of gravity is added to that of the spring. If its spring constant be designated by c, (see Fig. 7-8. pages 449 and 581), the equivalent spring constant of gravity Reversible (force per unit elongation) would be mg sin 6/a. Sincesin 6 ~ poaaae a/r, the resultant spring constant c, =c,-+mg/r. It follows further from the equation for the elastic line that the equivalent axis of rotation is Fic. 7-7. Physical pendulum. 19 Comptes Rendues, 186, 1827-1830 (1928); 188, 1089-1091 (1929); 190, 1387-1388 (1930); 192, 1116-1118 (1931); 198, 1399-1401 (1931); (1933). 100 Fic. 7-9a. Sus- pended _ elastic pendulum. Fic. 7-96. In- verted elastic pendulum. Fic. 7-10. Le- jay-Holweck pen- dulum. GRAVITATIONAL METHODS [Cuap. 7 located approximately one-third of the spring length from the point of suspension. Substituting, there- fore, 21 for r and 3EJ/l for the spring constant c, (where # is Young’s modulus of elasticity and J the moment of inertia of the spring section), the resulting spring constant c, = 3EJ/l + 3mg/2l, so that by sub- stitution into w = ~/c/m: =a tH fe = mE Tt 8 (7-17a) In the inverted pendulum the action of gravity tends to drive the mass away from the rest position instead of toward it (Fig. 7-9b) ; hence, w= [oe mE 2 or (7-176) 2mi8 Sil oer / 6ET — 3mgl The change of period with gravity is given by dT = dg Tol/(2EJ — mgl’). T becomes infinite when m = 2EJ/Uq. In a derivation not involving the approximations made here, the factor is 7/4 instead of 2.” Numerical eval- uation of eq. (7-176) shows that in order to obtain any advantage in sensitivity, the mass has to be made so large that the buckling strength of the spring is approached. This can be avoided by using a long bar and a short spring; in the Lejay-Holweck pendulum the length I is several times smaller than the distance L (see Fig. 7-10). With K as the moment of inertia of the pendulum mass, the period and its change with gravity Tika Vg fp tid Co — mgL r (7-17c) pag te tc ie a df 2 c — mgL With the dimensions used in the Lejay-Holweck pendulum, a change in period of 1-10 ° seconds corre- 20 A. Graf, Zeit. Geophys., 10(2), 76 (1934). Cuap. 7] GRAVITATIONAL METHODS 101 sponds to a change in gravity of 1 to Z milligals. This inverted pendulum is therefore 1000 to 2000 times more sensitive than the ordinary gravity pendulum. 2. Pendulum on moving support. The theory of the pendulum on mov- ing support is of equal importance for gravity measurements on vessels and floats and for land observations in connection with the elimination of the flexure of the penduium support. Details of the theory are given in two publications by Vening Meinesz;” only the principal formulas are discussed here. On a moving support three factors alter the period of a penduium: (1) horizontal accelerations, (2) vertical accelerations of the suspension point, (3) rotational movements of the apparatus. When rotational movements are kept down by suspending the apparatus in gimbals, horizontal accelerations cause practically the only interference with the movement of the pendulum. This interference may be com- pletely eliminated by swinging two penduiums simultaneously on the same support in the same vertical plane. By extension of eq. (7-166) the equations for two pendulums may be written d’ 6, 2 dy 1 aes ‘ia. Sahil eh ate 2 Fae (7-18a) 0. ey de + 26. + dt ‘ls = 0, where y is the horizontal coordinate in the plane of oscillation of the pendulums, w: and we their angular frequencies, 0, and 62 their amplitudes, and J, and I, their lengths. When an optical arrangement is provided whereby only the differences in the amplitudes of the two pendulums are recorded, the following equaiion is obtained for two isochronous pendulums (w = We and hi = lp): 2 a a eo (7-186) This relation is identical with the equation of motion of a single undis- turbed pendulum. It holds for a “‘fictitious’’ pendulum with the elonga- tion 6; — 62, the same length / and the same frequency w as the original pendulums. . A correction is required if the two pendulums are not iso- chronous. Denoting the period of the fictitious pendulum by 7, that of the first pioramnel pendulum by 7) and that of the second by T», the devia- 21 F. A. Vening Meinesz and F. E. Wright, ‘‘The gravity measuring cruise of the U.S. Submarine S 21,’”’ Publ. U. S. Naval Observatory (Washington), Vol. XIII, App. I (1930); F. A. Vening Meinesz, ‘‘Theory and Practice of Pendulum Observa- tions at Sea,’’ Publ. Netherlands Geodetic Comm. (Delft, 1929). 102 GRAVITATIONAL METHODS [Cuap. 7 tion from the isochronous condition may be expressed by an equation of the form T = 7; + AT, with @2 — OI DH AT = [ 008 (g — @) (7-18¢) 0 2w where a2 and a are the amplitudes of the second and of the fictitious pendulum, and ¢e and g, respectively, their phases. Since, in practice, 2 the difference I. — 7 is usually small compared with T, = may be neglected. Letting w2/w. = 1,w2 — ow. = —a (T2 — T1)/ T’, and con- sidering a2, a, and cos (gv; — ¢) as constant, we have from eq. (7—-18c) AT = —(T2 — T:) =-cos (v2 — ¢). (7-18d) The Vening Meinesz pendulum apparatus is designed to record the move- ments of the fictitious pendulum by reflecting a light beam from one pen- dulum to the other. In addition, one pendulum is photographed sepa- rately to obtain 72 for the above correction. Vertical acceleration of a pendulum is equivalent to a change in the value of gravity and produces little change in period, provided the ampli- tude is kept reasonably constant during the observation. Relative move- ments of knife edge or slippage on bearings. are negligible, provided the amplitude remains sufficiently constant. Rotation about a vertical axis does not affect the period. Rotation about a horizontal axis (inclination of the plane of oscillation) changes the gravity from g to g cos 8 if 6 is the angle of inclination. The resulting change in period is AT = 2 (Bconat. + 4a,), (7-18¢) where Beonst. is the constant tilt and a, is the amplitude of oscillation of the gimbal frame about this position. Acceleration imparted to the pendulum in the plane of oscillation by rotation about both horizontal and vertical axes produces a change in period, Ti 2 AT = ——,a (7-18f) ATE so that by combination with eq. (7-18e) AT = £7 1(Beonst. aS Cai), where (7-189) ey! a) e=5(1 7 Cuap. 7] GRAVITATIONAL METHODS 103 T,, (the period of oscillation of the frame in the gimbal suspension) and B (the tilt angle) are recorded separately by a highly damped pendulum in marine gravity apparatuses. Lastly, the customary reductions for ampli- tude, chronometer rate, temperature, and air pressure are applied. B. OBSERVATION AND ReEcorpDING METHODS; PENDULUM APPARATUS The high accuracy required in pendulum observations is attained by using the “‘coincidence’’ or ““beat’’? method. This method may be likened to a vernier. ‘Two nearly equal periods are compared by observing which time “divisions” coincide. The gravity pendulum is compared with a chronometer (or an astronomic clock or reference pendulum) of very nearly the same (or double) period, and the number of chronometer seconds are measured which elapse between two subsequent coincidences, that is, bm Pend. (27) n Chron. {-7,) Ip “fy ‘hy Pend. (=7,) Coincidence Interval Fic. 7-11. Coincidence method. between two successive instants when pendulum and chronometer are “‘in phase.” The pendulum may lag behind (Fig. 7-1la) or be ahead (Fig. 7-11b) of- the chronometer. In case a, the pendulum makes (n — 1) oscillations for 7 oscillations of the chronometer; in case b, (n + 1) oscil- lations. The pendulum period is 7, = Pe in the first case and n se ai eel pieces are a small integer multiple of each other, that is, if the ratio T,/T. = q, the coincidence method is applicable if q is slightly less or greater than 1, or slightly less or greater than 2, and so on. Letting T, (the period of the chronometer) equal one second, the following relations apply in the general coincidence case: -T, in the second case. When the periods of the two time pee Ts, (7-19a) 104 GRAVITATIONAL METHODS [Crtav. 7 By substituting 1/q = v: n oT we ged where n is the coincidence interval. In these formulas the inom sign 2 Oe pear | <1 : applies if q s and v Sa (or 2 any other integer). They may also be written q , T,=q+ aah (7-19c) and, by substituting the reciprocal of gq, 1 on ie fe — aC) —] pt AV, a v(vn + 1) (eolee) Hence, for a half-second pendulum, compared with a full-second chronom- eter, v = 2 and therefore n Vy 2n+1 and 1 1 If the pendulum swings slower than the chronometer, tensa Oe eee . di — ae aces and dg = pat. (7-19f) If the pendulum is so made” that — = (./8vg 1+ 2), (7-199) dg = dn and one millisecond change in coincidence interval corresponds to one milligal change in gravity. Coincidence intervals may be observed visually (stroboscopic method) or be recorded photographically. In the first method the gravity pendu- lum is observed only during a short interval when the reference pendulum or chronometer passes through its zero position. Therefore, the image of the gravity pendulum appears in the telescope every second with a dif- 22 H. Schmehl, Zeit. Geophys., 5(1), 1-15 (1929). CuapP. 7] GRAVITATIONAL METHODS 105 ferent phase, that is, a different distance from the crossweb, and “‘coinci- dence’”’ occurs when the pendulum image coincides with the crossweb. For observation of the flashes, light is shone intermittently through a diaphragm upon the pendulum mirror and thence to the telescope; the diaphragm is attached to the armature of an electromagnet actuated by the electric contact in the chronometer or astronomic clock. Light source, electromagnet, and telescope are all mounted in one box (flash box). For photographic registration of coincidences, Martin” has described the arrangement shown in Fig. 7-12. The filament of an electric light bulb is projected by means of lens Z; and mirror M on a slot placed in the focus of the pendulum lens, L5. From the pendulum mirror the light is reflected and passes through a cylindrical lens to the photographic plate Light Bulb ~~ ~ 1 mar See ey, / Slot Ae a =f | | | Clock Contact rd ee ae [ Mirror M — ~~ ~~ Cylindrical L malt Phatographic Plate Pendulum Fig. 7-12. Stroboscopic photography of pendulum by comparison with contact clock (after Martin). which advances at a slow rate. The mirror M is fastened to the armature of an electromagnet actuated by the chronometer contact. The flashes so recorded (see Fig. 7-13) are arranged in a sine curve; one-half period is the coincidence interval. The photographic plates are evaluated with an accuracy of +0.01 mm; the error in determining the coincidence in- terval is +0.03 sec. By observing a sufficient number of coincidences (usually ten), and repeating the procedure after fifty intervals, the ac- curacy is increased to the point where the mean error of the result is +0.0001 (see Table 19). This corresponds to an error in 7’ of + 1.2-10 ° sec., or 0.1 milligal in gravity. In another photographic method, the pendulum oscillations are photo- graphed directly on the same film with accurate time marks and (radio) time signals, transmitted by a chronometer or reference pendulum. The accuracy is increased if two pendulums, swung on the same support with *3 Zeitschrift fiir Geophysik, 5(8/4), 148-151 (1930). 106 GRAVITATIONAL METHODS [CHaP. 7 opposite phases, are photographed simultaneously. Since the passage of the pendulum through the rest position, with reference to a radio time signal, may be determined with an accuracy of about 2-10“ sec. and ten successive passages are observed at intervals of about 40 minutes, the period may be measured with an accuracy of about +2.10° seconds. ae er Oo ee See Rapa Ee A vs ae o_o wots 4-6 - oy Get baie E 7 . : Fic. 7-13. Stroboscopic coincidence record (after Martin). TABLE 19 EVALUATION OF STROBOSCOPIC COINCIDENCE RECORD: Amp.- 50 n Corr. No 205 217 6.92 205 58™ 33.778 2246.85 44.9370 0.0192 44.9178 sec 51.88 59 18.71 2246.83 44.9366 .0189 44.9177 ‘* 22 36.82 21°70 “3:65 2246.83 44.9366 .0186 44.9180 ‘‘ PAY APA AD 48.59 2246.84 44 9368 .0184 44.9184 * 24 6.69 iL a8}sG83 2246.84 44 9368 .0181 44.9187 ‘‘ 51.65 2 18.46 2246.81 44 .9362 .0178 44.9184 ‘‘ 25 36.61 Sed ago) 2246.78 44 9356 .0175 44.9181 ‘‘ PAS DALEY 48 .32 2246.78 44.9356 .0172 44.9184 ‘é 27 ~=—«6..47 Cs 8 45) 2246.78 44 9356 .0170 44.9186 ‘ 51.438 5 18.18 2246.75 44 9350 0.0167 44.9183 ‘S 44.9182 sec ¢ After Martin. In the Vening Meinesz method, the coincidence record (Fig. 7-14) is obtained by interrupting the light beam twice during a full swing. In the actual record (see Fig. 7-15), more vibrations occur between successive passages than indicated in Fig. 7-14, since the difference in period between Cuap. 7] GRAVITATIONAL METHODS 107 the pendulum pair and the chronometer is very slight. If the period of chronometer and pendulum pair were exactly alike, the chronometer breaks would always occur at the same relative positions in the pendulum curves and the phase-lag-sine curve passing through the breaks would be a straight line. If the period of the pendulum pair is greater = __ a d than the chronometer interval, | ntl Lf i teohecay cine \ the chronometer breaks occur eal ri [Va at intervals less than a com- 1-4 is Ve \r ay ‘ plete cycle (or } cycle). The ~~ a A U~ tnd sine curve of the breaks IS. Fig. 7-14. Vening Meinesz pendulum record therefore an expression of the (schematic). re anea N is Han nun SEA ecan NS SUR NIG GN ata Sea EON RENN Fic. 7-15. Photographic record of Vening Meinesz pendulum apparatus. Upper record: First fictitious pendulum with marks of two chronometers. Middle record: Second fictitious pendulum with chronometer marks and record of air temperature and of auxiliary damped pendulum 1, recording the tilt angle. Lower record: Record of pendulum 2 recorded with reference to auxiliary damped pendulum 2. (The latter swings in the plane of oscillation of the regular pendulum while auxiliary damped pendulum 1 swings at right angles to that plane.) receding movement of the pendulum vector whose angular velocity is the phase lag of the pendulum pair. The evaluation of the record is made as follows. By an automatic mechanism a mark is left off every 60 seconds on the record (for instance, before A in Fig. 7-14). In determining the time of passage of the phase-lag 108 GRAVITATIONAL METHODS [Cuap. 7 curve (or the coincidence time interval n) these 60-second markers are used as reference lines. Instead of the breaks themselves being counted, the excursions on the upper or lower side of the record, such as d or a in Fig. 7-14, may be used. If Ag is the angular phase lag of the pendulum pair for a complete cycle 27, the number of oscillations required to complete the 360° cycle is 27/Ag, and the period of the pendulum pair differs from that of the chronometer in the proportion 27/27 — Ag; thus, 1 2r 0.25 Morea pena where 27 = 22/Ag = the coincidence interval. For absolute and relative determination of gravity, various forms of pendulums have been developed which are described in detail by Swick.” Two widely used forms are illus- trated in Fig. 7-16. A is the Sterneck-type quartermeter pendulum. ‘The top part isa stirrup holding a knife-edge made of agate or quartz and two mirrors. 8B is a more re- cent form known as the “rod’’ or ‘/mini- mum” pendulum. In it the knife edge is so placed that a change in its position has a minimum effect on the period. In a physical pendulum the moment of inertia, K = IMs (see page 99), may be considered as the sum of two moments, one with the radius of gyration s about the knife edge and the other with the radius of gyration r about the center of gravity so that K = sM + r’M andl = (r’ + s*)s. Hence, it follows Fic. 7-16. (A) Sterneck pen- _ py differentiation that dulum; (B) Meisser bar pen- dulum. T= (7-20) 2r. sr dl = —-dr + —.—-ds. (7-21) S s For the least change of period 7’ and therefore of reduced pendulum length 1 with s, the factor of ds must be zero. This gives s = r and therefore 1 = 2s. For “minimum” pendulums, (1) the reduced length must be twice the distance of the center of gravity from the knife edge, s; (2) the radius of gyration in reference to the center of gravity must be equal to the distance s. It is not difficult to do this for circular rods, since 7” = L’/12 + R’/4, where L is the geometric length and R the radius. 24H. Swick, Modern Methods for Measuring the Intensity of Gravity, U.S. Coast and Geodetic Survey, Serial No. 150. Cuap. 7] GRAVITATIONAL METHODS 109 Pendulum apparatuses have gone through a process of slow development. Although they have been largely replaced by the gravimeter in geophysical exploration, they still retain a fairly important place for deep water marine exploration where it is impracticable to lower remote indicating gravimeters to ocean bottom. The pendulum apparatus for regional geodetic work on land generally consists of an evacuated receiver with one to four pen- dulums, a lens and prism arrangement for visual observation and recording, a flash box, and a chronometer or reference pendulum. The carlier representatives are the U.S. Coast and Geodetic Survey apparatus, the e f mee (ae Beer a see Eee |m bo pee ci ee a Se yee NS by eo cd A pees opti ~~~ opin =~. Cs | py Be set ! i a vrue fete 45123 45123 Fic. 7-17. Optical paths in Vening Meinesz pendulum apparatus. No. 1 records 6: — 02. No.2 records 6: — 63. No.3 records 62 (the prisms a and b are fastened to the first auxiliary pendulum, moving in a plane parallel to the plane of oscillation of the principal pendulums). No. 4 records air temperature (prism c is fastened to a temperature recording device). No. 5 records the position of the second auxiliary pendulum moving in a plane perpendicular to the plane of oscillation of the principal pendulums (prism d is fastened to this pendulum). The horizontal projections of the rays numbered 4 and 5 coincide; the other prisms have a height of 30 mm, but c, d, n, and o have a height of only 12 mm and are above one another. The prisms e, f, g, h, 2, k, l, n, 0, and p and the lenses are attached to the top plate of the apparatus. Fechner-Potsdam pendulum, the Askania-Sterneck apparatus, the Meisser 4-pendulum instrument, the Numerov pendulum apparatus. Reference is made to the literature” for descriptions and illustrations of these types. Only the. Vening Meinesz marine apparatus, the Askania 3-pendulum instrument, and the Brown gravity pendulum of the U.S. Coast and Geodetic Survey will be briefly described here. In the Vening Meinesz pendulum apparatus, three pendulums are sus- * H. Swick, loc. cit. A. Berroth, Handb. d. Phys., 11(9), 447 (1926). H. Schmehl, Handb. Exper. Phys., 26(2), 216-238 (1931). 110 GRAVITATIONAL METHODS [CHapP. 7 pended in the order 7m, me, ms (see Fig. 7-17) from left to the right, and an optical arrangement is provided to record two fictitious pendulums, one representing 6, — 62, the second @. — 63. In addition, pendulum 2 is recorded independently with reference to a highly damped auxiliary pendulum in the plane of oscillation of the other pendulums. A fourth record is obtained from a second highly damped pendulum, which swings in a plane at right angles to the plane of oscillation of the regular pendu- lums, giving the angle of tilt 8. Altogether five pendulums are contained in the apparatus. The regular pendulums are as nearly isochronous as possible, the differences in periods not exceeding 50 X 10" sec. at normal pressure and temperature. In the damped pendulums, one unit is mounted inside the other, the outer pendulum being filled with oil. The entire pendulum apparatus is suspended in a frame in which it may be leveled by means of four screws. This frame, in turn, is suspended in gimbals. Many desirable features of the Vening Meinesz pendulum apparatus have been incorporated in the Askania three-pendulum apparatus, shown in Fig. 7-18. The receiver is rigidly anchored with three leveling screws and clamps (4) to the base plate (3) and consists of a roughly rectangular case (1) with a hood (2), both made of duraluminum. An air-tight seal is provided between them so that a pressure of about 0.1 mm may be main- tained inside for 6 to 7 hours. The three pendulums are arrested and released by three movements (10). During transportation from one station to another an additional mechanism (8) is provided, which secures the pendulum in three sockets; two of these are seen below the mirrors (14) while one of them has been taken out and is shown separately in front (11). Three impulse disks (7) are provided to start the pendulums at the desired time with a phase difference of 180°. The pendulums are of the invariable type, about 430 mm long and 26 mm around. The knife edge is located about 120 mm from the center. The upper surfaces of the pendulums are polished to act as mirrors, reflecting the light on the mirrors (14) through a lens (15) into a recording apparatus shown in the center of the picture. This apparatus may be used with time signals transmitted by radio from a pendulum located at a central station. If the latter is adjusted to match the field pendulums within 2-10~° seconds, concidence intervals are around 120 seconds and are determined with an accuracy of 0.2 second. For a two-hour set, an accuracy of +0.6-10’ seconds and thus a mean error in gravity of only 0.2 milligal is claimed. The Brown pendulum apparatus of the U.S. Coast and Geodetic Survey represents a considerable improvement over their earlier type. As in the latter, only one pendulum is used, housed in an air-tight receiver (Fig. 26 See eq. (7-18e) and (7-189). "dig viupysp upoisam y ‘snqvisdde wuin[npusd-se14} vIUBYsSy “ST-2 ‘DI 111 112 GRAVITATIONAL METHODS [CHap. 7 7-19). On top is a photo cell arrangement for the transmission of the pendulum oscillations. U.S. Coast and Geodetic Survey Fic. 7-19. Brown gravity apparatus. Upper part contains recording device and photoelectric cell; lower (evacuated) part contains the (4 m, invar) pendulum. The Lejay-Holweck pendulum apparatus is distinguished from other pendulum instruments by its small size and weight. The pendulum is Cuar. 7] GRAVITATIONAL METHODS 113 inclosed in an-evacuated glass bulb not much larger than a radio tube (see Fig. 2-1), consists of a fused quartz rod 4 mm in diameter and 60 mm in length, extends into a pin, P, for observation or photoelectric recording, and is fastened at the bottom to an elinvar spring, EL, which at the thinnest point has a thickness of only 0.02 mm. An ingenious arresting mechanism clamps the pendulum by a slight movement of the diaphragm, D. In this manner, the vacuum inside the tube is not disturbed. The period of this pendulum is about 6 to 7 seconds; the time required for a single observa- tion is about 4 minutes. A 40- to 60-minute observation period gives better than one milligal accuracy in gravity. C. TimME-DETERMINATION AND TIME-SIGNAL—ITRANSMISSION METHODS For an accurate determination of the pendulum period some sort of a standard timepiece must be used, such as a contact chronometer, a contact clock (Riefler), or a gravity pendulum. None of these (with the possible exception of a well-protected gravity pendulum at a central station) retain a sufficiently constant rate and must be compared with absolute time standards. This comparison may be made (1) astronomically, with a zenith telescope, (2) by recording of observatory time signals transmitted by wire, or (8) by radio. The following discussion of time-determination and time-signal-transmission methods will include a description of pro- cedures used for transmitting pendulum oscillations from a base to a field station or vice versa. 1. Astronomic time determination is now used in emergency cases only when reception of time signals is impossible. With a zenith telescope the time is determined when a star (or the sun) passes the astronomic meridian. At that instant the hour angle of the star is zero and its right ascension is equal to the local sidereal time; therefore, the “time correction” of the chronometer is right ascension minus chronometer time. 2. Reception of observatory time signals. In most of the U.S. Coast and Geodetic Survey pendulum work until about 1932 the telegraphic noontime signals of the U.S. Naval Observatory were used. They were recorded on a chronograph, together with the beats of the contact chronometer. Relays were employed throughout to save the contact points in the chronometers, since their time lag does not affect the chronometer rates as long as it remains the same in successive time signal observations. If the telegraph office is too far away from the pendulum room where the chronometers are located, a hack chronometer is compared with the stationary chronometers, then carried to the telegraph office, and afterwards compared with the stationary chronometers. It is now the more common practice to record radio time signals on a chronograph toegether with the beats of the comparison chronometer. 114 GRAVITATIONAL METHODS [Cuap. 7 A standard radio receiver and a variety of circuits and instruments may be used for recording. With chronographs, relays must be employed; an ordinary headphone receiver may be changed readily to a relay by attach- ing a bridge with an adjustable contact spring to its top. In some chrono- graph recorders thyratron arrangements have been applied (see Fig. 7-20). 3. Reception of time signals from a central station. With observatory time signal reception, a pendulum station requires 24 hours, since this is the interval at which these signals are usually transmitted. However, if a chronometer at a central station were connected by wire to the flash box at each field station, time comparisons could be made as frequently as desired. Berroth was the first to apply this method in a pendulum survey of a north German salt dome. For larger surveys, wire connection is impracticable and radio transmission is used instead. Transmitters range at B (/ Fia. 7-20. Radio receiver with thyratron and mechanical relays for time-signal recording (after Weber, Richter, and Geficken). G, , Detector circuit; G: , amplifier circuit; Gs, thyratron; Gs, mechanical relay and circuit breaker. in power from 50 to 200 watts and in wave length from 40 to 100 meters. In the transmission of chronometer beats, the contact circuit feeds through an input transformer into the grid of the modulator tube or operates a relay which controls the B-supply of the transmitter. If a gravity pendulum is the time standard, capacitive or photoelectric transmission of its beats is employed. As shown in Fig. 7-21, the pen- dulum itself, or a pin fastened to its bob, is one plate of a condenser and passes the fixed plate when the pendulum goes through its zero position. This change in capacity may be made to control a transmitter in various ways. In the arrangement shown, the pendulum passage changes the tuning of a regenerative oscillator. ‘The resulting changes in plate current are amplified and operate a relay, which in turn controls the B-supply of the transmitter. In the photoelectric method, the light beam reflected from the pendulum mirror is used to make contact. The light source and Cuap. 7] GRAVITATIONAL METHODS 115 the photo cell shown in Fig. 7-22 are in the focal plane of the lens attached to the front of the pendulum receiver. When the pendulum passes through the rest position, the photoelectric cell receives a light flash and passes current, which is amplified and operates the transmitter through a relay. Fig. 7-23 shows a photo cell connected to a four-stage resistance-coupled amplifier and a transmitter without relay. Central Pendulum Transmitter Fig. 7-21. Transmission of pendulum beats from central station by capacitive method (adapted from Mahnkopf). Radio time signals may be hd) PE Cell picked up at the field stations by standard short-wave re- ceivers provided with some sort of a recording device in the output stage so that the signals may be photographed on the same film with the os- Fie. 7-22. Arrangement for photoelectric cillations of the field pendu- transmission of pendulum beats. lums. A simple recording . device may be made of a telephone receiver (2-4000 ohms) by removing the diaphragm and replacing it by a steel reed with a mirror. To reduce static and other interference, the reed should be tuned to the signal fre- quency. In the Askania mirror device (Fig. 7-24), an armature with mir- ror is so suspended between the poles of a horseshoe magnet that it adjusts itself parallel to the lines of force and is deflected as plate current passes through the coils fastened to the one pole piece. A regular oscillograph coupled to the output tube by a step-down transformer is likewise ap- Light Source 116 GRAVITATIONAL METHODS [CHaP. 7 uN OO NOQQ009000 (4 }HH_G ) Fic. 7-23. Photoelectric cell, amplifier, and transmitter. A OTF “me: ad American Askania Corp. Fic. 7-24. Mirror device (Askania) in ampli- fier stage added to receiver. 7, transformer; H, horseshoe magnet (end view); M, mirror. Fic. glow tube. battery; B, B battery; MA, milliammeter; G, glow tube. 7-25. Amplifier stage with recording T, Transformer; C, bias battery; A, hours, or with radio time signals. the chronometer rate is plicable. Any inertia in the recording system may be eliminated by a glow-tube osciilograph as shown in Fig. 7-25. Its cathode is a slotted cylinder. The length of the light glow in it is pro- portional to the current. D. INSTRUMENT CORREC- TIONS IN PENDULUM OBSERVATIONS Corrections are required in pendulum observations because of (1) variations in the rate of the comparison chronometer, (2) dependence of period on amplitude, (3) temperature, (4) air pressure, and (5) flexure of the sup- port. 1. The correction for rate of the chronometer is deter- mined by comparing it with astronomical time determi- nations at least every 24 The pendulum period reduced for Cuap. 7] GRAVITATIONAL METHODS 117 S Re chron. — obs. TS ie —22 doch Bat late 86,400 Bee (7-22a) where S is the rate of the chronometer in seconds in sidereal time per sidereal 24 hour day (positive if losing, negative if gaining), so that the rate correction itself is 0.00001157 ST. The correction for chronometer rate on the coincidence interval n is S n(2n — 1) Nred.chron. — 1) — 86,400 au ) (7—22b) teeny 2 provided the pendulum swings more slowly than the chronometer does. For rates less than 25 seconds per day, equation (7-22b) may be simplified to Nred. chron. = 1 — sii n(2n — 1) (7-22c) If S < 23 sec., the effect is less than 0.1 milligal. No correction for chronometer rates and no time comparisons are necessary if measurements are made simultaneously on two field stations and if their flash boxes are connected to the same chronometer, or if radio time signals sent out by a central astronomical clock or pendulum are recorded simultaneously. Of course, rate corrections are likewise unnecessary when a gravity pendulum is used for radio transmission from a base station. 2. The amplitude correction follows from formula (7-16h), so that the reduced period Trea. «2-0 = 7'(1 — a’ /16 ----), in which @ is the average am- plitude during an observation. It may be considered as the arithmetic or geometric mean of the extreme amplitudes or may be obtained from “Borda’s relation.’’ If ao is the initial amplitude and a; the final amplitude, ets) 2 (b) a = anay (a) o& or (c) oNei sin (a + as) sin (ao = ay) (7-232) 2(log. sin ap — log. sin ay) which, for small angles, is 2 2 DN waits Oo — af ite 2(loge ap — log, ay)” 118 GRAVITATIONAL METHODS [Cuap. 7 With the last expression, the are correction is 1 an ay 2.3 X 32 logis ao — logiy ay If the effect of this reduction is to be less than 0.1 milligal, the amplitude must not exceed 14°. With a simplification permissible for such ampli- tudes, the reduced coincidence interval is 16 sal (7-23) (7-23c) Nred.a—0 = N =F a The correction may be further reduced if referred to (constant) average amplitude am and a mean coincidence interval nm:” Nred. an = N ap — [2(an ra Qm Nm) ae (a oa Qm)]. (7-23d) 3. In the temperature correction it is sufficient to assume a linear change of period with temperature. The change in length of invar pendulums ranges from 1.2 to 1.6 w per meter and degree Centigrade. Quartz pen- dulums expand much less, while brass or bronze pendulums increase in length as much as 20 » per meter and degree Centigrade. The reduced period is f Le = 7T— Co(O TF .), (7-24a) ‘ . . . 28 where Cg is the ‘temperature coefficient,’ determined by experiment. The correction on the coincidence interval is Tred. temp. = 1 + Co(.— 8), (7-24) where the relation between Cg and ¢g is 1 / Co or Cg = (2rrea. — 1)? *€g: (7-24c) PCa ye 4, The air-pressure correction arises from the fact that the period of the pendulum is lengthened by the buoyancy of the air, by its hydrodynamic effect, and by its viscosity (interior friction). The buoyancy effect is the most important and depends not only upon the pressure of the air but also upon the amount of water vapor in it. That is, the buoyancy effect is less for saturated air than for. dry air at the same pressure. For this reason a ‘“hygrometer correction” has to be applied to the observed air pressure and the reduced air density is computed from the relation a ps — 0.377 py-h 760[1 + 0.003665(6 — @,)|’ 5 (7-25a) 27H. Schmehl, loc. cit. 28 H. Schmehl and W. Jennie, Zeit. Instrumentenkunde, 49(8), 396-406 (1929). Cuar. 7] GRAVITATIONAL METHODS 119 where p, is the manometer or barometer reading in millimeters, p, the saturation pressure of water vapor, h the relative humidity in per cent. Then the period as reduced for air pressure is Divedvaic =T-c pd a 50), (7-25b) where 6, is the mean density of the air (constant) and c, is the pressure coefficient to be determined by experiment.” The coincidence interval reduced for air pressure is Nredair = 2 + c,(6 ae 50) (7-25c) where the relation of c, and ¢, is given by 1 (QT sca)?’ Cy: (7-25d) Cp = (2mrea, — 1)’tp, OF Cp = 5. The flexure correction is due to the fact that the vibrating pendulum produces oscillations of the receiver case, of the pillar, and of the surface soil. Rather complex coupled vibration phenomena arise and the period of the pendulum itself changes. Numerous methods have been suggested to correct for this influence or to eliminate it. Since the correction is of the order of 10 to 40-10 ‘ on solid rock or cement and may increase to as much as 500-10’ sec. on marshy ground (Berroth), it must be determined accurately. The displacement of the point of suspension of the pendulum is y=-, (7-26a) where Y is the horizontal tension produced by the pendulum and e the elasticity of the support. The tension, Y, may be assumed to be equal to the restoring force. Hence, from equation (7-16a), Y = Mgs sin 6/l and ey = Mgssin @/l. Then the differential equation of motion, Te eR ae ldy dz + 7 sin 6 + 7p dt is identical with the equation given for the Vening Meinesz pendulum (7-18a) and the “disturbed”? pendulum length and the change in period are given by I Mgs l ¢ als s Mgs 2e/2 © = 0, ~ ~ (7-26b) AT = T aiid: 120 GRAVITATIONAL METHODS [Cuap. 7 Since the flexure of the support produces an increase in period, the flexure correction (sometimes called only flexure), is always negative. Flexure is determined experimentally (1) by applying an external force (producing a deflection of the pendulum apparatus), or (2) from the displacement caused by the moving pendulum itself. Since (according to eq. [7-26a]) the elasticity of the support is given by the ratio of horizontal force and corresponding displacement, the horizontal stress may be applied statically to the pendulum receiver by weights and pulley and the resulting displacement may be measured by a micro- id scope or an interferometer. The external im- pulses may also be produced periodically; then the forced oscillation amplitude of a light aux- 5, iliary pendulum (at rest at the beginning of the Sl mM test) is measured. Methods employing external forces are now superseded by those making use of the effect of the oscillating pendulum itself. They meas- ure the corresponding displacement of the re- | ceiver or the effects of the “driving” upon a companion pendulum. For making direct flex- Fic. 7-26a. Interferometer Ure observations, the pendulum apparatus is so (after Wright). set up that the pendulum swings to and fro in respect to the telescope of the flash box. A mirror, P (see Fig. 7-26a), is attached to the “hi head of the pendulum receiver and an inter- ferometer is placed between pendulum and i flash box on an independent support. From a ! i source, SL, of monochromatic light (sodium- chloride in an alcohol burner) the light beam : travels through the lens, L, to the two plane- 5 “A parallel giass plates, S and C. S is provided Fic. 7-26). Fringes and : j : aN : faneoudisplacementai(aiver with a semireflecting backing of silver so that Wright). part of the light is reflected to the mirror, P, and from it into the telescope, 7’, while another portion goes through the plates, S and C, to a stationary mirror, M, and thence into the telescope. The giass piate, C, is a compensator to make the two light rays travel through exactly the same substances and the same thicknesses on their way to the telescope where they unite under conditions producing inter- ference. As shown in Fig. 7—26b, a number of dark and light bands appear, the former corresponding to a phase difference of one-half wavelength and the latter to a full-wave phase shift. When the pendulum mirror, P, Cuap. 7] GRAVITATIONAL METHODS 121 moves periodically, the distances traveled by both rays change and the fringes shift periodically. If light changes to darkness and back to light, the movement has been one fringe, the phase shift one wavelength, and the displacement of the mirror one-half wavelength, or 0.29 microns (since the wavelength of sodium light is 0.58 microns). The shift of the fringes dz, is expressed in terms of fringe width, x, and all observations are reduced to 5 mm arc (not semi-arc) of pendulum movement. The correction on the pendulum period is determined by measuring periods 7’ and correspond- ing fringe shifts (F) under varying conditions of stability of the pendulum support so that the flexure “coefficient” c; = AT/AF. Then the flexure correction AT iiestre = (PF) “Cha = a ae “Cy. (727) A set of flexure observations with calculations is reproduced in Swick’s pamphlet.” The actual displacement of the pendulum support is very small; for firm ground and pillar it varies from 0.06 to 0.10 fringe width or 0.017 to 0.029 microns. Twin-pendulum procedures give greater accuracy than the interferom- eter method in the determination of flexure. Observations may be started with the companion pendulum at rest or with both pendulums in opposite phases and identical amplitudes. The second method is more accurate, since theoretically the influence of flexure is completely elimi- nated. Only a small correction remains, because of the impossibility of keeping the amplitude and phase relations of the two pendulums constant throughout the entire observation period. If, in the first method, one pendulum is at rest at the time & (a2 = 0 and yg: — g; = 7/2), and if at the time ¢ the amplitude a2 of the driven pendulum and the amplitude a, of the driving pendulum is observed, the effect a flexure on period and coin- cidence interval respectively is 2 AP ae: = 3: hee Saas QQ a(t a to) 4 (7-282) Antex. = 2 i Pr (en i provided the phase difference at the end of the observation period is still nearly 90°. If two pendulums swing against each other on the same support, the flexure corrections for each pendulum on period and coin- . . ° 3 cidence interval are, at any instant ¢, : 30 Toc. cit. 31H. Schmehl, Zeit. Geophys., 3(4), 157-160 (1927). 122 GRAVITATIONAL METHODS [Cuap. 7 St (AT1): = Fs|1 ot (22) -c0s (y2 — ee | (aE Fe|1 He (2) hoe ae ee| ‘ (7-28b) (Am): = F.| 1 -+ (22) -cos (ge — git 1 (Ane): = F.|1 =e (22) -c0s (go — oe| in which F; and F,, respectively, are approximate values of the flexure corrections obtained from equation (7-28a). The values of these cor- rections for the entire observation period are found by integration between the limits t; and t., reckoned from the time tf when the phase difference is exactly 180° and the amplitude ratio is (a2/a1)) and (a1/a2)o: ans ~ —¥41 ~ (3), + 5] (Seo (n — in), Gomi Fr if (ae w\\][b—-i b—-t +m. — 19] (22) 2-1) +F(1 -3(@),) || c | (7-28c) T. has the same equivalent as eq. (7-28c) with a:/a2 instead of ae/ax. The correction for the coincidence interval, with nn» = (m + ne)2, is An = F, + (2 COs (¢g2 — )), Ae (2 cos (gy: — »)) | “ ~ (te ae ti) [rm ar peal | (em ine oy) (2) a= F,, (3 Ga Soa 1)} n Qa1/0 1/0 (7-28d) The nz has the same equivalent as eq. (7-28d) with a1/az instead of ate/a, and (Mm, — Mm) instead of (Mm, — Mm). The elimination of flexure by the simultaneous oscillation of two pen- dulums is so perfect that, although the flexure itself may be 20-50 X One seconds, the corrections seldom exceed —1 X 10 ' seconds, provided the phase differences do not deviate more than 30° from 180°. 6. Examples of pendulum observations have been published by various authors for different instruments and procedures. A complete set of U.S. Coast and Geodetic Survey observations has been reproduced by Cuap. 7] GRAVITATIONAL METHODS 123 Swick.” For the Potsdam apparatus, observations with the one-pendulum and twin-pendulum methods are found in Schmehl’s publication;* Vening Meinesz has illustrated the application of his method by photographs of records and calculation examples.” E. GRAVIMETERS The pendulum methods discussed in the preceding section are sometimes referred to as ‘‘dynamic”’ gravity procedures since they involve the meas- urement of time. Other possibilities in the same category are: (1) the determination of the time and distance characteristics of free fall in vacuum; (2) a comparison of gravity with the centrifugal force of a rotating body by measuring the slope of a surface of mercury subjected to rapid rotation in a vessel. None of these methods has been perfected to the same degree of accuracy as that found in pendulum or gravimeter methods. The term “gravimeter,” or “gravity meter,’’ is customarily applied to an instrument involving a statzc method of comparing gravity with an elastic force and a measurement of the deflection or position of certain “indica- ’ tors’? when gravity and comparison force are in equilibrium. In the barometric method, atmospheric pressure as measured with an aneroid (or boilmg-point thermometer) is compared with the reading of a mercury barometer; in the volumetric method (Haalck gravimeter), both sides of a mercury barometer are connected to two vessels with the air under different pressure. In all remaining static gravity methods, the elasticity of springs is used for comparison with gravity. The mechanical gravimeters fall into two groups: nonastatic and astatic. Gravimeters that are modifications of horizontal seismometers” may be called horizontal seismo-gravimeters, while those resembling vertical seismographs may be designated vertical seismo-gravimeters. 1. Barometric method. Jf atmospheric pressure is measured at different localities with an aneroid and a mercury barometer, discrepancies result because the mercury barometer is affected by variations in gravity. Since the aneroid does not give sufficient accuracy, the boiling point of water is measured instead to give atmospheric pressure. The barometric method was the first to make possible determinations of gravity on board ship and was perfected principally by Hecker. To obtain a mean error of +40 milligals it is necessary to read the boiling point with an accuracy of 1/1000° C. and the barometer with an accuracy of 0.01 mm. How much az OCA Ct. 33 Schmehl, Zeit Geophys., loc. cit. est oc: cit: % See page 580, Fig. 9-94. 124 GRAVITATIONAL METHODS [Cuap. 7 the error could be reduced on land has probably not been determined. In any event, this method is not likely even to approach a modern gravimeter in accuracy. 2. Volumetric method (Haalck gravimeter’) is illustrated schematically in Fig. 7-27, where v and v’ are the two volumes and z and 2’, respectively, are the positions of the mercury menisci. If pis the pressure in the volume v and 7p’ is the pressure in the volume v’, then the difference in pressure Ap must be equal to the weight of the mercury column so that Ap = Az-6-g, where 6 is the specific gravity of the mercury. To obtain sufficient sensi- tivity, use is made of vessels of greatly increased section, of a lighter liquid (toluol) on top of the mercury, and of small capillary tubes, C and C’, for reading the menisci. The increase in the accuracy is proportional to the ratio of the sections of the ves- sel and the capillary (about 10,000 in the Haalck apparatus). A dis- placement of the menisci by about 1 mm corresponds to a change in gravity of one milligal. In the first experimental model, the mean error was +10 milligals. The lastest model is a quadruple ap- paratus, has an accuracy of about one milligal, is suspended in gim- bals, and may be used on board ship. 3. Unastatized mechanical grav- imeters utilize the elastic force of springs and the torsion of wires for comparison with gravity. Me- chanical, optical, or electrical means of magnification are applied to obtain the necessary accuracy of 1 in 10 million. In a spring gravimeter, the deflection, d, is inversely pro- portional to the square of its natural frequency, w. Since the relation wy = +/c/m may be written” w) = m-g/d-m, the variation of deflection d and of the reading a with gravity (V = static magnification) is given by Fic. 7-27. Haalck gravimeter. Ad = "9 and Aa = V%. (7-29) Wo Wo 3° H. Haalck, Zeit. Geophys., 7(1/2), 95-103 (1931); 8(1/2), 17-30 (1932); 8(5), 197-204 (1932); 9(1/2), 81-83 (1933); 9(6/8), 285-295 (1933); 11(1/2), 55-74 (1935); 12(1), 1-21 (1935). Idem, Beitr. angew. Geophys., 7(3), 285-316 (1938). 37 See page 581, eq. (9-83). Cuap. 7] GRAVITATIONAL METHODS 125 It is seen that for high (mechanical) sensitivity an increase in period (astatization) is of advantage. However, not all gravimeters are astatized. The Threlfall and Pollock gravimeter’ is one of the earliest examples of an unastatized gravimeter. It consists of a torsion wire about 0.0015 in. in diameter, supporting in the middle a quartz bar about 5 cm long and 0.018 g in weight, whose position is read by a microscope. One of the studs holding the wire is fixed; the other is rotated until the bar end coin- cides with the crossweb in the microscope (horizontal position). The corresponding stud position is read on an accurate dial. The Wright gravimeter closely resembles the Threlfall-Pollock instru- ment, two tapering helical springs taking the place of the torsion wire. Between them a small boom with a mirror is adjusted to horizontal position by turning one of the studs supporting the springs. An illustration based on a patent drawing is given in the author’s publication on gravimeters.”’ In the most recent type’ measurements are made as follows: The springs are wound until the boom is horizontal, at which time the reading of the spring-supporting frame is recorded. Then the spring is unwound so that the boom passes through its vertical position and reaches a horizontal position on the other side. The corresponding reading is recorded; the difference between readings for the horizontal boom positions is a measure of gravity. Since the boom is used near the upsetting position, this instrument may be included in the group of astatic gravimeters. Accurate temperature and pressure control is required; the accuracy is about 1 milligal. The Lindblad-Malmquist (“Boliden’”’) gravimeter” consists of two springs carrying a light mass with two disk-shaped extensions (see Fig. 7-28a). The upper disks act as the variable condenser in an “‘ultramicrom- eter” circuit. Using a spacing of. 2-10 ° cm, the authors claim to have been able to detect displacements of the order of 3.5-10-° em. A gravity change of one milligal corresponded to a displacement of about 5.5-10 ’ em, so that variations of the order of 1/100 milligal would be detectable. Because of various interfering factors, however, the mean error in the field was 0.1 to 0.2 milligal for a single observation and 0.05 to 0.1 milligal for five to ten observations. The ultramicrometer circuit acts merely as an indicator, the deflections being compensated by electrostatic attraction between the upper plates. The distance between the lower plates is so adjusted that a potential difference of 10 volts corresponds to a gravity variation of 1 milligal. 38 Phil. Trans. Roy. Soc. (A) 198, 215-258 (1900); (A) 231, 55-73 (1932). 39 C, A. Heiland, A.I.M.E. Tech. Publ., 1049 (1939). 40 F. E. Wright and J. L. England, Am. J. Sci., 365A, 373-383 (1938). 41 A. Lindblad and D. Malmquist, Ingen. Vetensk. Handl., No. 146, 52 pp. (Stock- holm, 1938). 126 GRAVITATIONAL METHODS [CHap. 7 In the Hartley” gravimeter the mass is supported approximately from the center of a beam hinged on one end. The movement of the beam is transferred to two rocking mirrors that rotate in opposite directions when the beam is displaced. The main spring supporting the beam above the mass is made of an alloy of tungsten and tantalum, carries 99.9 per cent of the total load, is wound with high initial tension, and:in extended position is about 10cm long. A small additional spring is provided for compensat- ing the beam deflections by rotation of a micrometer screw. In the Gulf (Hoyt) gravimeter, Fig. 7-28b (U.S. Patent 2,131,737, Oct. 4, 1938) a spider weighing about 100 grams is suspended from a helical spring of rectangular section. A spring section whose width is much greater than its thickness produces a rotation of the suspended mass when the weight changes, this action being comparable with that of a bifilar suspension (see below). The dimensions may be so selected that a change of 0.1 CLG LLLLLLG LAD ME rrceaierss a Fic. 7-28a. Lindblad-Malmquist gravimeter (schematic). milligal produces a deflection of the order of 1 arc-second. Deflections are measured by a multiple reflection setup involving two semireflecting lenses. One of these is attached to the spider. Scale and light source are in the conjugate foci of the lens combination. Reading the tenth multiple reflection, a deflection of 1 arc-second corresponds to about 20 scale divisions. In the Askania-Graf gravimeter” a mass is suspended freely from a helical spring. Its deflection is measured with an electrical displacement meter (presumably operating without amplifier) with a magnification of about 4-10°. Temperature compensation and a double battery-operated thermostat is provided. The accuracy is of the order of 0.1 milligal. It 42 Physics, 2(8), 123-130 (March, 1932). 43 A. Graf., Zeit. Geophys., 14(6/6), 154-172 (1938). Cuap. 7] GRAVITATIONAL METHODS 127 follows from eq. (7-29) that a deflection of 2.5-10-'u is produced by a gravity anomaly of one milligal, since the natural frequency is 1 sec. This displacement, with a magnifica- tion of 4-10*, gives a galva- nometer deflection of 10 mm. 4. Astatization of gravimeters is equivalent to lowering their nat- ural frequency. It involves the application of a negative restor- ing force in such a manner as to drive the mass away from its rest position and to aid any deflect- ing force. While unastatized gravimeters are invariably vertical seismo- graphs, the process of astatization makes it possible to utilize hori- zontal seismographs for gravity measurements. Virtually all horizontal seismo-gravimeters are inverted pendulums, analogous to the Wiechert astatic seismo- graph (Lejay-Holweck and the Ising gravimeters). Vertical seis- mographs may be astatized by attaching the suspension spring below the horizontal axis of the lever arm (Ewing), by using the spring at an angle of less than 90° with the beam (Berlage,“ La- Coste”), by combining a hori- zontal pendulum with a vertical balance (Schmerwitz*), by fas- tening an inverted pendulum per- manently to the center of the beam (Tanakadate, Thyssen), or by providing an additional ° Fic. 7-28b. Gulf gravimeter (after Hoyt). 44H. P. Berlage, Jr., Handbuch der Geophysik, IV(2), 385. “L. J. B. LaCoste, Physics, 6(3), 174-176 (1934); Seis. Soc. Amer. Bull., 25(2), 176-179 (April, 1935). 46 Zeit. Geophys., 7(1/2), 95-103 (1931); Beitr. angew. Geophys., 4(3), 274-295 (1934). 128 GRAVITATIONAL METHODS [CHaP. 7 “period” or “pull-back” spring through the axis of rotation (Truman, Mott-Smith). In vertical and horizontal seismo-gravimeters, the restoring and labilizing forces act in the vertical plane with rotation about a hori- zontal axis. it is also possible to produce a labilizing gravity moment with action in a horizontal plane and rotation about a vertical axis (bifilar suspension). ‘The tendency of such a system to come to rest in the lowest position of the mass. produces a horizontal torque. Bifilar systems may be astatized by “twisting” the bifilar suspension 180° (Fig. 7-30), or by addition of a helical spring (‘‘trifilar’ gravimeter, Fig. 7-31). By astatization the sensitivity to gravity variations is greatly increased. If 7 is the (positive) restoring force and x the (negative) labilizing force, then the resulting restoring force, N, is N=yn-k. (7-30a) Ii the system is to be stable, 7 must be greater than x. The degree of astatization, A, may be defined” as the ratio of the labilizing force, x, and the resultant force, N: A = «/N. (7-30b) The degree of astatization, A, increases, therefore, with the labilizing force and the difference between the restoring and the labilizing forces. Small differences in either may be observed with great accuracy. In some astatic systems differences in stabilizing force are the object of observation; in others it is differences in the labilizing force (inverted gravity pen- dulums). If the labilizing forces are held constant arid changes in the stabilizing forces are observed, the resultant restoring force and the degree of astatization change in accordance with Sete ie n | (7-30c) aA Pook dn ane (A + 1) aa On the other hand, if changes in the labilizing forces are observed, the cor- responding relations are aN dk Noe ae (7-30d) a seh (etn ES K 47 G. Ising, A.I.M.E. Tech. Publ., 828 (August, 1937). Cuap. 7] GRAVITATIONAL METHODS 129 5. Horizontal seismo-gravimeters resemble in principle the well-known Wiechert astatic seismograph. In the Ising gravimeter a quartz fiber is stretched between the prongs of a fork-shaped support and forms the horizontal axis of rotation of an inverted quartz rod fused rigidly to the fiber (Fig. 7-29). The pendulum assembly is mounted on a heavy metal block hung from two leaf springs in such a manner that it can be turned slightly about an axis parallel to the fiber by tight- ening a spring attached to one side of the block. When the block is tilted at an angle ¢, the pen- dulum is deflected from its verti- cal position by the angle @. In the position of equilibrium, 10 = x(0 + ¢) as (7-31a) ee U) sae tS Assuming that the gravity at a (base) station is g) and that a tilt, g, has produced the deflec- tion, 6, the labilizing force at that station xo = 74/(¢ + 60). If, at another station with the gravity gi, the same tilt angle is used, the labilizing force is x, = 79:/(e + @,). Then the difference in gravity is Ag = g(x — ko)/ko or, in terms of (small) deflection angles for constant tilts, 0; 2) 6 IN = ieee UG bs Vana eee : pe g | ; i | (7-31b) The deflection of the inverted pendulum is read with a micro- \} 'q reves AL) aN v4 gaa ) Res Sea as \\ 10. LR B mare ATT ST HE zs rec Wee l |} D SS SSS SSS b= NANA MALE 27 ON NAR NO Fic. 7-29. Ising astatic gravimeter (section). scope, and the tilt of the block is measured with the micrometer screw that controls the tension of the tilt spring. In the instruments described in the published reports the mean error was 0.5 to 0.6 milligal. The Lejay-Holweck pendulum with some modifications also could be used as a static gravimeter to operate like the Ising instrument. 130 GRAVITATIONAL METHODS [Cuap. 7 The N¢grgaard gravimeter” has two inverted quartz pendulums leaning toward one another, with an index rod between them. The distance between the ends of the quartz rods is read with a microscope and is a measure of gravity. The entire system is immersed in water of constant temperature and is thus highly damped and insensitive to vibration. The mean error is about 0.3 milligal. 6. Vertical setsmo-gravimeters fall into two groups: (1) inebreenenye in which gravity changes produce rotations about a vertical axis (bifilar or trifilar suspensions) ; (2) gravimeters in which this rotation takes place in a vertical plane and about a horizontal axis. In the bifilar gravimeters, the restoring force is due to the torsion of the suspension wires (equivalent torsional coefficient 7) as well as to gravity, since the suspended mass is raised upon rotation. If 2a is the distance of the suspension points above, 2b the distance below, and d their vertical distance, the effect of gravity is given by the expression mg-ab/d and, therefore, the resulting restoring force is iy Se 9 (7-32a) where d’ is the vertical distance corrected for a reduction in length which occurs because of the bending of the wires. With a moment of inertia K, the period of oscillation of a mass on bifilar suspension is f= In / K if (24% ee ma); (7-32b) which, however, is much too short to give sufficient sensitivity to gravity variations. A bifilar system can be readily astatized by changing the sign of the second term in the denominator of eq. (7-32b), that is, by making gravity the labilizing force (reversing the suspension 180° as shown in Fig. 7-30). Then T =r yx [ (2 = 2? ma): (7-82c) With high astatizing factors this procedure increases the sensitivity to gravity variations about 1000-fold, which is an-improvement of similar order as in the Lejay-Holweck pendulum, where gravity likewise acts as a labilizing force. Bifilar gravimeters have been constructed by Berroth,” Ising,” (Fig. 7-30), and Hart Brown. Bifilar instruments with crossed wires appear to be inferior to the 48 G. Ngrgaard, Dansk Geodaetisk Inst. Medd., No. 10 (Kgbenhavn, 1938). 49 Zeit. Geophys., 8(8), 366 (1932). 50 Loc. cit. Cuap. 7] GRAVITATIONAL METHODS 131 trifiiar gravimeters which are capable of the greatest sensitivity yet at- tained in such instruments. The trifilar gravimeter consists of a disk supported by a helical spring at its center and by three equally spaced wires at its circumference. It was first described by A. Schmidt.” Fig. 7-31 is a schematic showing only one of the suspension wires, fastened at the ceiling at C and attached to the disk at A. The vertical distance of C above the disk is CB = d, and its horizontal distance from the center is OB =a. The radius of the disk is OA = r and the horizontal distance AB =e. When a disk deflection, ¢, has been brought about by a torsion- head rotation, a, the suspension wire is deflected by the angle, 8, from the vertical. The total weight, W, is so dis- tributed that the coil spring bears a weight W — w and the suspension wires each w/2 or w/3, depending upon whether two or three wires are used. If w/2 is re- solved into its components, Q and H (see Fig. 7-31), it is seen that Q is ineffective and H = w/2 tan B = we/2d. Its tan- gential component, H cos ¥, produces the couple 2Hr cos y. In the triangle OAB, e-sin (90 + ¥) =asing. With cosy = a sin g/e, the couple Dz = wra sin ¢/d. It is opposed by the moment of torsion of the main coil, Di: = t(a — gy). Thus in the equilibrium position, ay x f> ix ) f Piece SSS 4 dn XZ SaaS Ss TO Fs er es an S i es +) GEE LL nal LeeLee dca ne ASI | AN x Y RYO SS r(a — 9) — “sin ¢ = 0. (7-33a) \ z Small changes in the weight of the disk and hence in gravity will produce large deflections, since Fia. 7-30. Ising bifilar gravimeter. #) d sin (2) “q cS ¢ +r It is seen that maximum sensitivity occurs when the denominator is zero or when cos ¢ = —7d/war. As 7 is small, the position of maximum sensitivity is very close to 90° from the position of zero deflection. With a trifilar gravimeter, Tomaschek and Schaffernicht” have recorded the 1 Beitr. Geophys., 4, 109-115 (1900). 52 Zeit. Geophys., 9(8), 125-136 (1933). 132 GRAVITATIONAL METHODS [CHap. 7 Fic. 7-31. Action of trifilar gravimeter. = «<” < <— <> <> <> <> <= Objective, WE Lens ) , Index Plate ZS Ground 6la.s—7 © Light Fic. 7-32. Truman gravimeter. changes in gravity brought about by the changes in attraction of the moon with an accuracy of about 0.001 milli- gal. A portable instrument for gravity exploration has not yet been developed. The Truman gravimeter (see Fig. 7- 32), used chiefly by the Humble Oil Company and associated companies, is similar in construction to a Ewing astatic vertical seismograph. The beam consists of a right triangle with the right angle at the axis of rotation. The mass is attached to the end of this triangle, and near it a vertical coil spring supports most of the mass and the beam. An astatizing spring is at- tached to the other corner of the tri- angle, approximately below the point of suspension. The accuracy is of the order of 0.5 milligal.” The Thyssen gravimeter (Fig. 7-33) is likewise a beam-type vertical seis- mometer. The beam is horizontal and suspended in the center on a knife edge, the balancing spring being housed in a tube surrounded by a water jacket expanding downward with an increase in temperature to offset the increase in spring length. An astatizing arm is fastened to the center of the beam which is made of fused quartz and has a length of 15 to 20cm. Two beams are arranged side by each in antiparal- lel arrangement as in a torsion balance. They are clamped by a mechanism operated from the top of the instru- ment and are read separately by the optical arrangement shown in the figure. The zero position is calculated from reversal readings. The mean error of one station is 0.25 milligal, 53 A.B Bryan, Geophysics, 2(4), 301-308 (Oct., 1937). Cnap. 7] . GRAVITATIONAL METHODS 133 that of repeat stations about 0.5 milligal.“ The drift in one day is 1 to 1.5 milligals. The Mott-Smith gravimeter” (Fig. 7-34) is essentially a torsion-wire gravimeter with astatization. The torsion fiber (2) is made of fused quartz and carries a weight arm (1) to which is attached the pointer (8). A negative restoring force is supplied by a fiber (4) passing through the axis of rota- tion of the weighing arm. Defiections of the system are read by a microscope. Gravimeter readings are affected by tem- perature, air pressure, humidity, abrupt changes and slow drift of the base reading. These efiects must be corrected for and be determined by experiment; furthermore, the sensitivity (scale value) of the instrument must be known. The effect of temperature is complex, cannot always be calculated, and is generally determined by experiment. In most gravimeters some sort of temper- ature compensation and thermostat protec- tion is provided. If this were not done, the temperature effect would be tremendous. In a spring gravimeter a change of 1°C. would produce an apparent change in grav- ity of 200 to 300 milligais. In a volumetric gravimeter the same temperature change would correspond to an apparent gravity anomaly of 3000 to 4000 milligals. Changes in air pressure affect some gravimeters, depending upon _ construc- tion of the case and the weight of the moving member. The buoyancy in- creases with barometric pressure, and its effect on the reading is determined by experiment. Changes in humidity may produce large effects in gravimeters whose mass is small, since water condensation will 54 A. Schleusener, Zeit. Geophys., 10(8), 369-377 (1934); Oel und Kohle, 2(7), 313-318 (1934). St. v. Thyssen and A. Schleusener, Oel und Kohle, 2(8), 635-650 (1935); Beitr. angew. Geophys., 6(1), 1-13 (1936). St. v. Thyssen, Zeit. Geophys., 11(3), 131-133 (1935) ; 11(4/6), 212-220 (1935); Beitr. angew. Geophys., 6(2), 178-181 (1935) ; 6(3), 303-314 (1935); 7(3), 218-229 (1938). A. Berroth, Oil Weekly, 76(13), 33-37 (March 11, 1935). F. Lubiger, Beitr. angew. Geophys., 7(8), 230-244 (1938). 56 Geophysics, 2(1), 21-32 (Jan.. 1937). Fig. 7-33. Thyssen gravimeter (schematic). 134 GRAVITATIONAL METHODS _ [CHar. 7 produce large changes in equivalent mass. In some instruments, calcium chloride in solid form or as supersaturated solution is used to keep the air dry. Although the sensitivity of a gravimeter is proportional to the square of the period, determinations of scale values by period observations are not in use (except for qualitative observation while adjusting an instru- ment), since there are numerous other methods with which scale values can be determined more easily and accu- rately. Some gravimeters may be calibrated by tilting. For an inclination, ¢, the effec- tive gravity changes from g to g cos g; there- fore, the apparent difference in gravity is 2 Ag = g(1 — cos ¢) = 29 sin’ 5 ~ i> (7-34a) Many gravimeters lend themselves readily Fra. 7-34. Mott-Smith gravi- to scale value determinations by addition of meter (schematic). weights (see Fig. 7-35). If the total gravi- meter mass is M, the apparent change in gravity produced by an addition of mass m is _ dm arg: (7-840) 4g Gravimeters with condenser plates may readily be calibrated electrostatically. If the two con- denser plates have equal surfaces of S square centimeters at a dis- tance of d centimeters, the ap- parent change in gravity brought about by a voltage difference, E, is Scale divisions neSE 8rd? MW’ Ag (7-34c) Load, mgrams Fic. 7-35. Gravimeter calibration by addi- : tion of mass (after Schleusener). In terms of capacity C = S/4rd, which is more readily deter- mined,” the apparent change in gravity is E’ Cc = —— 7-34d Ag = 2" oi ( ) 56 A. Lindblad and D. Malmquist, loc. cit. Cuap. 7] GRAVITATIONAL METHODS 135 Almost ‘any kind of gravimeter may be calibrated by measuring the change in reading with elevation. A sufficient difference exists in most office buildings between basement and the highest floor (Fig. 7-36). From the formulas given in the next section for the “free air’”’ reduction, the change in gravity with elevation is Ag (in milligals) = —AA. (in meters) -0.3086. (7-34e) Because of the elastic hysteresis of the suspension material, most gra- vimeters show a more or less appreciable ‘“‘drift’’ of the zero position with time. Furthermore, abrupt changes ¢n base position may result from mechanical changes in the moving systems. Both kinds of changes may 38 4h 642m. Below heen we Sy Scale divisions qj Be . 0 116° 1200 132 1400 Time Fic. 7-36. Calibration of gravimeter on building (after Schleusener). be corrected for by checking with a base station or a number of them at regular intervals.” F, CoRRECTIONS ON OBSERVED GRAVITY VALUES In relative gravity determinations with pendulums, the values at a field station (g.) are calculated from the base station values (gp) as follows: one cee le Ca i Ja = Yp i and jn — Joo (Cray (7-35a) where 7’, as before, is the period and n the coincidence interval. By series expansion, these equations take the more practical form: T, —.T 1 Ny aye Bee = 2p Ep, Dp ; \ (7-852) Nea — 1 Nae — 1 = Gg eS 7 4ng 3 2 Lu Soa i a 4? ig(2M» — 1) do(4ne oe Rae raphy is assumed to be — Ip i eS amc composed of masses which , aif have the shape of cylindrical a b segments. Hence, the mass Fic. 7-37. Terrain sectors. of such an element is dm = 6-rdg-dr-dh. Since the po- tential of a mass element at the origin is U = k.dm/r, the potential due to the entire topography surrounding the station is given by c-w [ff [See (7-386) The integration is here extended for distances from 0 to infinity. In practice the calculation is carried only to the point where the terrain effect is less than the probable error. The integration may be carried out by introducing a terrain angle yy = tan h/r. Then the vertical component of the attraction follows from a differentiation of eq. (7-385): fH aU e @ 2r Ag = rolee Ks | i (1 — cos y) dr-dg. (7-38c) The mass elements are now so dimensioned that within each of them the terrain angle may be assumed to be constant. If each mass element is bouhded by the concentric radii r~, and rmyi and by the angles ¢, and Pnt+1) ™m+1 p?ntl Ag = —ké(1 — cos y) ih i dr-dy, (7-38d) ™m en which is Ag = —ké(1 — cos V) (Tmt =a Tm) (Pn+1 ae ’n)- 58S. Hammer, Geophysics, 4(3), 184-194 (July, 1939). 59K. Jung, Zeit. Geophys., 3(6), 201-212 (1927). Cuap. 7] GRAVITATIONAL METHODS 139 The diagram must obviously be drawn at the reduced scale of 1:p, which means that the scale must be considered in the calculation. The elements are so calculated that their effect remains the same regardless of distance and direction. In this case it is convenient to make rm — Tfmi = 4/7 and ¢, — ¢a41 = 7/40, so that the resultant constant for each mass element becomes 0.1. If the numerical value is substituted for the gravitational constant, the effect of each mass element as shown in Fig. 7-38 is Ag = —6.67-10 °-5-p-(1 — cos W) microgals. (7-38e) It is seen that the spacing of the concentric circles and of the angles is the same and that the effect is independent of azimuth. In application to ea -HECEEE ESS B Fic. 7-38. Diagram (horizontal quadrant) for calculating terrain effect on gravity (after Jung). If y (terrain angle) = tan! f,/r, the effect of each field is —6.67-10-3-5-p(1 — cos y) microgals, where 1:7 is the scale to which the diagram is drawn, and 6 is density. terrain calculation, the diagram of Fig. 7-88 is first completed for the three remaining quadrants. The surrounding terrain is surveyed by rod and alidade. When the above diagram is used, the elevations are most con- veniently taken in the form of terrain angles. Lines of equal terrain angle are then drawn on transparent paper and superimposed on the diagram, and the number of elements is counted between two adjacent contour lines. The function 1 — cos y is taken from the diagram in Fig. 140 GRAVITATIONAL METHODS [CHap. 7 7-39 for each of these areas and multiplied by the element number. The sum of these figures is taken and multiplied by the density, provided the latter is uniform around the station. This product is multiplied by the factor given above, which includes the unit effect, gravitational constant, cs ee ee eo ES SS SS SUEDE AAAS OS BE MS LARANAAAARALLAAA 8 BBB BERR RARAAL ARR SAARAAARASSSSSS = SSS SS SS SSS Se MOB RRA RARER SAAS S22 SSS Se ES SS ee SANS = RAVSRASAS ANAS SHAN ABARSERSSasaarnaBraSrasrSaBEBanaarr ser arar reser wrsrBeers se esses Sy Se ee eee ee Sees seme ewes Sn SD SS ES SOEAS SE GSssare q3° Fig. 7-51a. Pendulum observations of relative gravity in East Azerbaijan (southeast Caucasus) (after Schlumberger). Details of the anticlines on which these fields are situated are not visible. The general trend of the strata from NW to SE is indicated by the steep gradient portion in the SW part of this area. The gravity map of the Wichita and Arbuckle Mountain area shown in Fig. 7-51b is discussed at this time, although the greater portion of the gravity data was derived from torsion-balance observations. The gravity anomalies are caused largely by the crystalline basement rocks, Cxap. 7] GRAVITATIONAL METHODS 161 to which is probably added the influence of the old Ordovician land surface. The main features of the map are a series of maxima corresponding to the Arbuckle Mountains, the continuation of the Wichita Mountains (Walters Arch) and the Minster Arch. A pronounced minimum is found between the Arbuckle Mountains on one side and the Wichita Mountains and their south-eastward continuation on the other, lending strong support to the theory first advanced on the basis of geologic evidence that the Arbuckle Fig. 7-51b. Gravimetric map of Wichita and Arbuckle mountains and of structural trends along the Oklahoma-Texas border (after Van Weelden). and Wichita Mountains are separate systems separated by the Anadarko and Ardmore basins.” A comparison of the gravity data with the results of magnetic surveys made in the same area is of interest (see page 431). Where overburden is shallow and veins comparatively wide, gravimeter observations will give good results in ore prospecting. Accuracy require- ments are high and corrections for adjacent formations often necessary. 66 A. Van Weelden, World Petrol. Congr. Proc., Sec. B. I., 174-176 (1934). 162 GRAVITATIONAL METHODS [CHap. 7 It is not believed that this method will give so distinct re- sults as electrical prospecting, although it would be useful to segregate electrical anomalies due to noncommercial mineral disseminations from commercial ore indications. Fig. 7—52 shows the results of gravity measure- ments made on the ice at Men- strisk in Sweden. The ore bodies below the lake, dis- covered by electrical prospect- ing, consist of three parallel len- ticular sulfide veins of steep north dip; the thickness of the southern vein is about 30 feet, that of the others from 10 to 13 feet. Leptite formation oc- GB Ore i -\ curs in the south, black schists EA / Hite bd oe = ° . Rock Shales , 'S in the north. Owing to their [3 Graywackes j difference in density (0.2), a C3 Overburden * ° ° : 0 ee correction was applied. The in- dications are shifted to the north (b) with respect to the suboutcrop Fic. 7-52. Gravimeter observations (a) on of the veins. This shift may Menstrisk Lake, and (b) at Lake Langsele, partially result from the dip and wataenche Sweden (after Lindblad and partially from the effect of the contact. The shift above the southern ore body may be explained by the occurrence of an additional body to the north. VI. TIME VARIATIONS OF THE GRAVITATIONAL FIELD Variations of gravity with time may be divided into periodic and non- periodic phenomena. ‘The former are related to the position of sun and moon, the latter are caused by natural changes of geologic origin or by artificial mass transports. While magnetic variations are of the order of 10°* to 10* of the normal terrestrial magnetic field, gravity variations represent only a 10 to 100 millionth part of normal gravity. As a rule they do not interfere with gravimeter exploration but may be recorded by stationary instruments. Observations of gravity variations are of scien- tific value in the analysis of geologic forces bringing about slow changes in Cuap. 7] GRAVITATIONAL METHODS 163 elevation (epirogenic movements). They are of practical importance in determining corrections for (torsion balance) coast stations, in ground subsidence problems, and in the investigation of subsurface mass dis- placements leading to earthquakes and volcanic eruptions. The following discussion deals not only with variations of gravity itself but also with re- lated variations of torsion balance quantities and the deflection of the vertical. A. PLANETARY (LUNAR) VARIATIONS Planetary variations of the gravitational field and the well-known “oceanic” and “bodily” tides are related phenomena. Tidal forces are due to the fact that the attractions of sun and moon at the earth’s surface deviate in direction and intensity from those attractions effective at the earth’s center. They would be present even if the earth did not rotate, would be approximately constant for any given surface point, and would have but semimonthly or semiannual periods. The earth’s rotation pro- duces a migration of a double tidal bulge with a period of one-half lunar day, the maximum am- Fic. 7-53. Tidal forces. plitudes occurring if the tide-generating body is in the zenith or nadir. Superposition of the semidiurnal, semimonthly, or semiannual periods brings about ex- cessive or abnormally reduced tidal amplitudes, the more important of these being known as “spring” and ‘‘neap’’ tide. The variations in intensity and direction of gravity which can be caleu- lated from the distance and mass of the sun and the moon are modified by the change of distance of a surface point from the earth’s center, brought about by the bodily tide. The observed variations in the direction of the vertical (recorded with horizontal pendulums) are about 3 to # the theoreti- cal values; the observed variations in gravity are about 1.2 times greater than the theoretical variations. In Fig. 7-53, let M be a heavenly body (sun or moon) at a distance r from the earth’s center, C, and at a distance e from a point P at the earth’s surface in the latitude yg. The angle between r and e is the parallax of the star, or x. If the star is in the zenith, the attraction on Pis — (kM /e’) (negative in respect to gravity), and at C itis —(kM/r’). To deduct the latter from the former, it is convenient to resolve either force into its ver- 164 GRAVITATIONAL METHODS [Cuar. 7 tical and horizontal components. For P the vertical component is then proportional to cos (gp + x) and for C, proportional to cos y. The hori- zontal component is proportional sin (p + x) for P and proportional sin gy for C. The resultant deflection of the vertical, Ay, is equal to the dif- ference of the horizontal components divided by gravity, so that . cos(y +x) cos¢ r2 ae kM r “Seiad eal Bean aca RNR ea [1-2 Fos» + (4) | r i Ag, = kM ae i a (7-45a) kM sin : = ie lpia [UENCE ee i [1-2 F cose + (*) | r r sin gp A EME ae ra As the earth’s radius, R, is 6.37-10° km and r for the moon = 3.8-10° km and for the sun = 1.5-10° km, it follows that R/r is 1.7-10° for the moon and 4.3.10” for the sun (and may, therefore, be neglected). Then 3kMR d\n Ag: = — Ori (cos 2e¢ + 4) milligals Agn = wee sin 2 milligals, and (7-45b) 3kMR . Ay = — Igri sin 29 The coefficient 3kMR/2r’ is 0.0824 milligals for the moon and 0.0376 for the sun, and the coefficient 3kMR/2gr* is 0.0173 arc-sec. for the moon and 0.0079 arc-sec. for the sun. Tabulations of lunar and solar tide-components have been published by K. Jung.** R. D. Wyckoff® calculated the total amplitude for the two principal lunar and solar semidiurnal, the principal lunar and solar di- urnal, and the lunisolar diurnal tides for Pittsburgh, and found 0.167 66a Handb. Exper. Phys. 26(2), 322 (1931). 87 Trans. Amer. Geophys. Union, 17th Ann. Meet., pt. I, 46-52, July, 1936. Cuap, 7] GRAVITATIONAL METHODS 165 milligals. Therefore, the maximum possible variation between the maxi- mum and minimum of the curves would have been approximately 0.34 milligals. The theoretical values agreed well with the records of a sta- tionary vertical seismo-gravimeter. B. SEcULAR (GEOLOGIC) VARIATIONS In the course of geologic time, considerable changes in mass distribution occur near the earth’s surface because of erosion, deposition of sediments, glaciation, removal of ice caps, orogenic and epeirogenic movements, fault- ing, volcanism, magma migrations, and the like. That some of these factors bring about changes in elevation has been definitely established. A well-known example is the uplift of Fennoscandia, whose postglacial rise is assumed to amount to a maximum of 275m. Areas in which such movements occur are generally characterized by strong gravity anomalies, indicating incomplete isostatic compensation. Since the earth’s crust tends to re-establish the isostatic equilibrium disturbed by geologic factors, it must be expected that the greatest gravity changes occur in areas of large gravity anomalies. However, definite proof of this appears to be scarce. Virtually the only corroborative material has been supplied by measurements in India in 1865-1873 and their repetition in 1903 and 1904. The observed differences average 54 milligals, which is equivalent to an increase in gravity by about 13 milligals per year. Some authors have expressed doubt as to the accuracy of the earlier measurements, and confirmation of such gravity variations in other regions is urgently needed. Subsurface mass displacements brought about by faulting, volcanic phenomena, and the like may also be expected to cause gravity variations. With an increase in the accuracy of recording gravimeters it is probable that useful information may be accumulated over a period of years in active earthquake regions and may lead to a solution of the problem of earthquake prediction. Combination of recording gravimeters with recording magnetometers and seismographs would be particularly useful. As is shown below, subsurface mass displacements can likewise be recorded by the torsion balance. C. CHANGES IN WaTER LEVEL (TIDES AND THE LIKE) That changes in water level have a definite effect on the torsion balance has been shown both theoretically and by actual measurements.” If a torsion balance is set up on the edge of a quay having vertical walls, so that the center of gravity of the balance is 13 feet above water level 68K. Jung, Handb. Exper. Phys., 25(3), 158 (1930). A. Schleusener, Beitr. angew. Geophys., 5(4), 480-518 (1936). 166 GRAVITATIONAL METHODS [Cuap. 7 at ebb tide, a rise in water level of 6.5 feet causes a change in gradient of the order of 90 Eétvés units;” however, this effect declines rapidly away from the edge and is only 1 Eétvos unit at a distance of 100 feet. The variation in the curvature values above the edge is 0. The maximum is observed about 10 feet from the edge; thence, the effect declines slowly and reaches 1 EKétvés unit about 1000 feet from the edge. These values may be cal- culated by applying the formula for the two-dimensional effect of a vertical step given on page 264. If the coast is sloping, the tide effects must be calculated by using the formula for an inverted sloping edge. The gra- dients and curvature effects are less in this case. The gravity anomalies directly above the edge follow from formula (7—42e). It is seen that, for the same conditions assumed in the calculation of the torsion balance Fig. 7-54. Gravity gradients and curvature anomalies produced when the water level in a lock is raised by 8.2 feet (after Schleusener). ~ anomalies, the gravity anomaly at the edge is 0.05 milligal, which is within the limits of accuracy of present gravimeters. Fig. 7-54 shows the gravity gradients, as well as the curvature values, for a water rise of about eight feet in a lock, all determined by a torsion balance, the distance of which from the edge ranged from 1 to 20 m. At 1 m distance the gradient reaches a maximum of about 100 E.U. At 3 m distance a maximum in the curvature occurs with 47 E.U., and at 20 m distance the gradient is 1 E.U. and the curvature 7 E.U. De- flections of the vertical may be calculated from an integration of the curva- ture variation; near the edge the deviation is 1.2-10~” arc-sec. De- observed values for all quantities were in good agreement with values calculated from the theory. 69 Hétvds unit = E.U. = 1-10-* Gal-em™!. Cuap. 7] GRAVITATIONAL METHODS 167 D. ARTIFICIAL Mass DISPLACEMENTS (MINING OPERATIONS) AND THE LIKE There can be no doubt that mass displacements, brought about by the removal of commercial minerals (salt, coal, sulfur, ore), and rock formation underground, and by filling of subsurface cavities produce variations of gravity anomalies with time. Actual measurements of such variations are apparently lacking. The only information now available are some calcula- tions concerning the maximum deflection of equipotential surfaces of gravity to be expected in such cases. For a coal seam 66 ft. in thickness, occupying a square 7.1 km wide, A. Schleusener” has calculated that the maximum deformation would amount to only 3.4 mm. In the Ruhr district where 4 billion tons of coal have been removed in an area of 1000 to 1500 square km., a drop of 3 mm of the niveau surfaces was calculated, assuming the average seam thickness to be 3 m. It should be observed that in these calculations the effect of refilling emptied pillars has not been considered. For a lignite open-pit mine of 50 m depth and 500 m breadth (200 m length), the maximum drop would be 2 mm and the maximum deflection of the vertical at the edge would be 0.77-10 ” arc-sec., corre- sponding to a maximum curvature anomaly of about 140 E.U. at that point. VII. DETERMINATION OF THE DEFLECTIONS OF THE VERTICAL Deflections of the vertical, or “plumb-line deviations,” are as the name indicates departures of the direction of gravity from some reference direc- tion. As there is no absolute way of establishing a constant reference direction all over the earth, the direction of gravity is referred to an arbi- trarily adapted standard. It is easier to visualize the attitude of these two directions by considering the surfaces to which they are perpendicular. The first is a niveau surface of gravity (a surface in which no gravity components exist), called a “geoid.’”’ This has no regular geometric shape and is affected by all visible and invisible irregularities in mass distribution. The second is an ellipsoid of revolution, also known as reference ellipsoid, since all accurate geodetic surveys are referred to it. The deviations in the direction of the perpendiculars to these planes are, therefore, the deflections of the vertical, that is, the deviation in the direction of actual gravity from that of normal gravity. The meridional deflection of the vertical is equal to the ratio of the horizontal gravity component in the meridian to gravity. It is frequently convenient to refer the deflection of the vertical to a point (P in Fig. 7-55) in which the directions of the normal and actual gravity are assumed to be identical. The magnitude 7° Schleusener, Beitr. angew, Geophys., loc. cit, 168 GRAVITATIONAL METHODS [CHaP. 7 of the gravity vectors is not defined by the direction of the niveau surface alone, but by the number of niveau surfaces per unit distance in the direc- tion of gravity. There are altogether four methods of determining deflections of the vertical. The first consists of a comparison of astronomic and geodetic measurements to establish a difference in the direction of the geoid and reference ellipsoid. The second measures the time variations of the direction of the vertical with horizontal pendulums. The third is based on field measurements of the horizontal component of gravity and is at present of theoretical significance only. The fourth is an indirect determi- faces iveau SU es Actua 5 oid) Undisturbed niveau surfaces ae bef. Ellipsoid CB = %-q = Ag Ag, = meridional Cell. of the vertical Fic. 7-55. Relations between deflection of vertical, geoid, reference ellipsoid, and gravity components. nation by integration from curvature values measured with the torsion balance. Only the first and last methods are discussed in this section. In the astronomic or star observations, instruments used for the deter- mination of longitude and latitude are set with their axes of revolution vertical, by means of accurate spirit levels which adjust themselves into a niveau surface of gravity. Therefore, astronomic observations give co- ordinates of a station on the geoid. If these coordinates, on the other hand, are determined by geodetic triangulation, the calculation of arcs, distances, and angles is based on the geometric figure of the reference ellipsoid. The difference of astronomic and geodetic latitude, therefore, gives the deflection in the meridian. From differences in astronomic and geodetic longitudes, deflections in the prime vertical may be obtained. Cuap. 7] GRAVITATIONAL METHODS 169 The accuracy is +0.03 arc-sec. in the meridian and 0.10 arc-sec. in the prime vertical. Much greater accuracy is obtainable by using torsion-balance observa- tions. Since the torsion balance measures the rate of change of the horizon- tal gravity components in the directions of minimum and maximum curva- ture, differences in the horizontal gravity components may be obtained by integrating their variations with distance between stations. With division by gravity, the corresponding differences in the deflections of the vertical can be calculated. Since the torsion balance does not measure the vertical gravity gradient and furnishes the gradients of the horizontal components only in the combination @’U /ay’ — aU/éaz’, relative deter- minations are possible only when deflections of the vertical are known at two points, at the end of a torsion-balance traverse.” According to Oltay” a comparison of astronomic and geodetic deflection observations with torsion-balance measurements in the Hungarian plain gave anaccuracy of 3-10 °° arc-sec. per km. In practice the determination of deflections of the vertical from torsion- balance observations is simplified when geologic bodies are essentially two-dimensional. In that case, the curvature values correspond to cylin- drical niveau surfaces, which are fully defined by one radius of curvature, and a variation of the horizontal gravity component in only one (2’) direction. Then the deflection of the vertical is 1paeu Agz’ — g ax? dx (7-46) The integration is carried out numerically by using averages of curva- tures between closely spaced stations or by integraphs. In this manner Schleusener” obtained an accuracy of about 1-10~* arc-sec. per meter of horizontal distance. The maximum deflections calculated from curvature values, reaching a maximum of 50 E.U., were of the order of 1-10” are-sec. Such deflections cannot be detected by the astronomic-geodctic method. Observations of deflections of the vertical must be carefully corrected for the effects of near and distant topography. ‘Terrain effects may be calculated by the use of diagrams composed of sectors bounded by radial lines and concentric circles, such as those calculated by Hayford”™ and Schleusener.” For the interpretation of anomalies in the deflection of the 1 R. v. Eétvés, Verh. 15. Allg. Conf. Internat. Erdmess. (Budapest, 1908). 7K. Oltay, Geodet. Arb. d. R. v. Eétvés Geophys. Forsch. Inst., Vol. II (Buda- pest, 1927). 73 Beitr. angew. Geophys., loc. cit. 74 John F. Hayford, ‘‘The Figure of the Earth and Isostasy from Measurements in Loa S.,”’ U. S. Department of Commerce (1909). 75 Loc. cit. 170 GRAVITATIONAL METHODS [Cuap. 7 vertical, graphical methods or integration machines are employed. Since deflection of the vertical is horizontal gravity component divided by gravity, diagrams and integraphs developed for the (vertical component of) gravity are applicable with 90° rotation of geologic section or diagram. e VIII. TORSION-BALANCE METHODS A. QUANTITIES MEASURED; SPACE GEOMETRY OF EQUIPOTENTIAL SURFACES The torsion balance measures the following physical quantities: (1) the “gradient,” or rate of change of gravity, related to the convergence of equipotential surfaces and to the curvature of tlie vertical; (2) the so-called “curvature values,” or “horizontal directing forces,” which give the deviation of equipotential surfaces from spherical shape, and give the direction of the minimum curvature. The curvature values represent the north gradient of the east component of gravity and the difference of the east gradient of the east component minus the north gradient of the north component. From the previous discussion of gravity, gravity potential, and surfaces of equal potential,” it is seen that the distance between the latter is inversely proportional to the gravity. Hence, a convergence of equipotential surfaces corresponds to a horizontal change or a gradient of gravity. If the change between two points is uniform, g’ = g + (dg/ds)-ds where (dg/ds) is the gradient of gravity at right angles to a line of equal gravity (isogam). The gradient may be resolved into a north and east component so that 2 2 STUN? ie og = /( ) + aa and tana = oN (7-47a) Os Ox 02 dy OZ og 0x Gradients are expressed in Eétvés units = E.U. = 10° C.GS. units or 10° Gals em”. Isogams are usually drawn at intervals of 1 or 4 milligal. A change in gravity by 1 milligal for 1 km distance corresponds to a gra- dient of about 10 E.U. If h and h’, respectively, represent the spacings of two equipotential surfaces with the convergence « between two points whose horizontal separation is ds, then dh — dh’ = dh = cds. If r is the radius of curvature of the vertical, dh = c-r. Since gdh = g’dh’, gdh = (g + (@g/ds)-ds)-(dh — ids). Substituting 1 = dh/r, gdh = 76 Page 89. Cuap. 7] GRAVITATIONAL METHODS 171 NA SS Fig. 7-56a. Horizontal gravity components and lines of force corresponding to a niveau surface with equal principal curvatures (after Rybar). Fic. 7-56b. Horizontal gravity components and lines of force corresponding to a niveau surface with unequal principal curvatures (after Rybar). 172 GRAVITATIONAL METHODS [CHaP. 7 dh(1 — ds/r) (g + (0g/ds)-ds). Dividing by dh and ds, 0 = dg/as — g/r — (ds/r)-dg/ds, so that, by neglecting second-order terms, ag a (7-47) which states that the gradient of gravity is proportional to the curvature of the vertical or to the convergence of the equipotential surfaces. 2 and from beam II: y. = As tar _ —(4r + 42) Aah” 1.414b”” ai id Mt a (7-536) U _ os + Ar _ —(Ae + Az) ue 1.414b”’ 1.414b” — In these equations U {? / / 1 mt m+ ns + Mm no 4 and my +m tn +04 a= oe Therefore, Use = +(ns — ne)/2b and Uy, = +(ns — m)/2b, where the upper signs are for beam I and the lower for beam II. If only one balance beam is functioning and if both gradients and curvatures are desired, observations in five azimuths are required. Then for beam II: ” nh = Cuap. 7] GRAVITATIONAL METHODS ‘ 183 (1) a= 0% nm — m = 2a"Uy + by, (2) a= 72°; m —m =a" sin 36° Us — 2a” cos 36° U2, + b” cos 72° Uy, — b” sin 72° U2, (3) a= 144°; ns — m =a’ sin 36° Us + 2a” cos 72° U,, — b” cos 36° Uy, — b” sin 36° Uz, (4) a = 216°; nd — m = a’ sin 36° Us + 2a” cos 72° Uxy — b” cos 36° Uy, + b” sin 36° Uz, (5) a = 288°; np — m = a” sin 36° Us — 2a” cos 36° Usy + b” cos 72° Uy. + b” sin 72° Uz. For beam I reverse only the signs for gradients. Hence, for beam II: Un = [M (ns — nm) + N(n4 — ns)| Uye = —[P(ns + me — 2m) — O(ms + 3 — 2m1)] (7-54a) Us = —2 IN (ne — m) — M(ru = ns)] 2Uy = - [O(ns + mz — 2m) — P(r + ns — 2m)], where i sin 72° ~ 2— cos 72° + cos 36° is sin 36° ~ 2— cos 72° + cos 36° ia 1 + cos 36° 5(cos 72° + cos 36°) M or 0.38042 N or 0.23511 or 0.32361 1 — cos 72° Pi 5(cos 72° + cos 36°) or 0.12361. With the foregoing coefficients, the instrument constants a and b may be combined for convenience in calculation. Equations (7-54a) contain 184 GRAVITATIONAL METHODS [CHapP. 7 only readings n and no m. With deflections A from the torsionless posi- tion, the equations are: Use = Uy. = — Wie 2 Sie -* [0.2351(As — A.) + 0.3804(A2 — As)] - [0.7236(4s + As) + 0.2764(A2 + As)] (7-54b) 4, [0.2851(As — Ax) — 0.3804(42 — As)] = (0.1382(4s + A.) + 0.3618(4 + As)], where the numerical factors represent combinations of trigonometric func- tions, as given before, and where ™m + Mm + m3 + m4 + 5 4. Horizontal gradiometers and similar instruments. 5 Because gradients are more readily interpreted than curvature values, and since the latter Fig. 7-61. Gradiometer. ring; p, arm; m, masses (after Lancaster—Jones). R, Damping are very erratic in certain types of work (rugged topography, and irreg- ular density distribution near the surface), a number of attempts have been made to design torsion balances which furnish the gradients alone or give them at least in fewer posi- tions than are required to obtain both gradients and curvature values. This objective may be accomplished by balance beams of different designs or by suitable combinations of stand- ard beams. In any beam with sym- metrical mass distribution the in- fluence of the curvatures is zero. If one of these masses is placed at a different elevation, the beam will be affected by the gradient forces alone. In the gradiometer of Shaw and Lancaster-Jones” three masses 78 J. Sci. Instr., 49(11/12), 1-20 (Nov. and Dec., 1932). Cuap. 7] GRAVITATIONAL METHODS 185 are spaced at angles of 120° (Fig. 7-61). All masses are equal and balanced. Since the moment of the curvature forces on each mass is D, = mpF (p = radius arm), the sum of the three moments to be used in eq. (7-50b) would be zero for any value of a. This may be demonstrated readily for the position a = 0: D+D) + dD’ = 5 me'{Us sin 60° — Us, sin 60° + 2U.,, — 2U.2, cos 60° — 2Uz, cos 60°} =-0. Therefore, formula (7—51b) for the standard balance reduces to n — m = b (cosa U,, — sin a Uz), (7-55) where b = 2fmph/7 and which contains three unknowns. These may be determined in three azimuths so that when a— 0, m— m = bU,,2; (2.3 120°, ta —- Nm = b (-3 OFS Sr we ay and a=240° m—m= b(-} Uae v3 Un). 2 2 Hence, 1 Un = V3 [(ns — mo) — (me — m)] and Uy = & (tm — me) ae where Mo = 3(m + ne + ns). For four positions (0°, 90°, 180°, and 270°) the readings become ™m — % = bU,., ng —- mh = —bU,,, Mm — mm = —bUz, Mm — m = Uz, so that ng — m = Mm — m and ne — m = Mm — m. The nm is thus half the sum of the opposing readings. Then Ue — = [(ms — mo) — (ne — no)] (7-55c) Use = se [lem — 10) — (5 — r0)] 186 GRAVITATIONAL METHODS only two azimuths are required. Fic. 7-62a. Haalck bal- ‘ ance (gradiometer). With formula (7-51b) (position 1): (1) balance I: nN — my =a 204 +b! Uys, (2) balance II: ni — m =a"'.—Way +b” i—Un, (position 2): (3) balance I: m2. — mo = a’-2Ux, + b’-—Uy., (4) balance II: ny — m =a’.—2Uy +b”-+Un. Subtracting equation (3) from (1), 1 / / Use = ae (ni — ne), and subtracting equation 2 from 4, 1 / Oz: ae 2b” (ne 7 mi) Curvature values may be obtained by | setting up the balance in three azimuths. In Hecker’s balance (Fig. 7-62b), four beams are used in such manner that two standard sets make an angle of 60° with each other. Only two azimuths are re- quired to obtain both gradients and curvature values. The formulas for this instrument may be derived by substi- tuting the values in Table 21 in eq. (7-510). balance. [(CHap. 7 If two balance systems are used in a gradiometer, In the Haalck torsion balance (see Fig. 7-62a) two standard beams are used at right angles to each other; only two azimuths are necessary to cancel the curvatures and to determine gradients. The arrangement is seen from the following scheme: BALANCE I Bauance II = Reading Reading Azimuth 1, a = 0°. ny a = 90°. Te “2 @ = 180°. ni a = 270°. ni! (7-56) Fig. 7-62b. Hecker four-beam Cuap. 7] GRAVITATIONAL METHODS 187 TABLE 2] ‘ BALANCE I Batance II Batancos IIt BaLance IV EOSIN SC Ni peeee | eee eee ees a ee ek ef ot ee eee Ag. Read. Az. Read. Az, Read, Ag. Read. 1 ee ae 0° ny’ 60° ny"! 180° “lea 240° ny" Dem rc\t 180° Ny! 240° Ne"! 0° ne!!! 60° eid Fig. 7-63 shows the Numerov” three-beam balance. With it, gradients may be determined in’ the 0° and 180° or 90° and 270° positions. An intermediate azimuth is required for curvatures. The beam azimuths and readings in these positions are shown in Table 22. The equations for the six possible combinations (canceling the torsionless-position reading) are:” (1) From positions 1 and 2: m — ™ = Aj-2 = 4aU, + bU,. + bUy my — Me = Aye = —2aUy + arv/3 Us +5 (VB ~ 1) — 8 (V8 + 1)U ee m —M = Ay. = —2aU, — av/3 Us Fia. 7-63. Nu- b ¥ b 2 merov - Askania — ~ (73+ 1)U,.+ = (V3 — 1)U.z, three-beam _bal- 2, 2 ance. TABLB 22 BALANnceE I Baance II Bauance III PosITION es Eee (aR py NON Tee Az. Read. Ag. Read. Ag, Read. IU ea teae 0° ny! 120° ny" 240° my!" DAS Gs OIA 90° No! 210° ne!’ 330° n!"’ SMG Ree 180° n;' 300° ns’! 60° ns!!! AMR Rec a 270° Ns! 30° ns!" 150° na!" 7? B. Numerov, Astron. Inst. Leningrad Bull., 30, 103-108 (1932). %a For simplicity, the constants a and b are here taken to be alike for all three eams. 188 GRAVITATIONAL METHODS (2) From positions 1 and 3: ° ni wna = Als = 2bU 4s ” my — 13 = Ay_3 = —bU,, — bv/3 Uss m — 1s = Avs = —bU,. + bV3 Ux (3) From positions 1 and 4: nm —m = Ais= 4aU,, + bU,, — dU —2aU., + ar/3 Us yf a ut Mm —NM = Ars (Cuap. 7 — 3 (VB + Un - 5 (V3 — NU mt mt mr Vie Noy — Ay, —2aU., arv/3 Ua + 2 (V3 -1)Un +5 (V8 + 1)Un (4) From positions 2 and 3: ney —'n, = Ass = —4al/,, + bU,. — DU, ” la — 13 = Ags = 2aUy — av/3 Us — : (3 + 1)U,— : (/3 — 1) Us m 1 aD Aoc_3 2aU 2, + arv/3 Un S | I “ ° (4/3 —1)Uy. + (V/3 + 1)U 2s (5) From positions 2 and 4: nm — 1 = Ao4 = —20U, —2b+/3 Uy. + dU: My — ng = Aes = +bV/3 U,. + Uz (6) From positions 3 and 4: mm = A,4 = 4aUZ = bu, — dU. ny —m = Az. = —2aU., + av3 Un II Vt ’ a Ng — Ns = Ao4 : (/3 — 1)U +3 (v3 lee mr UMP oon 2 wm A3-4 —2aU., = av/3 Us S | be Il +3 (VB + 1)U yn — 3 (V3 - 1)Us Cuap. 7] GRAVITATIONAL METHODS 189 It is seen that from the diametrical positions 1-3 and 2-4, the gradients alone may be obtained, but that for curvatures an additional intermediate position is required. Hence, for the gradients, wt 1 ” Ue = 2bv/3 (Ay_3 ae Ai-3), and [Ue = eV AG es or (7-57a) 1 Uz. = ap Ae, and a) 1 dA Uy = ~ obv/3 (Ac_4 — Ao-4). From combinations 1, 3, 4, and 6, we have the following equations for the curvatures: wt 1 ” b (1) Us a 2ar/3 (Aj_2 a Ai-2) =e 5g Us Te U,z) 1 b 20 oy 7a 54°41 ‘Ga 2a (Cis ao U2) Mt i) 1 " b (3) Ua = 2ar/3 (Ai-4 ee Ai-4) =F 34 (Us AF We) 1 b A OF = 54°44 + 5q (Us oe Oi) (7-57) ai 1 ” mr by (4) Us as 2ar/3 (As_3 = Az-3) a 2a (Us == Uys) ae, b oa am 5q Us ar U2) ier ie mt ou b ey (6) Us aa 2ar/3 (A3_4 A3_4) 2a (Use (OP) ta, 7) tear Us 2a Although it is not a gradiometer, the continuously rotating balance proposed by Kilchling” may be mentioned here. It consists of a single combined gradient and curvature balance, which is suspended from a 80 K. Kilchling, Zeit. Geophys., 2(4), 134-187 (1926); 3(6),- 281-285 (1927). 190 GRAVITATIONAL METHODS [CHap. 7 slowly rotated wire while a record is taken of the beam position with respect to the instrument case. As the gradient effects are proportional to the single azimuth, and the curvature values proportional to the double azimuth, one revolution yields an irregular curve whose positive and negative portions have different amplitudes. Evaluation is based on a determination of two equal ordinates of the same sign having an interval of.r. These ordinates are proportional to the gradients in the two direc- tions. Curvatures may be calculated from two pairs of equal but opposite ordinates of the interval +. The total period of observation was intended to be 2 hours with a 40 minute wait period to allow the beams to come to rest. Extensive experimentation with this balance did not show any superiority over the standard instrument. 5. Vertical gradiometers and similar instruments. The opinion has been expressed in the literature that a determination of the vertical gradient of gravity would be very desirable for a more complete interpretation of gravitational data. However, the geologic importance of the vertical gravity gradient has possibly been overstressed since for two-dimensional geologic bodies it may be readily determined from the corrected curvature values. Be that as it may, several attempts have been made to determine the vertical gravity gradient directly. These date back to 1880 and were continued in subsequent years in connection with measurements of the gravitational constant and of the mean density of the earth. Assume that in a sensitive balance the pans are replaced by a weight fixed to one end of the beam and by an equal weight suspended at a lower level on the other end (Fig. 7-64). Compared with the weight positions in the same level, the beam is unbalanced_because of the increase in weight of the suspended mass. If the addition of a weight, Am, is required to rebalance the beam, if the masses are m, and their difference in elevation is h, (m + Am)g = m(g + 0g/dz-h), and therefore Mn = (7-58a) In this manner Jolly found that with 5 kg (mercury) weights at a differ- ence of elevation of 21 m, an addition of 31.69 mg was necessary to re- balance the beam, which gave 3.01 X 10°° for g/dz. The normal value of the vertical gravity gradient may be obtained (1) from Clairaut’s theorem; (2) from the curvature of the reference ellipsoid. Since in Clairaut’s theorem, gravity is expressed as a function of the earth’s radius, the vertical gravity gradient may be obtained by differentiation with respect to the radius, so that” 81 See also F. R. Helmert, Higher Geodesy, Part 2, pp. 94-98, and formulas (7-36a) and (7-360). Cnap. 7] GRAVITATIONAL METHODS 191 o = 3.086 (1 + 7.1-10 *.cos 2y) microgals-em™. (7-58b) The second method” uses Laplace’s equation (7-5) and the curvatures of the reference ellipsoid in the meridian and the prime vertical, which are given by 1 1a°U 1 10°U == >=, and /— = ——\-—_,, Pz g Ox Py g oy so that 1 og = 9 a + *) + Qu’, (7-58c) dz Pr Py where 2w = 10.52 E.U. For g, pz, and p,, their values as function of latitude must be used (see Fig. 7-73b). The vertical gravity gradients calculated from eq. (7-58c) agree with those obtained from (7-58b) to a tenth E6tvés. Forty years after Jolly’s experiments, Berroth” proposed to use a standard torsion balance for the measurement of vertical gravity gradients by suspending it on nearly horizontal wires. Deflections were to be measured in different azimuths and at different starting angles of the beam against the horizontal. Another design proposed by Schmerwitz™ aims to increase the sensitivity of a regular balance by the addition of a hori- zontal pendulum, that is, by astatization (see page 127). A horizontal pendulum oscillating about a vertical axis is in labile equilibrium, but when it is tilted forward by an angle ¢, it will assume a definite rest posi- tion. If the axis of revolution is then tilted sideways by the angle @, a deflection y = 6/¢ from the rest position results. When a horizontal pendulum is placed on a balance, as in Fig. 7-64, the deflection 6 is duc to an increase in weight of the suspended mass. The deflection y throws additional weight over to the right, the moment being m’l’ sin y. For an ordinary balance with (equal) lever arms L, beam mass Mp, and vertical distance of center of gravity from the axis of rotation d, the sensitivity > = L/Mid. With the horizontal pendulum, x! Le Ty, Mode Sal ~ With a horizontal pendulum balance (l’ = 14 cm, m’ = 100 mg, sus- pended by two 17u wires [Zoellner suspension] at an angle of about 2°), a sensitivity of 10° mg per mm scale deflection could be obtained at a (7-58d) 82 R. v. Kétvés, op. cit., p. 362. 83 A. Berroth, Zeit. Instr., 40, 210-211 (1920). 8G, Schmerwitz, Zeit. Geophys., 7(1/2), 104 (1931). 192 GRAVITATIONAL METHODS [Cuap. 7 scale distance of 2.5m. Accuracy of 1 Eétvés (1/3000 part of the normal gradient) would require that the apparent change in weight be determined to 1-10 “mg. In that case it would be necessary to observe the vertical gradient in different azimuths, since gravity varies not only in vertical a | Fia. 7-64. Schmerwitz balance for determination of vertical gravity gradients. but also in horizontal direction. Thus, the action of all three gravity components on the beam is given by i, dm|(gz cos a + g, sin a)-2 + g.(x cos a + y sin a)]. C. INSTRUMENT TyPEs, INSTRUMENT CONSTANTS 1. Types. Although numerous types of torsion balances have been proposed and designed, comparatively few have attained commercial sig- Cuap. 7] GRAVITATIONAL METHODS 193 nificance. A detailed description with instrument constants has been given by Jung. In 1888 and 1890, respectively, K6tvés constructed the first curvature and combined curvature and gradient variometers for laboratory use. In 1898 he followed this with a combined single beam field instrument. Its dimensions and constants were (in round figures): m (single beam mass) = 30 g, h (distance of weights) = 60 cm, J (4 beam length) = 20 cm, K (moment of inertia) = 21,000, 7 (torsional coefficient of suspension wire) = 0.5, d (thickness of wire) = 40u, L (length of wire) = 56 cm. These dimensions have been maintained by all designers of large visual and automatic torsion balances. Fig. 7-65. From left to right: small Suess balance, large Suess balance, small Askania balance. The single balance was replaced in 1902 by a double variometer (see Fig. 7-65) with visual observation. Most large instruments developed after that, such as the Fechner, Oertling, and Askania (see Fig. 7-66) balances, used photographic recording devices and automatic azimuth rotation. Repeated attempts were made to reduce the dimensions of the large torsion balance. Edétvés himself went to the extreme with an in- strument in which m = 1.4 g,h = 20,1 = 5, K only 90, and 7 = 0.0046; but this instrument was a failure. Similar in dimensions was the Tsuboi 86K, Jung, Handb. Exper. Phys., 26(2), 103-123 (1930). 194 GRAVITATIONAL METHODS [CHapP. 7 ‘Photographic attachment Torsion head Platinum wire level Mirror Balonce-beam mirror petals praia Said weigh Contact clock Drang clock fateh Tube American Askania Corp. Fia. 7-66. Large Askania photographic recording torsion balance. tempted (Gepege, Haff, Hecker, Rybar) have not been very successful. The Z beam has recently been superseded by the quartz balance with m = 0.25, h = 20,1 = 10, K = 66, d = 5u, and L = 20. It was soon found that a geologically useful torsion balance cannot be decreased in dimensions beyond certain limits. For instance, the Eétvés-Suess small visual balance (Fig. 7-65) has the dimensions m = 8,h - 30, l= 10, d = 20n, L = 40 cm. Very effective in the reduction of overall dimensions was Schwey- dar’s invention of the Z beam (Fig. 7-67). This balance has the following dimensions: m = 22, h = 45, | = 20; d —*20-367 L- = 28 cm, K = 19,500, 7 = 0.23-0.47. Other small bal- ances in which a further reduc- tion in dimensions has been at- tilt beam (Fig. 7-68), with the following con- stants: m = 40g, h = 30cm,/ = 10cm, K = 9150, d = 33-48u, / dmhl = 13,800. Torsion balances completely deviating in dimensions from those mentioned are: the Tang] balance (curvature vari- ometer floated in water), Nikiforov’s short-wire balance (r = 16, L = 2 cm), and the gravity gradiometer previously discussed. 2. Constants. The instrument constants m, h, 1, f, L are readily determined before assembly in the factory by measurement of lengths and weights; they are not subject to change, are usually given in the calibration certificate, and require no recalibration. More involved are the American Askania Corp. lig. 7-67. Z-beam Askania balance. determinations of K and +r. In an assembled instrument, K/r may be obtained from oscillations and 7 from defiections. More convenient is the independent determination of these constants before assembly. 86 H. Imhof and A. Graf, Beitr. angew. Geophys., 4(4), 426-436 (1934); Rev. Sci. Instr., 6(10), 356-358 (1934). Cuap. 7] GRAVITATIONAL METHODS 195 The ratio K/r follows di- rectly from the (undamped) period 7 = 22 +/K/z, which co eee may be determined to a high feam system degree of accuracy (1/100 of a second) by using a coincidence method. Since in most base- Bi-filar ment laboratories the gravity suspension field is disturbed by adjacent walls and excavations, it is necessary to make period ob- servations in two directions at right angles to each other my fi (a, and as = a + 90°) to eliminate such effects. Then ; American tAskanio Corp, the equations for two periods Fic.7-68. Balance beam of tilt-beam balance. are 2 (1) = 7 — (KU, cos 2a, — 2KU-2, sin 2a) i as (7-59a) (2) oat = 7 — (—KU, cos 2a + 2KUz, sin 2a). 2 Addition of the two equations gives 2 72 s fits (7-59b) FOG ETA By observing the deflection of the beam due to a known mass at a known distance, 7 can be determined independently from the equation TES (Y (7-59c) 1 where ¢ is the deflection angle; C is a constant (C = a aaa , With / Wiss 4p? ln = length of cylindrical mass m); p = the distance between center of gravity of m and M; and k = gravitational constant. Since p is difficult to measure, the mass M is used on a swivel and rotated from one side of the weight to the other. For equal deflections on both sides, the radius of the swivel arm is equal to p and (7-59d) 196 GRAVITATIONAL METHODS [CHaP. 7 The more common practice is now to determine both K and 7 before the instrument is assembled. K is obtained by oscillating the beam on a calibrated wire with known +. For this purpose an oscillation box is made, usually of wood, provided with extensions for the lower (and upper) parts of the beam and of sufficient capacity to keep air damping down. Observations are corrected for (wire) temperatures and amplitude of oscillations. Where large gravity anomalies exist, observations are made in two positions of the box. Wires are very thoroughly tested. The following characteristics are of practical importance: (1) torsional coeffi- cient, (2) carrying capacity, (3) temperature coefficient, and (4) elastic hysteresis. The carrying capacity of a wire varies with the square of the diameter, while the torsional coefficient varies as the fourth power of the radius and inversely as the length: 4 r= 0, (7-60a) where r = radius, / = length, and w = modulus of rigidity. For other wire sections (ribbons, and the like) the torsional coefficient is given by the relation ¥ Cus’ y= en (7-60b) where S = section, C a constant, and J, the polar moment of inertia. For a rectangular section, Jp = (ab? + ba’)/12, where a and b are the sides of the rectangle. For ratios of a/b = 1, 2, 3, 4, and so on, the con- stant C takes the values 234 x 10° (for a/b = 1), 238, 249, and 260 X 10°. For thin ribbons in which the one dimension is less than one-third the other, the torsional coefficient is closely enough a= ao (1 — 0.63.°), (7-60c) in which the last term may be generally neglected. Ribbons have the advantage that for a given carrying capacity the torsional coefficient is less, but they are more difficult to obtain. In practice torsional coeffi- cients of torsion balance wires are determined from oscillation observations with calibrated weights. For this purpose a specially built instrument is used, consisting essentially of an upright tube with torsion head above and observation window below, and provided with a heating coil and ther- mometer. After a wire has been cut to length, provided with its clamps, and heat- treated, it is placed in the instrument with a mass of calibrated moment of Cuap. 7] - GRAVITATIONAL METHODS 197 inertia K. The period is determined by reading the time required for ten complete swings and repeating five to six times. This gives an accuracy in T of better than 1/100 of a second and a torsional coefficient 7 = 4r°K/T’. The moment of inertia, K, is determined by calibration with a ring of calculated moment of inertia. If the mass of the ring is m, its outer radius R, and its inner radius 7, its moment of inertia is Kg = 1m(R’ — r°’). If T, is the period without the ring and 7. with the ring, 2 Ar’ Ti e (K + Kr) and 2 T = pall K, T from which Aerie l Te (7-60d) R T a T? 2 The torsion coefficient changes with temperature, 0: To = Tol + B(O: — 20°)], (7-60e) in which the temperature coefficient, 8, of the torsional coefficient follows from period observations at different temperatures. In the field the variation of + with temperature is disregarded, but in selecting torsion wires in the factory, wires with excessive temperature coefficients of + are discarded. Equally undesirable are wires of excessive variation of the rest position, n, with temperature. If the reading is m at a tempera- ture 6), and nz at a temperature Oo, the variation of n with 9 is defined by NM. = m — a(Og — O,). The temperature coefficient a of a good wire should not exceed 3-5-10-* mm per degree C (referred to the same optical magnification as used in the field instrument). The temperature coeffi- cient of a wire depends largely on the method of clamping and heat treatment.” Platinum wires are heat treated electrically under load; tungsten wires are annealed in an atmosphere devoid of oxygen. Fig. 7-69 illustrates the improvement brought about in a wire by heat treatment. Curve A is the zero shift of an untreated wire, curve B that of a wire tempered under load fifty times a day. It should be noted that in a test instrument the change of the zero position with temperature is generally not the same as in a torsion balance 87 Concerning the effect of annealing and baking on temperature coefficient, see N.N. Zirbel, Physics, 2(3), 134-138 (March, 1932). GRAVITATIONAL METHODS — [CHaP. 7 — © (oe) = since beam deflections aré-produced by & convection currents in the narrow in- & 18 terior compartment. It has been $ Wire A found that this effect can be nearly 8 y, eliminated by determining an optimum transverse position of the beam in the ” interior compartment. When a wire breaks in the field and : a new wire is inserted, the coefficients 6 0, Pp, q, and r, as well as s and t, are : Wire B changed (see formula [7-52f]). If 7; is the torsion coefficient of a broken 0 20 3% & 50 fas wire in balance I, 7, the t.c. of a Fra. 7-69. Change of rest position broken wire in balance II, 72 the t.c. of torsion wires with treatment (after of a new wire in balance I. and TT) the Shaw and Lancaster-Jones). Kane : t.c. of a new wire in balance II, the new coefficients are: / Povt ae cas a gk Ta ai) | T) T2T1 a re | 7 Vr 4 Uy. = p [lai + ad -s oe (AG +40) | | T) T271 rT Tid Mi A } (7-61) U, = —q 4 7) (as aR Et (Aa ay) | 11 T2711 Aes ee suse St | as $a peTt (aly at) | 71 T2T1 and similarly for other beam positions. The replacement of a torsion wire must be done with great care to avoid kinking or overstraining the wire. Directions given by the manufacturers should be closely followed.” 3. The sensitivity of a torsion balance is a function of its geometric dimen- sions, of the torsional coefficient of the suspension wire, and of the optical magnification. According to eq. (7-51la), the angular deflection increases in the proportion K/7 for curvatures and in the proportion mhl/r for gradients. The optical magnification is given by 2f/y for single and 4f/v for double reflection, where f is focal length and » scale interval. Since the latter is generally so chosen that 1/10 division may still be 88 C. A. Heiland, Directions for the Askania Torsion Balance, American Askania Corporation (Houston and Chicago, 1933). H. Imhof and A. Graf, loc. cit. A. Schleusener, Zeit. Geophys., 9(6/8), 301. 8° For a description of steps necessary to readjust the beam after insertion of a new wire, see Directions for the Askania Torsion Balance, op. cit. Cuap. 7] GRAVITATIONAL METHODS 199 read conveniently, the sensitivity for curvatures is proportional 20fK/vr and for gradients 20fmhl/vr, where for double reflection the factor 40 takes the place of 20. The reciprocal of the sensitivity is the ‘‘scale value”’ of the instrument, VT eee (curvatures) (7-62) VT ~ 20¢mhl where 40f instead of 20f is used for double reflection. 4, Calculation of instrument readings of a standard torsion balance proceeds in accordance with formulas (7—-52b) to (7-54b). A number of positions are generally repeated. Deflections are averaged in such a manner that the variation of the torsionless position with time is elimi- nated. In visual torsion balances, beam readings are entered against ég (gradients) and es Fig. 7-70. Evaluation of torsion-balance record (large Ask&nia balance). azimuth, time, and temperature (see Fig. 7-71). Calculation is the same as in photographic balances. Fig. 7-70 illustrates a record taken with a recording balance. On the left is the fixed mirror record, then follows the record of the second balance, first balance, and temperature. For evaluation, a graduated scale is placed over the record and its O-line aligned with the fixed-point line. Deflections for positions occupied are read for beams II and I, giving nj, nz, 3, 71, m2, and n3, and so on, in seale divisions. These are entered for three positions in Table 23. The temperature record is not evaluated. The torsionless position is calcu- lated by averaging successive readings in the following manner: 1. mo = F(mi + nz + 73) Ie fg A ee ae ae) 2. mo = 3(m2 + m3 + mi) 2. no = 3(ne +3 + 1) 3. mo = 3(ns + m + m) ete. 3. my = 4(ns + ny + m) ete. 200 GRAVITATIONAL METHODS [Cuap. 7 By this procedure a linear change of the zero position with time is ° ° ° 7 , / , / y eliminated. After that the differences nj — m0, m2 — mM, 13 — no and / wt Mu ai Ul , / / ut ‘ft M1 — NM, Ne — Mm, M3 — Mo (or Aj, Ag, Az, and A;, Ae, and A;) are TABLE 23 CALCULATION OF THREE-POSITION TORSION BALANCE RECORD Station No. 10 Location: Fort Bend County, Dats: July 10, 1935 Texas OsBsERVER: J. A. S. ge = 29° ist READING: 9 h., 55 min. Notes: Instr. set due north Ba.Lance [ Ba.anceE IT No. No. Cd n A, A, A, 1 Te 5422 aes 2 74 || GVAail || SPsal i 0 3 3 | 50.0 | 51.9 AN ee -—1.9 1 tL} S38n0. |8OL.8: | 3029 2 Ze lecOl Oe cold wea | OR 3 3 | 49.7 | 51.6 th —-1.9 1 1 o3e5e 2 Sle oalee2-0 2 Qo oleae) ol 4 hss 0 3 3 | 49.4 hoe 1 1 2 2 3 3 1 1 2 2 3 3 “a Mean A” +2.0| —0.1 |} -—1.9 > =0 / , A, +4, = +2.2 a? ‘tr 4, +4, = —2.0 Difference Xo = Ue Difference Xp eat (Ulric —3.0 +1.45 | —4.4 +4.2 2.51 +10.5 Sum can SAN; \X \ SAUAENS on the left side of the A; + A: axis, go N to 2.2 on the A; + Ag axis, thence SW to +11.8 for U,, and SE to —0.5 for Uz In connection with the form shown in Table 23, a second form is used for the terrain correction, which contains also additional columns for far terrain, planetary correction, and calculation of final results (see Table 32). The following example is an illustration of calculations made for a station with very large gradients and curvature values, on which records Cuap. 7] GRAVITATIONAL METHODS 203 in three, four, and five positions were taken. The formulas used in the calculation of the three-position record \were Besa 26|(Ag As) — (As As) O101044(0Ag) "A; )] Uye = 2.18[(Ag + As) — (Ae + As) + 0.01044(A2 + As)] Un =) .—3.60[(Ae — Az) + (As. + As) — '0:01233(As — A; )] 2Uy = —6.24[(Ag + As) + (Ay + As) — 0.01233(A2' + Az)], where 0 = 1.26, p = 2.18, q = 3.60, andr = 6.24, 0.01044 = 1 — s, and 0.01233 = 1 —t. These formulas are derived from the standard formulas AY ‘+45 ————> Wax XIX KL PRD IOOP ARAN ax V4 di | cu 4 ava ROBES Fig. 7-72b. Torsion-balance calculation chart for Uz, and Uy, (after Slotnick). (7-52h), which may be written Uz, = 0(A; — SAe) = 0(A; — Ap + Az —SAz), and so on, so that Use = o[(Az — As) — (Ae — AZ) + (1 — s)(A2 — Ag)]---- 204 GRAVITATIONAL METHODS [CHap. 7 _ In the example (Table 24), (Az — A;)(1 — s) is designated as C.., (Ar — A;)-(1 — t) as Ca, and so on. TABLE 24 CALCULATION OF THREE-POSITION TORSION-BALANCE RECORD (LARGE DEFLECTIONS) Batancp I Batance Ii No n! n, A, A, A; No mn! nr, ‘s A, A, 1 | 141.7 7 1 81.5 LAE ee 2 90.0 | 116.8 —26.8! ... 2 34.5 53.6 —19.1 ihe 3 eat .7- A117 0n +1.7 || 3 | 44.9 | 53.7 ane ’ —8.8 1 | 142.2 | 117.0 |+25.2 io 1 81.7 53.7 |4-28-0) ee 2 90.0 | 116.8 ce —26.8) ... 2 34.6 53.8 . ta Oo — LOR2 | ee 3 | 118.2 | 116.1 Be +2.1 3 45.0 BBs? —8.7 1 | 140.0 | 115.8 |4+-24.2 ese 1 81.6 53.9 |+27.7| ... 2 89.2 | 115.8 nS —26.6) ... 2 35.2 54.0 —18.8] ... 3 | 117.5 | 115.5 +2.0 |; 3 | 45.2 | 54.0 an Be —8.8 1 | 139.8 | 115.5 |+24.3 ae 1 | 81.5 | 54.0 |427.5) ... 2 89.5 | 115.8 —26.3 2 | 35:2°|..54.0 } ... 401888 SMS OF ae 4520 1 5 Bs 1 me 2 2 3 a 3 ee Mean A’ +24.6) —26.6) +1.9 Mean A” +27.7| —19.0) —8.8 z= —0.1 == —-0.1 A= A=! =28.6 A, +4, = -247 ae, via a ae x ad = s) = (O55 a " ts x qd od s) = Cys A, 4, 10.2 ope t)’=C, 4, +4, = —27.8 te (Laue ee Diff C., | Res SOs ane. Diff C,. | Res xp | = Uy: —18.3) —Q.1 | —18.4] 1.26 | —23.2 +3.1 |) —0.3 |} +2.8 | 2.18 +6.1 Sum Ca Res. Xq | = Ug Sum Ci Res. xr 2Uzy —38.7| +0.1 | —38.6| —3.60| +139.0 —52.5 | +0.3 | —52.2| 6.24 | +325.7 In the calculation of the four-position record in Table 26, the numerical values in Table 25 were used. TABLE 25 b 414b ee = BES : m= (414b m= 14140 has Ate ay a 0 .2289- 10? 0.3237-10° 3-089). le” eee 1 ee eee 0.2318-10° OFS278- 10858 AL eg tee 3.051 Cuap. 7] GRAVITATIONAL METHODS .: 205 Z 2 PONE PONE RON PWD TABLE 26 CALCULATION OF FOUR-POSITION TORSION-BALANCE RECORD 3 (FROM LARGE DEFLECTIONS) Beam II Beam I no AY Ay A; Ay ||No.| 7’ nr Ai A; A; At 5 1 | 99.5 .2| 52.9 —2.7 2 | 92.1) 99.9 —7.8 .0) 53.3 +0.7 3 {110.2} 100.2 +10.0 .0| 53.3 —7.8|| 4 | 97.6} 100.3 —2.7 .6| 53.0/+10.6 1 |101.0) 100.3) +0.7 .0| 52.9 —2.9 2 | 92.5} 100.2 —7.7 .O| 52.7 +0.3 3 {110.1} 99.9 +10.2 .8) 52.6 —7.8|| 4 | 97.1] 99.8 —2.7 .9) 52.5/+10.4 1 |100.0} 99.8) +0.2 .6| 52.4 —2.8 2 | 92.1} 99.9 —7.8 .6) 52.5 +0.1 3 |110.1} 100.2 +9.9 .0| 52.5 —8.0|| 4 | 97.3) 100.5 —3.2 .2| 52.6/+10.6 1 {101.5} 100.8) +0.7 .8) 52.6 —2.8 2 | 93.1} 100.8 —7.7 al 3 {111.2 4 4 | 97.5 = +0.2/+10.5) —2.8| +0.4) —7.9 = = —0.1) +0.5) —7.8/+10.0/—2.8 Uzs Uyz Us: Uye Mi ESSSESSSRESSSESSS Ai + Ai = —7.3m = —22.5 or = —(As3 + Aj) —7.2m = —22.2 A: + A; = +2.2m = +6.8 or = —(Ai + Aji) = +2.3m = 47.1 —(Al + AY) = —7.7m’ = —23.5 or —(AZ + AZ) = +2.4m’ = +7.3 or As + Aj = —7.5m’ = —22.9 ai Al + Ad = +2.6m’ = +7.9 For five positions, calculations from deflections A with respect to the torsionless position, and from the readings 7 are possible. Both calcula- tions are given in Tables 27 to 30. The following formulas were used for the calculations from deflections: Balance I: Us, = —1,03 (Ai =—-Ag) = 1:66 (Az) ="As) Uo e816 (ne As) el (Ae Ae) Un = +4.73 (A, — Az) — 2.93 (As — A2) DU Baai(Age-- Az) — 9102\(Apat dg) Balance II: Use = +1.01 (Ai) — As) + 1.64 (As — Az) Wt 5 IAG AAC) ad AOA be) Us = +4.69 (44 — As) — 2.90 (As — Az) 2Uy = —3.40 (As + Ai) — 8.93 (Az + As) 206 GRAVITATIONAL METHODS [Cuap. 7 TABLE 27 CALCULATION OF FIVE-POSITION TORSION-BALANCE RECORD (FROM A’s) Part 1 n” | no AY A, | A; AS A; n nb Ai A; A; At A; 2 || ne a ea Cn OF 77h i 124.0).60.4 27 al ol eee 701 4 pea VP MR Tent a co 79.2)... doch 22. OR a ROP O15S Ole welt ae (Ale reek Q5A2190F Sia Lae — 471 0e eee 66295380412. 0 ee. |p eel ee Se ) T2192 (992 Ole. 2 eee ae 22 2a >) lee 9) 15 5 29 | oe aD I ni RC NI) SS = 32 Ol 7627/98: 91.2% 0 leee ee lel eel ee —22.2 C1 D5 Ol OT Tie oc oll eas chee kone ee ee 122..5/98:. 8) 23 8): .. oh.. 1. of ee ee AALG|SSeD ieee Sets Pa | Reet lh meee gl en TOVOOS Oise ee =19.6) 72). Ss ee SRV AB Molly orale lieu. Co SY? haiet Ream ean 9453 9826) vealise meee = 4:53| Ss Ale eee 6626) 53e4 2 sea ee eee ce be ya See ee T2IONZIOS Tle, coeredl eis eel Cee 2 Oe ae QOEGT DSS. hy mall ces, te cll's coche ee = 3214-16 7 |98e Tle oles ck sale o atl eee —22.0 SU Ol5s Al Om eal. et alcke wp leean, Wy ein ee 123.5/98.8/+24.7|......|..... hica, i Ue 441531, ee =O: (1... Mets Peake 79 0199 :2) = 0 |427.9|—9.0)/—0.1/+13.4|/—32.2||5 = —0.2|/424.3)/—19.9)—4.3/4+21.8)/—22.1 Beam II: Beam I: Ay + Af =4138.3 AY + Ag = —41.2 AS + AG=+17.5 Az + A; = —42.0 Al — AJ =4+13.5 Ay — AY = —23.2 Ai — AS=+26.1 As —Az:= —2.2 Table 28 shows the calculation of gradients and curvature values for each beam from the sums and differences in Table 27, in accordance with “the formulas given on page 184. The same numerical coefficients apply to the calculation of gradients and curvatures from the n’s as from the A’s. The calculation is shown in Tables 29 and 30. Table 31 contains a summary of results obtained for both beams combined or individually in three, four, and five positions. 5. Operation of torsion balances. First, an observation site that is flat, at least in the immediate vicinity, should be selected. Next, the differences of elevations on concentric rings are measured at eight or sixteen points, as described in the next section. Three wooden stakes are driven into the ground, and their tops are leveled and placed at an elevation such that the center of gravity of the beam is at a height for which the terrain correction has been calculated. A base plate is so laid on the wooden stakes that its north groove points north, and the differences in elevation for the inside terrain circles against it are determined. It is advantageous to set out a stake about ten feet north of the station site to facilitate orientation of the base plate, house, and instrument. After the hut is erected, the instrument 9°sT¢+ "= CG t+ 2a a or Oa C2) Pate 6° 96— 60° T= G'09— WW e— e°s¢+ g1°é+ €rL95- 06°%— 0°8E— 9° I+ 6° L9E+- &6' 8— 0 6h+ 61° T— Z Lavg | Calt= UY shy. =O) Geers Nea (Vv WOUd) GHOOUN AONVIVA-NOISUOL NOLLISOd-AAIA dO NOILVINOTVO QZ ATAV I], 207 208 GRAVITATIONAL METHODS [CHapP. 7 pedestal is placed in position on the aluminum base plate. This is followed by the center piece, which in the automatic instruments is provided with stops for three, four, and five positions and which must be set according to the azimuths selected. The upper part of the instrument containing the beams is secured in place, and tubes for the hanging weights are attached where necessary. After the instrument has been assembled, it is carefully leveled. In automatic balances the driving clockwork is wound and engaged andthe upper part allowed to rotate until it reaches the first stop. The compass TABLE 29 CALCULATION OF FIVE-POSITION TORSION-BALANCE RECORD (FROM n’s) Part 1 Beam II ; Beam I if 82.2 are MA 124.0 A Ma soo sae 2 44.2 PA ers Rome Fe AN As old 79.2 ey rae cc ion 3 ae Do 2 le Seen sl eae nee aes 9532) =|. vcton Ses 4 sank G6: Sic aa een ollbeocire 28s. POT | eee 5 ae 7A VES inal IN popeeneee 5. Ma eee 76.7 1 81.2 ate SBE 122)6-i) 2 Ree tery ics bc 2 44.6 any Be e8| | better ra 79.0 Bee eee 3 53.5 seer ell vec ne 94-3) «|. SRE 4 ae 66.6 Be || (Geen 3 aa 4(\el20 Re: 5 mae 2059) IIh aiyorss Se Jee 76.7 1 81.2 ae 123).5))|" tse. al) ae eee 2 44.1 SEP SIE | Plots Sireered LN cate ees hl || Metoneese 1980 | hs 522 | eee 3 52.7 5 ee A eeenimi| (beta i oe: 94.5 | ..... 4 nae 66.5 BP ts) | ee ce ates ve PIZZA eee 5 Se: LOS euler. sdaet Hock Al eee 76.5 81.5 | 44.3 | 53.1 66.7 | 20.7 123.4 | 79.1 94.7 | 121.2 | 76.6 ny" n,"' ns!’ mn" nz!" ny! ng! ns! na! ns! needle is then released and the upper part, together with the turntable, is turned clockwise until the side of the balance case is in the astronomic meridian. After the beams have been released, a visual instrument is ready for observations in the first and all other azimuths at about 50- minute intervals. In an automatic instrument a plate must be inserted, the recording clock wound, and a trial run made before the instrument can be left to itself. Further details are given in the author’s torsion- balance manual.” 9 Directions for the Askania Torsion Balance. GrG1es28 Lr — 6° 0&— €° 1298+ Tt 16— €°Sze+| 1°S9— G Sh— 0° 168+ 0°86— “NZ \9FG I+ tug —fu+ u |7e0'r— tug — tu + fu "2G |G I+ | tug — ,u+ ,uleee— | jus — tut ,fu g°o¢+ b Sh— 6'0g— 2 6r+ 1 16— 98+ | ¢°09+ Z &h— 6° 1¢— 0'86— “a lelh I+ ug — ju + lu l0rg'0- jug — fu + fu 72 NOW TS. SUS Se ee a ere. |e ce = aes 62eI+| 9°SZI+ ¢°9¢+ Sl+ GZ— @ ZeI+| 8° e9+ 9°€I+ 89+ 9°&%— YS rar jue £6°6— pa Ya |69°%+ pt — {yu 06°Z— psa Oes— | ZL2- G°9¢+ oF+ oe o-ss— | 2°8I+ 9°SI+ L 8%- 9°8Z— 72 |120'1- tu — vu 99° I— ty — Su 7 |10°I+ A ae t9° I+ ae ie [J Aveq II Rvag (4 Luvd (8% WOUA) GHOOUU AONVIVG-NOISUOL NOILISOd-HAIM FO NOILVTINOTVO of A1avy 209 210 GRAVITATIONAL METHODS [Ciap. 7 TABLE 31 PosiTIONs Bram Une Uyz Ua 2U zy Bh ahd I& Il 95 9 6.1 139.0 325.7 eben ii. —23 .2 4.5 129.9 318.6 Bee Ty Aromas —24.4 7.5 130.6 322.7 Reet I\ ; —23.0 5.8 132.9 319.5 Rae Mm orn oa E95 A() 8.6 132.2 325.3 4 I Sos 658). oe ee —22.2 7A ae Il —23.5 PZ ee. | —22.9 7.9 D. CoRRECTIONS After torsion-balance readings have been calculated in the form of gradients and curvature values as shown in the preceding section, a number of corrections must be applied. These may be divided into corrections required for every station and corrections required only in special cases. In the first group fall (1) the planetary correction, and (2) the terrain correction; in the second are (8) corrections for regional effects, (4) cor- rections for coast effect, and (5) corrections for fixed masses other than terrain, underground openings, and so forth. 1. Planetary corrections. As in measurements of relative gravity with the pendulum or gravimeter, the normal or planetary variation of gravity must be considered in both gradients and curvature values. It is here again sufficient to consider the earth as an ellipsoid of revolution with a major (equatorial) axis and a minor (polar) axis. The planetary variation in the gradient may be obtained by differentia- tion of formula (7-15b), disregarding the longitude term so that the plan- etary gradient is HEC OONY eb 18g) |) Op: : (Ue) cra: a ey a ae = Bae (7 63) where p; is the radius of curvature of the meridional ellipse, which in this case is sufficiently close to the earth’s radius so that after substitution of the numerical values from eq. (7—-15b) (Use)norm. = 8.16-10 °-sin 2y. (7-64) The variation of gravity and gravity gradient with latitude is shown in Fig. 7-73a. It is seen that the north gradient is zero at the equator and the poles, is always directed toward the north or south pole, and has a maximum at 45° latitude. Under the conditions assumed (two-axial ellipsoid of revolution), there is no variation of gravity along the parallels of latitude, and hence no correction need be applied for planetary variation to the observed values of U,.. If the instrument is oriented into the Cuap. 7] GRAVITATIONAL METHODS 211 magnetic meridian, a correction would, of course, be necessary. However, this can be avoided by allowing for the declination, and setting it in the direction of the astronomic meridian. For calculating the planetary effect on curvature values, formula (7-487) may be used, which relates the curvature U, to the two principal radii of curvature of the equipotential surface. The normal surface is assumed to be that of a two-axial ellipsoid of rotation, in which case the planes con- Southern Hemisphere Northern Hemisphere Latitude Fic. 7-73a. Planetary variation of gravity, gradients, and curvature values. taining the principal radii of curvature are in the astronomic meridian ! : 1 1 and the prime vertical, so that \ = 0. Hence (Ua)norm. = -9(4 = aT) Py Pz where p, and p, are the principal radii of curvature. For the meridian ellipse the radius of curvature” in the latitude ¢, is given by Gees WOKEN +/ (a? cos? y + c? sin? y)3 Pz = % K. Jung, Handb. Exper. Phys., 25(3), 150 (1930). 212 GRAVITATIONAL METHODS [CHapP. 7 with a as equatorial and c as polar radius, while the radius in the prime vertical is 2 a +/a? cos? g + c? sin? ¢ Py Southern Hemisphere Northern Hemisphere G0? 60°" — aa LO” A 0" NB Latitude Fia. 7-73b. Planetary variation of curvature radii of reference ellipsoid in meridian and prime vertical. The variation of these radii with latitude is shown in Fig. 7-736. There- fore, with sufficient approximation where the second factor is approximately twice the flattening, or 2-(a — c)/a (see eq. 7-14a). By substitution of the numerical value for the equatorial radius, (Ua)norm. = 5.15-10°° (1 + cos 2g). (7-65) Cuap. 7] GRAVITATIONAL METHODS 213 The planetary variation of the curvature value is shown in Fig. 7—73a. U., is zero, since } was assumed to be zero. The maximum value of (U4)norm. occurs at the equator; it is zero at both poles. 2. Terrain corrections. Since the torsion balance is a very sensitive instrument for the detection of certain types of subsurface mass irregulari- ties, it is readily understood why it also reacts very perceptibly to the visible, that is, topographic masses around it. As it measures variations in gravity components rather than gravity itself, it is seen that it must be more sensitive to terrain variations than is the pendulum or the gravi- meter. Finally, the variations of the horizontal gravity components (curvature values) are much more affected by terrain than are the varia- tions of the vertical components (gradients). In order to correct for terrain effects, it is necessary to know the shape of the topography surrounding the instrument. This is done for close distances (up to about 200 or 300 feet) by leveling. For greater distances, existing contour maps may be used with sufficient accuracy. It is cus- tomary to refer to the correction for the short distances as terrain or topo- graphic correction and to the correction for the greater distances as carto- graphic correction. It is obviously impossible to survey in detail all the small terrain irregu- larities around the instrument. As will be shown below, any method of terrain correction can do no more than substitute a more or less idealized surface for the actual terrain surface. Hence, the field survey need not be carried beyond the limits of accuracy inherent to the mathematical representation of terrain effects. The principal requirement is that the calculation of the terrain effects be within the limits of error with which gradients and curvature values can be read on the instrument and inter- preted. Terrain effects are therefore calculated in flat country (oil explora- tion) with a probable error of several tenths to one E.U., while in hilly country (mining applications) the probable error is several to 5 or even 10E.U. In any event, there is no need for carrying the accuracy of terrain surveys to extremes, since most analytical terrain methods are based on the assumption of uniform densities. This assumption is not always correct for the surface layer, to say nothing of the effect of a denser medium beneath the weathered layer. Experience has shown that it is generally sufficient to smooth out the ground immediately adjacent to the instrument (out to 1.5 m radius) as much as possible and to measure elevations in eight azimuths from the setup, along circles whose radii depend on terrain and correction method used. In most terrain methods the radii are fixed; and, in very unfavorable terrain, elevations are determined in sixteen instead of eight azimuths. Terrain correction procedures may be divided into (a) analytical, (b) 214 GRAVITATIONAL METHODS [Cuap. 7 graphical, and (c) integraph methods. In the first, elevations measured in the field in predetermined azimuths and radii about the instrument are substituted in formulas with fixed coefficients for such azimuths and dis- tances. In the second method, evaluation diagrams, or ‘‘graticules,”’ are used which are superimposed upon a terrain contour map or upon terrain sections in predetermined azimuths. A count is made of the number of diagram ‘“‘elements’” which are included within adjacent contour lines, or between the terrain profile and a plane through the center of gravity of the balance beam. In the integraph methods, contour maps or terrain profiles are evaluated directly by specially constructed integraphs. Terrain correction methods are numerous, and only those differing sufficiently in mathematical principles or procedure will be discussed. dm o/ Fig. 7-74. Mass element in relation to center of gravity of torsion balance. Their description will proceed in the order given above and will be con- cluded with a discussion of application and field practice. (a) Analytical methods. The fundamental principle underlying not only the analytical but all other terrain-correction methods is to divide the surrounding terrain into sectors bounded by angles and concentric circles and to sum up their effects. The action of each sector is calculated in the analytical methods by assuming definite variations from one azimuth to another and from one circle to another. Within two successive circles all sectors have the same opening. (In the graphical methods the sectors are all different and so calculated in respect to azimuth and distance that they exert the same effect on the instrument.) The action of each sector follows from the effect of a mass element dm (see Fig. 7-74). Since its gravity potential at the distance ris U = Cuap. 7] GRAVITATIONAL METHODS 215 (kdm)/r, the gradients and curvature values, or the second derivatives of the potential, are , 2 fae 2 ty = 3k [ dm.% Ue 3k [ dm.¥ z: , (7-66) Uy = ak { am.% Usy = 3k [ am.72. Assume that the center of gravity of the balance beam is at a distance ¢ and the mass element at an elevation h above ground. Then by substitu- tion of r = ~/p? + (¢ — h)?andz’ =¢—|h os Dia It) br Os, = 3k fam —* eee ee 3k [dm 2 ae y e+ 6 — hype in y(¢ — h) a zy Uyz = 3k | dm [o2 + (¢ — A)? Uy ia 3k | dm [p? + (¢ = h)?]5/2° With polar coordinates x = pcosa andy = psina: p cos a(t — h) p cos 2a Uae = Bh J am ne | Ue 8 me ap aye psin a(f — h) ra) p sin 2a Cy; = 3k | dm [p? = (¢ a: hy?]8/2 20 = 3k [ dm [o? + (t — hye” Fic. 7-75. Sectorial mass element. For a sectorial mass element (Fig. 7-75), dp-pda-dh-6 (6 = density) bounded by two concentric circles with the radii py and p,+1 and angles Om aNd m4, @m+1 penti ph deny i [ i dagaedn. (7-67) am en 0 216 GRAVITATIONAL METHODS [Cuap. 7 Extending the limits of integration over the entire surrounding topog- raphy, rs} 2n iS p cos ada dp dh(¢ — h) Use = 3kd | I fi ae 2 *r fr" 5 sin adadp dh(t — h) Uyz = aia | i ee [p? at (¢ wae h)?}5/? (7-68a) o @ h wy pcos 2a da dp dh ~Ua= ais [* J of +E WP o 2m\ ph 93 + p sin 2adadp dh Um = at | CL tae Re In practice the integration of the effects of the concentric circles is not carried to infinity. The circles are calculated individually; the calculation is stopped when a circle exerts an influence of less than 0.1 E.U.; and all circles are added. Within each circle the effect of the elevation A is a function of azimuth, as shown further below. For the last integration the denominator in eq. (7-68a) is more conveniently written a ; he 2eh\ a 2 2]—5/2 2 2 et Caw C++ % For fairly gentle slopes not exceeding 8°-10°, the last term is generally small and the above expression may be expanded in the form of a power h series, so that after multiplication by | dh (¢ — h) = 3 (2th — PW’) the 0 series is 1 .. 5 (h’ — 2ch)” gli + ye) an - ae Only the first two terms of the last factor are considered. This approxima- tion is made in all analytical terrain-correction methods. Carrying out h h the integrations if dh(¢ — h) and [ dh, the four derivatives are: 0 2a Un = —368 | [ p_cos ada dp (h® — 2¢h) | + | (7-68b) Gt Oe * sin adadp Un = —3h 5 i fees ea ae a 7-69 ** 6° cos 2ada dp —Us = +60) | je ear ** * sin 2ada 0 sin 2a da dp 2U ey = +603 [ ie aaa Cuap. 7] GRAVITATIONAL METHODS 217 From this point on, various analytical terrain methods make different assumptions regarding the variation of h with azimuth and radius. For greater distances it is permissible to make no assumption whatever regard- ing a variation and to assume merely that the elevation measured in the field is representative of the mean elevation of a sector which is so bounded that the station at which the elevation is measured is atts center” (and not at its corners as assumed in other analytical methods). The effect of each sector is then obtained by integration between the limits p, and py+1 and ag and amy. Considering that Qa in Qr 2a ° cosada = [ sin ada = i € cos 2ada = ii ¢ sin 2ada = 0 0 0 0 and that, therefore, the substitutions Lo 2h he and phenol (7-70) are permissible, the azimuthal effects of all sectors in a concentric ring are given by 2x 2 20 2 i cos ada H Sia) iG 2 cosa =c’ 0 Mn I 2r / sin ada H’ = = >> H’ sina =b’ 0 m (=a) / Qa i ea eR SpE: apenas e 0 10 Qn iL sin 2adaH = “TY Hsin 2a = d’ 0 where m is the number of azimuths (eight or sixteen) in which the eleva- tions are measured. Then the effect of one ring bounded by the radii py and py,, is 6 (p?ntl p * dp Tee gi |S eae ys 2 Ph (p e+ ne’ Pnt+l * dp Oe = eof p b’ "2h, @Fae” (7-72) rs 1 Pnt+l p 3 dp e Us = 6h; ait ee ey p * dp ’ 2Uy = = 6k oie (p? a (po? + @)5? -d %C. A. Heiland, A.I.M.E. Geophysical Prospecting, 554 (1929). 218 GRAVITATIONAL METHODS [Cnap. 7 Coefficients for each ring resulting from the evaluation of these integrals and the expansion of the coefficients c’, b’, e’, and d’ in terms of elevations in eight and sixteen azimuths are given in the article referred to.” As stated before, this procedure is permissible only for greater distances (cartographic correction). In the application of terrain methods to smaller distances, some variation of elevation between successive azimuths and radii must be assumed in order to arrive at a mean elevation of a sector. The simplest assumption has been made by Eétvés.” If the sector is bounded by angles a; and az and by radii p’ and p’’; if the elevations hi and hz have been determined on the radius p’ in the azimuths a and az ; and if the elevations hi’ and h; have been determined on the radius p”’ in the same azimuths, the mean elevation is assumed to be given by h = (; + Coa + Cspa + Cap, so that the coefficients €:(a2 — a)(p” — p’) = p'’(a2h — ayhz) — p'(aahi — ashe) C2(a2 — a) (p” — p’) = p" (he — hi) — p'(he — hy) & ” ” ’ ’ (7-73) C3(ar2 — a1)(p’’ — p’) = he — hy — (he — i) Ca4(aa — au)(0” — p’) = as(hi we hehe ie — ia): The effect of each ring is calculated from integrals similar to those contained in eq. (7-72). However, Eétvés does not use the squares of the elevations as in eqs. (7-71) to represent the azimuthal variations but breaks off the power series of (7-686) after the first term, which makes it possible to use the first powers of elevations. By considering only the first term in eq. (7-68b), eq. (7-69) therefore takes the following form for the gradients: Oy ie ** cos adadp Use = —38kd i i oe (hg — Q), where Q indicates a quadratic term Q = h’/2. Because of this simplifica- tion, the formulas are applicable to small elevations and gentle terrain only. In the Eétvés formulas given below, the innermost ring of 1.5-m radius is considered a plane with the inclination of — in the north and . in the east directions. A quadratic term is included for the 5-m radius, which is generally negligible for the gentle terrain to which Eétvés’ formula is applied. The radii are P1 p2 P3 ps Ps 1.5m 5m 20 m 50 m 100 m Density is assumed to be 1.8 and ¢ is 100 cm. % Ibid. © Op. cit., 358. Cuap. 7] GRAVITATIONAL METHODS 219 Us = [5.77 £]p, + [0.00379 £(hi + hs) + 0.0061 &(hs + hr) + 0.0221 E(he + ha + he + he) +0.0160c(he + he — hg — hs) + 0.13046(hi — hs) + 0.09225 (he + hg — ha — he) + Qo, +[0.01173(hi — hs) + 0.00831 (he + he — ha — he), +[0.00108(hi — hs) + 0.00077 (he + he — ha — he), +[0.00028(hi — hs) + 0.00020(h2 + he — Aa — he) Jo, Uys = [5.77 do, +[0.0379 u(hs + hr) + 0.0061 (hi + hs) + 0.0221 « (he + ha + he'+ hs) + 0.0160 E(he + he — he — hg) + 0.13046(hs — hr) + 0.09225 (ho + ha — he — he) + Vo. (7-74) +[0.01173(hs — hr) + 0.00831 (he + ha — he — hs) Jos +[0.00108(hs — hz) + 0.00077 (he + ha — he — he) Io, +[0.00028(hs — hr) + 0.00020(h: + ha — he — he) og —Up = [0.4826(h: — hs + hs — hr)Ipe +[0.08194(hi — hs + hs — hz)]os +[0.03181(hi — hs + hs — hr), +[0.03077(hi — hs + hs — hr)Ip, Dey = (0 4826(h, — ha + he — ha) lp. +[0.08194(he — ha + he — hes)]>5 +[0.03181 (hy — ha + he — hs)]p, +[0.03077(h: — ha + he — hes)]o, These formulas have been simplified yet extended to more unfavorable terrain by Schweydar.” He eliminated the separate calculation of the innermost ring and developed two methods for calculating gradients for: (1) gentle terrain and elevations not exceeding the height above ground of the center of gravity of the instrument; (2) any topography. The first method follows E6tvés’ procedure and considers only the first 97 W. Schweydar, Zeit. Geophys., 1(1), 81-89 (1924) ; 4(1), 17-23 (1927). 220 GRAVITATIONAL METHODS [CHaP. 7 and linear elevation term in the power series of eq. (7-680); the second uses the squares of the elevations as in eq. (7-69). In both methods the varia- tion of elevation with azimuth is represented by Fourier series. This makes the method more flexible and it is possible to apply the formulas to any desired number of azimuths. In any given azimuth, the variation of elevation is assumed to be linear between rings in the first method and quadratic in the second. In both methods the variation is assumed to be linear in the curvatures. Considering the linear variation between rings first, the following propor- tion exists: © Pniit — Pn P — Pn Therefore the elevation is hp (Pn a Pn) or hapass oa hovPn a p(n a aa) Substituting this in eq. (7-68a), and considering in the expansion of eq. (7-68b) only the linear terms, the terrain effect of one ring between the radii pp, and py is 3k6 as Uz = es UNOS [tf cos ada(hy pay: — hay Pn) Pony — Pn 0 2a ne if cos dain haw) | 0 3k6 Ee, z Uy. = ee | sin ada(hapay — May Pa) Pn41 — Pn 0 Qe + ca sin ada(h, — haw) | 0 (7-75a) 3k6 an ap 00 = toner meee We & i cos 2a daha Pay: — Aas Pn) Pn+1 — Pn 0 2x _ 1 f cos 2ada(h, — haw) | / 3k6 a 20 3; aay Leni Nt E [ sin 2a da(ha Pn = ReaD) Oni: — Pn 0 2x Si i, SPE. haw) | 0 The integral J; is the same as the integral in the gradients of formula | (7-72), and integral J, is the same as the integral in the curvature expres- Cuap. 7] GRAVITATIONAL METHODS 221 sion of the same formula. They involve the second and third powers of p, while J, involves the fourth power: ae | Ge Wap o<. p. pa : CUP i LPC en epee Bopha thee ae ee So, (OF FL (2 + 29872], (7-75b) ee ee of Pp (p? =e ae 4 2 352) Ppa Sogn oa Se The integrals expressing the azimuth variation are represented by Fourier series of the form h=a+bsina+ccosa+dsin 2a + e cos 2a so that the four coefficients are Qn 2x Tb = i hsin ada rd = | hsin 2ada 0 Qe Qe re = [ h cos ada re = if h cos 2a da. 0 0 Like the coefficients in eq. (7-71), these are obtained from observations of elevations h in m azimuths on one circle: so that in eight azimuths b = 0.25[0.707(he + hy — he — ha) + hz — hi] c¢ = 0.25[0.707(he — he — he + hs) + hi — hel (7-76) d = 0.25[he as ha ok he = hs] e= 0.25[A1 = hs + hs rm h7]. 222 GRAVITATIONAL METHODS [(CHaP. 7 For sixteen and thirty-two azimuths, the formulas are calculated in the same manner.” ‘The final terrain formulas then take the following form in Schweydar’s first method: Un = 5 [2.36e1 + 0.643c2 + 0.239c3 + 0.082c, + 0.0186c; + 0.00467c, + 0.00187c; + 0.001204c, + 0.000803c, + 0.0004284c ----] tee 5 (2.360, + 0.643b2 + 0.23903 + ----] (7-77) Be ee 5 [3.3024 + 1,962e. + 1.348e + 0.844e, + 0.357¢; + 0.147e, + 0.0805e7; + 0.0686es + 0.0616¢, + 0.0472e10 eoe FA 2U., = 5 (3.302d; o Poead at seat: In these formulas the indexes of the Fourier coefficients refer to the following distances (in meters): e2ajes 04 | 5 Gea Slo eae 1.5 | 3 | 5 | 10 | 20 | 30 | 40 | 50| 70 [100m The formulas are calculated for an elevation of 90 cm of the center of gravity of the beam above the ground. The constants give the terrain effects in E.U. Formulas for other beam elevations are given in the Aska- nia publication referred to previously. Table 32 represents the calculation of a terrain correction in accordance with eqs. (7-76) and (7-77). Above are the ground elevations in reference to the height of the base plate (22.5) and the telescope axis of the alidade (125 cm). With formula (7-76), the coefficients a, b, c, and d are cal- culated and multiplied by the factors in (7-77) to obtain the effects of each ring, whose sum gives the gradients and curvatures. The form represented by Table 32 is used together with the form given on page 200 and con- tains also the calculation of final results with planetary and terrain cor- rections. Schweydar’s second method is applied when the elevations of the sur- *% C. A. Heiland, Directions for the Askania Torsion Balance; also A.I.M.E. Geophysical Prospecting, 5383 (1929). Cuap. 7] GRAVITATIONAL METHODS 923 rounding terrain exceed the height of the center of gravity of the instru- ment above ground. Then the first two terms in the series of formula TABLE 32 TERRAIN CORRECTION A 4b = 0.707(hs + ha — he — hs) + hs — hz 4d = ho — hit he — hg 4c = 0.707 (he = hh as he + hs) + hy — hs 4e = hy =o hs + hs = hy Density: 2.0 Plate = 22.5 Instrument = 125 em p 1.5 3 5 10 20 m p as) 3 5 10 20 m h ] II Ill IV Vv h I II Ill IV Vv 1 +0.7| +0.7) +7.0 | +10.7| —4.0 1 21.8 | 21.8 | 118.0} 114.3) 129.0 2 +0.9) +1.1) +0.7 | +5.0 | +7.0 2 21.6 | 21.4 | 124.3} 120.0) 118.0 3 —1.2) —4.3) +1.6 | +1.7 | —5.2 3 23.0 26.8) | 12384 0 12353] 13022 4 —3.5| +2.7/+10.3 | +0.3 | +5.5 4 26.0 | 19.8 | 114.7} 124.7) 119.5 5 +0.3} —1.1) +1.6 | +4.3 | +0.2 5 22).2° (23.67) L234 0120.47) 12453 6 +1.5) +3.2) +3.2 | +3.8 | +8.8 6 2120) DOSS L218) 120 2) 1632 7 +1.5) +9.5) +0.7 | +3.5 | —6.0 Uh 21.0 | 13.0°| 124.3) 121.5) 131.0 8 +0.3) +8.3) +6.6 | +5.8 | —9.0 8 22.2 | 14.2 | 118.4) 119.2) 134.0 c +0.6) +1.1) +0.3 | +2.8 | —4.0 e +0.2; —1.4) +1.6) +2.5) +2.0 b —1.5) —4.8) +0.4 | —1.2 | 42.4 d +1.4) —1.7| —3.3) +0.7| +4.8 times | 2.36 | 0.643 0.239 | 0.082 | 0.0186 Ff | 3.302 1.96 1.343 0.844 0.357 | equals c’ +1.4| +0.7) +0.1 | +0.3 | —0.1 e’ +0.7) —2.7| +2.2) +2.1|) +0.7 b’ —3.5| —3.1}/ +0.1 | —0.1 0 d’ +4.6) —3.3) —4.4) +0.6] +1.7 6 6 Keay CUM 5. hee Bs came 5 8-0 ) 6 K,, = Sum b’ X 9 = —6.6 || 2K,, = Sum d’ X 3 = —0.8 NEGATIVE CORRECTIONS FLECORDED Wn |prvesits ir Maem een US Ve te I a eR CoRRECTED VALUES Terrain Topog. Planet. —4.4 +2.4 = +6.9 —13.7 Uz: IN +10.5 —6.6 = = +17.1 Uy —24° —2.5 —3.0 — +7.9 —7.4 Ua R —1.4 —0.8 — — —0.6 20 xy 7.4 (7-68b) are used, which leads to formula (7-69). As shown in (7-70), it is then more convenient to use the squares of the differences, (kh — ¢)° = H’. 224 GRAVITATIONAL METHODS [CHar. 7 Their variation with azimuth is again represented by Fourier series, so that the new coefficients (comparable with those given in [7-71]) are: NB 2 esp acini and iC = a areas (7-78) mm Mmm Instead of introducing again a linear variation between two rings, it is now more convenient to assume a variation of their squares between three rings, so that 2 2 H” = % + Cop + Czp. The coefficients are determined from the variation of H’ in one azimuth in three distances, pp, Pni1, ANd pp,2, So that the gradients 2a Ue = —3k g [tf C; COS a da 2 0 Qr 2r + Ba Co cosa da + hn { C3 COS « dae| 0 0 (7-79) 5 Serer Uy. = —3k - El c, sin ada 2 0 2x Qn +n f Ce Sina da + hf C3 sin ada, 0 where the integrals J, 2, and [3 are as given in (7—75b) except that the limits are py, and pp, Substituting numerical values for the same distances as in the first method the gradient formulas of the second method are: (ge 5 [172.9 IC jy + 11.64] C 2 + 17.92|C |p + 3.020 |C |, + 1.454 |C |; + 0.031 |C |, + 0.1404|C |, (7-80) + 0.0399 | C |s + 0.0592 | C |) + 0.0152 | C |r] Te — 3 (172.9 [Bh =e 41 G4 B leche al These formulas hold for ¢ = 0.9m. All elevation (differences) must be expressed in meters. The formulas for curvatures originally given do not change. Table 33 illustrates the calculation of terrain corrections for both curvatures and gradients (second Schweydar method) for very rugged terrain. Fig. 7-76 gives an idea of the magnitude of terrain effects under such conditions. In concluding the discussion of analytical methods, brief reference should be made to a method for calculating the effects of remote terrain features 0'S = ¢ Ajisuap 9oRJAINg z §cF- = a My lee| ss ST $ 6lé= aac X ps = "AZ z Hele ty ey al |S gosit = 2 - x ec = "x Bot I+ [ost | FOF |F6t BS+ ort] 20+ | Os+ | .| a] |g'1z—le'ot—|s'6— lo-ze—l9's8—l6'49—|e'16—| 80+ | e'o+ | .P e'1— |pt— jee— | e°0— jet+ lus— jees—| got feet} slo} |e-2+ lo-or—le-6— |z-ez—le-re—l6-¥¢—|-6¢—| 9'0—- | 0 2 sjenba 2620" of6se0"olrort’o| 120° | g¥°1 | zove feo-ar | v9'tt | 6zet | | a |*| 9 | |\z0'0 (6900 |180°0 |261'o |zce'o |rr°0 lere't | zaet | zoe'e | P ‘a SOUT} 9'Lb+|L 6&+|P'6Z+|Z1'6+ |Sh°9+\26°0+|6L°0+|190'0+|6z0'0+ a! lese— lert— |zt1— losz— lore— | z— | 9o—| rot | rot] Pp €°ZZ—|0'Se—|2'€Z—|96' O1— [98° 0+|68°I—|98"I—\ez0'o+|et0'0+, {D1 |zet+ lest— |ett— lzoz— |s9— | so— | %F-|e0-| 0 a ; W Wo Z'st |8'0 | $'°0 | 10 | 0°0 | 12:0 | ogo | ez: | 282: | 8 |6'et |6-0+ |z-0+ |e'0+ |z-0+ lor'o—|e¢-0—|sg8°— |esg'-— | 8 06 jo'6r | oo | To | g:2t| 90°0 | ze°0 | zoz° | |82: L |0°€+ lo'2+ |L0— je0+ |s'e— |rz'0—|19°0—joz8"— |ogs'— | 2 #88 j0'sz | 0'Gz| o'F9 | T'8c | 272] 26°9 | 2o2° | FLL" 9 |*'6— |o'g— jo’¢— jo's— |e's— |sz°e—|p9°2—jozs’— | g8'— | 9 Qe \Z-e2I | $98] €°6S | 2°62 | OFZ | 099 | 82° | e842. | ¢ — |lg'9— jt-tt—le6— |z:2— lrg— |ez'z—l29'2—[s88"— |ess'— | ¢ gee (92h | 9°02] O'9T | 06 | ¥2'e | 96°% | G98" | szs° | =F __iig-e— 6'9— |r-8— |o'¥— lo-e— |os'1—lzz't—loes:— | 16° — | + 0°61 /8°8ST | $°98 | 92h | O'OT | 29°Z | 6S°% | G98" | 88° | =f sig" #1—|9'zt—[@-6— |6 9— Jo'y— [zo'1—|t9°1—joge'— | 16° | ¢ gab |g 2h | 8'¥o | S'ze | F:09 | 00'9 | z9°¢ | gos | 8zB- Z |g9— |o9— |r'z— |2'o— [tz |tg-e—|zez—loee7— | 16 - | z 00 |r'0 | 1:22 | o'er | O'8z | 66°2 | 66°T | 9¢8°0 | 8z8"0 1 |it0— |9'0— [ae jo'z— [se |ea't—|1% t—|906°0-| 16°0-| 1 XE | TMA) ITA) TAR AL] AL | IT |] IT ‘| AI j=) = llext LantA| TA )-A (oA | AD i) a ot Oe 09s) Ore 0e- Ve Oct 0 | Gi elo oe Of: i 02: | 30% | 08 |20c; | Of |G a. eh eieodr | em Ww Ww cH — 7H + (CH — 7H — (H + (H)10L'0 =| a\F SH Histo! de ae He =e Py aH — iH ACH tH — 1H — *H)10L'0= | 0: F OHS i lee ates d NOILOGUYOO NIVYYAL €@ AIAV, 226 © GRAVITATIONAL METHODS [CHaP. 7 Eotvés Units eee ee} | 0 200 400 Fic. 7-76. Terrain effects and contours at Caribou, Colorado (compare with Fig. 7-119). on gradients and curvatures. from contour lines (cartographic correction). The procedure is illustrated in Fig. 7-77. The terrain is divided into elements bounded by successive contours (interval dp) and subtended by an angle da, so that the coordinates of the center of the element are p and a. Then the corresponding gradients and curvatures may be obtained from (7-69) by neglecting ¢ compared with h so that vee 34° he dp cos a da 2 p® ie aa? I? dp sin a da 2 p? (7-81) oan dp cone da p OU), vahsn oe eae (b) Graphical methods. The essence of graphical terrain correction methods is that the influence of the terrain isevaluated not by measure- ments in fixed distances and azimuths but by the use of contour lines and Cuap. 7] GRAVITATIONAL METHODS 220 terrain profiles. For this purpose diagrams are used which contain the outlines of mass sectors of such dimensions that their effect on the instru- ment is identical regardless of distance or azimuth. Hence, the determina- tion of terrain effects is accomplished by ‘‘counting” the number of “grati- cule’ elements encompassed by the successive contours or the terrain profile. In the first case we speak of “horizontal’’ diagrams; in the second, of vertical diagrams. The construction and use of horizontal diagrams is based on the calculation of sector plans of such dimensions that for equal y Fig. 7-77. Cartographic correction with contour lines. elevation their effect on the instrument is equal. An approximation method (Numerov”) and a rigorous method (K. Jung’”) have been de- veloped. Numerov’s method of calculating terrain diagrams rests on eq. (7-69), which, for an element bounded by successive radii py and pp41 and angles Om and Gm41, May be written in the following form, provided ¢’ is negligible compared with p’ in the denominator: 99 Zeit. Geophys., 4(3), 129 (1928). 100 Zeit. Geophys., 3(6), 201 (1927). 228 GRAVITATIONAL METHODS [CHaP. 7 om+1 Pn+1 Use = 3k5(th — 4h?) | mis as oe / nn dp am 3 pn p 2 @m+1 Pn+1 dp Use = kath — 8) [ sinada f f % (7-82) @m+1 Pn+1 dp a ee 3ki-h [ cos 2o da [ a am ° pn p @m+1 Pnt+1 Uy = 3h f sin2Qadaf 2 am pn p Carrying out the integration for a sector of constant elevation h, 3 : : 1 Us: = g ka(ch — 4h’)(sin amy, — sin ca) 4 = =) in Pn+1 Pn Pn41 (7-83) —U, = kéh(sin 2em4. — sin 2an)(+ — =) 2 Pn Pn+1 204 = — iy Sn 20m: — COS 2an)( + = +) 2 Pn Pn+1 Assuming now that ¢h — 3h” = constant = 1; that 6 = 1; that the unit effect is 10°” for gradients and 10° for curvatures; and further that (sin am, — SiN am) = const. and # — cea =const.; (7-84) Pa Pn+i it is possible to divide the entire surrounding topography into elements so dimensioned that regardless of distance and azimuth all produce the same effect. It is not necessary to construct separate diagrams for the east gradient and the northeast curvature. The north gradient and north curvature diagrams may be used for the purpose by rotation through 90° and 45°, respectively. Fig. 7-78a shows a diagram for the calculation of terrain gradients. With the arrow north, the diagram is used for Uz.; with the arrow east, for Uy. The unit effect of the five interior rings is 10”, that of the others 10°“ C.G.8. The diagrams are applicable from 50 to 500 m or 5 to 50 m; however, ¢ must be expressed in the same units ash. If the elevation be- tween two successive contour lines is h, the effect of the contour “‘strip”’ is né(¢h as th’), Cuap. 7] GRAVITATIONAL METHODS 229 where n is the number of ‘‘compartments’’ (or dots) covered and 6 the density. Fig. 7-78) is a diagram for the curvature values, likewise for 50 to 500 linear scale units. The unit effect of five inner rings is 10°”; that of the outer rings, 10°" C.G.S. The calculation of a “‘strip’’ of mean elevation h covering n dots proceeds in accordance with: effect = né-h. In the application of the Numerov diagrams, it must be remembered that they do not hold for very rugged terrain or for very short distances from the instrument, since ¢” is disregarded compared with p’. A rigorous Dope FRO TIX OS \ se Fic. 7-78a. Numerov diagram for terrain gradients. method has been proposed by Jung. Its only inconvenient feature is that lines of equal terrain angle (from the instrument) must be drawn about the station. This method was described before in connection with terrain corrections for gravity measurements (formulas [38c to 38e]). The rigorous mathematical representation of the terrain variation is made possible by figuring all elevations in respect to the center of gravity of the instrument, which eliminates ¢ from eqs. (7-68a). With the angle y = tan (h/p), the gradients and curvatures due to one segment are > SSS CL LTT SSE | WAM 28 Se A SS SSK PATH Fig. 7-79a. Jung diagram (D) for terrain gradients. 230 Cnap. 7] GRAVITATIONAL METHODS 231 Pn+1 fPom+1 dp Us. = — Ks | i (1 — cos’ y) — cos ada en am p pn+1 @m+1 “ dp A Uy = --K5 | | (1 — cos’ ¥) — sin a da n am p t (7-85) pn+1 femti } : dp Uy, = kb / (3 sin y — sin’ y) — cos 2a da pn am p pn+1 fom+i do 2U 25 = k6é / / (3 sin y — sin’ y) — sin 2a da. en am p In these expressions the terms 1 — cos y = G(y) and 3 sin y — sin’ y = K(y) may be obtained for any terrain profile from Fig. 7-39. Carrying out the integrations in eq. (7-85), the following equations are obtained —kiG() log. Pat! (sin Om y — SiN am) Use —kéG(y) log. Pat (cos Om, — COS Am) Po Uy: (7-86) Us = 4k6K (p) loge pai (sin 20mi1 — sin 2am) Pn —1kiK(y) log. Pa! (aos 2am 41 — COS 2am) 2Uy Again only two diagrams are necessary, since the N gradient diagram may be used by rotation through 90° for the E gradient, and the curvature diagram by rotation through 45°. The graticules shown in Figs. 7-79a and 7-79b were calculated by making Pn+1 py Seca Po log = const. = 0.1, sin am, — SiN ag, = const. = 0.05 and 3(sin 2am+1 — sin 2am) = const. = 0.05, so that for both diagrams the product of distance and azimuth factors is 0.005. Hence, for the curvature diagram C the unit effect is 0.333-10 °-6-K(y), and for the gradient diagram D the unit effect is 0.333-10°-5-G(y). For calculating Ua, the C diagram is oriented with the M axis toward N, E, 8, and W. The effects of the N and S quarters are negative and those of the EK and W quarters positive when elevations are positive, and vice versa. For calculating 2U.,, the M lines are oriented NE, SE, SW, and NW. The NE and SW quarters are positive and the SE and NW quarters negative when elevations are positive. Diagram D, for calculating U-., is oriented 232 GRAVITATIONAL METHODS [CHaP. 7 with B north and south and A east and west. For U,,., A is north and south, and B east and west. SN Te < ON EEX PERES wees. LTA con SX SS os, ty TH Ss Se Ley ler TT, Fig. 7-796. Jung diagram (C) for terrain curvatures. The evaluation of lines of equal elevation becomes unnecessary in a method using vertical diagrams proposed by the author.” These dia- Fig. 7-80. Mass element in ref- ’ erence to torsion balance. for y, and r cos ¢ for z, the equations grams are placed through the surrounding terrain in sixteen azimuths; the terrain profile is superimposed on the diagram; and a count is made of the number of elements which are included between the horizon (through the center of gravity of the in- strument) and the terrain profile. The om calculation of these diagrams is based on a determination of the effect of a segment of a spherical shell, such as that shown in Figs. 7-80 and 7-81. Substituting in eqs. (7-66) r sin w cos @ for z, r sin ¢ sin a 101 A.A.P.G. Bull., 18(1), 39-74 (Jan., 1929). Cuap. 7] GRAVITATIONAL METHODS 233 are sin ¢ COS g COS @ Us, = 3k i dm Se STR Tm es 3k [ dm sin ¢ COS ¢ SiN a ae eee Lon Lica, . (7-87) se sin’ ¢ cos 2a Us => 3k it dm eR eee on) 5 3k [ dm gy sin 2a 2U 2 a Since the mass element dm = : : Fig. 7-81. Sphericai shell mass- 6-dr-rdp-r sing-da, the gradients and element. curvatures of one element are @m+1 ¢pt+1 Tn+1 <2 cos ada sin’ y cos gdygdr Use = 3k6 i | | SOY Oe a ae STR am YD ™ rT @m+1 Opti mrn+1 3 ° 2 sin ada sin’ » cos gdyvdr U,. = 3kb i i i sin ada sin’ ¢ cos ydy dr am ¢D fn Ts am+1 Opti Tn+1 OER) cos 2a da sin” edgdr Us, = 3k6 i [ [ yO Oe EO ie Ei aie eae am 9D mn r @m+1.p?pt1 fTnti1 os oo 3 oe = aks | | i sin 2a da sin gdp dr @m YD n r r These four equations may be reduced to two because the azimuthal differences (sin, cos) in the components can be taken care of by rotation of the diagrams. Then the effect of one mass element is Tay Use = k6 (sin amy — SIN am)(sin® v4, — sin® gy) log. on n Us, = —43k6 (sin 2am,, — sin 2am)(cos’ gp — COS’ % (7-88) I r — 3.COS gp, + 3 cos ¢,) log. = : n Evaluation of gradients and curvatures in eight sections, that is, in sixteen azimuths, does not require thirty-two but only six diagrams. Of these, the GI and the CI diagrams are reproduced in Figs. 7-82 and 7-83. Unit effect is 1-107"; scale is arbitrary; and assumed density is 1.0. Their application above and below the horizon is indicated in the scheme in Fig. 7-84. [Cuap. 7 GRAVITATIONAL METHODS 234 Q S: = = Ly Lp Fia. 7-82. Terrain and interpretation diagram GI. \) \) \\ \\ x» 00, Fig. 7-83. Terrain and interpretation diagram CJ. There are a number of other terrain correction methods in addition to those described above which also make use of vertical diagrams. Haalck’s method,” for instance In diagrams are prepared for given azi- ? However, the mass elements are muths as in the author’s methods. 178 (1928). 102 Zeit. Geophys., 4, 161- Cuap. 7] GRAVITATIONAL METHODS 235 treated as cylindrical and not as spherical shells; hence, in any azimuthal section their outlines are rectangles.” The effect of the segments depends on their angular opening and varies with the number of azimuths (eight, sixteen, thirty-two, and so on) in which the diagrams are to be used. The azimuthal effect is then considered by relations resembling formula 6 (6radient) Diagrams C (Curvature) Diagrams Fig. 7-84. Application of vertical diagrams. (7-76). The number of elements between horizon and terrain profile are substituted for the elevations h. Two diagrams are required, one for gradients and the other for curvature values. In a modification of Haalck’s method by Gassmann™ the effects obtained by the evaluation 103 See also H. Haalck, Die Gravimetrischen Methoden der Angewandien Geophysik, pp. 116 and 117 (1929). 104 Beitr. angew. Geophys., 6(2), 202 (1936). 236 GRAVITATIONAL METHODS [CHap. 7 of the diagrams in different azimuths are combined by vectorial addition to a vector of the azimuth a for gradients and another vector of the azi- muth 2a for the curvatures. The justification for this procedure is seen by reference to formula (7-86), since the azimuth terms may be written in the form 2 sin Ae muna: gradients and 2 sin Aa os ae for curvatures. 2 (sin a) (sin 2a) The gradient and curvature vectors of the terrain may then be resolved into their z- and y-components to obtain the corrections for all four gradient and curvature components. (c) Planimeter and integraph methods. If planimeters or integraphs are used, terrain effects are determined by outlining the terrain profile or terrain contours with the stylus of one of these instruments rather than by counting elements as in the graphical methods. Two procedures are applicable: (1) use of ordinary planimeters with contour lines or terrain profiles distorted in respect to horizontal azimuth or vertical angle and distance scale in such a manner that the effect of the mass area is inde- pendent of azimuth and distance; (2) use of special integraphs with contour lines or terrain profiles drawn to undistorted scale. The first procedure was proposed by Below and has been described before in connection with the interpretation of gravity anomalies (page 155). Its applications have been worked out: (a) for the entire surrounding topography; (b) for small elevations at greater distance.” The relations that apply in the first case have been given in eq. 7-85. They contain integrals of the form i ae for both gradients and curvature values which p sin ada (cose) for gradients express the effect of distance, and of the form iL and ih sin ade for curvatures which express the effect of azimuth. (cos 2a) These integrals may be reduced to surface integrals of the form | Hi RdR d® by the substitution R = ~/2 log, p and = sin a, cos a, sin 20/2 and cos 2a/2. These substitutions result in a diagram which is distorted in respect to both scale and azimuth (see Figs. 7-85 and 7-86). On such diagrams lines of equal elevation angle y are plotted and the area S between successive lines is determined with a planimeter so that for the gradients cos a dp =2/f aig (sin a) Pieler eRe ra 106 K. Jung, Zeit. Geophys., 6(2), 114 (1930). Fig. 7-85. Scale distortion for gradients in Below-Jung’s planimeter terrain correc- tion (after Jung). and for the curvatures cos 2a dp Se f ee Gineaa eae) too, 36 For small elevations at greater distances, when the square of the height of the instrument above the ground is negligible compared with the square of the distance, formulas 7-82, containing the integrals cosa | 2 (sin a) “° J 8 238 GRAVITATIONAL METHODS [CHap. 7 for gradients and cos 2a dp (sin 2a) ~~ 5 for curvatures, apply. Hence, the substitutions R = 1/p for gradients and R = +/2/p for curvatures, ® = sin a, cos a for gradients and @ = sin 2a cos 2a 5 and —>» for curvatures may be made. en FR ST AEP ES ION 7. NO LI TG, Fig. 7-86. Scale distortion for curvatures in Below-Jung’s planimeter terrain correc- tion (after Jung). Distortions of diagrams may be avoided by the use of specially con- structed integraphs. The Askania Werke have constructed a special integraph’” for the evaluation of gravity and torsion anomalies which may also be applied to calculations of terrain effects. If the topography around the station has been represented by lines of equal elevation angle, the terrain effects which contain the double integrals ‘| Hl Mite CTS de (sin a) p cos 2a : da uP for curvatures may be written sin 2a) for gradients and | / ( 106 F, Kaselitz, Zeit. Geophys., 8(3/4), 191 (1932). See also p. 269. Cuap. 7] GRAVITATIONAL METHODS 239 in the form of eq. 7-85. The general form of these integrals is / dp cos Na p (sin na) integral of the form alg da, which may be evaluated by the integraph as surface dp sin ng(p) p [cosn¢(p)]’ of this integraph is given in the following section on interpretation of torsion balance anomalies. (d) Field practice in terrain survey; preparation of station site. The accuracy of a torsion balance may be enhanced considerably by a judicious selection of the station site. The location should be as flat as possible, at least to a distance of about 20 meters. Vicinity of ditches, bluffs, embankments, and houses should be avoided if possible. In forests it is advisable to set up the instrument in such a manner that large trees are symmetrically arranged with respect to it. If setups in rugged terrain have to be made, the site should be so selected that the effect on gradients is a minimum. ‘The site should be leveled with a shovel to a radius of 3to5m. In the filling of depressions, the dirt should be tightly tamped to preserve approximately the same density around the station. Leveling the immediate vicinity has the further advantage of avoiding difficulties in setting up the house. After the site has been leveled, a plane table or transit is set up and the ‘far terrain”? determined first (at 5, 10, 20, 30 m, and so on). On the plane table sheet, eight or sixteen azimuths are laid off. If a transit is used, it is advisable to mount a compass on top and to read the angles on it instead of on the horizontal circle. The instrument 1s set up over the station point. One man reads the elevations and takes them down, the other goes around the station and places the leveling rod where directed. A rope or chain with the proper measurements marked on it is used in obtaining distances. It is advisable to carry a rope 20 m long for the average terrain and an extension out to 100 m for more complicated terrains. The rope is laid out first in the north direction and the rod is placed at 5, 10, 20, 30 m, and so on. Then the rope is moved over to the next azimuth and the rod is placed at 30, 20, 10, 5 m, and so on. In some terrains the use of ropes or chains may be impracticable. Some companies have trained their men to pace the distance accurately. In brush country it may be necessary to cut lines for the terrain survey (Fig. 7-87). The rod should be graduated in centimeters; it may be so made that differences in elevation may be read directly. For this purpose the rod is graduated both ways from zero, with red divisions below and black divisions above, red indicating positive elevations and black negative. The foot of the rod carries an adjustable shoe. Before elevations are taken, the rod is placed close to the telescope of the transit and so ad- justed that the zero point coincides with the optical axis of the telescope. A more detailed discussion 240 GRAVITATIONAL METHODS [CHap. 7 After ‘‘far’’ terrain has been taken, three pegs are driven into the ground, and the aluminum base plate is laid on it and so oriented that the north mark is in the astronomic meridian. The “near” terrain (1.5m and 3 m radii) is then taken by placing the leveling rod successively in the eight directions marked on the plate and leveling it with a carpenter’s level. Distances to ground are read at 1.5 m and 3 m distances with a ruler (see Table 32). The density of the surface soil is taken by filling a 1000 cc container and weighing it. If considerable contrast exists between the density of the surface weathered layer and the formation below, its density may Fie. 7-87. Aerial photograph of torsion-balance stations in Mexico. have to be determined separately. Further details on terrain field meth- ods, selection of station, calculations, and the like are given in Directions for the Askania Torsion Balance. The brief directions given above apply to the Schweydar method and may be modified for other terrain methods. Different companies have adopted slightly different techniques in the field and in the calculations (use of nomographs, and so on), but the fundamentals of procedure are more or less the same. With calculation diagrams involving units of equal elevation angle it may be advisable to measure angles directly on the vertical circle of the transit or alidade. 3. Correction for regional gradient. In torsion balance surveys it happens that the gradient and curvature anomaly due to a structure or geologic body Cuap. 7] GRAVITATIONAL METHODS 241 is frequently superimposed upon a larger anomaly due to regional geologic structure or some other larger geologic body. Examples of such regional effects are monoclines, deep-seated intrusions, regional attitude of base- ment topography, geosynclines, and the like. When a local structure is superimposed on such regional features, it is possible that its effect is not immediately recognized in the gradient picture. For instance, in the case of an anticline or dome, the familiar reversal of gradients may not appear in the torsion balance map at all. It can be produced, however, by sub- tracting (vectorially) the effect of the regional geologic feature (see Fig. 7-93). It1is impossible, however, to give general directions for the applica- tion of such correction. The magnitude and direction of the “‘regional”’ gradient depend entirely on distance, depth, and configuration of the regional geologic feature involved. The regional effect may be deter- mined (1) by field measurements and (2) by calculation. Where sufficient well-information is available to establish definitely the absence of local structure and the presence of nothing but regional effect, the regional gradient and its variation with distance may be determined from a suffi- cient number of torsion balance observations. The regional gradient may also be derived from regional surveys with the gravity pendulum or gravimeter. If the geologic feature producing the regional gradient is definitely known, its effect may be calculated by the formulas and procedures given in the following section on interpreta- tion. An instructive example for the application of the regional gradient. correction is given by D. C. Barton’ for the Fox and Graham oil fields in Oklahoma. In mining exploration the “‘regional” feature to be elimi- nated is frequently of very restricted extent and often a geologic body which in the regular usage of the term would likewise be called a “‘local”’ structure, for example, a contact zone, a fault, an intrusion, or the like. What is considered a regional feature depends, in other words, entirely on what geologic feature is sought by the survey. The procedure of correcting for a regional gradient is, therefore, comparable in every detail with the subtraction of a “normal” value from magnetic anomalies. 4. Correction for coast effect. Coast effects are due to (1) the slope of the coastal shelf and (2) variations in water level (tides). The second of these has been discussed before (pages 165-166) in connection with time variations of gravity, and it need not be considered here. That fairly appreciable gravity anomalies accompany the continental shelf had been observed by Hecker. An analysis and theoretical explanation of the effect was given by Schidtz and Helmert.’” Whereas above a buried slope of dense material the gravity anomaly rises gradually from its lowest 107 A.I.M.E. Geophysical Prospecting, 458 (1929). 108 Encycl. Math. Wiss., VI 1 (7), 143 (1906-1925). 242 GRAVITATIONAL METHODS [(CuaP. 7 to its highest value, a negative peak occurs over the foot and a positive over the upper edge of a continental shelf in isostatic equilibrium. For a slope of about 1° inclination, Helmert calculated a positive peak of 53 milligals above the upper edge of the shelf, dropping to about 25 milligals Fic. 7-88. Lines of equal gradients in infinite rectangular tunnel section (after Meisser). 100 km inland. Hence, a coastward gradient is pro- duced along a wide zone which for the slope men- tioned is of the order of 3 E.U., increasing to 5 and more units near the coast. For shelves of steeper slope the effect is correspondingly greater. Like other regional effects the coast effect may be determined by direct ob- servation or calculation and may be deducted (vectori- ally) from the observed gradi- ents. 5. Corrections for fixed masses (other than terrain), effects of underground open- ings (tunnels and the like). Corrections for fixed masses other than terrain are re- quired only in exceptional cases when setups near them cannot be avoided. Fre- quently it is sufficient to cal- culate their effects by assum- ing point masses, linear masses (trees), slabs, or para- llelopipeds. The formulas given for these in the section on interpretation (pages 258- 265) areapplicable. Ifseveral fixed masses are present, it is often possible to reduce or virtually avoid a correction by setting up the instrument so that their effects are com- pensated. On gradients two or more equal masses in symmetrical dis- position cancel; on curvatures three symmetrical, equal masses compensate. In underground work a similar precaution reduces corrections for tunnel Cuape. 7] GRAVITATIONAL METHODS 243 sections appreciably. In the two planes of symmetry of a rectangular section the gradients are zero. However, the curvatures cannot be made zero. The effects of a tunnel of rectangular section, infinite in its longi- tudinal direction, on gradients and curvatures follow directly from the formulas for a vertical step given in the section on interpretation. Figs. 7-88 and 7-89 (after Meisser’”) show the gradient and curvature distribution inside a tunnel which is infinite in the y’ direction. With the notation of Fig. 7-90, Uyz and 2U,4, = 0 and Uy = 2kd(a + 8B) (7-89) Uy. = 2ké log. i ee 14 if the center of gravity of the torsion balance is below the center of the section. When setting up an instrument in the center line of the tunnel so that its height above the tunnel floor can be varied (i.e. along the z aes 0: U2, =, 0, cand Us = 8ké tan | h/a. If the tunnel section is not rectangular or nearly rectangular in section, it is advisable to use the graphical or integraph meth- ods given in the interpretation section for two-dimensional fea- tures and to calculate the effect of the actual tunnel outline. In any event, the instrument should be set up as nearly in the center Fia. 7-89. Lines of equal curvatures in : infinite rectangular tunnel section (after of the section as possible. Al- Meisser). though the curvatures are not zero, their variation with location is least and the correction (if curva- tures are used at all) may be determined with fair accuracy. The tunnel outline can be measured with a device used in excavation, sometimes 109 Zeit. Geophys., 6(1), 17-18 (1930). 244 GRAVITATIONAL METHODS [Cuap. 7 called the ‘‘sunflower.” It consists of a graduated arm rotatable about a horizontal axis, which is shifted until it makes contact with the tunnel wall, thus giving the distance of the wall at any vertical angle from the center of gravity of the torsion balance. The vertical angle of the arm may be read on a dial. If the tunnel is not straight, or if the shape of other subsurface cavities is to be determined, the sunflower may be provided with a vertical axis permitting the variation of section with horizontal azimuth to be obtained. E. GrapHicaAL REPRESENTATION OF ToRSION BALANCE DATA For convenience in interpretation, torsion balance results are plotted as vectors or as curves. The corrections discussed in the preceding section are applied to the instrument z readings algebraically or vec- torially. Geologic interpreta- S SWSSRSULISULS NUS UU SUBS tion is based on the corrected > G values represented by vectors NYY or by curves of gradient and curvature components in ge- ologically significant direc- g tions (usually at right angles a ES SYy NY 4 f Z to the strike). For more y qualitative interpretation or D comparison with gravimeter P Be \ or pendulum data, relative gravity is calculated from gradients and represented in the form of isogams. 1. In vector representation, WOR Mel Ab hacer eee the east gradient (see Fig. Se ge 7-91a), U,z, is laid off to the east if it is positive and the north gradient, Uz, to the north if it also is positive. The resultant vector is the total gradient dg/ds. Its azimuth, a, gives the direction of maximum change of gravity. In plotting curvature values, —U, is laid off toward north and 2U., toward east. The resultant vector is the ‘‘differential curvature,’ R, and it makes the angle 2\ with north. Therefore, it must be replotted. In deing so, it is customary to shift the R line on itself so that the station NY LS NY, Fic. 7-90. Tunnel section. Cuap. 7] GRAVITATIONAL METHODS 245 is in its center. The same procedure is recommended for gradients (Fig. 7-91c). Therefore, tana =" tan 2). = —— (7-90a) 0. OFF Uw R= VUE OU For plotting the vectors, the coordinate axes are drawn through the station in astronomic or magnetic directions, depending on how the in- strument was set up in the field. Use of astronomic coordinates is pref- erable. The scale is generally 1 mm per E.U. Replotting of curvatures may be avoided by using the diagram of Fig. 7-92. The radial lines = : s (b) (c) Fic. 7-91. Method of plotting gradients and curvatures. divide each quadrant into 45° sectors, so that the resultant differential curvature, R (concentric circles) and its azimuth are obtained directly. 2. Vectorial addition and subtraction of gradients and curvatures is useful for visualizing the effeets of (terrain, regional, and so on) corrections. In the case of gradients, vectorial subtraction is possible without difficulty. Fig. 7-93a shows the addition of two gradient vectors, Fig. 7-936 the subtraction of a regional gradient vector. For curvatures, vectorial addi- tion and subtraction must be made by auxiliary vectors of twice the azimuth. In Fig. 7-93c, Ri and R, are the original vectors to be added; Ri and R; are the auxiliary vectors of double azimuth that combine to form the vector R;3. This vector, when plotted at half its azimuth, gives Rs, representing the vectorial sum of R; and R,. Subtraction of curvature values follows a similar procedure. 3. A transformation of coordinates may be desirable for changing observed 246 GRAVITATIONAL METHODS [Cuap. 7 values from magnetic to astronomic directions, or, in certain interpreta- tion problems, for referring different sets of vectors to a uniform system. ONC LERL Fea Re eZ eens Seas SEE HERS g *2Uny E +l, (@) Fic. 7-93. Vectorial addition and subtraction of gradients and curvatures. (b) g The transformations may be made analytically or graphically. If two systems, (x, y) and (z’, y’), make the angle a with each other (positive Cuap. 7] GRAVITATIONAL METHODS 247 from north by east), the two sets of transformation equations for gradients and curvatures are: Use = Uz, cosa — Uy, sin a Uy = Uz. sin a + Uy, cosa Un = Ug cos 2a + 2U zy sin 2a | 2U2y = —Ua sin 2a + 2U zy Cos 2a and : (7-90b) | Uy, = Uz cosa + Uy, sin a Uy. = —Uz sin a + Uy, cos a Uy = Ua cos 2a — 2Uz, sin 2a QU = Us sin 2a + 2U 2, cos 2a. Graphical transformation follows a similar procedure as shown previ- ously in Fig. 7-93, that is, single azimuth projection of components for gradients, double azimuth projection for curvatures. 4. Conversion to curves. Conversion of torsion balance data to curves frequently gives considerable interpretational advantages, particularly where these curves are used with geologic sections through “two-dimen- sional” geologic bodies. Therefore, field traverses and interpretation pro- files are laid out at right angles to the strike when possible. Because of regional or other effects, the directions of gradient and curvature vectors may not coincide with the direction of the profile. In this case they should be projected on the profile, which may be done analytically or graphically. If in Fig. 7-94, ¢ is the azimuth of a gradient vector with reference to the profile direction x’, and y is the azimuth of a curvature vector, the projected values are ag 1 09 COs ¢ and —U) = Reos 2y. (7-90c) Ox 0s In the corresponding graphical construction the gradient vector is pro- jected upon the profile direction as shown. For the projection of the curvature, the construction of the auxiliary vector at twice the angle with the profile is again necessary. For two-dimensional geologic features of virtually infinite extent in the y direction, the (corrected) gradient vectors make the angles of 0° or 180° with the profile direction. The corresponding angles of the curvatures are 0° or 90°. If the subsurface feature is infinite in the y’ direction, ag/dy’, 2U zy, and aU /ayi = Oand —U,, = 0’U/az}. A gradient vector in the z’ direction is then plotted as positive ordinate and a vector pointing 248 GRAVITATIONAL METHODS ~— [CHaP. 7 in the —z’ direction as negative ordinate. A curvature vector at 0° angle is plotted as positive ordinate (0°U/daz}) and a curvature making an angle of 90° with the profile as negative ordinate. 5. Calculation of relative gravity, construction of tsogams. Since the horizontal gradient of gravity represents the slope of the gravity curve, it is possible to calculate the difference in gravity between two points when the rate is reasonably uniform and the distance between them is small. A number of procedures are in use to accomplish the “mechanical integra- tion” of the gradient curve. For close spacings of stations and uniform gradients it is satisfactory to project the gradient vectors on the profile line, to average the projections at successive stations, and to multiply the average by the distance. If gradients are expressed in E.U. and distances in kilometers, g x the gravity anomaly is ob- ae tained in tenth milligals. Cal- culation of the projection of (a) the vectors upon a line con- necting the station is facili- tated by the use of a gradu- ated glass scale or transparent graduated paper. Gravity dif- ferences are added from sta- tion to station along closed loops, and the error of closing . is distributed at the end. A js Yi; aa least square adjustment of the entire net of stations can be (bh) made if desired.” Fia. 7-94. Projection of gradients and curva- A second method of caleu- tures on profile direction. lating gravity differences be- tween stations is based on the construction of tangent polygons (Fig. 7-95b), with the assump- tion that the rate given by the gradient at one station prevails half way to the next. Between two stations, A and B, the projections of the vectors U;, and U;, are plotted as ordinates against unit distance. This procedure, beginning with A, gives the point D on the “Ag curve” for the half-way point E. Hence, the gradient for the second station, B, is plotted as ordinate against unit distance and the point F is obtained on the gravity curve. The procedure is again applied to several sets of stations arranged in closed loops or polygons. Three stations arranged 102, C. Barton, A.A.P.G. Bull., 18(9), 1168-1181 (Sept., 1929). I. Roman, A.I.M.E. Geophysical Prospecting, 486-503 (1932). Cuap. 7] GRAVITATIONAL METHODS 249 for simplicity at the corners of a triangle are shown in Fig. 7-95c. They happen to show a large error of closure which has been adjusted graphically as shown in Fig. 7-95d. The adjustment follows the rule that the tangents at the points B and C must be kept constant, and that the curve must close at A. When gravity differences have been so calculated, “isogams’’ may be plotted as shown in Fig. 7—95e. (¢) (e) Fie. 7-95. Calculation of relative gravity from gradients in station triangle (after Jung). A third procedure is based on a graphical integration of the gradient curve. Stations are arranged on straight lines, and projections of gra- dients are plotted as ordinates in a continuous gradient curve. The station lines should be so laid out that they close back to the original station. The gradient curve is then integrated numerically or by the use of an integraph (such as those designed by Abdank-Abakanovicz, Harbou, 250 GRAVITATIONAL METHODS [CHap. 7 and others) for tracing the curve J f(x) dz, if the curve y = f(z) is given. The error of closure in this method naturally depends much on how closely the integrated gradient curve approaches the true gradient varia- tion. In any event, some sort of an adjustment of the errors of closure is required, as in the other two methods. In areas where gradients are very erratic and near-surface anomalies overshadow deeper effects, a better isogam picture may be obtained by arranging the stations in clusters of three or four, calculating the average vector for the center of gravity of the station polygon, and using this average vector for the isogam construction.” F. THEORY OF SUBSURFACE EFFECTS, INTERPRETATION METHODS 1. Interpretation methods. Interpretation of torsion balance results is based on gradient and curvature maps, isogam maps, or gradient and curvature profile curves constructed as described in the last section. Whether all of these maps and curves or only some of them are used de- pends entirely on the nature of the geologic objects under survey. In oil exploration, a representation of torsion balance results in the form of a gradient, a curvature, and an isogam map is best suited for interpreta- tion. If such a gravitational survey reveals definite geologic units (such as an anticline, a salt dome, or an intrusion), it is better to plot the results as profile curves, since they lend themselves better to quantitative analysis. Gradient profiles are usually more reliable than curvature profiles. In rugged country the latter are often disregarded entirely. Interpretation methods are qualitative, semiquantitative, or quantita- tive, depending upon the nature of the survey, the complexity of the geologic situation (number of effective geologic bodies), and, generally, the amount of geologic information available. Naturally the first step in almost every torsion balance survey is preliminary interpretation by inspection. For this purpose gradient and isogam maps are most suitable. From the appearance of the indications it is possible to determine whether the geologic features mapped are extensive or of local significance, whether they are of three-dimensional proportions or extended in the direction of strike, whether they occur at great or at shallow depths, whether their outline is well defined or gradual, and so on. An observer acquainted with the regional geologic possibilities will be able to arrive rather rapidly at a preliminary interpretation of the geologic significance of the anomalies. The reliability of these preliminary findings is enhanced considerably if local geologic or geophysical information is available from outcrops and 11 J. Koenigsberger, A.A.P.G. Bull., 14(9), 1222 (Sept., 1930). Cuap. 7] GRAVITATIONAL METHODS 251 wells, or from magnetic, seismic, and electric surveys. Even the pre- liminary interpretation of a torsion balance map requires close cooperation of the physicist and the geologist, or else the geologist must acquire a good working knowledge of the theory of subsurface effects (that is, he must be able to appreciate the physical possibilities), and the physicist must be familiar with the geologic possibilities to avoid misinterpretation of the results. In any event, it is advisable, wherever possible, to start a survey in an area where geologic information from outcrops, well records, or underground workings is available. The preliminary interpretation of an isogam or a gradient map will often indicate the need for a revision of the map by allowing for a regional gradient. How this correction is applied depends entirely upon the geologic situation. It is a trial-and-error proposition and may require a considerable amount of work, which, however, more than pays for itself in the quantitative analysis. The qualitative interpretation of such a corrected gradient or isogam map has as its first objective a delineation of the areas which are structurally high and low or which represent oc- currences of heavier and lighter masses. In this preliminary phase it is quite permissible to consider an isogam map as the equivalent of a geologic contour map. Subsequent quantitative analysis will then determine whether the gravity anomalies are due predominantly to one or several geologic features. It is evident that the deviation of the isogam map from the equivalent contour map increases with the number of effective geologic bodies or formations. Further determination of the type of geologic body or structure produc- ing a gravitational high or low is possible by estimating its outline, strike, dip, and approximate depth from the anomaly. The outline is given by stations characterized by the longest gradient arrows, by a crowding of the isogams, and by small curvature values (located between stations with different directions of the R lines). The strike of geologic bodies may be expected to be parallel with the trend of the isogams, at right angles to the gradient arrows, and parallel with (or at right angles to) the R lines. The dip of geologic bodies is frequently indicated by the isogam interval, the length of the gradient arrows, and the magnitude of the R lines (com- pare, for instance, Fig. 7-99h with Fig. 7-992). Regional dip is indicated by uniform magnitude and direction of gradient arrows through consider- able distances. An indication of depth may be obtained from the rapidity of changes in the gradient and curvature values in horizontal direction. The type of change in direction and the magnitude of gradients and curvatures in the direction of strike indicates to what extent geologic bodies may be considered two-dimensional. Fortunately, most forma- 252 GRAVITATIONAL METHODS [Cuap. 7 tions and ore deposits are of two-dimensional character; they allow repre- sentation of the field findings by gradient (or curvature) curves, and a somewhat more quantitative interpretation. The following rules apply in semiquantitative interpretation of anomalies due to two-dimensional and some three-dimensional bodies: (a) If but one density contrast is effective, the Ag curve is approximately parallel with the outline of the subsurface feature and the isogams represent approximately its surface contours. (b) The gradient arrows point toward the highest point of the sub- surface feature. Their magnitude is approximately proportional to the rate of change of subsurface density in horizontal direction. Maxima occur above points or areas of greatest dip; zero points occur above the lines of symmetry of anticlines, vertical dikes, and the like. When a gradient curve has only positive values, a subsurface feature rises,in one direction only. The curve is symmetrical if there occurs a vertical face. Positive and negative values are observed in the gradient curve if the subsurface feature is limited across the strike. If the positive and nega- tive gradient anomalies are symmetrical, the boundaries of the subsurface feature are vertical on both sides or dip equally in opposite directions. If the anomalies are unsymmetrical, the two boundaries dip equally in the same direction (inclined dike) or unequally in opposite directions (anti- cline with unequal flank dips). (c) The (curvature) R lines are parallel with the strike of heavier sub- surface features above them, but they are small and perpendicular to the strike beyond them (see, for instance, the curvature anomaly of a fault block in Fig. 7-99b). The magnitude of the lines depends in a general way on the curvature in the outline of the heavier masses below the surface; or, if the outlines are straight for short distances, on the rate of change in their direction. Hence, the curvature values are greatest above the center of a dike or plug-shaped mass, above the crest of an anticline, or above the trough of a syncline. Zero points of curvature values frequently occur above abrupt subsurface changes from light to heavy masses. They coincide sometimes with points of maximum gradient, and vice versa. In semiquantitative interpretation, extensive use is made of “type’’ curves calculated for geologic features most frequently encountered, such as vertical and inclined faults, vertical and inclined dikes and slabs, sym- metrical and asymmetrical anticlines and synclines, and so on. How these are calculated is further explained below. An extensive file of such curves for a variety of depths, dimensions, and dispositions of geologic bodies is of considerable help in a preliminary analysis of torsion balance data and reduces the work required for a quantitative analysis. Cuap. 7] GRAVITATIONAL METHODS 253 Contrary to semiquantitative analysis, quantitative analysis requires an evaluation of the anomalies by calculation in each particular case. The approach may be direct or indirect. The direct methods are applicable only where one geologic feature exists, where the geologic situation is simple, and where the geologic features have or approach the shape of simple geometric bodies. Direct methods make use of the magnitude of the anomalies in gradients, curvatures, and relative gravity at the points of symmetry or maximum anomaly; or they utilize the abscissas of zero, maximum, minimum, or half-value anomalies to calculate depth, dimen- sions, and disposition of geologic bodies. The application of direct methods of interpretation is confined largely to mining problems and to ore bodies of simple character. Its application in oil exploration problems is the exception rather than the rule. Indirect interpretation methods are applicable in all interpretation problems. Their principle is as follows: From the results of qualitative and semiquantitative analysis the assumption is made that a gravitating body has a definite shape, depth, and density. The anomalies of this body are then calculated and the results of such calculations are compared with the field data. The assumed body is then changed with regard to its different parameters until a reasonable agreement between field data and calculated anomalies is secured. This is a trial-and-error method, and fairly laborious; however, it has been very successful when applied with patience and supplemented by geologic data. It is the only interpreta- tion method that can be used when a number of geologic bodies or forma- tions are effective. It is superior to qualitative analysis where sufficient geologic or geophysical information is available to limit the number of possible combinations of bodies capable of producing a given anomaly. In all semiquantitative and quantitative torsion balance interpretation methods, it is necessary to know what type anomalies are produced by geologic bodies of a given shape, density, and depth. They may be cal- culated (1) analytically, (2) graphically, or (8) by integration machines. Regardless of calculation method, the fundamental relations are the same in all methods, but they differ depending upon whether they apply to two- or three-dimensional bodies and are derived from the expressions for the Newtonian and logarithmic gravity potentials given in eqs. (7-39b) and (7-39e). It was shown before that gravity was obtained from these po- tentials by differentiation with respect to z. Likewise, the horizontal gravity component would be obtainable by differentiation with respect to z. Therefore, the gravity gradients and curvature values follow by dif- ferentiation with respect to x and y, respectively, of the vertical (eqs. 254 GRAVITATIONAL METHODS [CHaP. 7 [7-39c] and [7-39f]) and horizontal gravity components. Then the gradi- ents and curvatures are (a) for three-dimensional bodies (v = volume): a= a0 ff] giv = ans {ff aeavde = ou fff '$ar~u fff U,. = 3ké [Tf 7 dv = 3ké = dx dy dz (7-91a) vem aie [J as av = 3m f ff" Bs Bee ee CY ty 2U., = 36 | { {Hao = aes [ff ™ axayae (b) for two-dimensional bodies (S = surface): Uv. = 48 [| [ as = 445 [ | avac ip fe s s Uy. = 0 2U2, = 0 (7-91b) LU, = or in polar coordinates: oe Soe 2 dy i (7-91c) 2 ieee a I ee aes 2. In analytical methods of interpretation, the above equations are used for calculating the anomalies of bodies of simple geometric shape. To illustrate the development of these formulas, it is useful to begin with the simpler forms (point element, line element, spherical body, cylindrical body), although it is, of course, realized that geologic bodies occurring in nature never have such shapes and rarely approach them. The gradients and curvatures of a point element are given by eqs. (7-66) CuapP. 7] GRAVITATIONAL METHODS 255 and (7-91la). In polar coordinates, x = p cos a, y = psina, p = T cos g, and z = r sin g, so that Uz = 3kdm cL ae = = 3 kdm sin 2¢ COS a 2 7 eran ee egg te elite yz 7 5) a (7-92a) U, = —3kdm pee = —3kdm pee eee 2a 2U x, = 3kdm ® pS Ae = Bind EGA bradients GS 4HI27 12353 4 5 meters (Curvatures Fic. 7-96a. Effect of three-dimensional mass on gradients and curvature values (after Jung). The following conclusions may be derived from these equations: The torsion balance anomalies of three-dimensional masses are (1) inversely pro- portional to the cube of the distance, other things (horizontal and vertical azimuths) being equal; (2) proportional to the single horizontal azimuth for gradients and the double horizontal azimuth for curvatures; (3) pro- portional to the sine of the double vertical angle for gradients and the square of the cosine of the single vertical angle for curvatures. By comparisor. with eqs. (7-91a) and (7-91c) it is noted that for two-dimen- sional features the effects are inversely proportional to the square of the distance and to the sine and cosine of the double vertical angle. For the anomaly of a sphere, the same formulas ((7-66], [7-91a], and [7—92a)) apply by substitution of the total mass, M, for the differential mass, dm. 256 GRAVITATIONAL METHODS [CHaP. 7 K. Jung’” has published a number of diagrams showing the effects of spherical masses on gradients and curvature values (see Fig. 7—-96a). If C (= curvature) is an abbreviated notation for —U4/2ks and G (= gradient) for U,,/2k6, then the depth, D, to the center of the sphere is DiS 226 max. a 1.232 inax.3 its radius is (7-92b) R = 0.949 Cnax.-D = 0.823 Ginax,-D. : . . 7 C 113 For cylindrical disks, cones, and paraboloids of rotation ~ the curvatures : : : 114 and gradients for points on the axis are zero. Lancaster-Jones ~ has Fig. 7-96b. Rectangular unsymmetrical slab. calculated the gradients and curvatures of a vertical line element and of a thin cylinder in order to arrive at a correction for the influence of trees in densely wooded country. For the development of graphical interpre- tation diagrams, the following relations for rectangular slabs are of im- portance. If in Fig. 7—-96b z, is the depth to the upper surface, 22 the depth to the lower, x; the distance to the south, and z2 the distance to the north face of a rectangular slab whose extension in the strike is given by toward east and y2 toward west, and if distances to the corners are indi- cated by numerals 1 to 4 in the east and by 5 to 8 in the west, integration of eq. (7-9l1a) results in 12 Handb. Exper. Phys., 25(8), 160-161. 113 Tord. 114 A.I.M.E. Geophysical Prospecting, 508-509 (1929). Cuap. 7] GRAVITATIONAL METHODS 257 testo es ret yo tye | ee ‘irs tye ety Tat yi Ts + Ye Ta steele Eat toes Nrecte ae he atc) CA Un = bo tog.| i a z| < = + 2 “te + 21 ouctae Diw te =e" Le ta re + 2 Ta + 22 a] U, = ké lo ah C © oe . : : Yo + 22 75 + 2% 13 + 21 73 + 22 —U, = ké | tan vege tan fm 5 tame YI tang (7-92c) L278 Yor L273 Y173 ee tans ee tan: ee ee ane? cane X15 Y2rs Li72 Yire eet eta ete tetris 171 yrs 2176 Y2T6 Sani ean ita | tan eal L274 Yr L277 Yor7 When the slab is symmetrically disposed in respect to the profile plane, Y=) = —Ye,m1 = 75, = 1,73 = 77, and m% = 7g; the U., and U,, components vanish and the gradients and curvatures become = a UO Re] Ta Fy Use = ké lo le : ; 2 Tk OR oa Oe ein ea ate a tH Wii 2ks | tan HE) tama) & dane ae + tan a a (7-92d) : 3 L214 Yr4 Lig es eee Salon La ag a 2171 yr} %172 Ylo It is convenient to consider the gradients and curvatures due to a hori- zontal line of limited strike extent since this gives the possibility of deriving an approximate formula which will indicate when it is permissible to con- sider a three-dimensional feature as two-dimensional. If p is the radius vector from the station to the line of the section dS in the profile plane and if + b is its extension at right angles thereto, then Uy, and 2U,-, are zero, and the gradient and curvature component follow from integra- tion of eq. (7-9la) and series expansion of the expressions involving = b(1 + p/b)': 258 GRAVITATIONAL METHODS [CHap. 7 +b , 2 Us. = 3 hb-d8-p sin 2¢ [= 4h5.a8.7 ar -3(°) i =| pt 8\b +b 22 2 2 ign = —3kb-d8 [ Ey eae) 3 pe p 2 canto! (149. Ca (7-92e) When the extension of the line is +, the second terms in the brackets vanish and the two-dimensional values as given in eq. (7-91b) remain. Hence, these terms indicate the error committed when limited features are considered two-dimensional. According to Jung’” an error of 1 per Gradients 54521 123435 wmlers Curvatures a 5* 564m? ; d=1 Fia. 7-97. Effect of two-dimensional mass (cylinder section) on gradients and curva- ture values (after Jung). cent is produced in gradients when b is less than 2.5p, and the same error arises in curvatures when 0 is less than 12. For gradient calculation it is therefore permissible to consider most geologic features of elliptical out- line as two-dimensional in interpretation calculations. As an example of a two-dimensional feature, consider the torsion balance anomalies due to a horizontal cylinder. These anomalies follow directly from eq. (7—91c) and are Us: = 2kdR x a and (7-93a) iar Uy = QksR? x sos ee J "8 Handb. Exper. Phys., 25(3), 184 (1930). Cuap. 7] GRAVITATIONAL METHODS 259 where F# is the radius of the cylinder. Fig. 7-97 illustrates the action of a horizontal cylinder in the form of lines of equal position for a given effect on gradients and curvatures. It is seen that the curvature is insensitive Fig. 7-98. Two-dimensional bodies: (a) cylinder, (b) slope, (c) symmetrical anti- cline, (d) symmetrical syncline, (e) inclined dike, (f) vertical step, (g) rectangular slab, (h) infinite vertical dike. to masses 45° below the horizon and most sensitive to those directly be- neath and in the horizon. The gradients, on the other hand, are insensi- tive to masses in the horizon and directly below, and most sensitive to 260 GRAVITATIONAL METHODS [CHaP. 7 masses 45° below the horizon. The gradient anomalies of two- and three- dimensional masses are therefore quite similar in respect to vertical angle and differ only in regard to distance power. In the curvatures, an exten- sive strike dimension produces sensitivity in the vertical direction in addi- tion to that in horizontal direction. The depth to center, D, and radius may be determined, as in eq. (7-92b), from the relations” De BK ls J 1.7326 = 0.5782¢ max. max. Rech Le (7-93) R = 0.564V Cinax.:D = 0.700W Ginax.-D, where Zc, is the abscissa of the point of zero curvature anomaly (see Fig. 7-99). Other two-dimensional features are illustrated in Fig. 7-98, such as anticlines, synclines, inclined dikes, vertical steps, slabs, and vertical dikes. Their anomalies may be calculated readily from those of a slope (Fig. 7-98b). The calculation involves essentially the integration of formula (7-91b). For the gradient this may be written, with the notation D -) of Fig. 7-98b, Uz, = 2ké if zdz i, ae where x = 2 on the sloping d Zo edge. Using ro = 2 + 2, ¥ =a —@, mdy = ds sin a, and dz = ds e sin a, we have Uz, = 2k6 i : dgo Sin a sin go/sin y or Uz, = ké |2 sin’ a wy loge = — sin 2a(¢g2 — o) | Thus, with the dip angle 7 = a — a, and 1 similar analysis for the curvature, U,, = 2ké sin i| sin z log. ~ + cos z(g2 — o | 1 (7-93c) —Uy, = 2ké sin i| sin i(¢2 — gi) — cos 7 log, = L For direct interpetation it is useful to know that the center between the extremes in the curvatures is situated above the center of the sub- surface slope. With this point as origin, the abscissas of the maximum gradient and curvature values are given by PRES Ne Gmax. —_ 2(D ahs d) = 1W4Dd + (D — d)’ cotan? i. cotan 1; Ic max. For complete depth and dip determinations, diagrams have been con- structed by Jung.” 116 Jung, Zeit. Geophys., 3(6), 267-280 (1927). U7 [bid. Cuap. 7] GRAVITATIONAL METHODS 261 (a) AN SST TAN RR (c) (€) Fig. 7-99a-e. Gradients and curvatures for two-dimensional features (after Jung). (Fig. 7-99f-7 on page 262.) G=Gradient, K=curvature value. 262 GRAVITATIONAL METHODS [CHap. 7 Above an extended slope (see Fig. 7-99) log. 5 =Oandm—-g=r 1 so that Us. = kia sin 2 (7-93d = Qkde sin’ 7. ) | eal a I (h) Fic. 7-99f-7. Gradients and curvatures for two-dimensional features, continued (after Jung). G=Gradient, K=curvature value. For small angles sin 7 & 7; therefore, the gradient on extended slopes is Un. = Qhirt = 7.36° E.U., (7-93e) which is a useful formula for correlating regional dip and regional gradient. In all these formulas, 6 signifies, of course, difference in density. If 7 is expressed in radians, the coefficient in eq. (7-93e) is 419 E.U. Cuap. 7] GRAVITATIONAL METHODS 263 In the calculation of symmetrical anticlines, the curvatures due to two opposite slopes given by eq. (7-93c) are added and the gradients sub- tracted so that Uz. = 2ké sin i| sin 1 log. = + cos 1(@,; — ®) 2 (7-93f) che al meee re ; T1712 —Uy = 2ké sin 2 sin 1(@; + bd.) — cos 7 log, Hl 3 For a symmetrical syncline, Uz, = 2ké sin i| sin 7 log. ~ — cos 2(@; — Bo) 2 (7-939) Thies Wee ; T1T2 —Uy = 2k6 sin 2 sin 1(@; + 2) + cos 7 log. a 3 It should be noted that in Figs. 7-98c and 7-98d ® stands for difference in angle. K. Jung’ and H. Shaw’ have calculated a number of diagrams to assist in direct determinations of the characteristics of anticlines and synclines from gradients and curvature values. To obtain the gradients and curvatures for an inclined dike as in Fig. 7—-98e, two slopes (eq. [7—93c]) are deducted from each other, so that with the notation indicated in the figure, Ue, = 2ks-sin i| sin 1 log. ao + cos i(ge — 1 — gs + ¢3) 1/4 (7-93h) Sule) Mae ae ‘ rer —Uy = 2k6 sin é sin i(e2 — g1 — gs + 3) — cos 7 log, ae : 1/4 Usually the depth extent of the dike is considerable, so that Uyz = 2k6 sin i sin 1 log. 2 + cos 2(y3 — o | 1 —U,: = 2ké6 sin isin 1(¢3 — v1) — cos 7 log. = 1 If the gradient at the origin (x = 0 above the center of the upper face) (see Fig. 7-99) is Go = Gmax. + Gmin. and if the curvature Cy = Cmax. + Cmin., then cotan 7 = Co/Go, and Go = 3 sin 27h) (&) = ©& for xz = 0); d = (w/2) cotan @/2. For the last calculation, special diagrams 118 Tbid., 3, 257-280 (1927) ; 5, 238-252 (1929). 19H, Shaw, A.I.M.E. Geophysical Prospecting, 336-366 (1932). 264 GRAVITATIONAL METHODS [Cuap. 7 using the distance between the extremes in gradients and curvatures have been constructed by Jung. The dip angle may also be calculated from the ratios of gradient maxima and minima. The direct interpretation of torsion balance anomalies of vertical and inclined dikes has been dis- cussed in detail by H. Shaw.’” By letting 7 = 90° in eq. (7—-93c), the gradient and curvature anomalies of*a step with a vertical face (fault, escarpment, or the like) are obtained. With the notation of Fig. 7—98f, Uy: = 2ké log ike ue (7-94a) —Uxn = 2k5(¢2 — ¢1). The upper and lower depths follow, therefore, from the amplitudes and abscissas of the extremes in gradients and curvatures, thus: aD = (te Ne = (t¢,) max, (7-94b) d logio D = 0.4388Ginax. The anomalies of a block with vertical faces, as in Fig. 7-98g, may be ob- tained by subtracting two faces, as in eq. (7-94a) or by letting 7 = 90° in formula (7-93h). Then Ug, = 2ké log, tals ala (7-94c) ap Ae a 2k (yo oa OV G4 a 3). For direct interpretation, it is helpful that the curvature at the symmetry point, z = 0, is equal to twice the angle subtended by the upper and lower edges. Hence, Cmax. = 2¢., where go = (¢1 — ¢2)r=0 = (4 — $3) 2=0- The complete determination of depth and outline is possible by means of diagrams constructed by Jung.” When the dike is of infinite depth extent, rs ® re and gs & ¢2, so that with the notation of Fig. 7-98h, Us, = 2ké log. ze | me | (7-94d) —Us,: —2k5®. 120 Tbid, 121 Zeit. Geophys., 3, 257-280 (1927); 5, 238-252 (1929). Cuap. 7] GRAVITATIONAL METHODS 265 Since Crax, = ® and rg ,,, = 7, the depth and the width, according 122 to Jung, ~~ are P d = 79 cos . and (7-94e) nD, w = 270 sin a : It is possible to approximate the outline of two-dimensional masses of irregular shape by using a polygon with straight sides and applying formula (7-93c) repeatedly, as proposed by Matuyama and Higasinaka.”” How- ever, it is easier in such cases to use the graphical methods described in the following paragraphs. 3. Graphical interpretation methods make use of diagrams containing mass elements in section or plan view in such an arrangement that their effect on a station (0-point) is identical irrespective of distance or azimuth (see also pages 153 and 227). For three-dimensional subsurface features of moderate relief the diagrams calculated by Numerov, discussed on page 228 and illustrated in Figs. 7-78a and 7—78b, are applied in connection with subsurface contour maps, and strips bounded by successive contours are evaluated. Then the height of the instrument above ground ¢ cor- responds to the depth, D, of the effective geologic feature beneath the in- strument. The mean “elevation” of a contour strip with respect to this point is h = D — d whered = (d; + de)/2, or the mean of the depth values of two contours. 61s the density contrast. If n,is the number of elements comprised by a contour strip in the curvature diagram and n, the cor- responding number in the gradient diagram, the effect of one strip, (sub- script st), is (Uzz)et 7 4§.n,-(D° a d’) (7-95a) (UA = b- nips a)s For determinations of U,, and 2U,, the diagrams are rotated 90° or 45°, respectively, as in the terrain applications. For steep slopes of subsurface features the accuracy of horizontal (contour line) diagrams is insufficient, and vertical diagrams such as shown in Figs. 7-82 and 7-83 must be applied with geologic sections through the geologic body in a number of azimuths. Although the diagrams under discussion have been calculated 122 Thid. 123 Japan. J. Astron. and Geophys., 7, 47-81 (1930). 266 GRAVITATIONAL METHODS [Cuap. 7 for sixteen azimuths, they may readily be modified for fewer directions by changing the azimuth factor in eq. (7-88). These diagrams are particu- larly suited for the calculation of.salt domes, cap rocks, irregular ore bodies, mine cavings, and the like. Certain two-dimensional diagrams are applicable to such geologic features as domes or anticlines if a definite variation of strike extent with depth of the elements (Barton) is incorporated. u; Yer Fria. 7-100. Orientation of two-dimensional interpretation diagram (Fig. 7-79b) for gradients and curvatures (after Jung). Diagrams for two-dimensional bodies are readily calculated, since their surface effects depend on section only. Calculations are a minimum with cylindrical coordinates. Integration of eq. (7-9lc) gives Uz, = —ké log. me (cos 2¢m,, — COS 2¢m) ? (7-950) Us = —kéd log, ae (sin 2m: — SiN 2gy_) for an element bounded by radii r, and ry,, and angles gp, and gm. (as in Fig. 7-79b). A comparison of these equations with the last two in eq. 7-86 shows that the curvature terrain diagram of Fig. 7-79b may be used for calculations of gradients and curvatures of two-dimensional masses. Eq.. (7-95b) indicates 45° symmetry and therefore the orientation for gradients and curvatures differs by 45°, as shown in Fig. 7-100. The unit effect is ? E.U. For evaluating horizontal or nearly horizontal forma- tions, it is more convenient to arrange the mass elements along horizontal lines and therefore base the calculations on formula (7-94c). In a form Crap. 7] GRAVITATIONAL METHODS 267 better suited for determining the vertical boundaries of mass elements in a horizontal bed this may be written 2 2 2 2 Xi +22 t+2Z nein los ( aT a ‘) LORS erates cera (7-95c) —Uy = 2ké (tan™ fa + tan? a — tan 2 21 = tan? 4 nal T2 V1 Xo Fic. 7-101. Interpretation diagram for two-dimensional features (after Barton). Diagrams based on these equations are shown in Figs. 7-101a and 7-101b."™ In the calculation the vertical sequence of formation boundaries is deter- mined by the assumption that zp41 = (10/9)z,. Therefore in semilog- arithmic representation, as in the figure, the vertical formation interval is 124 1), C. Barton, A.I.M.E. Geophysical Prospecting, 489 (1929). 268 GRAVITATIONAL METHODS [CHaP. 7 constant which, however, necessitates a replotting of the geologic section to that scale. A limited strike extent proportional to depth (as in salt domes and anticlines) may be introduced as shown in Figs. 7—iOlc, d, e, and f. Calculations of the anomalies are then based on formulas (7—92d). 4. Planimeter and integraph methods may be used for the calculation of torsion balance anomalies from known or assumed outlines of a geologic body. Since, according to eq. (7-91c), the action of a two-dimensional feature depends not only on area but also on distance and vertical angle, the area to be evaluated must be replotted to suitable scale before a regular OY ee ete MeO ee Fig. 7-102a. Scale distortion in Below-Jung planimeter interpretation method for two-dimensional bodies (after Jung). planimeter can be applied to give the torsion balance anomaly (Below method,” see eq. [7-44b] and Figs. 7-46 and 7-47). To convert the double integral in eq. (7-9lc) into a surface integral independent of azi- muth and distance, the substitutions R for +~/2 log. p, ® for $ sin 2g, and 3 cos 2y, respectively, are necessary so that the gradients and curvatures are proportional ff R d@dR after the scale distortion has been accom- plished, as shown in Fig. 7-102a. A direct evaluation of gravity integrals without scale distoriton is pos- 125 Jung, Zeit. Geophys., 6(2), 114-122 (1930). Cuap. 7] GRAVITATIONAL METHODS 269 sible with the instrument illustrated in Fig. 7-102b. It gives the surface integrals sin ng it / sin ng dr 5 {| if ee ae fog and ee ae", (7-96a) s s where the apparatus will take multiples up to n = 3. The first integral applies in the first derivatives of gravity (horizontal and vertical gravity American Askania Corp. Fie. 7-102b. Torsion balance interpretation integraph. TABLB 34 APPLICATION OF GRAVITY INTEGRAPH E Quantity £ Quantity E Quantity au : oU P Pendulum; : az! « ff sine de ar ; oz « ff sin 29 dp ar Gravimeter au 2 i oa J f cos v dy dr |3 ~ a J f c0s 29 dy dr 3} Uzg « ff ein apes 2} Us'g & [fein 290 = 3| Uz & J fein Spee Torsion ui y r Bal meat 3 Urs « ffoospay= 2 Ua’ « ff co 2p ay = 3 Ua « ff cw sede components); the second in the second derivatives (gradients and curva- ture values). The factor n depends, among other things, on whether the integral applies to a two- or three-dimensional body as illustrated by Table 34. For three-dimensional bodies the volume integrals are reduced to surface integrals by evaluating the sections of geologic bodies in various azimuths, plotting the effect as a function of azimuth (polar diagram), and evaluating the resulting area with the same integrometer. 270 GRAVITATIONAL METHODS [Cuar. 7 With one of the integrations carried out, the gradients and curvatures as measured by this instrument are, therefore, for two-dimensional bodies: Tr. $2 ub} We. = 2k6 it if sin 29 ag Ko ik _ (cos 2¢1 — cos 2¢e) TI ¥1 T1 (7-96b) rape? dr ads ae 4 Ug: = 2kb cos 29 dy — = ké — (sin 2g. — sin 29;) ry %¢1 r nye hy ) and for three-dimensional bodies: ae #2 r2 A dr Use = 3k6 / / if cos a da (sin y — sin* vg) dg — aio ny r i fail; 1 3 1 3 = ké cos ada a (cos 3¢1 + 2cos v1 — +. cos 3¢y2 — 2 cos ge) ay uss Uy. = same with sin a instead of cos a. (7-96c) ag 2 r2 3 dr —Us = 4h | | / cos Za da-cos’ » dg. — | a, %o, “rh r 7 Sra PR ditvciie aa tite fi =k] cos2ada a ({sin get++sin 3¢go—#sin g,—4sin 3¢1) ay ry U,, = same with sin 2a in place of cos 2a. J The mechanism of this integraph is enclosed in a circular case and pivots about a point near the supporting base, this being equivalent to rotation about the angle ¢. The variation in the r direction is brought about by radial motion of the pointer touching the board, which by a rack and pinion movement rotates a keyed shaft shown in the center of the arm assembly. This instrument is probably the most advanced means for a rapid determination of torsion balance anomalies and has an ac- curacy of 1 to 2 per cent. A simple integraph for the evaluation of two- dimensional features has been constructed by Gamburzeff.’” G. Discussion oF ToRSION BALANCE RESULTS 1. Measurements on lakes. The logical approach to the verification of the theory of subsurface effects discussed in the preceding section is a measurement of the anomalies due to known subsurface mass distributions. Most suitable for this purpose are frozen lakes, whose bottom contours are usually well known from soundings. Measurements on the ice are readily made. The instrument can be moved from one point to an- other on skids, and terrain corrections are usually negligible. Edtvés, 126 Gerl. Beitr., 24, 83-93 (1929). Cuap. 7] GRAVITATIONAL METHODS 271 himself, was the first to realize the merit of lake measurements.” Even before he had developed his double gradient and curvature variometer, he surveyed thirty-three stations on the ice of Balaton Lake in 1901 and twelve stations in 1903. Similar measurements were made in 1924 by Holst’™ in the Black Forest on Lake Titi. This lake is of glacial origin. Its greatest depth is 39 meters, and the bottom formation is gneiss covered S| oe o eo @ o ¥0 50 0 $0 100 150 200 250m EE SS ee | SCALE Fic. 7-103a. Bottom contours (in decimeters) of Lake Shuvalovo (after Numerov). by a thin layer of morainal material. The observed torsion balance anomalies were large because of the large density difference between water and rock (1.7). Since the lake profile was well known from soundings, the observed indications could be compared with theoretical anomalies (calcu- lated by means of the slope formula [7-93c]). 127 R. v. Kétvoés, Result. wiss. Erforsch Balatonsees, Vol. I, Geophys. Appendix (1908). 128 EH, Holst, Zeit. Geophys., 1, 228-237 (1924-1925). 272 GRAVITATIONAL METHODS [CHaP. 7 Fig. 7-103 illustrates the results of very careful measurements made by B. Numerov™ on Lake Shuvalovo near Leningrad, which proved to be a suitable study object since its maximum depth is only 13 meters. In its middle a sand ridge comes within 1 meter of the surface. There is an almost complete identity of the isogams and isobathic lines. Since in the formula Ag = 2k7é6h, the factor 27k is equal to 42 E.U., the variation in Fic. 7-1036. Isogams and gradients (in 0.01 milligals) on Lake Shuvalovo. depth of the lake bottom may be predicted from Ah = Adg-10°/426. The density difference wasone. An anomaly of 1.37 milligals corresponded to the sand bank previously mentioned. 2. In oil exploration the torsion balance has found undoubtedly its greatest commercial application. Its possibilities for mapping subsurface 129 B. Numerov, Zeit. Geophys., 5, 276-289 (1929). Cuap. 7] GRAVITATIONAL METHODS 273 geologic structure were realized at an early date by Hugo von Boeckh™” who gave an interpretation of some of Eétv6és’ earlier surveys and sug- gested to him and his assistants the study of oil structures. Fig. 7-104 illustrates relative gravity values calculated from torsion balance measure- ments for a profile in the Maros Valley in Hungary. It is seen that the Scale 100 —-— 100 Fig. 7-108c. Curvatures on Lake Shuvalovo. gravity minima correspond closely to the uplifted positions of the salt beds and to the salt anticlines. Following Boeckh’s publication, attempts were made in other European countries to utilize the torsion balance for the mapping of salt domes and salt anticlines. In 1917 W. Schweydar™ observed the gravity gradi- 130 H. v. Boeckh, Petroleum, 12(16), 817-823 (1917). 131 W. Schweydar, Zeit. Prakt. Geol., 26, 157-162 (Nov., 1918). 274 GRAVITATIONAL METHODS [Cuap. 7 ents on the Nienhagen-Haenigsen salt dome and oil field (northern Ger- many) and found them to be larger on the west side because of the steep dip of the Mesozoic beds and the overhang of the dome. The Wietze oil field of northern Germany was studied extensively with geophysical meth- ods. Fig. 7-105 shows seismic refraction profiles, the outline of the dome deduced from them, and the results of torsion balance and pendulum measurements. The outline of the dome given by the torsion balance checks closely with that furnished by the seismograph. Another north German structure studied extensively with seismic-refrac- tion, electrical, magnetic, and torsion balance methods is the Litbtheen salt dome, whose section is well known from borings and potash mines.” As shown in Fig. 7-106, the outline of the dome is very well indicated by the gradients and curvature values. Contrary to Gulf coast experience, no gravity maximum occurs, despite a well developed cap rock. The main purpose of the survey was to determine the extent of (potential ZAC a ane TLE ccere CPO eg eer rie A 1 kin Fic. 7-104. Gravity anomalies on salt anticlines in the Maros Valley (after v. Boeckh). oil-bearing) Mesozoic strata around the dome. These strata are well developed on the east flank of the dome, give rise to a reversal of the gradients, and are estimated to be about 500 meters wide there. They broaden on the north flank to 700 meters, increase to 1300 meters width in the northwest, but they are then reduced considerably on the west flank of the dome. Torsion balance work in northern Germany has been con- tinued and supplemented of late by gravimeter observations. Fig. 7-107 shows the torsion balance results for the deep-seated dome of Schneeheide, whose gravimeter anomaly was previously illustrated in Fig. 7—50a. In Russia, B. Numerov’’ made a study of the salt deposits near Soli- kamsk in the northern Urals and correlated the torsion balance anomalies with well data. The variation of gravity anomaly with salt depth (see Fig. 7-108) was found to be linear. Numerov used an equation derived 132 H. Seblatnigg, Mecklenb. Geol. L.-A. Mitt., 49-58 (1930) 133 B. Numerov, Zeit. Geophys., 5(7), 261-265 (1929). Cuap. 7] GRAVITATIONAL METHODS 275 previously in connection with his experiments on Lake Shuvalovo to ex- press the above relation. The difference in density between salt beds and overburden was assumed to be 0.35. From 1925 to 1928 extensive gravity measurements were made in the Emba district on the northeast shore of the Caspian Sea.’ Numerous Old PN as Wielze g = a ° om \ a ” et w| b Seismic Shothole and Depth in Profile _----~ 60ologically assumed ag Outline 27 | \ Gulline of Salt Dome / from seismic work , f } Lf. ie “/ i a NG Onan Melze ZB sn —- ~ ee / aunties, Gravity Anomaly in pendulum traverse Fic. 7-105. Seismic refraction depths, seismic outline gravity gradients, and gravity profile on Oldau-Hambuehren (Wietze) salt dome in northern Germany. salt domes have been discovered there by the application of geophysical methods. It appears that the whole region between the Ural and the Volga rivers is fairly studded with salt domes. The Soviets estimated that by 1934 they had discovered more than 400 salt domes by geophysics. 134 Tbid., 268-270. 276 GRAVITATIONAL METHODS [Cuap. 7 Fig. 7-109 shows a small portion of this region between the oil fields of Dossor and Iskin. At Dossor, where the depth to salt is of the order of 400 meters, the gravity anomaly is 31 milligals. Other domes in this area produce anomalies of the order of 15 to 25 milligals. Since 1935, detail er: U \\ Probst-Jesar by Lubtheen Mi oe x | x 4 yr» aA N= / x re os on oy o 500 200Mefers AS 50 20 Lotres I yey a Mri N 7 > . oa Xi pose Fig. 7-106. Torsion balance results and geologic section, Liibtheen-Jessenitz salt dome (after Seblatnigg). work on the geophysically discovered domes has been under way with torsion balance and reflection seismograph. In another salt dome country, Rumania, the torsion balance has like- wise been very successful. The first measurements there were probably made by W. Schweydar in 1918. Geophysical work of increasing scale was then initiated by commercial companies. In 1928 the Geological Cuap. 7] GRAVITATIONAL METHODS 207 Institute of Rumania began a study of various salt domes and anticlines. The Floresti salt dome’ was surveyed with various geophysical methods. It was found to produce a negative magnetic anomaly of the order of 40 gammas and to show distinctly in equiresistivity surveys. Fig. 7-110 represents the gradient and curvature values along a profile across the dome which is of the mushroom type and is covered with only about 20 meters of terrace gravels of the Prahova River. Further studies of this aw .¥ ¥ 4 nae Ly / =) pe Ae \ 4 ¥ / S N . - x \ ws = pee Ns S g : tS ' aoe. SA pao ~. Lies < e « a i ~T Oe Edtves Units 0 / 2 3Km Seismos Company Fig. 7-107. Torsion balance results on (deep-seated) dome of Schneeheide, northern Germany. (Compare with Fig. 7-50a). and adjacent domes and anticlines were made in subsequent years by the Rumanian Geological Institute.”° Among those investigated were the domes of Baicoi-Tintea and the anticlines of Bucovul, Filipesti, Novacesti, and others between Ploesti and Targoviste. The torsion balance was introduced in this country in September, 1922, and used in an experimental survey of the Spindle Top salt dome in De- cember, 1922. The Nash dome was the first to be discovered by the 135 M. Ghitulesco, 2nd Congr. Internat. de Forage (Paris, 1929). 236 T, Gavat. Inst. Geol. Roumania Ann., 16, 683-706 (1934). 278 GRAVITATIONAL METHODS [Cuap. 7 torsion balance in the early spring of 1924. The results of the reconnais- sance torsion balance survey were published by Barton.’ The dome is of the “‘shallow’’ type, its cap coming to within 750 feet of the surface, and it is characterized by a positive gravity anomaly. In the same year the Long Point dome was found with the torsion balance; in 1925 the Allen, Clemens, and Fannet domes were located. . We Gradient of gravity Fig. 7-109. Gravity anomalies between Dossor and Iskin, Emba district, Russia (after Numerov). netic results for this dome (negative anomaly of about 20 to 25 gammas). The Sugarland dome, for which the torsion balance results have been published by the same authors, is an example of a dome of moderate depth, which shows a large minimum and a small maximum. The top of the cap is at a depth of about 3500 feet; salt was encountered at a depth of 4280 feet. 142 Tbid. 280 GRAVITATIONAL METHODS [Cuap. 7 Gravity minima aione are observed on deep-seated domes (depth to cap or salt, 5000 feet or more). An example is the Shepards-Mott dome illus- trated in Fig. 7-113. No salt was encountered at depths of 6000 feet. The regional effect is quite large and keeps the gradients from showing the typical reversal. The refiection contour map indicates a closure of 1400 feet. A well-defined gravity minimum has also been found on the Tombaiil field, showing good closure with and against the regional dip but weak closure in the direction y \ of strike, as is the case in other ihe, * ~ domes along the Conroe trend. ot ‘ “” No evidence of salt has been 7 found by drilling. Fig. 7-114 illustrates the pa / pea 3 ty / gravity picture of the Esperson BS a dome (discovered by the tor- wo sion balance late in 1928’) Curvature’ and the geologic section as- Nw ee sumed in the interpretation calculations. The gradients are of the order of 2 to 7 E.U.; the gravity minimum on the left is due to the Esperson dome. Because of the inter- ference from the salt mass of the adjoining South Liberty- Dayton dome, a maximum is produced between them. In the calculations, the average i density of salt was assumed / GY, to be 2.19 and that of the cap rock 2.6. For the sediments Fic. 7-110. Torsion balance anomalies on the assumptions were: from 0 Floresti salt dome, Rumania (afterGhitulesco). to 300 feet, 1.9 to 2.05; from 2000 to 4000 feet, 2.20; from 4000 to 8000 feet, 2.25; from 8000 to 12,000 feet, 2.3. This results in the ap- parent sait-density differences indicated in the figure. It is seen that a grav- ity maximum above a dome may be due not only to the effect of the cap but also to that part of the salt which exceeds the density of the surrounding sediments. Such interdomal maxima, as revealed by this survey, may be a source of interpretation difficulties. As a matter of fact, maxima of this om 143 PD. C. Barton, A.A.P.G. Bull., 14(9), 1129-1143 (1930). Cuap. 7] GRAVITATIONAL METHODS 281 type were first confused with the cap effects of moderately deep domes. Drilling these produced only negative results. As shown in Fig. 7-114, interpretation of the Esperson anomaly gave 6000-8000 feet for the top of the salt. It was actually encountered later at a depth of 7000 feet. In oil exploration the torsion balance has been equally successful in surveys of nonsalt dome-type structures, although fewer results have been published. It was recognized at an early date that anticlines and domes nee Ke 57 i aS 35 37 40 a [ASE Fiq. 7-111. Torsion balance gradient survey of Hoskins Mound salt dome (after Barton). with heavier material in their cores would give rise to a positive torsion balance anomaly. Fig. 7-115 shows the results of a survey made in 1915 to 1916 on the Egbell anticline by Eétvés and his associates.’ The oil occurs in the Sarmatian formations near the surface; denser Eocene and Paleocene formations are assumed in the core of the folds. While the maximum on the Egbell anticline is well defined, the Sasvar dome shows only as a terrace superimposed on the regional gradient. Subsequent 144 See footnote 130. 282 GRAVITATIONAL METHODS ‘[Cuap. 7 1000 7000 HORIZONTAL SCALE 500 1500 2 ° ‘OVD FE Fig. 7-112. Sections of Hoskins Mound salt dome, showing comparison of torsion balance predictions and results of drilling (after Bar- ton). torsion balance work on an- ticlinal structures has been more extensive than the pub- lished accounts would indicate. In 1919 and 1920 R. Schumann conducted torsion balance measurements in the Vienna Basin to determine potential oil structure in the Sarmatian formation and to trace the Leopoldsdorf fault.” A por- tion of the torsion balance surveys made on Russian oil structures has been published by Numerov;” gravity anom- alies in the Grozny oil field (Caucasian fold zone) are shown on the resistivity map of Fig. 10-67. The Grozny and Terek anticlines are in- dicated by gravity maxima. Results for the Rumanian fields have been discussed Fra. 7-113. Shepards-Mott dome, reflection seismic and torsion balance survey (after Clark and Eby). 145 R. Schumann, Montanistische Rundschau, June 1, 1923. M6 Op. cit., 271. Cuap. 7] GRAVITATIONAL METHODS 283 by Gavat;'” for anticlines in Persia, by Jones and Davies.” A recon- naissance torsion balance survey across the Fort Collins anticline was described by John Wilson That the torsion balance is ideally suited for the mapping of the topog- raphy of basement rocks was first recognized by Eétvés himself, whose See U Oo ggeags % sae . South Liberty - Dayfon Fig. 7-114. Torsion balance gradient curves (measured and calculated) for the Esperson-South Liberty-Dayton domes, with calculated section (after Barton). 49 10 nga! Lobell Saswer Well SR fittest RH ee eer ee tT {LLL Se = 5 QRS REZ 6* eI ANAL Saba SUES EO A ON Fic. 7-115. Gravity anomalies (calculated from gravity gradients) on the Egbell and Sasvar domes (Czechoslovakia) (after v. Boeckh). 1. Pontian; 2. Sarmatian; 3. Upper Mediterranean; 4. Schlier; 5. Lower Neocene; 6. Paleocene and Triassic. classical observations in the Hungarian plain near Arad (begun in 1903 and continued in 1905 and 1906) are too well known to be reproduced in detail. In the Midcontinent fields’” the torsion balance has been used 147 See footnote 136. 48 J. H. Jones and R. Davies, M. N. Roy. Astron. Soc., Geophys. Supp., 11(1), 1-32 (1928). 1449 John Wilson, Colo. School of Mines Magazine, 18(6), 23 (Oct., 1928). 160 T), C. Barton, A.I.M.E. Geophysical Prospecting, 416-466 (1929). 284 GRAVITATIONAL METHODS [CuaP. 7 extensively to map ridges of granite, gneiss, and Cambro-Ordovician rocks. Examples are the Amarillo granite ridge, the Nocona-Muenster-Bulcher ridge, the Healdton fields, the Criner hills, the Kansas granite ridges, and the ridges in Colorado and Nebraska. Some of these appear in the gravity map of Fig. 7-51b. Barton has reproduced the torsion balance results for the Muenster-Bulcher ridge,” which showed well in the gradient picture. However, in the Fox area, the Fox and Graham uplifts were Mie Tet, Se in le aT IGA IS SS oS a CJ eC Te ee in et Gt SS +e te ee eR Be aca a Mey eae ae eo hes Cea Lo aimcssoo ys re Tr el Ce ee ee, eG Sie pu eG Fig. 7-116. Torsion balance anomalies on Hull-Gloucester fault, Canada (after A. H. Miller). 1. Shale and limestone under 70’ of drift (6 = 2.6); 2. Limestone (6 = 2.7); 3. Chazy shale and sandstone (6 = 2.5); 4. Dolomite (6 = 2.8); 5. Potsdam sandstone (8 = 2.5); 6. Precambrian (6 = 2.8). hardly noticeable. Only after considering the regional gradient due to the adjacent Arbuckle Mountains could a better agreement between struc- tural and torsion balance data be obtained. In oil exploration the torsion balance has been widely used for the loca- tion of faults. Eétvés was again first to point out this possibility. The amount of published data is no measure of the actual scope of work on fault problems. In 1927 M. Matuyama investigated step faults in Meso- zoic slate (density 2.5) covered by alluvial material (density 2.0) in the Kokubu plain near the Sakurazima volcano in J apan.”” Results obtained 151 Thid. 162M. Matuyama, Japan. J. Astron. and Geophys., 4(8), 1-18 (1927). Cuap. 7] GRAVITATIONAL METHODS 285 with torsion balance, magnetic, and electrical methods in an attempt to delineate step-faulted blocks in the Limagne-Graben zone have been pub- lished by Geoffroy.” The torsion balance has been rather successful in the Mexia-Luling fault zone. In a profile illustrated by Barton,” the Edwards limestone, at a depth of between 1000 and 2400 feet, is in contact with lighter Kagle- ford, De! Rio, and Austin chalk, while the Eagleford, Del Rio, and Austin are against lighter Taylor and Navarro shales. Hence, the maximum gradient occurs above the subsurface point where this density contrast occurs, that is, down dip in the fault from its surface trace. Two faults in the Paleozoic area near Ottawa were investigated by Miller’” and 8 = s v g S T+ + + t+ te eet eet t Pe AS a heh 9 ICE ee Ch oeen she ee ete Hie cir Purity ah Os Ao rs ++ t+ttt BO Ne EN eS Ey eS ae IS , TI Deena ito Prws rie PYG ANC Sune EGRET chaalieg Hie 2 kc SP en) (arom ee ure U or tee Swe HL Suge eso trot toners 4) ET meg ge pe re: Fic. 7-117. Torsion balance results on Hazeldean fault, Canada (after Miller). 1. Black River, Chazy limestone (6 = 2.7); 2. Chazy shale and sandstone (6 = 2.5); iG SE aah dolomite (6 = 2.8); 4. Potsdam sandstone (6 = 2.5);5. Precambrian showed a distinctly different response. The Hull-Gloucester fault near Leitrim (Fig. 7-116) in the Paleozoic and Pre-Cambrian has a 900 foot displacement and produces large gradients (about 150 E.U.) because of a near-surface contrast in density. Theoretical values calculated for an assumed subsurface section agreed well with the experimental results. In the same Paleozoic section the Hazeldean fault (575 foot displace- ment) gave a distinctly different picture. A “minimum” gradient was observed, since the effects of the lower beds (density contrast in upthrow direction) are overcompensated by a near-surface effect of density contrast 153 M. P. Geoffroy, Ann. Office Nat. Comb. Ligu., 4, 617-647 (1929). 154 TF), C. Barton, A.I.M.E. Geophysical Prospecting, 416-466 (1929). 155 A, H. Miller, Canad. Geol. Survey Mem., 165, 197-208 (1931). 286 GRAVITATIONAL METHODS [Cuap. 7 in down-throw direction (Fig. 7-117). The Pentland fault near Porto- bello in the Edinburgh district was investigated by McLintock and Phem- ister’ (Fig. 7-118). This overthrust fault dips toward the west and separates a series of volcanic beds of 500 feet thickness and of east dip from the oil shale group of sedimentaries in the east; hence, a westward tendency of gradients is produced. A satisfactory agreement of theo- retical and experimental pot Fatras Units. Pr values was obtained by assuming a block with in- clined face, 0.42 difference in density, beginning at a depth of 100 feet, and hay- ing a superimposed syncline west of the fault in the lava beds. At Dossor (see Numerov, footnote 134) S. Mironov investigated a fault on the west side of the field, separating the Senonian from (productive) Jurassic beds overlying Permo-Tri- assic and salt formations.” Matuyama and Higasin- aka’ determined the tor- sion balance anomalies of a fault of 70 meters dis- placement in the Takumati oil field, and Vajk’” dis- cussed a survey in South America where a maximum in the gradients and curva- Fig. 7-118. Torsion balance results on Pentland tures could be explained fault (after McLintock and Phemister). by either an anticline or a i". ~~ Upper Old Red $5 = es ote Oeics normal fault. 3. Applications in mining. Although Edtvés made some experiments with the torsion balance and magnetic instruments on igneous dikes, it is 166 W.F. P. McLintock and James Phemister, Great Britain, Geol. Survey, Summ. of Progr., pt. IT, 10-28 (1928). 157 S. Mironov, Geol. Comm. Vestnic, No. 5 (Leningrad, 1925). 158 MI. Matuyama and H. Higasinaka, Japan. J. Astron. and Geophys., VII(2), 47-81 (1930). 159 R, Vajk, World Petrol. Congr. Proc. B I, 140-142 (London, 1933). Cuap. 7] GRAVITATIONAL METHODS 287 not known whether he actually investigated any ore deposits. His asso- ciate, Stephen Rybar, surveyed the contact-metamorphic iron ore deposits of Banat in Rumania around 1917. In 1919 R. Schumann mapped the area near Zillingdorf north of Vienna to determine the structure of the coal deposits there. In Russia the torsion balance was used by P. Niki- forov, Lasareff, and Gamburzeff in connection with the magnetic survey of the Kursk anomaly.” Several torsion balance profiles across this deposit are illustrated in Chapter 8 (Fig. 8-59). The gradients reach a maximum amplitude of 80 and the curvature values an amplitude of 130 SS “~N ~ -—— 200 400 600 -10°* cas. ——~—~ Outline of magnetite deposit — 20 — Magnetic anomaly in 10bby Fic. 7-119. Torsion balance results on Caribou magnetite deposit, Colorado. (Scale same as in Fig. 7-76) K.U. and can be explained on the assumption of a density difference of 0.8 between the iron quartzite and the surrounding metamorphic rocks. e The Swedish investigators, H. Lundberg, K. Sundberg, and E. Eklund,™ have used the torsion balance in conjunction with electrical and magnetic surveys and published the results of a reconnaissance survey on Mens- trask Lake. In Germany the torsion balance was tried at about the same time on some siderite veins of the Siegerland district.” Matuyama investigated 160 P. Lasareff and G. A. Gamburzeff, Gerlands Beitr., 16(1), 71-89 (1926), 19(2/3), 210-230 (1928). 161 Sveriges Geol. Unders. Arsbok, 17(8), 86 (1925). 162 Hf. Quiring, Glueckauf, 59, 405-410 (1923). 288 GRAVITATIONAL METHODS [Cuar. 7 = Mh fi Me Monzonite |! Sopbyry j} Gobiroy yy if th oS a LOS £00 aod ed Magneiste a Fic. 7-120. Gravimetric, magneiic, and electrical indications on Caribou magnetite deposit. G, gradients; K, curvature values; AV, magnetic vertical intensity; C, rei. conductivity. Fotves Units the vicinity of the Fushun Colliery and located a fault separating gneiss from sedi- mentary rocks.” Whether the coal seams were indi- cated remained doubtful on account of terrain interfer- ence. Shaw and Lancaster- Jones conducted a recon- naissance survey across a barite deposit about 50 feet in depth, which was known from underground work- G; ings.“ Mason observed a 50 Nee & \ ihe) aN. i oe bog 163 Op. cit., 2(2), 91-106 (1924). Fic. 7-121. Torsion balance and magnetic 164 FH}, Shaw and E. Lancaster- anomaly (AZ) on Swynnerton dike (after McLin- Jones, Mining Mag., Jan. & tock and Phemister). Feb., 1925. Cuap. 7} GRAVITATIONAL METHODS 289 moderate anomaly of 20 to 30 EHétvés amplitude on the weil-known Falconbridge ore body in Canada.” In the Tri-State district the torsion balance was tried with the hope of locating lead-zine ores directly.” However, it was possible only to outline the (lighter) chert pockets in limestone in which the ore bodies occur.. Fig. 7-119 shows torsion balance results obtained by the author at Caribou, Colorado, on a magmatic differentiation type of magnetite de- posit in gabbro. Despite unfavorable terrain conditions indicated in Fig. 7-76, the torsion balance indicates the individual concentrations Lotves Units 9 8 70 6 50 40 0 1] 60 @ MH 06 8% Om Fic. 7-122. Gradients and curvature values above lignite deposit bounded by sand- stone fault block (after Seblatnigg). (accompanied by magnetic anomalies ranging from 20 to 100,000 gammas) rather satisfactorily. Fig. 7-120 gives average curves for the gradients and curvatures across this deposit and also illustrates results of magnetic and electrical investigations. Fig. 7-121 indicates the results of a torsion balance traverse made by McLintock and Phemister™ across a dike of 165M. Mason, Geophysical Exploration for Ores, A.I.M.E. Geophysical Pros- pecting, 9-36 (1929). 166 P| W. George, A.1.M.E. Geophysical Prospecting, 561-571 (1929). 167 W. F. P. McLintock and J. Phemister, Mining Mag., Dec. 1927. 290 GRAVITATIONAL METHODS [CuaP. 7 nepheline basalt in Triassic Keuper marls. The vertical intensity anomaly is shown for comparison. In 1926 and 1927 the torsion balance was used in the investigation of magnetite deposits of Krivoj-Rog in southern Russia in connection with magnetic surveys.” Two cases are known where the torsion balance has been applied indirectly in the mapping of lignite deposits. The deposit shown in Fig. 7-122 occurs in Tertiary beds” (density 2.1) and is bounded on one side by Triassic sandstone (density 2.35). Hence, it was possible to outline it by locating the edge +300 +250 ~ _ mee. +150 ae °o O o fe) Values of gradient in Edtvds Units \ fe) Bar ke = = ‘ o ie] -!00) Distances in feet fe) OO 400 600 eg 800 Fig. 7-123. Torsion balance survey of Caldwell pyrite deposit (after Miller). Solid curve, observed; dotted, calculated anomaly. of the sandstone block. Edge and Laby have published a survey of similar character.” In the Gelliondale field in southeast Victoria the lignite bed occurs in horizontal stratification in sandy beds about 100 feet from the surface. Since it is terminated by the sloping surface of 168 P. Nikiforov and others, Inst. Pract. Geophys. Bull., 4, 299-307, 315-330 (1928). 169 H. Seblatnigg, Braunkohle, No. 23 (1929). 70 Edge and Laby, Principles and Practice, etc. (Cambridge Univ. Press, 1931) Cuap. 7] GRAVITATIONAL METHODS 291 denser Jurassic rocks, it could be outlined by mapping bedrock topography. In one of the profiles the lignite did not come up against the edge of bedrock. A broad gradient maximum, due to the superimposed effect of the lignite edge and the sloping bedrock surface nearby, was observed. The torsion balance is also useful for outlining placer channels. Edge and Laby investigated a portion of the Gulgong field in New South Wales with the object of determining the edge of a sloping channel filled with alluvial strata, underlain by granite. (Seismic data for this field are shown in Fig. 9-41.) A similar application of the torsion balance was =>. »|" 70-m . 100 Litvés Unis 60 40 Yi 4% 2 41 Jo Fic. 7-124. Underground torsion balance observations at Beienrode, Germany (after Birnbaum). made by McLintock and Phemister™’ who surveyed the buried channel of the Kelvin River near Drumry. Surveys of salt deposits have been made not only in conncction with oil exploration but also for mining pur. poses. An example is A. H. Miller’s survey of the Malagash salt deposit,” which revealed a dome-shaped anomaly of 3 milligal maximum ampli- tude. The thickness of the salt is about 300 feet. Fig. 7-123 shows a 171 W. F. P. McLintock and J. Phemister, Roy. Soc. (Edinburgh) Trans. ., 56(1), 141-155 (1929). 172 A. H. Miller and G. W. H. Norman, A.I.M.E. Tech. Publ., No. 737 (1936). 292 GRAVITATIONAL METHODS [CHap. 7 torsion balance survey of the Caldwell (Renfrew Co., Ontario) pyrite deposit.’ The theoretical curve (based on the assumption of a density difference of 1.7, a thickness of the deposit of 50 feet, depth 20 feet, and dip 60 feet) is likewise shown. Since it is calculated under the assumption of a two-dimensional body, its amplitude exceeds that of the experimental curve. A number of attempts to use the torsion balance underground have been made and published. The earliest survey of this kind was made with a curvature variometer by Brillouin in the Simplon tunnel in 1905. Subse- quent experiments indicate that gradient observations are more suitable underground. A. Birnbaum’* made some torsion balance observations on two levels of the Beienrode potash mine in Germany. As shown in Fig. 7-124, the gradients point toward the anhydrite in the 700 foot level but 100 bradient Grr. =~] Salt Basalt (aaa ieee ClO? LO Fig. 7-125. Underground torsion balance measurements on basalt dike in salt (after Meisser and Wolf). away from it in the 1000 foot level, this indicating that its major portion is located below the 700 and above the 1000 foot level. A rather unusual occurrence of basalt (density 3.0) in salt (density 2.2) was investigated by Meisser and Wolf’ 700 meters below the surface. Supplementary measurements of magnetic vertical intensity and seismic propagation speed were made at the surface and underground. The thickness of the basalt varied from 0.4 to 90 meters. As Fig. 7-125 indicates, its major portion occurs below the 700 meter level. As has been emphasized by Kumagai,” the effects underground are so large that the sensitivity of the instrument must be reduced; otherwise, its starting azimuth must be so selected that the effects of the adjacent tunnel walls are at a minimum. 173 A. H. Miller, Canad. Geol. Surv. Mem., 170(3), 99-118 (1930). 174 A. Birnbaum, Kali, 18, 144-148 (1924). 175 Q, Meisser and F. Wolf, Zeit. Geophys., 6(1), 13-21 (1930). 176 N. Kumagai, Japan. J. Astron. Geophys., 9(3), 141-206 (1932). 8 MAGNETIC METHOD I, INTRODUCTION ‘T= MAGNETIC method of prospecting is one of the oldest geophysical methods. It was applied to the location of ore bodies as early as 1640. Like gravitational methods and in contrast to electrical and seismic methods, it utilizes a natural field of force, consisting of the field of geologic (a) (6) Fic. 8-1. Vector diagram of the earth’s magnetic field (a) for the northern hemi- sphere, (b) for the southern hemisphere. bodies and the terrestrial magnetic field. Contrary to their gravitational attraction (which exists independently of the earth’s gravity field), the magnetic reactions of geologic bodies frequently depend on direction and magnitude of the earth’s field. The law controlling magnetic attraction (Coulomb’s law) is identical in form with that governing gravitational attraction. Hence, magnetic interpretation problems may often be handled by a simple adaption of the relations which apply in gravita- tional work. Because of the spontaneous nature of subsurface effects, it is not possible to control the depth of penetration in magnetic prospecting. 293 294 MAGNETIC METHOD SYMBOLS USED IN CHAPTER 8 B33 TF FP SSS SOLO aes rnegerar a S'S » American Askania Corp. Fig. 8-38. Large earth inductor. Europe by the Askania Company—a large type for observatory use (see Fig. 8-38) and a small type for field surveys (see Fig. 8-35). Details ab Op. crt. ug. 10) pitt. aS Op ecrts nee 2: Cuap. 8] MAGNETIC METHOD 363 of earth inductor observations with record forms are given by Hazard.” The use of the earth inductor as a compass is based on its ability to find the magnetic meridian by the zero-induction brush position (see page 361). In application (airplane) the brushes are so set as to make the required course angle with the axis of the ship; the pilot then navigates the ship in such a manner that the galvanometer on the instrument board shows no deflection. Magnetic intensities may be measured with the.earth inductor by using the ballistic method previously discussed, by keeping the speed of the coil constant, or by compensating the field so that the speed is no longer of influence. In the constant-speed method the coil is coupled to a syn- chronous motor driven from a valve-maintained tuning fork, and the e.m.f. induced in the coil is measured with a potentiometer.” The compensation principle is applied in an inductor” provided with a pair of Helmholtz coils mounted to the frame B in such a manner that the field of the coils opposes the earth magnetic field in the z2’’ direction. The compensation current is accurately measured by a potentiometer arrangement. A dis- advantage is the lack of homogeneity in the inside of the coil. This lack may be overcome by the new form of Helmholtz coils suggested by Fan- selau and Bock.” _In a compensation inductor suggested by the author,” a large magnet compensates the major portion of the field and a smaller magnet is moved along a deflection bar for compensation. This instru- ment is suitable for any intensity component. The possibilities of the compensation inductor are well demonstrated by the fact that it has been proposed as a primary standard in absolute magnetic observatory work.” The earth inductor gradiometer” is intended for the determination of “intensity gradients’ in the north and east directions. It consists of a horizontal frame in which two coils rotate about horizontal axes. They are situated on opposite arms of a Kirchhoff-Wheatstone bridge so that the ratio of the e.m.f.’s induced in the coils is observed. The Null instrument is a sensitive galvanometer set up on a separate tripod. When the coil frame is E-W, the axes of the two coils are N-S, which eliminates the 47 Op. cit., pp. 77-84. 48 F, M. Soule, Terr. Mag., 36(2), 103-110 (June, 1930). 49W. Uljanin, Terr. Mag., 34(3), 199-206 (Sept., 1929). 50 See G. Fanselau, Zeit. Phys., 54(3/4), 260-269 (1929). F. E. Smith, Phil. Trans., A223, 186-191 (1923). R. Bock, Zeit. Phys., 64, 257-259 (1929). R. H. Bacon, Rev. Sci. Instr., 7(11), 423 (Nov., 1936). 5t See P. Aguerrevere, Colo. School of Mines Quarterly, 27(3), 11-29 (July, 1932). la H, A. Johnson, Terr. Mag., 44(1), 29-42 (1939). 52 See I. Roman and T. C. Sermon, ‘‘A Magnetic Gradiometer,’’ A.I.M.E. Geo- physical Prospecting, 373-390 (1934). 364 MAGNETIC METHOD [CHapr. 8 horizontal intensity. Therefore, the E-W gradient of the vertical intensity is measured. When the frame is now turned into the N-S direction, the axes of rotation are at right angles to the horizontal intensity so that both H and Z (that is, the total intensity T) are now effective. Roman actually measures T by setting the brushes at right angles to the field (which requires a knowledge of the inclination) and calculates Z from it. This makes the method laborious, but it can be avoided if provision is made to turn the coils in their frame in such a manner that their axes of rotation always point north. 3. (Iron) induction instruments are designed to measure the inclination, the vertical intensity, and the magnetic meridian. Induction inclinom- eters consist of a magnetic needle suspended from a thread or wire, and two vertical iron bars mounted opposite each end of the magnetic needle. One bar is up from the plane of the needle; the other is down. There will be a south pole induced in the upper end of the lower bar and a north pole in the lower end of the upper bar. This deflects the needle from the mag- netic meridian. Naturally, opposite poles are also produced in the bars by the poles of the needle. This effect can be kept down and is neglected in the following formulas. If F is the force produced on the suspended needle from the induction in the bars, the deflection in the Lamont method is given by sin ¢ = F/H, where F = 2Zk’’/d’, k” is an induction factor, and d is the distance between needle poles and poles induced in the bars. Hence, (8-47) If an astatic magnetic system instead of the magnetic needle is used, the effect of the horizontal intensity is eliminated, and the torsion of the suspension wire furnishes the restoring force that opposes the effect of induction in the bars. In the vertical intensity magnetometer designed by MeNish,” the astatic system is represented by an armature consisting of two vertical bars mounted on the ends of a nonmagnetic vane (see Fig. 8-39). For magnetic meridian determinations, Rieber™ has designed a micro- magnetometer consisting of two iron bars mounted end-to-end with a small gap and the fiber of a string galvanometer between them. When alter- nating current of about 100 cycles is passed through the string, and if the bars are in the magnetic prime vertical, the induction and string deflection are zero. 58 Terr. Mag., 41(2), 161 (June, 1936). 54 A.I.M.E. Geophysical Prospecting, 410 (1929). Cnap. 8] MAGNETIC METHOD 365 4. Sine galvanometers are combinations of unifilar magnetometers and deflection coils so arranged as to give a horizontal comparison field in the magnetic prime vertical or at right angles to the needle. In the second case, the instrument is used as the “‘sine’”’ galvanometer proper; in the first, as a “tangent” galvanometer. The horizontal intensity gc Ona — As (8-48) tan ¢ sin ~ where C' is a coil constant and I the current, measured by standard re- sistance coil, standard Weston cell, and potentiometer. For field instru- ments the coil constant may be determined by measuring deflections at an observatory where H is known. Large instruments for absolute deter- minations of the horizontal intensity are described by Barnett” and Hazard;” a smaller field instrument is il- lustrated by Nippoldt.” 5. Compass variometers are instruments intended for the measurement of the horizontal intensity on moving support. They consist of two compasses mounted some distance apart above each other. The force acting on either compass is dependent on the horizontal intensity and the attraction due to the other needle. Generally, the angle of spread between the two compasses is meas- ured, from which the horizontal intensity oMk ) Fia. 8-39. In- athe duction vertical H = poe Gee 9? (8 49) magnetometer (after McNish). where JM is the magnetic moment of each magnetic needle, k a deflection constant, y the spread angle, and r the distance of the needles. The instrument is well adapted to the measurement of horizontal intensity anomalies on board ship and in aircraft. It may be made into a vertical intensity instrument by using two compasses oscillating.in vertical planes side by side with their plane of oscillation in the magnetic prime vertical. Details are given in publications of L. A. Bauer and others,” by E. B. Brammer,” by G. Angenheister,” and by K. Luyken.” 55 Pub. No. 175, Carnegie Institution, 373-394 (Dec., 1921). = O)p. Cil., ps oS: 57 Nippoldt, op. cit., p. 33. 58 Pub. No. 175, Carnegie Institution, V, 339-351 (1926). 59 Zeit. Instr., 45(12), 576-579 (Dec., 1925). 60 Handb. Exper. Phys., 25(1), 577-578 (1928). 61 Zeit. f. angew. Geophys., 1(6), 163-181 (Oct., 1923). 366 MAGNETIC METHOD [Cuap. 8 D. OBSERVATORY INSTRUMENTS Certain instruments now used in observatory practice are also applicable in regional magnetic surveying. Some of these may, by suitable modifica- tions, become of importance for magnetic prospecting. Observatory in- struments are employed (1) for the absolute determination of magnetic components, and (2) for recording magnetic variations. 1. Instruments for absolute determinations are sine galvanometers, mag- netic theodolites, and earth inductors. These require no further discussion here, since their principles have been described before. 2. Instruments for the recording of magnetic variations fall into two groups of different design, depending on whether they are intended for perma- nent observatories or for temporary setups in connection with magnetic exploration. In permanent observatories variation instruments are pro- vided for declination, horizontal intensity, and vertical intensity. Some observatories prefer to record north and east components of the hori- zontal intensity. The variometers are usually set up in a straight line in the magnetic prime vertical so that the declination variometer oscillates in the magnetic: meridian, the horizontal magnetometer in the prime ver- tical, and the vertical intensity variometer in the magnetic meridian.” For convenience in scale value determinations, Helmholtz coils are perma- nently installed on the instruments. Temporary observatories in magnetic exploration generally utilize the regular vertical or horizontal intensity magnetometers equipped with a mirror device. This device projects the light reflected from the magnetic system on a recording drum and carries a base-line mirror and a Bourdon tube for recording temperature. A portable recording device using only the magnetic system of a balance magnetometer is illustrated in Fig. 8-22. A method for remote recording of magnetic variations by means of a balanced photoelectric cell arrange- ment has recently been described by Graf.” IV. CORRECTIONS In magnetic prospecting it is necessary to eliminate or correct for tem- perature, daily variation, planetary variation, base change, influence of iron and steel objects, terrain anomalies, and regional anomalies. These corrections will be discussed in the order indicated. A. TEMPERATURE 1. Elimination. The action of temperature may be disregarded in instruments which are well insulated, are compensated for temperature, 62 See Hazard, op. cit. (2nd ed.), Fig. 14, and pp. 108-112 for directions for operat- ing a magnetic observatory. se A. Graf, Beitr. angew. Geophys., 7(4), 357-365 (1939). Cuap. 8] MAGNETIC METHOD 367 or have low sensitivity. The same is true for recording instruments when they are compensated or used in rooms of constant temperature. 2. Even when a temperature correction is applied, magnets and magne- tometers are usually well insulated in order to cut down temperature fluctu- ations and temperature hysteresis. An instrument finish of high reflecting power gives best protection against excessive temperature changes.” The procedure in determining temperature coefficients of Schmidt balances was described on page 331. Other magnetometers are treated in a similar manner. B. MAGNETIC VARIATIONS Magnetic variations may be divided into periodic (daily or diurnal varia- tion), nonperiodic (magnetic storms), secular variation, and artificial variations due to stray currents, and the like. 1. The diurnal variation is closely related to the earth’s rotation. It is greater and more irregular during the day than at night; its amplitude and phase varies with season and latitude (see Figs. 8-40 and 8-41). Pro- cedures for elimination or correction are discussed below in ascending order of accuracy. When large anomalies are encountered or when the sensitivity of the instrument is low, the variation is usually disregarded. Variations may be eliminated by simultaneous observations with two instruments on suc- cessive stations. In stationary instruments magnetic variations may be eliminated by the use of astatic systems and by shielding where applicable. Moderate accuracy in the elimination of the variation is attained by checking back at a base station as often as possible and by considering the daily variation as part of the variation of the base value. If measure- ments at the base are not possible at regular intervals, it is advisable to select times between which the change is approximately linear. Curves as shown in Figs. 8-40 and 8-41 can give reliable data for daily variation corrections, particularly when measurements are made fairly near a magnetic observatory for which such curves are available. Allow- ance must be made for differences in mean local time as shown in the next paragraph. Greater accuracy is attainable by arranging with magnetic observatories for tracings or photostatic reproductions of their records for specific days. The curve-amplitudes must be multiplied by scale value and must be corrected for temperature (unless the instruments are com- pensated or are set up in constant temperature rooms) and for difference in local mean time between observatory and area under survey (Ad of 63 For curves on magnetometers of different makes see J. B. Ostermeier, Zeit. Erdoel. Bergbau, etc., June 14, 1930. Honolulu fz Declination Lauinox —-—-— Winer Louiner —-—-- Winter -—~ I Dip Horizontal Intensity (b) (c) Fra. 8-40. Diurnal variation curves (a) for D, (b) for H, (c) for I (after Hazard). 368 Cuap. 8] MAGNETIC METHOD 369 15° = 60 min. of At). For some countries formulas are available giving diurnal variation as a function of latitude and longitude. With an in- crease in distance of the observatory from the area, these calculations decrease in accuracy, since the correction applies only to periodic and not to nonperiodic variations. This has been shown by Soske™ who found differences between records taken near Pasadena and observatory records of Tucson (AX = 7°) amounting to 10—20y on days of magnetic activity. To what extent local meteorologic and geologic conditions affect the Mn. 6 12 18 Mn. 6 12 18 Mn. 6 12 18 Mn. 6 J2 78 Man. oy 7 A N SLANT IAA (ENA UDINE &6 WE SWS aa =F O77. Nm VA SeW22 Saw. Paes... -& Man \s AVS BNAM SWS J Na@ BR Eee ae AM BOAR BSE Ree 20 eine RN Be ZAN ea Gb SE na 20° 0 WON VINCI NIE 40 eed a ual AVA mana ade Se 49° Bean ALIN NTI Nie AT BASS NSA NIE AN Ie 7, M. Component X E.Component Y Vert. ComponentZ Dipl Fig. 8-41. Diurnal variation curves for X, Y, and Z (after Bartels). magnetic variations has been the object of some discussion. H. Aurand,” in an analysis of survey data accumulated between 1928 and 1931 by the Midwest Refining Co., obtained conclusive evidence of the influence of meteorological factors (up to 50y). Whether variable static charges are produced on magnetic instruments by atmospheric electric fluctuations or whether magnetic fields originating from electrically charged particles in motion are responsible is difficult to decide. Inasmuch as there appears 64 J. L. Soske, Terr. Mag., 38(2), 109-116 (June, 1933). 65 Personal communication to the author. 370 MAGNETIC METHOD [Cuap. 8 to be a relation between fluctuations of the atmospheric electric potential gradient and magnetic variations, it would seem reasonable that local meteorologic factors can be of influence. Vacquier” has shown that, what- ever their cause, such local differences exist not only in the variations following local mean time but also in astronomical (nonperiodic, see 2, below) variations as well (see Fig. 8-42). It is also possible that local geologic conditions (rocks of high magnetic susceptibility) give rise to induction damping and smoothing of the curves. While Soske” could not find differences between variations recorded in Tucson and basalt areas in California, with local anomalies up to 3,500y; Koenigsberger” concluded from the rock susceptibilities in two Alpine valleys that variation corrections may be in error by as much as 10-15y. In such areas, however, his investigations were concerned primarily with nonperiodic variations. Because of possible discrepancies between observatory records and local magnetic variations, the only procedure which satisfies all accuracy re- quirements is the local determination of magnetic variations. This requires a second instrument which may be read by another observer at intervals of from 10 to 30 minutes (depending on magnetic activity) or may be provided with a recording attachment as previously described (see also page 356 and footnote 62a). The recording instrument should be free from all magnetic disturbances caused by electric power lines, tram- ways, automobiles, and the like, and be protected against temperature fluctuations. A recording hut or tent may be used for this purpose, or the instruments may be set up in mine tunnels where available. 2. Magnetic storms occur approximately at the same (or astronomic) time all over the earth. Because of their irregular character, rapid time change, and large amplitude, it is difficult to correct for them. To enable observers to distinguish them from possible local effects, announcements of magnetic storms having occurred the week before are published regu- larly in the Oil and Gas Journal.” Arrangements may be made with most observatories for collect telegraph report service. During a storm it is advisable to suspend operations, since stations occupied at that time would have to be rechecked in any event. 3. Secular variation is the slow change of magnetic elements in the course of centuries. It is not the same all over the earth. Charts of lines of equal secular variation are published by the U. S. Coast and 66 Terr. Mag., 42(1), 17-28 (March, 1937). 87 Loc. cit. 88 Zeit. Geophys., 6(2), 74-78 (1930). 69 For an illustration of a magnetogram of a magnetic storm, see Oil and Gas Journal, 28(41), 41 (Feb., 1930). Hours Local Time Hours Local Time 10 le 14 16 Group 1— July 10,1995 (a) Hours 0” Meridian Time (b) Fig. 8-42. Differences in magnetic variations recorded at various stations (after Vacquier) (a) in local time variations, (b) in astronomical time variations. (T, Tueson; C, Cheltenham; I, Eads (E. Colorado); III, Lumberton, 8S. Miss.; IV, between Quitaque and Plainview, N. Texas; V, between Millcreek and Randolph, S. Oklahoma; VII, Anadarko, Oklahoma.) 371 372 MAGNETIC METHOD [CHap. 8 Geodetic Survey. Approximate variation rates are also given on the charts of magnetic elements. This variation does not have to be con- sidered in magnetic surveying except when absolute values in relation to . government stations are desired. For calculations of the planetary correc- tion and for adjustments of a magnetometer to a different locality, charts for any year may be used. 4, “Artificial” variations are due to both power lines and power plants, surges in A.C. lines, magnetic separators, electric tramways, their return circuit through ground, and anticorrosion currents in pipe lines. A magne- tometer should be set up at least 1,500-3,000 feet away from such sources of interference. Near tramways a magnetic station outside the return circuit loop is generally much less disturbed than one inside. There are exceptions to this rule if stray currents are carried to the outside by pipe lines and wires.” Abrupt changes in the base value of a magnetometer may occur because of the demagnetizing effect of power lines. Koenigs- berger reports displacements as large as 140y when working near power lines. Transportation of magnetometers on electric tramways caused changes of from —5 to —35y, while transportation on railroads and auto- mobiles produced little, if any, effect. C. PLANETARY VARIATION Since the vertical intensity increases and the horizontal intensity de- creases toward the magnetic pole, the planetary correction is negative for the former and poSitive for the latter. The rate of change of magnetic elements with latitude and longitude may be taken from U. S. Coast and Geodetic cr other world charts. For a given area an average value may be assumed, or the magnetic lines may be transferred from such charts to the base map of the survey. For small areas and large anomalies (magnetic mine exploration) the planetary correction is generally neglected. ‘ D. BasE CHANGE This correction is applied to allow for changes in the base value of magnetometers between checks on base stations. Before the correction is calculated, base station readings must be corrected for temperature and diurnal variation. If the difference does not exceed 15-207 in one day, it may be uniformly distributed among stations occupied between base checks. Larger differences indicate abrupt changes and must be corrected for accordingly. The observer is generally in a position to tell from his 70 Much information has been published on leakage currents in connection with corrosion problems. See, for instance, U. S. Bureau of Standards Technologic Papers, No. 63, 75, 127, and so forth. Cuap. 8] MAGNETIC METHOD Wey travelog when such changes (shocks, demagnetizing effects, and so on) are likely to have occurred. Base readings should be:plotted against time to separate random from systematic changes (variations, changes in tem- perature coefficient, and the like). E. INFLUENCE OF IRON AND STEEL OBJECTS Since it is impossible to correct for the magnetic fields caused by iron masses, the only remedy is to keep at a distance commensurate with the accuracy of the survey. For objects extending in a vertical direction, the anomaly decreases approximately in proportion to the inverse square of the distance. For predominantly horizontal objects, the attraction is approximately proportional to the inverse first power of distance. 1. Interference from iron objects about the observer (watch, knife, key ring, belt buckle, steel frames of glasses, suspender buckles, steel rings in notebooks, and the like) can be avoided since it is a simple matter to determine their influence by approaching a magnetometer from various sides, and from above and below. Objects found to be effective at the customary operating distance should be taken off. 2. The vertical field of the instrument case of a magnetometer with compass and auxiliary magnets is about 1257 at 1 yard distance to the north and disappears at 4 or 5 yards. 3. A bicycle produces an anomaly of almost —60y at a distance of 1 | meter. An automobile has, at 3 yards distance, a vertical field of ahout —7007, which ‘disappears at about 25 to 35 yards. It varies somewhat with the direction in which the car is pointed and the position of the instru- ment with reference to it. 4. The field of a wire fence running N-S (the instrument being on the east side) is about —350y at 1 yard and disappears at about 36 yards. 5. The influence of a bridge varies considerably, depending upon con- struction and material, size and direction, and whether the observer is above or below it. | 6. Pipe lines can generally be spotted in the field by the overhead telephone lines which follow the course. For a N-S traverse across an 8 inch line buried 4 feet below the surface, running E-W, Barret’ observed a vertical intensity anomaly of —500y at about 2 yards (peak in curve) and a disappearance of the anomaly at about 30 yards. From 2 yards to a point directly over the pipe, the anomaly decreases sharply. This interference varies with the direction of the pipe, polarization at the ends, and existence of anticorrosion currents. : 71 Oil and Gas Journal, 28(22), oa 245-252 (Oct. 16, 1929); A.A.P.G. Bull., 16(11), 1371-1389 (Nev., 1931). 374 MAGNETIC METHOD [Cuar. 8 7. Near a railroad bed, running E-W, Barret observed on the south side a negative anomaly up to about 5 yards which then increased to a maximum of 4007, thence decreased and disappeared at 125 yards. 8. The effect of buzldings depends entirely upon size and iron and steel content. Brick buildings and brick walls are often magnetic, since the stones acquire magnetism in the process of roasting. 9. The influence of slag and gravel roadbeds, drain pipes, and the like, varies greatly with construction materials; it is difficult to give even approximate figures. 10. The influence of tank farms is generally complicated by associated pumping, power, and pipe line equipment; general figures are not avail- able. 11. When magnetic measurements are used for detailing or extending drilled or produeing fields, it is necessary to know the effect of well casing. The vertical and horizontal intensity anomalies of a tubular casing of uniform diameter may be written” di. nids AZ =" SkZo as a ee T1 ie) (8-50) 1 1 AH = SxZo-2 (: = ): Te Up where « is the susceptibility of the casing material, S its cross-sectional area, Zo the normal vertical intensity (SkZo = pole strength, or magnetic moment divided by the length of the casing), d; the depth to the upper and d, the depth to the lower pole, 7; the distance of the point to the upper and rz the distance to the lower pole, z the surface distance. This formula corresponds to that for a vertical magnet (formula [8—-53]). For a very long magnet the second term in the bracket is negligible and there occurs only a positive anomaly. A short magnet may produce an area of negative anomalies surrounding one with positive anomalies, as illus- trated in Table 43. In this example the anomaly disappears at about 200 feet from the well, regardless of the length of the casing. Barret”® and Clifford’ conducted surveys in oil fields before and after a change took place in the number of wells and concluded that the picture of the magnetic anomalies was not changed within the limits of accuracy. This is contrary to Van Weelden’s” contention that cumulative magnetic fields of wells may reach figures sufficient’ to explain the negative anomalies 72 Barret, loc. cit. 78 Loc. cit. 740. C. Clifford, A.A.P.G. Bull., 16(12), 1171-1176 (Dec , 1932). 75 A. Van Weelden, World Petrol. Congr. Proc., Sec. B. I., 86-90 (1933). Cnap. 8] MAGNETIC METHOD 375 frequently observed on developed fields. The influence of all wells in the Healdton field was theoretically sufficient to account for its negative anomaly (— 2007). TABLE 43? COMPARATIVE VERTICAL ANOMALIES OF A SHORT AND LONG STRING OF WELL CASING ‘SurFaAcEe DIsTaNcE 206’ or 10” CasINnG; 4,609’ oF ComposITE | SurFacE DISTANCE IN FEET AZ in GAMMAS | Castne; AZ In GAMMAS IN FEET 0 PAO GOT Mier eeu | 0 ae 19, 500 35, 200 | 5 6.6 6,700 | 10,700 10 12.0 2,000 5,500 | 15 22.0 434 2,990 | 20 32.1 158 | 1,220 30 46.0 37 300 50 56.0 : —6 Oe 81.0 —29 53 100 118.5 —29 11 150 147.0 —14 0 200 260.0 0 0 250 2 After Barret. 12. Derricks, electric line towers, and mine shafts produce negative mag- netic anomalies, being above the plane of observation. Depending on size and amount of steel involved, the fields range from several hundred to several thousand gammas at nearby points. F. TERRAIN ANOMALIES In magnetic prospecting, terrain interference is not nearly so important as in other lines of geophysical exploration. It is due to (1) a geo- metric effect resulting in a change of vertical distance of magnetic bodies from the plane of observation, (2) magnetic effects caused by surface rocks. 1. The geometric effect is of importance when changes in elevation along magnetic profiles are comparable with the distance of observation points from the magnetic body. For a three-dimensional body magnetized by induction (northern magnetic latitude), whose vertical intensity is nor- mally at a maximum above the body and whose horizontal intensity has a maximum and minimum to the south and north, the appearance of the anomaly curves is almost reversed if the slope is steep enough,” since the lower pole of the body comes closer to the surface. For uniform slopes the changes in relative position of instrument and subsurface poles may be 76 See Haalck, op. cit. 376 MAGNETIC METHOD [Cuap. 8 readily calculated.” In the interpretation of the results in irregular terrain, it is necessary to consider the relative position of each station with respect to subsurface bodies. In this case it is advisable to obtain additional data by observations at every station at two heights of the ~ instrument” or by the use of a compass variometer” which is very sensitive to rapid space changes of intensity. 2. Magnetic interference may occur even on a flat terrain surface by locally different weathering, by magnetic rocks in glacial drift, by surface float near iron and nickel deposits, by magnetite stringers in igneous rocks, and by outcrops magnetized by lightning. It is difficult to give even approximate general figures for these effects. On the other hand, the influence of topographic features of simple geometric shape may be es- timated” by assuming uniform magnetization in the earth’s field. If the susceptibility is x, the greatest vertical intensity field of a hill station (calculated on the assumption of an elongated ellipsoid) is AZ = +4nkZo. (8-51a) The approximate anomaly near the bottom of a vertical wall (quarry station) is AZ = —4mxZo. (8-51b) The vertical field in an elongated depression between walls of uniform slope on either side depends not on the absolute differences in elevation between summits and valleys, but on the degree of slope. For gentle slopes AZ = —2nkZo (8-51c) approximately, while for steep slopes AZ = —31xZy. (8-51d) The anomaly in the interior of a sphere (measurements in caves, tunnels) is AZ = —SaxZy. (8-5le) Koenigsberger” confirmed these theoretical values by numerous ob- servations. The greatest difference between summit and valley values in gneiss was 1307; in gneiss quarries the anomalies reached —50y; in 77 A. Nippoldt, Magnetische Mutung, p. 12 1930. 78 See A. F. Hallimond, Min. Mag., 41(1), 16-22 (July, 1929). Nippoldt, A. Mag- netische Mutung, p. 66. The formulas for platform observations or for different elevations of mine shafts apply (see pp. 407-408). 79 Phys. Zeit., 176-179 (1907); A. Nippoldt, Magnetische Mutung, pp. 68-70. 80 Koenigsberger, Gerl. Beitr., 20(3/4), 293-307 (1928). 81 [bid. : Cuap. 8] MAGNETIC METHOD 377 gravel pits they ranged from —13 to —20y. In valleys of granite, Koenigsberger observed anomalies of from —10 to —25y; in areas of basic schists, from —50 to —200y7; at the foot of glacio-fluvial terraces the effects varied from —20 to —30y. G. NorMAuL FIELDS Although interpretation of magnetic anomalies is based mainly on the shape of anomaly curves, it is frequently desirable to know the value of the undisturbed intensity in the area under survey. In some interpreta- tion problems it is necessary to differentiate between positive and negative anomalies; in vector and line-of-force interpretation the sign of the anomaly, and thus a fairly accurate determination of normal values, is of importance. There is no standard procedure for determining normal values since they depend on the type of anomaly surveyed. For large and locally limited anomalies it is sufficient to select a base station in geologically undisturbed terrain and to consider its intensity as the normal value. Elsewhere it is usually satisfactory to use the U. S. Coast and Geodetic Survey maps. Since regional anomalies are already included in their normal values, anomalies due to local deviations from regional structure appear as excess or deficiencies with respect to these. In extensive surveys conducted for the purpose of obtaining relations between magnetic anomalies and regional structure, it is better to use world charts in which only anomalies of continental order of magnitude remain. To simply form the average of all magnetic values in an area and designate this as the normal value is not recommended, since a given geologic body may not produce a balanced number of positive and nega- tive anomalies. The selection of a normal value is frequently a trial and error proposition. Its final value can often be chosen only with regard to the shape of the anomaly curve to be expected from theoretical and geological considerations. V. MAGNETIC FIELDS OF SUBSURFACE BODIES (INTERPRETATION THEORY) A. GRAPHICAL REPRESENTATION OF RESULTS For interpretation in geologic terms, magnetic data must be so plotted as to show the clearest indication of subsurface bodies. The following representations are in use: (1) lines of equal anomaly; (2) profiles at right angles to strike; (3) peg models, isometric maps; (4) anomalous vectors; and (5) magnetic gradients. 1. Lines of equal anomaly. For higher magnetic latitudes lines of equal 378 MAGNETIC METHOD [CHap. 8 vertical intensity anomaly are best suited. Their interval should be two to three times the probable error of the survey; greater intervals are pre- ferred for large anomaly gradients. ‘‘Isanomalic’? maps are comparable to contour maps; it is helpful to shade areas of equal anomaly, darkest shades corresponding to areas of greatest anomalies. The use of two different colors will be of assistance; red may be used for positive, and blue or green for negative anomalies. 2. Profiles at right angles to strike show magnetic values as ordinates and distances as abscissas above a known or inferred geologic section. For geologic features causing negative anomalies, inverted ordinates are used. Where a simple geometric relation between magnetic values and subsurface contours can be assumed, the scale of the magnetic ordinates may be made identical with the vertical scale in the geologic section. Parallel profiles across the same geologic feature may be cut of celluloid strips and mounted on a map (see Fig. 8-72). If horizontal intensity measurements have been made in the plane of the magnetic meridian, the anomalies must be projected upon a direction at right angles to the strike. This projected anomaly is hereinafter designated by the symbol H,. The conversion may be avoided by orienting a horizontal magnetometer at right angles to the strike or in a profile direction at approximately that angle. 3. Peg models, isometric maps. Magnetic anomalies may be represented on maps by pegs of proportionate length (see Fig. 8-71). For areas of small magnetic gradients, better visualization of the magnetic relief can be obtained in this manner. However, negative magnetic anomalies do not show to advantage. Isometric maps are prepared by using the 60° axis for the north, the 120° axis for the east coordinate of the map, and the 0° or vertical axis for the representation of anomalies. A difficulty with isometric maps is that large anomalies may obscure adjacent features and that negative anomalies cannot be shown advantageously. 4. Anomalous vectors. Interpretational advantages are often gained by representing the results in the form of anomalous vectors, since they are tangent +o the lines of force radiating from the poles of the disturbing objects. Their usefulness, however, depends upon a careful selection of the normal value. Horizontal vectors may be plotted from anomalies in declination and horizontal intensity. A convenient method is to calculate the north com- ponent X and the east component Y from the observations, to subtract X) and Y,, and to plot AX and AY. The anomalous vector F# is the resultant of the two (see Fig. 8-43a). In another method the normal Ho is plotted in the direction 6) , and the observed H is plotted at the observed angle (see Fig. 8-43b); the horizontal anomalous vector F is equal to the vectorial difference of Hy and H. The Tiberg method of the parallelogram Se Cuap. 8] MAGNETIC METHOD 379 of forces is virtually identical with the method just discussed. Under- ground measurements are made by stretching a cord between two points, A and B. The line AB may make the angle 6 with the normal meridian. At each point the actual magnetic meridian referred to AB, and the actual horizontal intensity are measured by using the Dahlblom sine arm. This gives H and y and, thus, R (Fig. 8-43c). Astrenemic aes | i Ste Pt iy) AZ ~ ! ag eee eM | eg) (e) (Ff) (9) Fig. 8-43. (a) Horizontal anomalous vector from X and Y. (6) Horizontal anomalous vector from Hy, 6, and H. (c) Tiberg’s ‘‘arrow’’ method. (d) Vertical anomalous vector from Hp and Z. (e) Vertical anomalous vector from To, Io, T, and I. (f) Total anomalous vector in isometric projection. (g) Total anomalous vector in two-dimensional representation (Jenny). (hk) Total anomalous vector in two-dimensional representation. Vertical vectors may be plotted from horizontal and vertical intensity observations with Schmidt balances or from inclination and total intensity observations with the Hotchkiss superdip. If AH has been reduced to the direction of the profile, the vertical disturbance vector, S, = A (AH,)" + (AZ)’ is obtained from the construction indicated in Fig. 8-43d. a \ ' | Niue cae 2000 Sy Vee SE eho x Aer iY MAES POT EEA i ¥ ipecietia ae So ae Se, SESS ee eee ae ie BY ce Surtace of Peridotile 4000 =~ Folded Paleozon / ge tks ey (wel! data) Oh eT = ts / aie ok e+ + ee are - + eer Ne ok Seale ae ‘ Peridotite Plug Fig. 8-65. Section across peridotite plug in Arkansas, showing depth finding by anomalous vectors (after Stearn). amphy” traced gold-bearing pegmatite dikes by their increased magnetiza- tion (negative anomalies, Southern Hemisphere), while Stearn’ surveyed gold-bearing rhyolite dikes that were intruded into monzonite and caused negative anomalies. In diamond-mine exploration, the magnetometer can be helpful in trac- ing the igneous plugs or pipes in which the diamonds occur. Stearn’ applied the magnetic method to the location of peridotite plugs in Arkansas 149 A.I.M.E. Geophysical Prospecting, 325 (1934). 150 Loc. cit. 161 Thid., 197. Cuap. 8] MAGNETIC METHOD 419 (see Fig. 8-65), Krahmann!®” on a Kimberlite pipe in southwestern Trans- vaal. In this survey the — 1200 gamma (Southern Hemisphere) anomaly followed very closely the outline of the pipe. Strong magnetic anomalies in the contact zone due to magnetized shales were also recorded. The stratigraphic association of sedimentary nonmagnetic beds of-:com- mercial value with magnetic members in the geologic section has been utilized to advantage in the Lake Superior region where strike, dip, and faults of the copper-bearing lava flows have been mapped by tracing mag- netic members in the series,” and in South Africa in connection with exploration for the gold conglomerates of the Witwatersrand system™ (see Fig. 8-66). These strata show evidence of considerable metamor- phism and consist of quartzites, slates and shales, the gold-bearing con- glomerates, and volcanic beds. Several dikes and faults cut through the area. In the west Witwatersrand the accurate stratigraphic relation of the magnetic beds (magnetic slates) to the main reef could be well estab- lished. During the experimental period a number of magnetic profiles were run on outcropping sections. Fig. 8-66 shows vertical intensity anomalies for the section near the main reef. The curves are quite irregu- lar because of changes in magnetite content. In the upper profile, at the point of greatest irregularity, magnetic material (extracted by electro- magnets) varied from 0 to 80 per cent, and susceptibilities from 0 to 10,000-10°°. When the overburden becomes comparable with the dis- tance of the magnetic shale members, their effects overlap, resulting in one major negative (Southern Hemisphere) anomaly (see Fig. 8-67). While in this particular area the magnetite shales were normally magnetized, syenite, dolerite, and granophyre dikes cutting through the area were abnormally magnetized. In another area” abnormal polarization was found on the magnetite shales (anomalies of 20,000 y for a depth of 477 feet). The susceptibilities determined in the laboratory were not sufficient to explain the magnitude of the anomalies.” It has been estimated that as a consequence of the magnetic surveys the potential gold production has been increased by at least one-eighth of its present amount. In the location of gold placer deposits, the stratigraphic association of placer channels with magnetic formations other than the concentrates can be helpful in locating the channel itself. Edge and Laby™” have demon- strated this at Gulgong, New South Wales, where the channels are filled with basalt flows, producing positive (Edge-Laby definition) anomalies 152 Min. and Met., 16, 342 (June, 1935). 153 Stearn, op. cit., 187. 154 Krahmann, Geol. Soc. 8. Afr. Trans., 39 (1936). 155 See F. Bahnemann, A.I.M.E. Contrib. No. 79, 1935. 156 See discussion on p. 401. 157 Op. cit., 189. 420 MAGNETIC METHOD [CHaAP. 8 +8000 04600 0 biabiatee tein. - 4000 1 3 Quartzite wn hale, not § magnetic -8000 7B Shale, slightly magnetic we roca HIGIC, Moderately 12000 ms Mmagneric Shale, tughly 5 magnetic 6 Ex) 7illite 7D Shaly Mudsyone 8 E23) Government heeft +4000 0 Seer ee = Gavernment Reef Shales -4000 1.234 324343 7 penne Jee eae | °£000 4 yh 0 ey Ne ee -2000 | Jeppesiown Beds beclogical Section not available Scale 0 50 200 500 4090 500 Engl Feet Fig. 8-66. Vertical intensity anomalies on outcrops of sections of lower Witwaters- rand system in West Wits area. The middle profile is 12 miles southwest of Krugers- dorp. (After Krahmann.) Ne 00° WITWATERSRAND SYSTEM Se 14000 Fig. 8-67. Interpretation of vertical intensity anomalies, western section, West Wits area, 33 miles southwest of Krugersdorp (after Krahmann). Cuap. 8] MAGNETIC METHOD 421 of about 5007. Placer channels may also be located structurally if the bedrock is magnetic. Fig. 8-68 shows a negative magnetic anomaly above a bedrock depression corresponding to an auriferous gravel channel in California. Structural magnetic prospecting has been applied in various countries in coal exploration. Edge and Laby’” surveyed the brown coal field at Gelliohdale, Victoria, with torsion balance and magnetometer. The brown coal is about 400 feet thick and occurs 50 to 100 feet from the Hotchkiss Superdip Scale Divisions Fig. 8-68. Magnetic lows over placer channels in California (after E. W. Ellsworth). surface, in troughs of Jurassic sandstone. Magnetic anomalies were caused by this sandstone and basaltic intrusions. Since Carboniferous deposits were formed in geosynclines, the regional depressions of the crystal- line basement and therefore negative magnetic anomalies have been found to be characteristic of productive Carboniferous in many areas in Europe (productive belt through Mons, Namur, and Luettich;’ Ruhr Basin be- tween Muenster, Duesseldorf, Elberfeld, and Soest; Carboniferous areas 168 Toid., 158. 159 Reich, op. cit., I, 20. 160 Joid., I, 31. 422 MAGNETIC METHOD [Cuap. 8 in northern France, near Aachen, in Hessen, Saxony, and Upper Silesia™™ in Germany). 5. Surveys for miscellaneous ores (chromite, manganese, and the like). As stated previously, direct magnetic prospecting for chromite may be successful if the ores are more magnetic than the basic igneous rocks in which they occur. Reference to magnetic work on chromite is made by Krasulin™” in the Urals, by Bagratuni’™ at Geidara (Kurdistan), and by Snelgrove™ in Newfoundland. A reference to Lundberg’s’® work men- tions magnetic effects of chromite ore in Newfoundland and surveys of chromite-bearing serpentines in Canada. Under favorable conditions, sedimentary manganese ores may be located directly at shallow depth. As shown by a survey made at Nickopol,’” Russia, the ore, consisting of pyrolusite, psilomelane, polyanite, and wad, occurs at depths of from 20 to 40 meters in clay on granite. Magnetic anomalies were small (of the order of 100 y in Z) and very irregular, corresponding to varying composi- tion of the ore and changes in the granitic bedrock surface. 6. For the location of meteors, the use of the magnetometer is, in most cases, uneconomical. An average iron meteorite, buried several feet deep, is not effective beyond a radius of 5 or 10 feet. Unless its location is known within very close limits, magnetic prospecting, even with a dip needle or cardan magnetometer, would require too many stations. When there is an accumulation of a large amount of meteoric material, the magnetic method may be used to locate areas of greatest concentration. For Meteor Crater, Arizona, Jakosky™” reports anomalies of surprisingly small magnitude (657) at the SW portion of the crater and assumes that the magnetic material begins at 200 feet and concentrates with depth. B. Maanetic Surveys IN O1L EXPLORATION Oil-bearing formations are rarely magnetic, and some other formation of a known structural or stratigraphic relation is mapped. Suchassociated formations are (1) salt domes, (2) magnetic beds in the sedimentary sec- tion, and (3) basement rocks and igneous intrusions. The exceptions where the ozl-bearing formations themselves produce magnetic effects are (a) granite wash on the flanks of ridges, (b) serpentine plugs and laccoliths, and (c) shoe string sands. 161 Reich, Zeit. Geophys., 2(7), 273-278 (1927). 162 Razvedka Nedr., 5/6, 18-21 (1983). 163 Thid., 19, 19-21 (Dec., 1933). 164 Chromite Deposits of Newfoundland, Dept. of Nat. Res., St. Johns, Nf. 165 Min. and Met., 16, 337 (Jan., 1935). 166 N. Trubiatchinski, Geol. and Prosp. Service, U.S.S.R. Fase. 166, (1932). 167 A _I.M.E. Geophysical Prospecting, 69 (1932). Cuap. 8] MAGNETIC METHOD 423 1. The magnetic location of salt domes was attempted shortly after the introduction of the Schmidt magnetometer. In northern Germany, salt domes produce negative anomalies by a combination of the following effects: (a) diamagnetism of the salt, (b) diamagnetism of gypsum and anhydrite in the cap rock where present, (c) paramagnetism of glacial strata if salt dome is near surface, and possibly (d) slight paramagnetism of Tertiary and Cretaceous sediments. Magnetic surveys on salt domes 5400-$0. Contour Top of Oligocene / “y 765 Fig. 8-69. Magnetic anomalies on Port Barre salt dome (after Barret). were made by Schuh” and Moll’” in Mecklenburg; by the author on the salt domes of Segeberg and Lueneburg; by Haalck and Brinkmeier’” on the salt dome of Wefensleben; by Kohl and Krahmann™ on the salt anticlines of Salzgitter and Benthen. Except on outcropping cap rocks, 168 Mecklenb. Geol. Survey, 32 (1920). 169 Mecklenb. Geol. Survey, 33 (1922). 170 Haalck, Die magnetischen Verfahren, p. 132. 171 Metall und Erz., 23, 583-586 (1926); 26, 571-582 (1928). 424 MAGNETIC METHOD [Cuap. 8 salt dome anomalies seldom exceeded 20 or 30y in any of the above surveys. On the salt dome of Hettenschlag, in Alsace,” the negative anomalies were of the same order. When magnetometers were first in- troduced on the Gulf coast, experimental surveys were made on a number of known domes. The author ran a number of traverses on the Barbers Hill and Esperson domes in 1925. In the following years the magnetom- eter found more application for the mapping of basement topography, and it was not until its accuracy was increased that it was used again in salt dome work on the Gulf coast. Surveys have been published by Barret”® for the Simmsboro area and for the Anse La Butte and Port Barre domes,” and by Jenny” and Clark and Eby” for the Fannet dome. The latter, comparatively near the surface, produces an anomaly of —25y. The Port Barre dome, at much greater depth, has an anomaly of only —15y (see Fig. 8-69). 2. Determination of structure by the mapping of magnetic sedimentary formations. While most magnetic anomalies in producing or prospective oil territory are due to changes in topography or composition of the base- ment rocks or to intrusions of igneous rocks, there are certain areas, particularly those distinguished by great thicknesses of sedimentary forma- tions, where the effect of sedimentary beds predominates. The effective magnetic members may be ferruginous shales, sandstones, volcanic tuffs, iron conglomerates, and the like. Uplifts of such formations are charac- terized by positive anomalies except where magnetic members thin out over the crest or have been eroded away. Such conditions occur in California’” where there is a marked variation in susceptibilities of sedi- mentary rocks. In the Tertiary formation, susceptibilities vary from 14.10°° in the Saugus of the Upper Pliocene to 4000-10 ° in the vivianitic sandstone of the McKittrick group in the Pliocene. The Cretaceous is, on an average, more magnetic than the Tertiary, and the Jurassic (Franciscan) is more magnetic than either Tertiary or Cretace- ous. The picture is further complicated by interbedded volcanics, and metamorphic and intrusive rocks. At the Raven Pass anticline with flank dips of 40° to 50°, Cretaceous beds in the center are more magnetic than the Miocene on the flanks, giving rise to positive anomalies of 1107 on the crest. On the other hand, on the White Creek syncline 20 miles northwest of Coalinga with strongly magnetic cretaceous beds on the 172 P. Geoffroy, Ann. Off. Comb. Liqu., 6, 1015-1021 (1929). 173 Barret, Mapping Geologic Structure with the Magnetometric Methods (Shreveport, Feb., 1937). 174 A .A.P.G. Bull., 19(7), 1070-1071 (July, 1935). 175 Oil Weekly, April 27, 1936. 178 A.A.P.G. Bull., 19(3), 363 (Mar., 1935). 177 EF. D. Lynton, A.A.P.G. Bull., 15(11), 1351-1370 (Nov., 1931). Cuap. 8] MAGNETIC METHOD 425 flanks and moderately magnetic Etchegoin beds in the core, a drop in vertical intensity was observed. The Kettleman Hills structure shows a series of highs on the upturned edges of the fold, magnetic lows along the axis of the north dome, and a series of highs on the axis of the middle dome, indicating that the magnetic beds were eroded from the north dome but are continuous across the middle dome. Similar conditions appear to exist on the Dominguez dome.” Erosion of magnetic formations from the crest of anticlines may also be responsible for magnetic lows found above uplifts in other states. The problem of their origin has not been settled and the following explanations have been advanced: (a) effects of well casing and derricks, (b) abnormal polarization, (c) erosion of magnetic formations from crests, and (d) ir- regular basement magnetization. Negative anomalies have been found in the Healdton, Oklahoma City, and Garber fields.” Conversely, Som- ers” believes that positive anomalies may be encountered on anticlines because of uplifts of magnetic sedimentaries as well as on synclines be- cause of an increase in thickness of magnetic sediments. According to Jenny™ both effects are in evidence on the Gulf coast. In the northern part of that area magnetic anomalies are presumably caused by structural uplifts, while along the coastal portion they are assumed to be due to changes in thickness of the magnetic strata. The magnetically active beds are assumed to be of Eocene age in the north and of lower Miocene age in the southern portion. In the former, the Conroe field produces a distinct positive anomaly’ (15 to 20y) (see Fig. 8-70). When magnetic formations are uplifted by a salt dome, the negative salt effect may be obliterated and replaced by a positive anomaly above the dome (Jenny™). The presence of magnetic members in a sedimentary column gives an opportunity for the location of faults. They may reveal themselves by a transition of higher to lower magnetic values or by abrupt depressions in the curve, all depending on thickness, depth and dip of the magnetic beds, and hade and throw of the fault. Fig. 8-71 (from Lynton™) shows a magnetic survey on the San Andreas fault and Fig. 8-72 on the Walnut Creek fault. The trace of the latter is indicated by a sharp drop in the profile curves, high values to the northeast corresponding to the more 178 California Oil World, April 30, 1931. 179 Oi] and Gas J., Nov. 15, 1928. 180 “‘Anomalies of Vertical Intensity,’’ Colo. Sch. Mines Mag., Aug.—Dec., 1930. Jan.—Feb., 1931. 181 Oil Weekly, July 16 and 23, 1934. 182 J. H. Williams, Oil Weekly, Aug. 21, 1934 183 Oil Weekly, April 27, 1936. 184 Loc. cit. 426 MAGNETIC METHOD ACuap. 8 magnetic Cretaceous sediments and low values to the southwest cor- responding to less magnetic Eocene strata. In the Pettus area (Bee -4990 Contour, top of the Conroe Sand Fic. 8-70. Magnetic survey of Conroe area (after Williams). Fig. 8-71. Magnetic survey of San Andreas fault, California (peg model) (after Lynton). County, Texas) Barret’” observed a definite minimum on the principal fault whose throw is some 500 feet in the Pettus sand (Eocene, about 4000 feet deep). Magnetic anomalies of faults are often greater than 185 Toc. cit. Cuap. 8] MAGNETIC METHOD 427 anticipated if basement rocks have been affected, if igneous sheets have been intruded into the fault fissure, or if the fault plane has acquired con- centrations of magnetic material or has been magnetized by other causes. J. Jung and C. Alexanian’” made surveys on faults at Allschwill (Meletta against Cyrene marls), at Niederhaslach (Triassic lime against sandstone), at Aubure (granite against sandstone) and at Guewenheim (Meletta marls against shales, and the like), and observed the typical depression in the vertical intensity curve also noticed elsewhere. They came to the con- clusion that this effect cannot be explained by the susceptibilities and ne RR BOE CRELK BREA Fic. 8-72. Magnetic survey of Walnut Creek fault, California (celluloid profiles on map) (after Lynton). disposition of the adjacent formations but must be an effect of the fault plane itself. Similar depressions in magnetic curves corresponding to the Leopoldsdorf and Sollenau faults in the Vienna basin were observed by Forberger, John, and Petrascheck.” 3. Mapping of basement topography and of igneous intrusions. In many oil-producing areas or prospective oil territories, structure in the sedimentaries is controlled by the topography of basement rocks due to deep seated folding or faulting, or by differential settling about pre-existing basement highs. Intrusions of igneous rocks, such as plugs and batholiths, 186 Ann. Off. Comb. Liqu., 4, 711-720 (1931). 187 Akad. Wiss. Wien, Sitz. Ber., 143(1), (5-7), 137-145 (1934). 428 MAGNETIC METHOD [Cuar. 8 and lateral injections into sediments in the form of laccoliths may produce doming of strata, and their magnetic anomalies will give an indirect indication of structure in the oil-producing section. Where basement rocks are uniformly magnetized, mapping of topography has resulted in the location of new oil fields and the extension of known ones. One of the best-known examples is the Hobbs field (Lea County, New Mexico, see Fig. 8-73). It was located in 1926 by a midwest mag- netometer party, surveyed by torsion balance, and drilled in 1927. Con- Fic. 8-73. Magnetic contours (after Lahee), structural contours (after DeFord), and torsion-balance data (after Coffin) for Hobbs field, discovered by a magnetic survey. siderable development followed in 1929. The magnetic contours are shifted in comparison with the structural contours at 4000 feet. Accord- ing to Barret’s interpretation, this is due to the normal induction in the earth’s magnetic field which places the maximum in Z south of the highest point of the subsurface feature. On other structures such displacements 188 A.A.P.G. Bull., 16(1), 51-90 (Jan., 1932). Cuap. 8] MAGNETIC METHOD 429 of magnetic and structural contours have been found to occur (a) when there is a shift of the structural axis; (b) when an igneous core acts as a buttress against lateral forces which pushed the sedimentaries over the igneous core; and (c) when the basement is not uniformly magnetized, for instance, when a buried hill consists of both sedimentaries and intrusives. Another instructive example of the successful application of the mag- netometer in locating oil structure by mapping basement topography is the survey of the Nocona field (Fig. 8-74)."” The magnetometer closure Leeeno IN SKETCH "A‘- 1SODYNAMIC LINES. IN SKETCH "B"- STRUCTURE CONTOUR LINES. PRODUCING WELL Fic. 8-74. Magnetic and structural contours of Nocona field, Oklahoma. The northern extension of the field was developed as the resuit of the magnetometer survey. (a) Magnetic contours, (b) structural contours. is small and the magnetic high is shifted with respect to the structural high. In the Lucien field a small magnetic anomaly is caused by the granite core of the Ordovician fold.” The buried Amarillo granite ridge has been the object of considerable magnetic study. Profiles over the ridge were made as early as 1925, and the results were published by Adams™ and the author.” The granite is about 3000 feet deep at the 189 Heiland, Terr. Mag., 37(3), 343-348 (Sept., 1932). 190 Jenny, Oil Weekly, 72(13), 16-18 (Mar. 12, 1934). 191 Oil and Gas J., Feb. 16, 1928. 192 Colo. Sch. Mines Quart., 24(1), 64 (Mar., 1929). 430 MAGNETIC METHOD [Cuap. 8 highest point, where the magnetic anomaly is some 300y. In the eastward extension of the Amarillo Ridge, the Wichita and Arbuckle Mountains and their buried forelands have been surveyed in detail by the Shell Oil Co. A portion of their magnetic map is reproduced in Fig. 8-75. The geophysical surveys and subsequent drilling brought out the fact that the Arbuckles form a separate folding system, are not connected with the Wichita Mountains, and are separated from them by the Ardmore basin.” The Wichita Mountains continue uninterruptedly as the Walters Arch into the Muenster Arch. The interval of the magnetic isanomalics (ob- tained with magnetometers) is 1007. The Arbuckle, Criner, Walters, and Muenster Arches are indicated by magnetic highs approximately cor- responding to gravity highs, while the intervening Ardmore and Marietta synclines are magnetic lows. While the magnetic anomalies are, in the main, caused by the contact of the sediments with the pre-Cambrian gneisses, granites, granite porphyries, and the like, changes in the com- position of the basement rocks also affect the picture. Sediments appear to have little or no effect on anomalies in this area. For Alabama, similar regional surveys and interpretations are discussed by Eby and Nicar,™ and for the coastal plains of Nort and South Caro- lina, by McCarthy.” Regular trends of highs and lows of considerable amplitude (up to 12007) were observed. The actual number of detailed magnetometer surveys made for oil exploration in Texas, Louisiana, Mis- sissippi, Alabama, Oklahoma, Kansas, Colorado. New Mexico, California, Wyoming, and the Dakotas is much greater than these few examples would indicate. The general conclusion to be derived from this work is that the magnetic method can be exceedingly useful in structural oil prospecting of such areas where the basement rocks are of uniform com- position and uniformly magnetized and where magnetic sediments, if present, are continuous and conformable to basement topography. Where there are rapid changes of igneous rocks in the basement, intrusions of irregular character, erosion of magnetic sediments, or irregular distribu- tions of magnetic materials within them, magnetic exploration should be replaced by a different geophysical method. As previously mentioned, faults may be located magnetically where they have affected the basement rocks. In the Amarillo field (N. H. Stearn’) the Potter County fault of 1200-1500 foot throw showed by an abrupt drop in Hotchkiss superdip readings. Over the Beckham County fault with a throw of 300-500 feet the intensity dropped about 400y. The 193 World Petrol. Congr. Proc., B(I), 174 (1933). See also Fig. 7-51b. 194 Geol. Survey Ala. Bull., 43 (June, 1936). 195 Jour. Geol., 44(3), 396-406 (April-May 1936). 196 A .I.M.E. Geophysical Prospecting, 189-191 (1932). ‘A QOL :[BAtoq}UI INOZUOD oTyoUTBYT “(UOPfIdA4 UBA 1904j8) Jap1Og SBX9T-VWOYR[YO 94} Suo[e’ spuos}, [eVanjonsys Jo puv surejuNo; spyonqiy pue Bylot Jo deur oyousvyy ‘¢7-g “DIZ i) Siw | VLIHOIM, 432 MAGNETIC METHOD [Cuap. 8 depth of the basement in the case of the Amarillo fault on the downthrow side was assumed to be about 4000 feet and the depth of the basement in the case of the Beckham County fault about 2500 feet. The Hazeldean fault (Miller’’) in the pre-Cambrian, with a throw of 700 feet, caused a positive peak of about 120y on the upthrow side and a flatter negative anomaly of — 160 7 amplitude on the downthrow side. Theoretical calcula- tions checked the maximum as to amplitude and position, but gave for the negative anomaly about half the observed amplitude and a negative peak much closer to the fault. Igneous intrusions have been frequently mapped in connection with magnetic oil exploration. Extensive batholithic intrusions may give rise to doming of the oil-bearing strata. Fracture and fault zones are often accompanied by intrusions; laccolithic wedges produce warping in the sedimentary beds. Examples of magnetic effects of intrusives have been frequently cited in the literature and but a few examples will suffice. Lynton” reports a number of surveys on basic igneous intrusions from California whose susceptibility is given as around 7000-10 ° units. In the vicinity of Paso Creek in the San Joaquin Valley the magnetometer out- lined a strong high (anomaly not stated). A well subsequently drilled encountered plutonic rocks at 2700 feet. In the Ventura basin near Oxnard an anomalous area with peak value of 700y was outlined, and a well put down in the high area encountered basalt at 1915 feet. The susceptibility of the basalt as determined on well samples was 700-10 °. On the Jackson uplift in Mississippi an extensive magnetometer survey was made by Spraragen.”” A difference of 9007 in vertical intensity from the lowest to the highest point corresponds to a difference in depth to the chalk of 560 feet. A similar survey was made by Barret” on the Caddo- Shreveport uplift. The maximum in vertical intensity is 2507 and a minimum of —250y occurs to the north. The structural high is much broader than the magnetic high, and there appears to be a considerable shift (to the south) of the place of maximum vertical gradient compared with the place of maximum structural gradient. The area of the 600-foot contour (on top of the producing sand in the Nacatoch formation) is dis- placed as much as 10 miles to the northwest from the area of the 225-y contour. A rather unusual condition exists in the serpentine fields of southwest Texas (Yoast field, Bastrop County; and Dale field, Caldwell County) because the oil occurs in the magnetically active formation. In the Yoast field™ the serpentine is at a depth of about 1500 feet 197 Canad. Geol. Survey Mem., 170, 99-118 (1932). See also Fig. 7-117. 198 Toc. cit. 199 Oil and Gas J., 30(26) (Jan. 21, 1932). 200 A.A.P.G. Bull., 14(2), 175-183 (1930). 201 TD), M. Collingwood, A.A.P.G. Bull., 14(9), 1191-1198 (Sept., 1930). Cuap. 8] MAGNETIC METHOD 433 and produces a positive anomaly of about 25,7. Studies of exposed igneous rocks in Uvalde and Kinney Counties, Texas, were correlated by Liddle®..with surveys of the Little Fry Pan anticline, where small magnetic anomalies were found. A well located on the _ highest point of the anticline encountered 150 feet of serpentine at 1000 feet depth. Other serpentine plugs in the same area (Yoast field, Dale field [serpentine at about 2000 feet]; Ellstone structure [serpentine at about 700 feet]; Buchanan field [serpentine at 1800 feet]) were outlined by Sprara- gen.” In the San Pedro area in Brazil, Malamphy™ studied the effects of laccoliths and sills of basalts, found anomalies of the order of 2007 maximum corresponding to susceptibilities of about 4000-10~° units, and compared actual depths (350 to 450 feet) with depths calculated from the drop of the vertical intensity curve (which gave from 300 to 400 feet). Where oil production is associated with intrusives along fracture and fault zones, detailed magnetic surveys to locate the igneous sheets will be of considerable help. Examples of such surveys in Mexico have been published by the author.” 4. For the location of shoestring sands, only one example is known. Stearn” has described results obtained on several profiles through the Bush City shoestring in Anderson County, whose depth is from 600 to 800 feet. Anomalies are predominantly negative and of the order of 20 to 407. As Stearn indicates, it would be difficult to locate shoestrings magnetically because of the small magnitude and lack of definition of the anomalies. C. MaGnetic SuRVEYS IN CIVIL AND MiniTary ENGINEERING The scarcity of magnetic surveys in civil and military engineering is due not so much to adverse conditions as to lack of information on the part of the civil engineer regarding the possibilities of geophysical exploration. The usefulness of magnetic methods has been demonstrated in a number of cases discussed below. 1. Water supply and drainage surveys may derive much assistance from magnetic exploration where water occurs in troughs underlain by crystal- line or igneous rocks, where-its circulation is controlled by structure of magnetic beds, where water occurs in porous magnetic igneous rocks, or where its circulation is blocked by faults or igneous dikes. An applica- tion of this sort is mentioned by Grohskopf and Reinoehl”” who found that 202 A.A.P.G. Bull., 14(4), 509-516 (April, 1930). 203 Op. cit., 28(62) 42 (May 15, 1930). 204 A .I.M.E. Tech. Publ. No. 696 (Feb., 1936). 205 Colo. Sch. Mines Quart., 24(1), 61 (1929). 208 A.I.M.E. Geophysical Prospecting, 192 (1932). 207 Miss. State Geol. Rep., App. IV (1933). 434 MAGNETIC METHOD [Cuap. 8 thinning and tightening of the water-bearing beds occurred on magnetic highs so that chances of increased water supply were greater on the flanks and in the lows. A report by Kelly’ states that a subsurface N 22007 S +12007 +8007 +4007 ° 100 200 300m +2003 +8007 +4007 to7 -4007 i a) 160 200 369 400m Fig. 8-76. Location and thickness determination of basalt flows for building and road material (after Ahrens). structural trough was mapped magnetically by Jakosky to investigate water supply conditions on the Kaibab plateau. 2. In the location of construction materials, magnetic methods have con- siderable chance of success in outlining occurrences of igneous rocks suit- 208 Min. and Met., 17, 10 (Jan., 1936). Cuap. 8] MAGNETIC METHOD 435 able for building stone, such as granite, basalt, and the like. Fig. 8-76 shows the magnetic anomalies of a lava flow above nonmagnetic Tertiary shales. The magnetic anomalies are proportional to the thickness of the lava cover; minima occur where the shales come through to the surface. Ahrens” and Schroeder and Reich” established by a detailed survey of a basalt quarry that it was possible to differentiate between solid basalt usable for construction purposes and unusable weathered rock, since the anomalies over portions of the latter were much reduced. Fic. 8-77. Location of buried ammunition by magnetic and electrical measure- ments. Anomalies are shown in profile view, together with equipotential lines of an electrical survey. (After Ebert.) 3. Dam site surveys. Magnetic surveys can be of much help in deter- mining structural conditions and rock properties on dam sites since they are much less expensive than drilling; at least, their use makes it possible to limit drilling operations to the absolute minimum. How the use of geophysics can reduce excavation and construction costs has been demon- strated in the case of the Bonneville Dam. It is reported that in the geological survey of that area the possibility of igneous intrusions was not recognized and that, after the first excavations encountered basalt, a geophysicist was called in to survey the basalt dikes. This subsequently 209 Beitr. angew. Geophys., 2(4), 320 (1932). 210 Beitr. angew. Geophys., 1(4), 432-436 (1931). 436 MAGNETIC METHOD [Cuap. 8 changed the construction plans and made it possible to use basalt pillars as foundations for a power house. 4. If the location of buried metal (pipe lines, ammunition) is known approximately, it may be readily found by magnetometers adaptable to rapid surveys, such as the dip needle and similar magnetometers. A Keuffel and Esser prospectus describes the location of two pipe lines, and an article by Ebert” discusses the location of a buried ammunition magazine by electrical and-magnetic measurements (see Fig. 8-77). Verti- cal intensity anomalies up to 400y were observed. Two lost magazines were found by combined electrical and magnetic measurements. 211 Beitr. angew. Geophys., 1(1), 9-14 (1930). 9 SEISMIC METHODS I. INTRODUCTION Srtsmic procedures are in the group of ‘‘indirect’”’ geophysical methods in which extraneous fields are set up and reactions of subsurface conditions to such fields are measured. Seismic exploration is concerned with the investigation of elastic forces. Contrary to other indirect geophysical methods—such as electrical ones—these fields of elastic forces are not stationary or quasi-stationary but vary and propagate with time. In common with electrical methods, the depth of investigation in seismic exploration may be controlled by varying the spacing between transmis- sion and reception points. This gives both the seismic and electrical methods great interpretational advantages over the gravitational and magnetic methods, since the indications furnished by the latter two repre- sent the integral effects of all masses from great depths up to the surface. Direct and quantitative determinations of depths are the exceptions in gravimetric and magnetic work, but they are common practice in seismic and resistivity methods. A further advantage of seismic methods lies in the fact that not only the depths of geologic bodies but also some of their physical properties may be obtained. Seismic and resistivity methods are, therefore, particularly well adapted to determinations of horizontal or nearly honzontal formation boundaries. This does not mean that other types of geologic bodies may not be well adapted to seismic exploration. Seismic refraction shooting has attained great practical significance in the location of salt domes because of the distinct geometric disposition and elasticity contrast existing in such domes. Like most other geophysical methods, seismic methods depend for their successful application on the size of geologic bodies to be located. Both the refraction and resistivity methods depend on the thickness of forma- tions compared with depth. This does not appear to hold for the reflec- 1 With the exception of the reflection method. 437 438 SEISMIC METHODS [Cuap. 9 SYMBOLS USED IN CHAPTER 9 asc va MSTA RSRDOVS SOROS Po Se RSS Sees SSS Sy SS at Ss Ss QS RDRN amplitude, distance amplitude, breadth distance deflection, distance, diameter, depth | distance frequency frequency factor gravity depth, height, thickness angle V—l1 incompressibility factor length mass tuning factor percentage, proportion, factor restoration coefficient distance, radius distance time displacement displacement displacement coordinate, displacement coordinate, displacement coordinate, depth distance constant, curvature distance, depth electromotive force force, load height, depth | current sectional moment of inertia moment of inertia length magnification turns force, pressure factor, amplitude ratio factor, amplitude period, time ultimate stress volume energy density amplitude depth angle angle angle Sep taHonrQoB PRNKMAddHoOwW VU Z ASH woOWD> coefficient, factor constant damping factor 2.718 friction number factor, number number number damping resistance refractive index ratio scale reading temperature salinity velocity vector amplitude vector amplitude vector amplitude couple Young’s modulus field strength intensity indicator length compressibility magnetomotive foree power resistance surface, area transmission constant transmission constant indicator magnification dynamic magnification stress component stress component stress component coefficient coefficient Crap. 9] SEISMIC METHODS 439 SYMBOLS USED IN CHAPTER 9—Concluded | 5 angle 6 density A increment € angle; damping constant £ dilation coefficient t friction factor n damping factor | ® | volume change nx wave length a Lamé coefficient A logarithmic decrement be (Galitzin) damping factor u | rigidity modulus \lenae, | velocity ratio II Poisseuille coefficient p radius, distance o Poisson’s ratio é | factor T torsion coefficient Fa 5 | time 9 angle © flux ® dip angle y angle | w angular frequency tion method, which has been found to be applicable to depths of 20,000 to 30,000 feet without any apparent relation to the thickness of the re- flecting formation (provided it exceeds a certain minimum value, such as 25-50 feet). As the principal objective of seismic methods is a depth determination of elastic discontinuities, it is necessary that these properties remain reasonably constant in horizontal direction. This is true for most oil-bearing structures in which formations have been changed compara- tively little from their original position, and it is one of the reasons why seismic prospecting has been applied so extensively in oil exploration. Uses of seismic prospecting in mining have been few. Regions in which ore bodies are found are generally folded, faulted, intruded by igneous bodies, and metamorphosed. The continuity of physical properties that is so prevalent in sedimentary oil-bearing regions rarely exists in mining areas. Further, ore bodies generally do not differ sufficiently in their elastic properties from the surrounding rocks. Exceptions are the seismic determination of overburden thickness, the location of gold-bearing gravel channels, and structural investigations of carboniferous regions and sedimentary ores. Applications of seismic methods depend on the degree of contrast in elastic properties of geologic bodies with respect to the surrounding media. In seismic exploration, differences in the speed of elastic waves in different formations are measured. These depend on certain combinations of Young’s modulus of elasticity, Poisson’s ratio, and density. The influence of density counteracts that of the modulus of elasticity. However, with an increasing degree of consolidation, the modulus of elasticity increases at a greater rate than does density so that formations of a greater degree of 440 SEISMIC METHODS [CHap. 9 consolidation, dynamo-metamorphism, and greater geologic age general exhibit a greater seismic wave speed. In regard to physical laws involved, seismic phenomena are comparable to optical phenomena since they deal with a type of energy propagated in the form of waves. Wave propagation may be said to be characterized by velocity, frequency, intensity, direction, and certain associated or de- rived characteristics and phenomena, such as travel time, wave length, absorption, refraction, reflection, and the like. In optics, only quasi- stationary phenomena are investigated, owing to the rapid rate of propa- gation of light, whereas in seismic work, virtually all interpretation is based on travel time. Comparatively little quantitative use is made of direction, frequency, and intensity. The chief objective is to determine the distance between the earth’s surface and one or more refracting and reflecting surfaces below. Sensitive detection devices are used to record the arrival times of first (refraction) or later (refraction and reflection) impulses. These detectors embody an inert mass which remains (at first) stationary in respect to the ground, and whose movement may be magni- fied mechanically or electrically. In addition, the instant of the explosion is transferred to the receiving station; accurate time marks are provided on the record so that the time elapsed between the shot and the arrival of the elastic impulses may be found. Together with a determination of distance between shot point and record, this permits of measuring the true and apparent velocities of elastic waves. The simplest method of seismic prospecting is the fan-shooting method. This consists of comparing the travel times from a single shot point to a number of pickups arranged approximately in a circle around it. The ex- istence and sometimes the nature of an intervening medium may be deduced from these data. More detailed information is derived from the refrac- tion method, which consists of shooting traverses with one (or two) shot points and a number of seismographs set up in line, and determining the travel time as a function of distance. The time-distance curves give in- formation on the paths of seismic rays below, their refraction, and depths to refracting surfaces. In the reflection method, the travel times of re- flected waves allow depths to reflecting surfaces to be calculated. Observation methods and instruments in seismic prospecting and earth- quake seismology are very similar in respect to time marking, time trans- mission, and recording procedures. The inductive electromagnetic seismo- graph, which is now widely used in geophysical exploration, was developed for earthquake seismology by Galitzin more than twenty-five years ago. On the other hand, important differences in instruments were brought about by the needs of adaptation to geological exploration. This resulted in a decrease of size, increase in portability, increase in natural frequency Cuap. 9] SEISMIC METHODS 44] and magnification, introduction of electrical amplification, increase in photographic recording speed and restriction of the record to the vertical component. However, the theory of wave propagation used in seismic prospecting is again quite similar to the theory developed in earthquake seismology. In the application of the seismic method to oil exploration, great suc- cesses have been obtained in locating salt domes, anticlines and faults, and in mapping the topography of basement rocks. Buried land surfaces and limestone beds are usually good seismic key horizons. While in oil exploration refraction methods dominated the field several years ago both for reconnaissance and detail, the picture has now changed completely. Ever increasing fields of application have been found for the reflection method. It was soon discovered that not only limestone beds but hard shales and other beds with seemingly small differences in elastic properties would give reflections. On occasion, their lack of continuity gave rise to serious difficulties, but these were overcome by the application of the dip- shooting and the continuous-profiling methods. The field of civil engineering has also seen the application of seismic ex- ploration in late years. Most foundation problems, such as determination of depth to bedrock and investigation of tunnel and dam sites, may be attacked by refraction methods. Another application of seismology in civil engineering (engineering seismology) has as its objective the design of earthquake-proof structures, the determination of dynamic response of models of proposed structures, the investigation of damage done by traffic and blasting vibrations, the determination of the elastic properties of foundation sites, and the analysis of the frequency response of roadbeds, bridges, dams, and buildings. A discussion of the fields of engineering seismology and of acoustic methods is given in Chapter 12. II. PHYSICAL ROCK PROPERTIES IN SEISMIC EXPLORATION ; SELECTED TOPICS ON THE THEORY OF ELASTIC DEFORMATIONS AND WAVE PROPAGATION A. GENERAL The elastic properties of rocks may be ascertained in the laboratory, and from such data the velocity of the elastic waves in formations may be determined. Direct velocity determinations may be made in the field (1) by shooting on exposed formations; (2) by shooting in or near a well at known depths (average velocity determinations in reflection work) ; and (8) from the travel-time curve. A direct measurement of velocity on rock samples in the laboratory has not been attempted. Elastic wave-producing forces are associated with two types of strains: 442 SEISMIC METHODS {(Cuar. 9 (1) volume changes, that is, compression or dilation; (2) shearing strains. These two strains propagate in'a homogeneous isotropic medium with con- stant but different velocities. It is true that geologic formations en- countered near the surface and in the interior of the earth are far from homogeneous and isotropic. However, this can be allowed for by assuming continuous or discontinuous variations of the physical properties and by applying the theory to small elements of an elastic substance. The deriva- tions given below presuppose, furthermore, a perfectly elastic body, that is, a body in which the stress is proportional to the strain (one to which Hooke’s law may be applied), and one in which there is no elastic hysteresis. B. ELEMENTS OF THEORY OF Evastic DEFORMATION AND WAVE PROPAGATION” 1. Relation of strain and stress; elastic properties; volume and shear de- formations (static problem). In considering an element of volume of an Fig. 9-1. Normal and tangential stress components in elementary parallelopiped. elastic body subjected to stress (Fig. 9-1), its orientation can be so chosen that the three stress components X,, Y,, and Z,, are at right angles to its surfaces; S,, S,, and S,. These stress components are known as “normal” stresses. Two stress components exist in each surface at right angles to each of the three normal stresses. These components are known as “tangential” stresses and are designated Z, , X. ; Y,, X, ; and Z,, Y. . 2 This section is not intended to go into the detail& of the theory of elasticity; and it has, of necessity, been limited to a discussion of the definition and relation of elastic moduli and wave velocities. The literature on theoretical physics contains numerous valuable treatises on the subject, for instance, L. Page, Theoretical Phystes, pp. 132-141, Van Nostrand (1928); A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity (2 volumes, Cambridge, 1892-1893); W. Thomson and P. G. Tait, Treatise on Natural Philosophy, vol. II, chap. vit (Cambridge, 1883). Cuap. 9] SE ISMIC METHODS 443 Since the elementary body must be in equilibrium against rotation, the tangential stresses in each pair referred to above are equal to one another. (a) Normal stresses. Under the influence of the normal stresses X, , Y, , and Z, , three sides of the element of volume suffer the displacements u in the x direction, v in the y direction, and w in the z direction. Then the deformations referred to unit length, or the specific strains, are du/dzx, dv/dy, and dw/dz. The change in volume AV, resulting from the deforma- tions in the three directions, is equal to the sum of the specific strains: AV i Ou Ov Ow YF If © is negative, reduction of volume or compression takes place; if positive, extension or dilation. The change in volume is accompanied ‘by a change in shape; when the length is extended, the section is reduced. In this type of deformation, the angles are preserved. Since the strains are proportional to the stresses, the relation between normal stress and the corresponding strain in the x direction may be written” ee = e-X,, (9-2) Ox ; where e is the dilation coefficient. A more customary definition of this coefficient may be arrived at by writing 1_% _P/s eau Al’ ax l E=--— (9-3) that is, load per unit area divided by relative elongation. The expansion du/dz in the x direction produces a reduction of section in the y-z plane. Assuming the reductions in width, dv/dy and dw/dz, to be equal and to be a fraction of and proportional to the elongation, we have ov ow ou tA tad ae tel 9-4a oy 0z ° Oa ( ) ‘ , ; : ow / du The factor o is called Potsson’s ratio. From eq. (9-4a), ¢ = ai / ae %¢ Assuming, for the moment, that X, alone is effective. The complete expres- sions are given in eq. (9-6). 444 SEISMIC METHODS [Cuap. 9 or as generally written, Ad /Al Solin) ar wii Poisson’s ratio is the ratio of relative reduction of diameter d and relative elongation. For many substances, o is in the neighborhood of }. Substi- tuting (9-2) in (9-4a), eke (9-5) The original extension in the zx direction given by eq. (9-2) is opposed by a reduction of the z-z section due to the normal stress Y,. Byanalogy with (9-5), this reduction is (du/dx) = otY,. A further reduction takes place because of the stress Z, , which is ceZ,. Therefore, the total specific strain is aus eX, — otY, — oeZ;. Ox Hence, the strain in the z direction: a = e[X, — o [Y, + Z,)] the strain in the y direction: oe = e[Y, — o(Z, + X,)] oy (9-6) and Ow the strain in the z direction: ape e[Z. — o(X. + Y,)]. Adding these three equations and considering (9-1), © = ¢{(1 — 2c)(X. + Y, + Z,)l. (9-7) Adding to the right side of the first equation of (9-6), + X.ce and — X,0e, the specific strain in the x direction 0 a = e[X.(1 + o) — o(X. + Y, + Z,)]. Re-substituting eq. (9-7), = cs e| x.(0 ur bon ass | Cuap. 9] SEISMIC METHODS 445 Solving for the normal stress and treating all equations of (9-6) in the same manner, > yee be vt eee * eg (1 +o)(L— 2c) e(1 +) da 0) 1 dv Y. = 9 SSS 9-8 "* ¢ (l-+ o)(1— 2c) e(1 + a) Oy ee) ra o 0] 1 ow 2 (1+o0)(1 — 20) * e(1 +) a2 The two coefficients in these relations are known as the Lamé coefficients: ie cE d ae E TS a) wae CST) If Poisson’s ratio is 1,2 = w = 2E. The quantity wu is also known as the shear or rigidity modulus. With these coefficients, eq. (9-8) become a Ou X, = @2 2 Tr “te ee dv Z. @2 + Qu These are the fundamental equations expressing the normal stresses as functions of the volume changes and of the specific strains in the same directions. Eqs. (9-9) state that the strains produced by normal stresses depend on both 2 and u whereas the tangential stresses, as shown in the following paragraph, depend on the rigidity modulus u alone. Eqs. (9-9) indicate further that the normal stresses become equal when the rigidity is zero. In that case all tangential stresses are zero and the normal stress is the hydrostatic pressure. If X, = Y, = Z. = —P in egs. (9-9), by adding eqs. (9-9) and substituting P we obtain —3P = 302 + 2u9; P= —@O(a + 2y). If + 3u = k, then (9-10) P= —-k® or —@ = P/k = PK. 446 SEISMIC METHODS [Cuap. 9 The factor k is the incompressibility factor or bulk modulus; its reciprocal, K, is the compressibility. In terms of Young’s modulus: E Gs 3(1 = 20)" If Poisson’s ratio o is 4, k = 2E. (b) Tangential stresses produce a change in the angles of an elastic body and preserve the surfaces. In the x-z plane of an elementary parallelo- Duz Ju (Cc) Fig. 9-2. (a) Shear deformation by X,; (b) shear deformation by Z,; (c) resultant deformation. piped, the tangential stresses X, and Z, produce the strains du and dw and the “shear” angles y,, and ¢,, , which are related to the stresses by a proportionality factor that is the reciprocal of the rigidity, wu. Thus, as shown in Fig. 9-2, g,. (1/u)X, and g., & (1/y)Z,. Since X, and Z, are interchangeable, the resultant change of shape is given by 1 2 os = — X,; : u ’ and, similarly, for the other planes, (9-11) Cuap. 9] SEISMIC METHODS 447 As dzg., = du and dty., = dw, Ges + Css = du — dtp and dz dx Ou ow ie eas) ena Misa a 0z oT Ox Ov ow Opes be Py az pt ay (9-12) Ou Ov 2 abe weg a Wa Sag. Oa Z Bez = (2 i a) (9-13) z(=¥) = »( + %), 2. Propagation of deformations; longitudinal and transverse types of waves (dynamic problem). For simplification of analysis, consider a plane wave resulting from displacements u in the zx direction. Then only the com- ponents X,, Y.,, and Z, shown in Fig. 9-1 have to be considered. These forces are referred to unit area and therefore their action on the y-z side of an elementary parallelopiped is given by expressions of the form X,-dy-dz, or 0X,/dx-dV. Although the primary deformation is in the x direction, deformations in the y and z directions result from contraction. The accelerations corresponding to these deformations are 0°u/dt’, d°v/at’, and @'w/dt. Since the force (@X,/dr-dV) is mass (dV -3, with 8 = density) times acceleration (6°u/dt’), the equations for a (plane) wave in the x direction are 5.2 _ aK. at? ax av aY. 9-14 ot? Ox ( ) aw _ a, at? ax In these equations, X., as given by formula (9-9), = @% + 2y du/dz. © follows from (9-1). Since the initial specific strains in the y and z 448 SEISMIC METHODS [CHapP. 9 directions are 0, ® = du/dz. Hence, X, = (4+ 2m) du/dzr. Y, follows from eq. (9-13). Since the problem is limited to propagation in the zx direction and the shears in the y and z directions are zero, Yz = uw dv/dx and Z, = udw/dx. By differentiation of these components with respect to x as required by (9-14), the following equations are obtained: au _ A+ 2Quau Ot 3 ax? a°v u a°y at 5 ant Or dw _ yaw at? 8 Oa?” The first equation indicates the gradient of the specific strain du/dx in the xz direction, that is, in the direction of propagation. It is thus the expression for a compressional é and longitudinal wave. The second equation gives the gra- MA dient or propagation of the shear dv/dz in the x direction; and the third equation, the 2 gradient or propagation of the SB li ab al x2 shear Ow/dx in the z direction. This applies to a plane wave traveling in one direction (see - Fig. 9-3); however, it can be Fic. 9-3. Propagation of longitudinal and shear shown that the equations deformations. here derived also hold for space waves. Eqs. (9-15) show that the acceleration in a longitudinal wave (or com- pression 0°u/dx”) is proportional to (4 + 2p) /6, while in the second case it is proportional to u/s. The two last waves are shear waves; they are not propagated independently. Figure and equations merely indicate the two (z and y) components of the wave whose relative amplitudes determine the plane of polarization. The proportionality factors in the last three equations my be designated by v, thus: v; = (a + 2y)/6 and vi = y /B. Then d°u/dt? = vi-d'u/dr ; dv/at? = v;-0'v/dx"; dw/dt’ = v;-d'w/dx. The velocities of the longi- tudinal and transverse waves are, therefore, v= = and v; = 4/*. (9-16) Cuap. 9] SEISMIC METHODS 449 When oc = 1}, 2 = yw, and v,/v, = ~/3; that is, the longitudinal wave moves faster than the transverse wave. The accelerations on the left side of eq. (9-15) may be set in relation to the ground amplitudes. Since the inertia force, m.d°u/dt’, must equal the restoring force (= force per unit displacement, or spring constant c, times displacement), we have m.d’u/at’ = —cu or (9-17) Fig. 9-4. Periodic motion. In this equation c/m = w ; w is the angular frequency of oscillation or the angular velocity of the motion of a given particle on the circumference of the circle of reference (see Fig. 9-4) or o= 2rf, (9-1 8a) where 1/7’ = f is the number of ndcillations per second. The solution of eq. (9-17) is u = Bo sin wt + Cy cos wt. (9-18b) Substituting for the two arbitrary constants, Aj = Bp + Co, sin y =Co/Ao, and cos ~y = Bo/ A) ; u = Aosin (wi + ¥) = Aosin (gy + ¥) = Aosinw(t + &), (9-19) in which ¢ and y are phase angles; y = wt) is the starting angle corre- sponding to the time & ; and g = wt is the phase angle at the time?t. The significance of the constants Ay, Cy, and By may be obtained from eq. (9-19) by solving for the limits g + y = 90°, g = 0°, and gy = 90°. Then, Ay is seen to be the maximum amplitude (peak amplitude) ; Cy is the initial amplitude; and By is the amplitude reached within a quarter period (e = 90°) after the start. These relations appear in Fig. 9-4, whose right side shows wave motion plotted against time, while on the left ampli- tudes are shown as function of phase angles on the reference circle. 450 SEISMIC METHODS [Cuap. 9 3. Harthquake waves. In the preceding section it was stated that in an isotropic elastic body only two types of waves exist, longitudinal and transverse waves. While the observed waves are actually longitudinal and transverse in character, there are a number of types in addition to the two mentioned. There is virtually but one longitudinal wave and several kinds of transverse waves. The explanation is that the above theory con- siders a volume element within an unbounded elastic solid and is not strictly valid for surfaces between media. It is readily seen that the trans- verse waves should be the ones to be influenced by such conditions, since they have an arbitrary direction of oscillation in a plane at right angles to their direction of propagation. This plane should depend, in its orienta- tion and other characteristics, on the orientation and elastic characteristics of a geologic or physical boundary. v retlecied incident retHlected long. refracted Love (@ Rayleigh (2) lacident longitudinal transverse Fie. 9-5. Wave types on boundaries. When a wave consisting of longitudinal and transverse impulses strikes a boundary, theoretically no less than twelve new wave types are pro- duced. As shown in Fig. 9-5, two refracted (longitudinal and transverse) and two reflected waves are produced by the longitudinal wave. The same is true for the transverse wave, so that in this manner alone eight new waves are accounted for. Further, each wave may generate the Love wave, Q, which is a special type of transverse wave with its plane of oscillation in the formation boundary, and the Rayleigh wave, R, which is a combined longitudinal and transverse wave with plane of oscillation at right angles to the surface and parallel to the direction of the propaga- tion. The last two waves are frequently observed at the earth’s surface; it is probable that the so-called “ground roll’’ observed in reflection seis- mology is of the Rayleigh type. Instead of distinguishing between longitudinal and transverse waves it has become the custom in seismology to speak of preliminary and surface Cuap. 9] SEISMIC METHODS waves. The preliminary waves, or forerunners, come to a seismic station through the interior of the earth, while the surface waves, as their name indicates, propagate along the earth’s surface. The forerunners in turn are divided into the lon- gitudinai and transverse preliminary waves, while the surface waves are divided in the same manner into the Love waves and the Rayleigh waves, named after the investigators who first described and analyzed them. Jsually there are three phases in a long-distance seismogram (see Fig. 9-6): (1) the primae, or normal longitudinal preliminaries, P; (2)° the secundae, or transverse preliminaries, S; and (3) the surface waves, L (= longae). Abrupt arrivals are designated by the subscript i (impetus); a gradual appearance is designated by e (emersio). The P waves, as well as the S waves, are divided into the (1) normal, (2) reflected,’ and (3) refracted waves. Alternatmg waves, mostly of the reflected type, are designated by the letters PS or SP, depending upon whether they were running first as longitudinal or transverse waves. The subscript n denotes the normal preliminaries; the subscript c designates waves which have passed the core of the earth. Bars above the symbols indicate refractions; double letters, reflec- tions. The main part of a seismogram is generally divided into (1) the arrivai of the surface waves, L; (2) the maximum, M; and (8) the coda, C. An analysis of travel-time curves makes it possible to determine the depth of penetration of seismic waves in the earth’s interior, their path, and their velocities along various portions of this path. Obviously, only the preliminary waves can be used for investigations of this character. As the longitudinal waves have the greatest velocity and arrive first, they can be more accurately identified and timed than can later impulses. Travel-time curves for the directly transmitted, for the once and twice reflected,’ and 2 Reflected at the surface. ‘Tt has been suspected that some unreasonably deep reflections recorded in seismic exploration are of a similar nature, that is, reflected once at the surface and twice on the reflecting bed. eR Th ed 45” SSS pp 7m p ‘Fig. 9-6. Typical long-range earthquake record (distance, 9800 km; Mexican earthquake, April 15, 1907) (after Gutenberg). 452 SEISMIC METHODS [CHap. 9 for the first and second preliminary waves have been published in various books on seismology. The time of arrival is not a linear function of the distance traveled. The velocity is not constant but dependent on distance and thus on depth of the strata traversed. 4. Characteristics of waves observed in seismic exploration. In seismic exploration one does not have to deal with as many types of waves as in earthquake seismology. This fact is due, first, to the smaller distances and shorter time intervals involved; and second, to the fact that not so many components are recorded, making it impossible to identify trans- verse waves with certainty. It is true that transverse impulses have been recognized in records of quarry explosions, but in such cases greater dis- tances were involved and horizontal components were also recorded. Three types of longitudinal waves are observed in seismic exploration: (1) directly transmitted; (2) refracted; and (3) reflected. Longitudinal waves transmitted at the immediate surface are rarely observed; vir- tually all first breaks, even those recorded close to the shot point, are refracted waves. Surface waves arriving at the end of a record are prob- ably not simple longitudinal but Rayleigh waves. Their frequency is generally low, from 10 to 15 cycles. The frequency of the refracted waves, on the other hand, covers a wide band from around 15 to 60 or 80 cycles, while the frequency of reflected waves is frequently near 50 and covers the range from 30 to 70 cycles. C. LABORATORY AND FieLD METHODS FOR THE DETERMINATION OF Evastic MoputiI AND WAVE VELOCITIES It was shown in the preceding sections that elastic moduli are the physical parameters relating stresses and deformations and that the elastic wave velocities are functions of these moduli. In the study of the elastic behavior of rocks and formations, it is thus possible to attack the problem in two ways: (1) by measuring elastic moduli in the laboratory; (2) by making velocity determinations directly in the field. Direct velocity deter- minations have the advantage that the speed of seismic waves is deter- mined in sztu, that is, under the natural conditions of moisture, pressure, weathering, and the like. Furthermore, unconsolidated formations cannot be moved and must be tested in the field. Elastic constants may be expressed in various units. Pounds per square inch is the unit most frequently used in the testing of construction ma- terials in this country. Another technical system uses the atmosphere; scientific publications employ dynes per cm’, megabars, and baryes. In many articles there is confusion as to the correct usage of the terms bars and baryes. In Europe the normal atmosphere and the technical at- mosphere (kg per cm’), the dyne per cm’, and kg per mm’ are preferred. Se £22 FT FOS FI 969 FI s-O1 OSPF T HON] aUVOadS aad saNnog Laas s0T870°S 201 -8h0'% 201 -680°% eOT-9TT'S 2-01 °680°% LOOg auvadg ugd SaND0g v-O1-°€0°2 9-OI 288 7 z-OI'T z-O1°0'T z-O1€80'T s-01°Z0'T | 7-AN -OF 2-O1°0°L r-O1 2887 201°T I c0'T €80'T 9-O1°20'T z-WO.DH ‘yenbe A[Iwau 218 s}UEUIZIEd WOD peul]zNO Ajoyeredes Ul SUId}] >ALON 2-01 °¢68'9 2-01: S08°9 r-OL 882° 7 v-OIl SL ¥ 10°86 81°96 186°0 896 °0 T 186°0 €10'T I 9-OT'T 1-01 6986 avg (VouIN) qugHASOWLY v0L 768 °9 8°8LP 201° L08°6 901-208 °6 901 'T oO E10 'T qAuvg WO 7_-WKO-GNAG 32 2s Se -2 eee ‘yout arenbs 1ad spunog -qoo} a1enbs 10d spunog Fe SO req (83ay\]) eee ee a19ydsoulzyy es afieq JO z_Wd-ouAC SS SLINO GANASSAUd AO SNOILVIGY TVOTHANON PP ATAVE (or) - 454 SEISMIC METHODS [CHap. 9 Table 44 is given to aid in the conversion of these units. The units based upon the acceleration of gravity are referred to its value in 45° latitude (980.665 cm-sec °) by international agreement. Although, in the technical system of this country, elastic moduli are usually expressed in pounds per square inch, the barye, or dyn cm, will be used in the following sections, since the parameters expressed in the C.G.S. system may be more readily converted into velocities of longi- tudinal and transverse waves. Wave speeds are usually given in meters or kilometers per second, although in seismic prospecting feet per second has been widely adopted. Several of the elastic constants are not inde- pendent quantities but may be calculated from one another. If Young’s modulus and Poisson’s ratio have been determined, the compressibility may be calculated. On the other hand, the compressibility may also be measured directly. If the two values differ, it indicates a deviation from isotropy and homogeneity. Furthermore, a comparison of values deter- mined statically and dynamically in the laboratory, with those calculated — from velocity determinations, is of value. Methods for the determination of elastic constants may be divided into laboratory and field methods. The latter are dynamic methods, since they involve the measurement of time, while laboratory determinations may be either static or dynamic or both. In the static determinations stress- strain relations are established, while dynamic measurements are based on observations of natural frequencies. Equipment for testing elastic prop- erties of construction materials has been developed to a high degree of perfection.” For the measurement of deformations the following devices are used: (1) extensometers, (2) deflectometers, and (3) detrusion meters; they may be (a) mechanical, (b) optical, or (c) electrical. Mechanical devices are generally not accurate enough for geophysical application. Closest in this respect are some of the more delicate types of Ames gauges, for which an accuracy of 0.000025 inch is claimed. The simplest optical devices for measuring extensions or deflections, microscopes, and cathetometers, are generally not accurate enough for rock testing. Rocking mirror arrangements, however, give satisfactory results. In the Martens mirror extensometer two rocking mirrors are clamped to opposite sides of a specimen. These are rotated when the specimen is extended (see Fig. 9-7) and are observed by separate telescopes. If the arrangement is so modified (Fig. 9-8) that the light travels from one mirror to the other, more magnification is obtained. If A is the distance from scale or telescope to the nearest mirror, D their distance apart, and n 5 Comprehensive descriptions may be found in J. B. Johnson’s Materials of Con- struction, Chapter II, John Wiley (1930), and in C. H. Gibbons, Materials Testing Machines, Instruments Publishing Co. (Pittsburgh, 1935). Cuap. 9] SEISMIC METHODS 455 the observed deflection in scale divisions, the deflection angle of each mirror is given by tan a = where A and D are expressed in scale divisions. To obtain the ex- tension of a bar, the angular mirror deflection must be multiplied by the effective lever arm of the rocking mirror. A rocking-mirror arrange- ment with a powerful telescope 4.5 m away from the scale has been employed by Zisman. He obtained magnifications of the order of one million. Interference measurements for strain determinations have been applied in two ways. In the inter- ference extensometer of Grueneisen (Fig. 9-9), two tubes are clamped to the sections whose change of dis- tance is to be measured. The ends of the tubes carry two closely spaced polished glass disks, between which interference patterns are pro- 4A + 2D » (9-20) RD Si HiiilhiZ ROOAY Fig. 9-7. Bauschinger Martens mirror duced. If the pattern changes by extensometer. Scale ae SS tort oc Bar Telescope ca aa A ae Sp SS — aS Mirrer l= Sorcha nee Mirror Fie. 9-8. Double mirror reflection arrangement. one fringe width, the corresponding change in distance is one-half the wave length of the light employed. 456 SEISMIC METHODS [Cuap. 9 Fig. 9-9. Extension measure- ment by interferometer (Gruen- eisen arrangement). Another interference method has been applied by Richards’ for testing deforma- tions of rectangular plates. If such plates are subjected to stresses at the ends, they will curve not only in the longitudinal direction but in the transverse as well (see Fig. 9-10). The upper surface of the plate or rock slab under investigation is polished, and interference patterns, as shown sche- matically in Fig. 9-11, are observed against a fixed plate. The simplest of the electrical devices is the wire-resistance type. An L-shaped lever arm magnifies the extension or de- flection of the specimen. Its end acts as the movable arm of a potentiometer which may be placed in any of the well-known bridge circuits to measure resistance or potential changes. An arrangement of this type is used in Zisman’s compressi- bility tester (Fig. 9-13). In the con- denser microphone extensometer,® small variations of distance of two condenser plates are converted into changes of ca- pacity; in the magnetic gauges® the induc- tance of iron-core solenoids is varied by changes in position of an iron armature. The solenoids may be energized with A.C. of intermediate fre- ey, quency and may be used in any one of the well- inductance known aa Fic. 9-10. Longitudinal and transverse curvature of bent bridges. Fig.9-12shows plate. a Westinghouse extens- ometer, which, for slow deformations, may be operated from a 60 cycle current source. Yow °'T. C. Richards, Phys. Soc. Proc., 45(1) (248), 70-79 (Jan. Fie. “9-11. Pat-!), 1) 1933): terns of interfer- 6¢ W. A. Zisman, Proc. Nat. Acad. Sci., 19, 653, 666, 680 (1933). ence fringes of rock % A detailed discussion of capacitance strain gauges, with slab when bent as __ literature, is given on pp. 931-932. in Fig. 9-10. 6 Inductance gauges are discussed further on pp. 932-933. Cuap. 9] SEISMIC METHODS 457 1. Laboratory methods. (a) Static determinations involve measurements of stress-strain relations, utilizing tension, compression, bending, or torsion. Tension and contraction tests: Samples are used in the form of long bars or drill cores in any of the Olsen, Riehlé, or Emery machines. The strains may be measured by rocking-mirror devices, interferometric gauges, or condenser-microphone attachments. The contraction is obtained by means of a lever device measuring the reduction in diameter with two contact arms, provided with mirror magnification. From the load P, the area S, the original length /, and the change in length Al, Young’s modulus may be calculated: ae ) Dy a) Ei ae [9-3] S Al Poisson’s ratio is: Ad ee dl Ci Al [9 4b] l These two constants are sufficient for isotropic media to calculate all other elastic coefficients and, together with the densities, the velocities of the longitudinal and transverse waves. Fia. 9-12. Westing- Compressibility tests: Although the compressibility house magnetic strain ) : recorder. (O, oscillo- may be calculated from Young’s modulus and Pois- Banh recunen son’s ratio, it is preferable to measure it separately. potentiometer.) For most compressibility tests the sample is used in some liquid which is compressed in a strong steel cylinder. A correction must be applied for the expansion of the steel cylinder and for the compres- sion of the liquid. Bridgman used chrome-vanadium steel for the cylinder; Adams used n-butyl-ether for the liquid. A simple way of determining the volume change is to measure the movement of the piston compressing the liquid. The distance the piston should move if the liquid alone were in the cylinder may be calculated from the dimensions of the steel cylinder and the compressibility of the liquid, or it may be measured directly. Since the volume of the sample is also reduced, the difference of the piston movement without sample and the movement with sample gives the volume reduction AV of the specimen. Then the compressibility, AV K ca V.P° [9-10] 458 SEISMIC METHODS [Crapr. 9 The piston displacement is measured by one of the optical or electrical methods described before; the pressure P is read (Adams) on a resistance pressure gauge meter immersed in the liquid. Other investigators have used the reduction in length of the specimen for a determination of the cubic compressibility. They measured the pressure of the liquid with a manometer and determined the reduction of length of the specimen by a contact bar whose motion was magnified by optical or electrical means. Amagat carried this rod outside the pressure cylinder and measured its displacement optically; Bridgman magnified its movement by a lever arm acting as the movable arm on a potentiometer; Zisman used the arrange- ment shown in Fig. 9-13 with the transmission mechanism enclosed in the pressure bomb. If Al is the reduction of length of the specimen, the linear compressibility may be reduced to the ey) cubic compressibility, since potentiometer spring te 3Al K = P ° (9-21) Because of the many variables and correction factors entering into such compressibility tests, it has become general practice to use an iron cylinder of known compressibility as a reference standard. Considerable magnifica- tion (of the order of one million) is required to measure changes of length accurately. Bending (transverse) tests: These tests may be divided into two groups. In the first, ER niaaor eee Young’s modulus alone is determined; in the Renee nearhc ER DEO RcOni: other, both Young’s modulus and Poisson’s pressibility tests. ratio are obtained. Tests in the first group are made with bending (beam testing) ma- chines. Rock specimens in the form of slabs are clamped on one end or supported on knife edges on both ends. The last procedure is not so favorable as the first because the deflection is only 7 of that ob- served at the free end of a clamped beam. Deflections are mea- sured optically by mirror devices or by condenser-microphone ar- rangements. If J is the moment of inertia of the beam section C7Ze27 272 6¢ D. Adams and E. G. Coker, Pub. No. 46, Carnegie Inst., 1906; Gerl. Beitr.; $1, 315-321 (1931). L. H. Adams and R. E. Gibson, Proc. Nat. Acad. Sci., 12, 275 (1926), 15, 713 (1929). L. H. Adams and E. D. Williamson, J. Frank. Inst., 196, 475-529 (1923). L. H. Adams, E. D. Williamson, and J. Johnston, J. Am. Chem. Soc., 287, 7-18 (Jan., 1939). Cuap. 9] SEISMIC METHODS 459 under test and if its deflection is d with the load P concentrated at its end, d=-—. (9-22a) Since the moment of inertia J = a’b/12 for a rectangular section, and J = rr/4 for a circular section, the deflections are: 4P°P gy Rail for a rectangular section, (9-22b) where b = breadth, a = thickness, and 4 UP d = ——— for a circular section. (9-22c) 3 Er’s If the specimen is supported on either end by knife edges, the deflection 3 ote (9-224) 48 EJ Hence Young’s modulus 3 i} = for a rectangular section and E = 1 UP for a circular section. 12 rad Deflections may be measured with two mirrors fastened to the ends of the specimen. If the light is reflected from one to the other, the angle is given by eq. (9-20), and Young’s modulus Bok oP Eq. (9-22d) holds for beams supported on knife edges; for fixed ends the factor is y$, instead of 7; By the second group of flexure tests, both Young’s inodulus and Poisson’s ratio are obtained. A slab is cut from the rock under investigation, sup- ported on either end by knife edges, and a load is applied on the extreme ends, outward from the supporting knife edges (see Fig. 9-10). Both longitudinal and transverse strains are measured with an interferometer. The top of the rock slab is polished, and a plane-parallel glass plate is laid on top of it. Interference fringes resulting from the bending of the beam are observed or photographed. A diagram of the apparatus has been 460 SEISMIC METHODS [Cuap. 9 given by Richards.’ Poisson’s ratio follows from the angle of spread of the asymptotes of the fringe hyperbolas (see Fig. 9-11), ¢ = tan’ a. The curvatures in the longitudinal and transverse directions may be determined from the fringe patterns, according to the relation C = 4\n/d,, (9-24a) where C is the curvature, \ the wave length of the interferometer light, n a given number of the fringe used to calculate C, and d, is the distance apart of the vertices of the nth pair of fringes. The ratio of the curvatures is Poisson’s ratio, c= 5; (9-24) and Young’s modulus _ 8D 1-6 ~~ 2bh?C, 1 + o?? where b = width, D = couple, and 2h = thickness. Torsion tests: For static torsion tests, the specimen is clamped in a hori- zontal position, and a twist is applied to one end in a torsional testing machine. The torsion of two sections with respect to each other is ob- tained by a detrusion meter provided with mirror multiplication. Since the torsion tests furnish the modulus of rigidity, and since Young’s modu- lus may be obtained from extension tests, Poisson’s ratio and all other desired constants may be calculated. The angle of twist between two sec- tions of a bar separated by the length 1 is Di MN (9-252) Jou (9-24c) where D is the rotational couple and J, the polar moment of inertia. Hence, the modulus of rigidity for a round bar with the radius r is u = ey —e— pP (9-250) (with p = radius of gyration, P = force), when the angle ¢ is expressed in degrees. (b) Dynamic laboratory tests. Elastic constants of rocks may be deter- mined from the natural frequencies of their transverse, torsional, and longitudinal vibrations. All these determinations are comparatively simple, since only one parameter, time (or its reciprocal, frequency), is 7 Loc. cit. Cuap. 9] SEISMIC METHODS 461 involved. The procedure is to drive the specimen with impulses of con- tinuously varying frequency until maximum amplitude is obtained. With sufficient accuracy, this resonance frequency may be considered equal to the natural frequency. Measurements of a complete resonance curve give interesting information on the damping within the specimen. Transverse vibration tests: These tests” are the dynamic equivalent of the tests referred to on page 459. They may be applied to bars supported on one end or on both ends. As was stated in connection with eq. (9-17), the natural frequency. w of an elastic system oscillating with the load m is given by m dm where the spring constant, or force per unit deflection P/d, im 1Fba’* - (9-260) c for a bar clamped on one end. For slabs suspended between two points, similar relations may be worked out from the formulas previously given for the static deflection. The above relations hold only if the mass may be considered as concen- trated on one end. The transverse frequency of unloaded bars clamped on one end is given by A * wo = Ae 1, E (for the circular [radius 7]) and (9-26c) a’ (n\ Vee OIE a 3 (for the rectangular) sections, a being the dimension of the side in the plane of oscillation. For the fundamental, n is 1.875; for the first harmonic, 4.694; ~/E/5 is known as the “bar” velocity (see eq. [9-29a]). Torsional vibrations: The specimens under tests are suspended in a ver- tical position and are loaded with a disk whose moment of inertia K is known or may be determined. This method is well adapted to long-drill cores. The general relation for the period of a torsional system is T = 2 ~/Kl/uJ,, where | is the length of the specimen and J, the polar Wo 7aG. Grime, Phil. Mag,, 20, 304 (1935), 28, 96 (1937). W. H. Swift, Phil. Mag., 2, 351-368 (Aug., 1926). 462 SEISMIC METHODS [CHap. 9 moment of inertia (}r* for a round bar). Hence, the modulus of rigidity for a round bar C= oa. (9-27) For a round disk attached as a revolving mass, the moment of inertia is K = ip'm (p = disk radius). The torsional frequency of a specimen and thus the modulus of rigidity may also be determined’ by a resonance method analogous to the one described in the next paragraph. In a drill core, a saw cut is made on one end and a strip of iron is fastened rigidly in it. This strip is placed between the poles of two electromagnets. An identical arrangement is provided at the other end of the specimen. The electromagnets on one side are excited by a variable-frequency oscillator, while those on the other side are connected to an amplifier and rectifier meter. The torque produced on one end is transmitted to the other. Its ampli- tude is greatest when the natural torsional frequency of the specimen coincides with the driving frequency. A bar clamped at its center has a node at that point so that its length / is one-half the wave length. Since the torsional wave velocity is +/ u/s and is equal to the product of wave length and frequency, UAL 4 fo = Oy / 5” (9-28) where fo represents natural frequency, | length, and u the rigidity modulus as before. Longitudinal vibrations: The specimen, preferably in the form of a rod or drill core, is arranged horizontally, clamped at its center, and excited to oscillate horizontally. This may be done by attaching a piece of iron to one of the faces and by exciting this end with an iron-core solenoid supplied with current of variable frequency. A better arrangement is to attach a light coil to each side of the specimen, each coil being suspended in the field of a dynamic speaker (Fig. 9-14). One coil is supplied with current of variable frequency and thus drives the specimen. In the other coil, currents are induced which depend on the frequency and amplitude of motion of the other end. Resonance is again determined by maximum amplitude.’ Another way of setting the specimen into oscillation is by electrostatic coupling. Fig. 9-15 shows an arrangement proposed by Ide™ for such ob- 8 J. M. Ide, Geophysics, 1(8), 349 (Oct., 1936). ° B. B. Weatherby and L. Y. Faust, A.A.P.G. Bull., 19(1), 12 (Jan., 1935). . % J. M. Ide, Proc. Nat. Acad. Sci., 22, 81, 482 (1936); Rev. Sci. Instr., 6, 296-298 (Oct., 1935); Jour. Geol., 45, 689-716 (Oct., 1937). Cuap. 9] SEISMIC METHODS 463 servations. The oscillations of the speci- ™ M men are picked up by a piezo-electric crys- tal cemented to the specimen (or by a sepa- : : o) rate microphone), are amplified and read on y, an output meter. Longitudinal “bar” vibrations do not de- 0 aN ES pend on Poisson’s ratio; their velocity is Fig. 9-14. Apparatus for given by electromagnetic determination E of natural bar frequency (after vin = / aah (9-29a) Weatherby and Fayst). (B, 3 bar; M, magnet; C, coil; O, os- . ; cillator; S, supporting knife Since, as before, for a bar of the length J, edge: A. aaanlition oe capece 1 = 4) and v= Af., the longitudinal bar _r, rectifier.) velocity Wiz ul (9—29b) Methods for determining damping from resonance curves are discussed on page 481. Rebound observations: Elastic properties of rocks may be determined by observations of physical parameters related to the rebounding of a steel ball dropped from a given height. Two methods have been used: (1) measuring the size of the imprint, and (2) measuring the height of rebound.” If a steel ball of radius p,, mass m , Young’s modulus E, (= 22-10"), dropped from a height H on the rock whose surface is blackened, leaves an imprint of the radius r, then Young’s modulus of the rock is given by E 13.5m,2gHp? Ey o-30) If a steel ball is dropped from a height H on the rock surface and re- bounds ‘to the height A (see Fig. 9- 16), the so-called ‘restoration’ coeffi- cient 1s nas h wo q= ft. (9-31) The exact relation between the resto- a 9-15. Apparatus for electrostatic ration coefficient and Young’s modu- eteymination of natural bar frequency ; 4 een Ot ealintee C. bon. lus has not been definitely deter denser; D, dielectric; F, foil; B, base plate; V, polarizing voltage; S, speci- 10 J. Roess, Union Geod. and Geophys. men; Cr, crystal; A, amplifier; M, out- Internat. Assoc. Seism. Ser. A, Trav. Sci., put meter.) Fasc., 18, 3-69 (1935). ~~ 464 SEISMIC METHODS [CHap. 9 mined. Roess established an empirical relation (Fig. 9-17) by determin- ing both g and E for the same rocks by the two methods described above. Rebound observations are applicable only to fine-grained materials. If the ball hits a large mineral grain, the elastic coefficient of the grain and not that of the aggregate is obtained. Another difficulty arises from the fact that | the surface constitution of the rock must not deviate from the composition of its in- terior; otherwise the restitution coefficient would express surface conditions only. As ill ARUERRAUUUANDOSRAOUOOORER —— ee ee nae transverse energy at the location of a de- IG. J-10. ecord of steel ba . Pe poundisig thom surface of nine tector set up at a measured distance. One ble slab (after Roess). shot point may be used with a number of a matter of fact, rebound observations are used in the metallurgy of steel for hard- ness determination. 2. Field methods (velocity determinations). Field determinations of horizontal velocities are made by measuring the time interval which elapses between the firing of a shot and the arrival of the longitudinal or 0.6 0.7 0.8 0.9 (Restoration coefficient) Fig. 9-17. Young’s modulus E as a function of restoration coefficient (q) for some homogeneous rocks. (Numbers refer to tabulation of rock specimens, pp. 11 and 12, Roess’ article.) (After Roess.) detectors, and the latter may be moved when one spread is not sufficient to cover all desired distances. Another method is to leave the detectors at their places and to move the shot point. In practice, the application of this method is not quite so easy as it may appear. Errors of instru- mental and geologic nature occur. The former arise from (1) inaccuracies in the determination of the exact instant of the shot, (2) errors in the tim- Cuap. 9] SEISMIC METHODS 465 ing device, and (3) errors in timing the impulses in the record. The shot instant may be transferred to the recorder by wire or radio. For short distances this method is generally not accurate enough; an insensitive seismograph near the shot point is preferable, as it will record the actual time when the energy is impressed on the ground. Errors in the timing device can generally be kept down sufficiently to make possible time determinations with an accuracy of 1 in 10,000 if necessary. The ‘‘timing” of the impulses in the record is generally the most difficult part of the problem (as seen in some of the records published by Weatherby, A.A.P.G. Bull., Jan. 1934). Unless the sharpness of the first impulses can be improved, there is no object in increasing the accuracy of the timer and shot instant transmission to more than z¢/o5 of a second. When a number of seismographs are used, it is necessary to balance their phase shifts and to determine the corresponding parallax corrections. More serious than these instrumental difficulties are geologic factors which often make it difficult to determine reliable velocities. The surface of the rock whose wave speed is to be determined must be free from cover and reasonably unweathered so that true velocities may be obtained. It is, of course, possible to obtain velocities of inaccessible layers from the travel time curve. However, these velocities are true velocities only if the layers are horizontal. Dip may be eliminated by shooting the profile up and down dip. Vertical velocity determinations through formation (that is, generally at right angles to the bedding planes) are made in connection with weathered- layer-correction shooting in shallow (25 to 150 foot) holes and in connection with average-velocity determinations in deep wells. For the latter a de- tector is lowered into the well to various depths and shots are fired either near the well or at a distance corresponding to one-half the general spread distance, to simulate the direction of the ray in its travel to or from the reflecting bed. By means of the travel time to various depths, the average velocity from the surface to the formation in question or the differential velocities between strata are calculated. This method is discussed further in Chapter 11. Tables 45 through 55 list the elastic moduli and wave velocities for the more important minerals, rocks, and formations. In Table 45 are listed the elastic moduli of minerals, and in Table 46 are given elastic moduli of igneous, metamorphic, and sedimentary rocks.’ ‘Table 47 shows velocities of longitudinal waves for the formations nearest the surface, particularly the weathered layer; Table 48, the longitudinal wave speeds for alluvium and glacial drift; Table 49, the longitudinal wave velocities for sands, 11 Largely after Adams, Adams and Gibson, Adams and Williamson, Zisman, Richards, Don Leet, Born and Owen. 466 SEISMIC METHODS [CHaP. 9 clays, and marls; Table 50, those for sandstones and shales; Table 51, the velocities in limestones, anhydrite, salt, and the like; and Table 52 repre- sents longitudinal velocities for igneous and metamorphic rocks. A num- ber of selected values for transverse waves are given in Table 53. Table 54 shows some values for Rayleigh waves, and Table 55 contains vertical velocities, that is, longitudinal velocities determined by meaguring travel times at right angles to the bedding planes in wells. CHap. 9] SEISMIC METHODS TABLE 45 ELASTIC MODULI OF MINERALS (at atmospheric pressure) 467 MINERAL Feldspar: Orthoclase CoMPRESSIBILITY X 10!2 | Youna’s MopuLvus X 10-4 Pyroxenes & Amphiboles: — Augite Olivine Mica: Phlogopite Other Minerals: Quartz Pyrite Magnetite Calcite Gypsum Rock salt Ice _ (=) Go or oS & &S Ve) worRNRF COON bo NI or _ TABLE 46 ELASTIC MODULI OF ROCKS Rock Quincy granite Tishomingo granite Diorite Gabbro Norite Extrusives Andesite Diabase Basalt Volcanic Glasses Obsidian Quartzitic slate (Ar- chean) Gneiss Chloritic slate Quartzite (Triassic) Graywacke (Devo- nian) LocaLiIty oe WHO HS OH RASCH = —_ a INVESTIGATOR Igneous Rocks Massachusetts Oklahoma Ontario Maine Leet Born & Hard- ing Adams & Wil- liamson Zisman Adams & Gib- son Zisman Adams & Gib- son cc Metamorphic Rocks Adams & Gib- son Zisman Adams & Gib- son CoMPRESSI- Youna’s Mopv- BILITY X 102 Lus X 10° 2.28 4.3 1.93 3.29 (field) 4.55 (lab.) 1.62 1.28 10.8 1.65 8.05 4.3 6.9 1.45 10.2 1.36 10.15 2.86 (4) 2.08 6.65 2.07 3.28 1.97 7.0 1.88 7.34 1.82 7.6 468 SEISMIC METHODS TaBLE 46—Concluded ELASTIC MODULI OF ROCKS [Cuar. 9 Rock Locatity INVESTIGATOR Commanent, Younes Mowe: Sedimentary Rocks Sandstones Sandstone (Triassic) Adams & Gib- 13.5 1.02 son Sandstone (Tertiary) 8.35 1.65 Weathered sandstone | California Heiland mh 0.25 (Tertiary) Limestones and Anhydrite: Limestone S. W. Persia Richards 2.99 5.3-5.5 Limestone (Devo- Adams & Gib- 1.70 8.15 nian) son Anhydrite S. W. Persia Richards 1.69 7.2-7.4 Unconsolidated Formations f R Youna’ Rock Locauity INVESTIGATOR MGDCIIG Monouts Fousonig x10 | xX 10-1 Overburden (river de-| Los Angeles, | Heiland 0.010 0.030 0.45 posits) Calif. Loess (dry) Leine Valley, | Ramspeck 0.011 0.033 0.44 Germany Gravel Werra Valley, ss 0.0059 | 0.017 0.47 Germany TABLES 47-52 VELOCITIES OF LONGITUDINAL WAVES TABLE 47 WEATHERED SURFACE LAYER, AIR, WATER LONGITUDINAL WAVE VELOCITY FORMATION LocaLity INVESTIGATOR m./sec. ft./sec. Weathered surface} E. Alberta, Heiland 169-305 555-1000 layer (Pleisto-| Canada cene) Dry surface sands | California Rieber 330 1083 Air | 330.8 + 0.66t2 | 1089 + 0.22t Weathered layer | E. Colorado Pugh 335-1690 1099-5545 Loess Jena, Germany| Meisser & 375-400 1230-1312 Martin Dry surface soil | California Rieber 600 1969 Weathered surface} Oklahoma Goldstone 610 2000 rocks Loam (wet) Australia Edge & Laby 761 2497 Water (iresh)ia A UND ess ae ea eisai uan | 1435 4708 Water at 14°C. at | Germany Beuerman 1475 4840 20 m WALEDNBEA) iii ek Ceuta WRIA th nates 1480-1490 4856-4889 *t = temperature. ALLUVIUM, DILUVIUM—GLACIAL DRIFT Cuap. 9] FoRMATION Alluvium Alluvium Tertiary alluvia Alluvium Alluvium Alluvium at depth Diluvium Diluvial sands Diluvial sands (wet) Diluvial sands (wet) Glacial Drift Glacial drift Glacial drift : | SEISMIC METHODS LocaLity Spain Str. Gibraltar Diaz Lake, Calif. Owens Valley, Calif. Spain Sperenberg, Germany Kummersdorf, Germany San Joaquin Valley, Calif. EK. Alberta N. Germany TABLE 48 469 INVESTIGATOR Sifteriz Devaux Gutenberg Buwalda & Wood Sifieriz Reich & Schweydar Reich Rieber Heiland Barsch & Reich ® Round figures such as these indicate values by investigator. These figures are the equivalent in feet (from conversion tables), Investigators in countries using. metric systems usually give velocities in m.sec.—1; those in countries using the English system, in ft. -sec.? TABLE 49 LONGITUDINAL WAVE VELOCITY m/sec. 550-6502 800-1500 900 1000 1100-2360 855-1011 1430 1650-1950 484-508 1700 SANDS, CLAYS, MARLS FORMATION Sands and Clays Dune sand Cemented sand Sandy Clay Pure sands Cemented sandy clay Clayey sands ft./sec. 1805-2133° 2625-4921 2953 3280 3609-7743 2805-3317 4692 5414-6398 1588-1667 5578 LONGITUDINAL WAVE VELOCITY Miocene sands and clays (wet) Oligocene clays Marls Eocene marls Marl Marl Eocene marls Calcareous marl Locatity INVESTIGATOR eu m/sec. ft./sec. Denmark Brockamp 500 1640 Australia Edge & Laby 802-975 2795-3200 iS of 975-1160 3200-3806 Gibraltar Devaux 1000 3280 Australia Edge & Laby 1160-1280 3806-4200 Gibraltar Devaux 1400 4593 N. Germany Reich 1600-1700 5250-5578 Jueterbog, Angenheister 1900 6234 Germany N. Germany Reich 1800 5906 Gibraltar Devaux 2000-2500 6562-8202 Spain Sifieriz 2000-3800 6562-12467 Gibraltar Devaux 2400 7874 Spain Sifieriz 3000-4700 9843-15420 470 SEISMIC METHODS [Cuap. 9 TABLE 50 SANDSTONES AND SHALES LONGITUDINAL WAVE VELOCITY ForMATION Loca.iTy INVESTIGATOR m/sec. ft./sec. Ribstone Creek | E. Alberta Heiland 931-1130 3055-3708 sandstone (Up- per Cretaceous) Tertiary sands & | Los Angeles | Wood & shales Basin Richter 0-200 m 1000+ 3280 200-320 m 1900 6234 320-860 m 2100 6890 860-1650 m 2900 9514 1650-? m 3500 11483 Sandstone Gibraltar Devaux 2000 6562 Middle Bunt sand-| Jena, Germany| Meisser & 2000-2800 6562-9187 stone (Triassic) Martin Pennsylvanian Oklahoma Goldstone 2130 6989 sandstone, shales, and limes Sandstone con- | Australia Edge & Laby 2400 7874 glomerate Upper Miocene (in| Texas Gulf | Barton 2400-2700 7874-8858 part) coast Middle Eocene Gulf coast 4200 137802 TABLE 51 LIMESTONE, GYPSUM, ANHYDRITE, CHALK, SALT ForMATION Limestone Cretaceous lime- stone Carboniferous limestone Gypsum Soft limestone Gypsum Limestone? sur- face velocities Cretaceous (Ed- wards) Pennsylvanian (Belle City) Mississippian (Mayes) Devonian (Hunton) LoNnGITUDINAL WavB VELOCITY Locaity INVESTIGATOR m/sec. ft./sec, Island of Ceccaty & 1, 000-1, 103 3, 280-3, 619 Djerba Jabiol France Maurin & 2,140 7,021 Eblé N. Germany Barsch & 3, 000-3 , 600 9, 841-11, 812 Reich Spain Sifieriz 3,100 10,171 Gibraltar Devaux 3,200-3,600 | 10,500-11,812 Spain Sifieriz 3,350-3,600 | 10,991-11,812 Locations in Weatherby & Miss., La., Faust Tex., N. Mex., Okla., 3,352 11,000 Kan., Colo., and Penn. " 4,572 15,000 E $ 3,810 12,500 < i 4,267 14,000 ® These velocities may be in error as much as 305 m./sec. (or 1000 ft./sec,) because of surface weathering and erosion. CuapP. 9] SEISMIC METHODS TaBLeE 51—Concluded 471 LIMESTONE, GYPSUM, ANHYDRITE, CHALK, SALT FORMATION Ordovician (Viola) Cambro-Ordo- vician (Ar- buckle) Anhydrite Zechstein gypsum Arbuckle _ lime- stone (Cambro- Ordovician) Leesport lime Chalk Chalk Pecan Gap chalk (Cretaceous) Chalk face) Austin chalk (Cre- taceous) Chalk (subsur- Salt Salt in 710 m depth (= 2,300 ft.) Salt and anhy- drite (Triassic) Rock salt of domes Salt beds Salt beds Salt beds Salt beds Salt beds Salt beds LocaLity Locations in Miss., La., Tex., N. Mex., Okla., Kan., Colo., and Penn. Spain Sperenberg, Germany Tishomingo, Okla. Pennsylvania Denmark Texas Texas Texas Austria Rhoen, Ger- many Jueterbog, Ger- many Texas Spain INVESTIGATOR Faust Sifieriz Schweydar & Reich Weatherby, Born, & Harding Ewing Brockamp Barton Brockamp Meisser Angenheister Barton Sifieriz LONGITUDINAL WAVE VELOCITY 3, 400-4 , 400 3,500 4,090 across bedding plane 5,320 along bedding plane 6, 400 2,200 3, 000-3, 600 3,020-4, 200 3, 600-4, 200 4,200 4,450 4,500 4, 720-5, 200 5000-7 ,000 5, 300-6, 300 5,500 5, 500-5, 900 5, 700-6, 950 6, 200-7 , 700 ‘Weatherby & 11, 155-14, 436 11,483 13,430 17,430 20 , 998 7,218 9, 843-11, 812 9, 908-13, 780 11,812-13,780 13,780 14, 600 14,765 15 ,486-17 , 060 16 , 405-22, 967 17, 388-20, 670 18,045 18, 045-19, 358 18, 702-22, 803 20, 342-25, 264 472 SEISMIC METHODS [CHap. 9 TABLE 52 IGNEOUS” AND METAMORPHIC ROCKS LoNnaITuDINAL WavE VELOcITY FORMATION Locauity INVESTIGATOR m/sec. ft./sec. Igneous Rocks Granite Gibraltar Devaux 4,000 13,124 Tishomingo gran-| Tishomingo, Weatherby, | 4,570-5,230 | 14,880-17,150 ite Okla. Born, & Harding Ronne granite Denmark Brockamp 4,800 15,749 Quincy granite Massachusetts | Leet & Ewing 4,960+ 20 16,2734 66 Westerly granite . i 5,000+ 40 16,4054. 131° Rockport granite . i 5,080+- 10 16,667+ 33 Granite Yosemite Val- | Gutenberg, 5,100-5,400 | 16,733-17,717 ley, Calif. Buwalda, & Wood Rockport granite | Massachusetts | Leet 5,140 16, 864 “‘Gestreifter”’ Denmark Brockamp 5,150 16,897 granite Igneous basement | Venezuela Allen 5,460 17,914 Crystalline rock | Gibraltar Devaux 5,500 18,045 Granite Australia Edge & Laby 5,630 18,472 Granite facies San Gabriel | Wood & Rich- 5,670 18,603 Dam to Pasa-| ter dena, Calif. Igneous basement | Venezuela Allen 6,510 21,359 (not defined) Granodiorite Australia Edge & Laby 4,570 14,993 Basalt California Rieber 3,600 11,811 Metamorphics Crystalline gneiss | Alabama Hills, | Gutenberg, 3,100 10,170 ~and schist Calif. Buwalda, & Wood Hard slate Australia Edge & Laby | 3,200-3,500 | 10,500-11,483 Hornfels slate os i 3,500-4,420 | 11,483-14,501 Green slate Denmark Brockamp 4,000 13, 124 Slates (Cambrian) | Spain Sifieriz 4,500-5,000 | 14,764-16,405 Slate and quartz- | N. Germany Barsch & 5,000 16,405 ite Reich Massive gneiss Spain Sifieriz 5,150-7,500 | 16,896-24,606 12 Rock types arranged in order of decreasing acidity. TABLE 53 ELASTIC VELOCITIES OF TRANSVERSE WAVES FORMATION Tishomingo gran- ite Rockport granite Locatity Tishomingo, Okla. Massachusetts INVESTIGATOR Weatherby, Born, & Harding Leet TRANSVERSE WAVE VELOCITY m/sec. 2,130-2,420 2,700 ft./sec. 7,000-7,950 8,858 Cuap. 9] SEISMIC METHODS 473 TABLE 58—Concluded ELASTIC VELOCITIES OF TRANSVERSE WAVES TRANSVERSE WAVE VELOCITY ForMATION LocaLItTy INVESTIGATOR m/sec. ft./sec. Basement rocks California Wood & Rich- 3,250 10,663 ter Sudbury norite Ontario Leet 3,490 11,450 Limestone S. W. Persia Richards | 2,710-2,800—- | 8,890-9,186- 2,930 9,613 Leesport lime Pennsylvania | Ewing 3,260 10,696 TABLE 54 RAYLEIGH WAVE VELOCITIES TRANSVERSB Wave VELOCITY ForMATION Locauity INVESTIGATOR m/sec. ft./sec. Overburden? Los Angeles, | Heiland 198 650 Calif. Gravel¢ Werra Valley, | Ramspeck 180 590 Germany Loess? Leine Valley, te 260 860 Germany Sediments (allu- | Ventura Basin, | Gutenberg, 330 1083 vium) Calif. Buwalda, & Wood Sediments (allu- | Los Angeles af 550 1805 vium) Basin, Calif. Limestone S. W. Persia Richards 2160 7087 Rockport granite | Massachusetts | Leet 2190 7185 Sudbury norite Ontario Hy 2790 9154 ¢ From vibrator measurements. TABLE 55 VERTICAL VELOCITIES OF LONGITUDINAL WAVES” FORMATION Pleistocene to Oligocene Hocenen ye sent.) eee Cretaceous iit. 4. oh ah. IBEGMTAT oe ihe ok eet Pennsylvanian.......... Mississippian Devomlanter Ae yy aelg iieem siehieljelde) ar rlehaytetie|Nelyatiee:ce VELOcITIES (ft-sec.—1) IN VELocITIES (ft: sec.) SHALES AND SANDSTONES In LIMESTONES zn, | 70,20 |S 00 acura] AS DOGO 6,500 | 7,200) 8,100 | 7,100 | 9,000 | 10,100 ate ie pe 7,400 | 9,300 | 10,700 || 11,000 | 13,500 | (8,300) 8,500 | 10,000 Bells eas 15,500 | (3,900) 9,500 | 11,200 | 11,700 || 15,000 | 15,500 | (3,000) la vals st 12,500 | 17,000 | (4,700) 13,300 | 13,400 | 13,500 || 14,000 | 17,500 | (4,500) aan ibe pte 16,700 | 20,000 | (4,000) 122 Data from fifty wells in Mississippi, Louisiana, Texas, New Mexico, Oklahoma, Kansas, Colorado, and Pennsylvania, from B. Weatherby and L. Y. Faust. 474 SEISMIC METHODS [Caap. 9 D. Factors AFFECTING ELASTIC PROPERTIES OF Rocks 1. In zgneous rocks, the rigidity, Young’s modulus, and the velocity of longitudinal waves all increase with a decrease in silica content; this be- havior is in harmony with that of the silicate minerals and holds for both intrusive and extrusive igneous rocks. Intrusive and coarse-grained rocks generally have a greater elasticity than do extrusive rocks, since they contain less liquo-viscous matter. It is possible that the difference is partially due to differences in porosity. The variation of elasticity with degree and depth of crystallization is less pro- nounced than its variation with silica content. 2. Sedimentary rocks show marked differ- ences in elasticity depending on petrologic composition. Clastic sediments, such - as sands, sandstones, and shales, are less elastic than sediments composed partly or wholly of crystalline matter, such as limestones, dolomites, and the like. Elastic properties of sedimentary rocks depend much more on texture and geologic history than on mineral composition. The effect of porosity and decomposition is to decrease the modulus of elasticity and the wave velocity of a sediment. In areas of great thickness of sedimentary rocks the porosity decreases with depth. Therefore, the modulus of elasticity increases and with _ Fie. 9-18. Calculated velo- it the wave velocity. Related to changes of pie ole caine peal toa porosity is the variation of Young’s modu- (after Lester). lus with pressure. For small pressures, rocks appear to be more compressible, since any cavities present have to be closed before the pressure can begin to act on the rock matter itself. Excessive compressibilities resulting from poros- ity are accompanied by high values of Poisson’s ratio. It must be ex- pected that the ratio of longitudinal and transverse wave speeds changes considerably with depth in unconsolidated sediments. The effect of poros- ity on wave velocity is of practical importance in the near-surface layer, inasmuch as the delay caused by the latter must be eliminated in reflec- tion shooting (‘‘weathered” or “aerated’’™ surface layer). The thickness of this layer is of the order of 5 to 50 feet, and velocities in it range from 500 to 2500 feet per second. Hence, wave speeds less than the speed of Composite velocity - meters per se. proportion alr te earth by velume 180. C. Lester, A.A.P.G. Bull., 16(12), 1230-1234 (Dec., 1932). t Crap. 9] SEISMIC METHODS 475 sound in air are possible in this formation. On the assumption that the layer is a liquid mixture of air and earth, the sound velocity “ ELE; ‘ Mie / [pk + Cl — p)EWipts + — peal’ 2) where E, = elasticity of air (1.2-10°);E2 = elasticity of earth; p = pro- portion of air to total by volume; 3; = density of air (0.0012) ; 82 = density of earth; and 1 — p = proportion of earth to total by volume. With a Young’s modulus of 5.58-10°° and a density of 1.9, the curve shown in Fig. 9-18 has been computed. The effect of moisture, or water content, on the velocity in sedimentary beds is rather involved. In consolidated beds (sandstones, limestones, slates, schists, porous igneous rocks, and the like) moisture appears to decrease the velocity; in unconsolidated beds moisture increases the ve- locity appreciably. In reflection work practical use is made of this increase in velocity (and improvement in the transmission characteristics) by Fig. 9-19. Location of ground water by refraction shooting (7.7. = travel time). (After data from Rieber.) placing the shots in or below the ground-water table. In California Rieber observed distinct breaks in near-surface travel-time curves on the ground-water (see Fig. 9-19). Many observations of elastic wave speeds appear to indicate a direct relation between geologic age and elasticity. However, the controlling factor is the amount of diastrophism to which a formation has been sub- jected in its*geologic history. An increased age merely increases the probability that it has undergone a greater degree of dynamometamor- phism. As a consequence velocities in geologic formations change less with depth of burial the greater their geologic age (see Fig. 9-20). Ce- mentation of clastic sediments by mineral solutions during their geologic history is likewise of considerable influence upon their modulus of elas- ticity. It follows from the above that metamorphic rocks have an increased elasticity compared with the rocks from which they were derived. Fur- thermore, their elastic constants are different in the direction of texture 14 See Lester, loc. cit. 476 SEISMIC METHODS [CHap. 9 than at right angles thereto. In metamorphics the speed of propagation of elastic waves is therefore greater in the direc- tion of strike than at right angles thereto.” This elastic aniso- tropy also plays a part in sedi- mentary rocks and accounts for some irregularities encountered : ate ity sane é i c a Mean depth of section in feet occasionally eS Dros pe Cts Fig. 9-20. Differential velocities (to 2000 ing. McCollum and Snell” feet, from 2000 to 3000 feet, and 3000 to 4000 found that in shales the veloc- feet) plotted against mean depths for sec- ity parallel to the stratification Bane different ages (after Weatherby and was as much as 50 per cent : higher than at right angles thereto. With an increase in depth of burial the porosities of sedimentary rocks are reduced. This decrease depends on the amount of porosity originally present and the type of sediment concerned. It is caused by the fact that collodial matter in sediments undergoes dehydration with increasing pres- sure and that their soft mineral grains become granulated. Jifferential velocity in ft-sec. a 2200 : velocity in meters’ $ec /600 200 4or 600 800 /000 /200 Gepth in feet Fig. 9-21. Variation of wave velocity with depth (California). (Adapted from Rieber.) Fig. 9-21 shows the variation of velocity with depth in the San Joaquin Valley in California for various unconsolidated members of the Tertiary formation (from refraction observations). Not only in sedimentary but 16 Tgo-time curves are elliptical and have the same shape as equipotential curves in anisotropic media (see pp. 700 and 706). 16 Physics, 2(3), 174 (March, 1932). Cuap. 9] SEISMIC METHODS 477 also in igneous rocks does the velocity of elastic waves change with depth; however, this change is less in the latter than in the former, since igneous rocks have a lesser initial porosity. By laboratory experiments, Adams and Gibson have shown that the compressibility of granites and gabbros drops at first rapidly with an increase in pressure and remains uniform later for greater pressures. The greatest change in compressibility occurs for the first thousand megabaryes, which is equivalent to the first 4 km of depth. E. PaysicaL Rock PROPERTIES RELATED TO SEISMIC INTENSITY To fully characterize the elastic behavior of rocks and formations con- sideration must be given to the intensity of elastic vibrations in addition to the velocity of propagation. The following physical parameters are significant in this connection: (1) specific acoustic resistance, (2) spreading and dispersion, and (8) absorption and dissipation of energy. 1. Acoustic (radiation) impedance. The seismic or acoustic intensity I may be defined as the average rate of flow of energy through a unit section normal to the direction of propagation, or it may be defined as average power transmission per unit area. Power being the flow of energy per second, the intensity is equal to the average energy content, or energy density, W, multiplied by the velocity of an acoustic or seismic wave, I = W.v. (9-332) Since the kinetic energy is }mv’ or, for a simple harmonic motion with the maximum amplitude A and frequency w, = 3mA‘w’, the energy density per unit volume is 4A’. By substitution of 4? for w, W = 27° A’f's, so that eq. (9-33a) becomes I = 29 A’v)-3-f". (9-33) If in this equation the factor R is substituted for the product v3, the intensity I = 2rf’AR. (9-33c) The intensity is thus proportional to the square of the amplitude and to the square of the frequency. Hence, vibrations of high frequency may be accompanied by great intensities, although their amplitude is small. Further, the intensity depends on the factor R, which by analogy with the electrical relation (power = J°R) may be designated as acoustic resist- ance (in the presence of a reactive component, acoustic impedance). The acoustic resistance referred to unit dimensions is the specific acoustic resistance. Following are the specific acoustic resistances for a number of substances: steel, 390-10*; rubber, 0.5-10°; water, 15-10*; and air, 42. 478 SEISMIC METHODS [Cuap. 9 The acoustic resistance of a medium determines the load or energy output of a sound source within, hence, also, the name radiation resistance or impedance. It also controls the transmission of energy from one medium to another and the ratio of reflected to incident energy. If the-specific acoustic resistances of two adjacent media differ considerably, almost no energy is transmitted and nearly perfect reflection occurs. In the case of energy transfer from water to air and vice versa, the amount transmitted is only about 0.12 per cent of the incident energy. The same holds true for the transmission of sound from an orifice or tubing of small diameter to another of larger diameter. The case is analogous to the transmission of sound from a rare to a dense medium. In the reverse case, when sound is trans- mitted from a dense to a rare medium, or from an orifice of large diameter into one of smaller diameter, the transmitted energy is still small as before (most of the incident en- ergy being reflected), and the transmitted amplitude is approximately twice that of the incident amplitude. If a wave passes from a medium with the specific acoustic resist- ance R, to another with the specific acoustic : resistance R,, if A; is the amplitude of the flected rays in two media of : 5 different specific acoustic re- direct wave, B, the amplitude of the reflected sistances. wave in the first medium, and A, the ampli- tude of the energy transmitted into the second medium (see Fig. 9-22) then” Ri Big tied A, Fig. 9-22. Refracted and re- B= A, = — 4 : "R: + Ri "rat 1 (9-34) < 2Ri 2 Ast Aulus 2) Se eidast : *Rea RS ree where r;2 = R2/R,.” The power transmission. ratio is given by the expression 4/(r_2 + 1)”; that is, the energy transmission from one medium into another is poor if the specific acoustic resistances of two adjoining media, such as air and water, differ widely. This may be remedied by placing a third medium of intermediate specific acoustic resistance between 17 See G. W. Stewart and R. B. Lindsay, Acoustics, Van Nostrand (1930). 18 Note the similarity of the coefficient eo with the reflection coefficient 2 1 (o2 — pi) (p2 + 1) potentials in media of different resistivities p (see p. 712). and the ‘‘dimming factor’’ 2p:/(o2 + p1) in the equations involving electrical Cuap. 9] SEISMIC METHODS 479 them. If the latter is the geometric mean of the other two specific acoustic resistances and if the thickness of the intermediate layer is one-quarter of the elastic wave length of the intermediate layer, the transmission ratio of energy from water to air may be made equal to unity. By using rubber for casing materials of listening devices, the intensity of sound reception may be increased considerably; certain types of geophones are not placed in direct contact with the ground but in holes filled with water which acts as an intervening medium to step down the acoustic resistance. The specific acoustic resistances of the more important rocks and min- erals shown in Table 56 have been computed from their velocities and densities. These values are of interest in connection with reflection shoot- ing, since the ratio of the reflected to the incident amplitude increases with the ratio of the specific acoustic resistances of the formations involved. TABLE 56 SPECIFIC ACOUSTIC RESISTANCES FoRMATION R-10-4 FoRMATION R-10-4 Basement rocks............... 176 Cretaceous formations......... 50 Mamestones ete ae 108 Glacialistratas.*-. 52. 20-30 inex Salt eH 7AsL). LACT Ales 100 Poppa a! By AAG WS. tee. 5-10 2. Spreading, selective scattering, dispersion. Since the intensity of sound decreases with the distance from the source, it varies, for spherical waves, inversely as the surface areas of concentric spheres. For cylin- drical waves it varies inversely as the surface areas of concentric cylinders. Hence, formula (9-33c) becomes, for spherical waves, 1a late = FR, (9-35a) and, for cylindrical waves, 2 = rs PR, (9-356) where R, as before, is specific acoustic resistance, r is distance, f is fre- quency, and A is amplitude. Selective scattering is due to reflections and refractions on prominent irregularities. It is greater for high frequencies than for low frequencies, since the dimensions of the disturbing objects become a controlling factor compared with the wave length. The amplitude of the scattered waves at any distance from the obstacle is directly proportional to the volume of the obstacle and inversely proportional to the square of the wave length. Hence, the intensity of scattered sound varies inversely as the fourth power of the wave length. In a medium consisting of numerous small objects, 480 SEISMIC METHODS [Cuap. 9 scattering accentuates the low and attenuates the high frequencies with an increase in distance. The effects of dispersion on the propagation of seismic waves have been observed in station seismology. The phenomenon is similar to the dis- persion of light by refraction. In optics the degree of dispersion depends on the substance and varies inversely as wave length; that is, the index of refraction is greater for small than for large wave lengths. Since light velocity is inversely proportional to the refractive index, the velocity in- creases with wave length. In other words, both refractive index and dis- persion are inversely proportional to wave length, period, and velocity. This is normal dispersion. If the velocity decreases with wave length, abnormal dispersion occurs. In seismology the effect of dispersion on intensity or amplitude has been observed for longitudinal and transverse waves.” In a wave with com- ponents having different periods, a maximum will occur at a given station because of interference. If the velocity varies with period because of dispersion, this maximum will travel to another station, not with the veloc- ity of the individual waves, but with greater or less velocity, called the group velocity, C. If no dispersion is present, C = v. If the velocity v increases with the wave length (or period), there is normal dispersion, and the group velocity C is less than v. For abnormal dispersion, if the veloc- ity decreases with wave length, the group velocity is greater than the individual wave velocity. Normal dispersion has been observed in the first longitudinal impulses; the occurrence of the maximum in this wave group has been found to be delayed with increasing epicentral distances.” The effect of dispersion is most pronounced in transverse surface waves; further details are given on page 927. 3. Absorption and dissipation. The decrease of seismic intensity with distance, due to geometric spreading, scattering, and dispersion, is ac- companied by losses due to energy absorption giving rise to damping. Hence, at the distance r the intensity I, = le (9-36a) where « is an absorption coefficient or the reciprocal of the distance at which I, is reduced to Iy/e. Hence, ees ne (9-368) r Jie where I,/Ip) may be designated as acoustic transparency and I)/I, as acoustic opacity and is measured in decibels: db = 10 log I,/Ib. Con- 19 B. Gutenberg, Handb. der Geophys., IV(1), 27-28 (1929). 198 Thid. Cap. 9] SEISMIC METHODS 481 sidering both spreading and absorption, IL ee” 7 Arr? (9-37) for a spherical wave. ‘The absorption coefficient a appears to increase with the second power of the frequency. Hence, high frequencies are largely eliminated with increasing distance from source of vibration and the low frequencies are left over. According to Stewart and Lindsay” the following relation exists between absorption coefficient and viscosity: i 8a If? Qa where II is the Poiseuille coefficient of interior friction. Damping constants may be determined in the field and laboratory from resonance curves. The latter are taken with the apparatus previously described (see pages 462-463), the former with vibrators. In both cases the medium under test is force driven, and its dynamic magnification W (see page 602) is given by —— 1 = — We Va — mtb een where n is the tuning factor or the ratio of impressed and natural frequency w/w, and 7 is the relative damping (see page 586) in per cents critical. Substituting in the above formula the resonance tuning factor n, = 4/1 — 2n?, the magnification at resonance We eee (9-396) PIE NOD A 1 (9-39a) For the determination of » from a resonance curve it is convenient to measure the frequencies at which, below and above the resonance peak, the maximum amplitude has dropped to 1/+/2 of its peak value. Then a combination of the last two equations gives ( W ) sis An? A 1— n? Wins ra (1 = n*)? =P 4n? n? IN 2y7 (Uae) Mad n and with W = Wmax./~/2: 1-—n hs f—f marae fo V 272 — fr 20 Loc. cit. 482 SEISMIC METHODS [Cuap. 9 Since, in approximation, f’ ~ fo in the denominator, the damping rates become, for two frequencies, fi and fz, at which the dynamic magnifica- tion has fallen off to one-half of its maximum value: 2 —— —- nm = fot and 2 = (fo kT Ga 7 fa) , so that, since ae = fo, _ ™m a= ne fe er fi " Uh oars He (9-39d) Since the damping resistance p, or the ratio between driving force and velocity of motion (see page 584), is given by p = 2me, with m as mass and ¢ equal to won, the damping coefficient ¢ is Af; therefore the damping resistance (or dissipative resistance) p = 2nmAf. (9-40) (For torsional vibrations the polar moment of inertia is substituted for the mass m). Table 57 gives the damping resistances of a number of substances in bar form at 10 ke (p in kilohms), as found by Wegel and Walther.” TABLE 57 DAMPING RESISTANCES OF SUBSTANCES IN BAR FORM Teed see 8 hind AN Re Lie 117-130 Silvers fob Ae Oe ee 2.8 Hardtrubberseys.. tart. 5%... « 25.5 Glass) s..6.sio. oe eee 2.45 IND OK GLE i voce en ceenructe conse 10 Steely cniscros doc hte we eee 0.84 Coppers Oona ids eee HES Steel -(annealed)......... 2. o.aee 0.215 Similar determinations for rocks have not been published, but they would undoubtedly add greatly to our knowledge of dissipation and ab- sorption of seismic energy. From the damping, an equivalent Poisseuille coefficient II may be derived if the vibrating medium has a simple geometric shape, such as a bar oscillating longitudinally. In such a case the viscosity coefficient is II = pl/2x’S, S being the area of the rod. Substituting m = 8IS for its mass, II = pl’é/2x°m. Since, from eqs. (9-29a) and (9-29b), ee I 3 SB ——————s rs af’ Bx? mfy’ and, since 7 dasa? it is seen that TIw The relative damping is thus represented by the ratio between a dissipa- tive modulus IIw and the elastic modulus. Hence, in a complex representa- 21 Physics, 6, 141-157 (April, 1935). Cuap. 9] SEISMIC METHODS 483 tion of Young’s modulus (or rigidity modulus) the damping 7 represents the tangent of a phase angle between elastic (E or u) and dissipative moduli (IIw and IIw) (see Fig. 9-23). The resulting elastic moduli, E = Ey + joll; and w = w + jwll, , are thus comparable with the apparent dielectric constant (see Chapter 10, page 641). The reciprocal of the tangent of the \ Mechanica/| Kesistance «|! 7 Mass Reactance, =m, Lf | Flastic Beactance, c £, | ! | | Conditions at Resonance Complex Llastic Moduli Fig. 9-23. Oscillation of elastic systems represented by complex moduli (after Wegel and Walther). phase angle has also been designated as ‘‘dissipation”’ constant,” although this definition does not appear well chosen, since materials with the greatest energy dissipation would have the smallest dissipation constants. III. METHODS OF SEISMIC PROSPECTING A. TECHNIQUE OF SHOOTING; SHOT INSTANT TRANSMISSION; REVIEW OF Seismic MrtTHops 1. Source of energy: weights, explosives. In seismic exploration dyna- mite is used almost exclusively. However, different energy sources have | 4H. Walther, Bell Lab. Record, 363-366 (Aug., 1934). 484 SEISMIC METHODS [CHar. 9 been used or suggested. Fessenden proposed the use of sonic transmit- ters, as applied in submarine signaling, for the location of ore bodies. Some commercial companies and scientific institutions have experimented occasionally with weights. Hubert,” using weights of 20, 50, and 117 kg dropped from heights of 1 to 11 m, could detect reflections from a number of beds down to 5 km in depth by means of a Wiechert seismograph with a magnification of 2 million located at a distance of 125 m from the weight tower. He found that (1) the travel times of seismic impulses generated by falling weights were independent of the masses and of the elevation from which they were dropped, (2) seismograms obtained with different masses and different heights could be correlated phase by phase; (3) the observed amplitudes were proportional to the square root of the height and to the weights of the masses used, hence, the amplitudes were propor- tional to the square root of the fall energy. Experiments made in this country with falling weights have shown that a 200-pound lead weight dropped from about 20 feet can be detected with a Schweydar seismograph under favorable circumstances up to about 300 feet. The energy liberated by falling weights is much less than that from a * dynamite explosion. To release the same energy produced by a confined buried charge of about 500 pounds of dynamite, an iron ball nine feet in diameter and weighing 75 tons would have to be dropped from a height of one mile. Nevertheless, weights have possibilities in reflection work. Unbalanced flywheel machines (vibrators) have been used for testing the dynamic response of buildings and surface formations. Details are given in Chapter 12. With the exception of vibration tests of buildings and surface formations, dynamite is used in virtually all commercial seismic exploration. Com- mercial dynamites fall into two group (A) Straight dynamites (dynamites proper). These contain nitroglyc- erine, in an amount equal to the grade-strength marking, and various absorptive materials. (B) Gelatins. Some of the nitroglycerine is replaced by nitrocotton, forming a gelatin. (a) Blasting gelatin: 91 per cent nitroglycerine, 8 per cent nitrocotton, 1 per cent chalk. (b) Straight gelatins: These are blasting gelatins, diluted with pulp and sodium nitrate. The Du Pont Hi-Velocity Seismic Gelatin and the Atlas and Hercules low-freezing gelatins are in this group. (c) Ammonia (or special) gelatins. These are equal in strength to the straight gelatins, but ammonium nitrate replaces a portion of the nitro- 23F. Hubert, Zeit. Geophysik, 1(6), 197 (1924-1925). Crap. 9] SEISMIC METHODS . 485 glycerine. The Atlas ammonia gelatins, Du Pont’s Seismogel A and B, and Du Pont Nitramon are in this group. For reasons stated later, straight dynamites and blasting gelatin are not so well suited for seismic applications as are ammonia and straight gelatins. Explosives for geophysical as well as other applications are characterized by the following properties: 1. Strength 6. Consistency 2. Density 7. Water resistance 3. Propagation effectiveness 8. Freezing resistance 4. Rate of detonation 9. Safety 5. Cost 10. Inflammability By strength of an explosive is meant the percentage of nitroglycerine in straight dynamites. For any other explosive, regardless of composition, the strength rating is obtained by comparing its effect with that of straight dynamite. The absolute strength of an explosive is of minor importance. While theoretically the effect of an explosion should be independent of the type of explosive used, provided the energy (weight-strength times amount) remains constant, it has been demonstrated in practice that, for the same amount, variations in strength and type of gelatin within the range of 40 to 80 per cent have little effect. Strengths are generally referred to unit weight or unit volume and are thus designated as weight-strength or bulk-strength. High bulk-strength is advantageous for reducing trans- portation costs and size of shot hole. Density is of importance in connection with strength. An explosive of both high density and high strength, that is, high weight-strength, is preferable. Propagation effectiveness is the ability of an explosion to propagate through the explosive itself, as well as through air gaps or other non- explosives, to another portion of explosive or cartridge. A typical indica- tion of ineffective propagation from one cartridge to another is shown in Fig. 2 of an article by N. G. Johnson and G. H. Smith.” Rate of detonation is the speed with which the detonating wave travels through a train of explosives. Experience shows that the percentage of energy converted into ground vibration increases with the rate of detona- tion and that the latter increases with the degree of confinement. This is caused by the peculiarity of the gelatin dynamites of having two velocities, one around 8500 feet and the other ranging from 13,000 to 20,000 feet, depending upon the grade of the explosive. In ordinary gelatins the high velocity will not be developed in the open but under close confinement in a 24 Geophysics, 1(2), 232 (June, 1936). 486 SEISMIC METHODS [Cuap. 9 drill hole; therefore, it is necessary to place shots in as firm ground as possible to insure good confinement and to tamp shot holes with mud or water. Again, high water pressures will prevent the high velocity from appearing in the regular ammonia gelatins. Therefore, both Hercules and Du Pont have developed Hi-Velocity—type gelatins for seismic work which give high unconfined velocities without special priming and with- stand such water pressures as occur in the deepest reflection shot holes. It is obvious that those explosives which will give the greatest explosive energy per dollar expended are the most desirable. In long-range refrac- tion work the cost of dynamite amounts to half the cost of operation of a seismic party; consumption of 1200 to 2500 pounds per day is not unusual. In reflection work the cost of hole-drilling exceeds the cost of dynamite. The price of special gelatins is around $17 per 100 pounds in carload and $20 in ton lots. Commercial dynamites vary in consistency from rubber-like constitution’ (blasting gelatin) to free flowing (Nitramon). For reflection work where charges have to be forced into deep holes, stiff cartridges are required. Therefore, special gelatins in stiff wrappers, or in tin cans (Nitramon) are used in seismic exploration. For special applications where very small charges (1/16 pound) are sufficient, a plastic gelatin of sticky rubber-like consistency, which may be molded around caps, is available. Lack of consistency or excessive obstructions in shot holes can be overcome by the use of tin torpedoes. Water resistance is one of the most important properties of explosives in geophysical work. Blasting gelatins, straight gelatins, and ammonia gelatins rank highest in water resistance; next follow the straight nitro- glycerine dynamites; and lowest are certain types of ammonia dynamites. By wax-dipping of wrappers or use of sealed cans (Nitramon), the water resistance is increased considerably. Both dynamite and caps must be highly resistant to water to be usable in the water-tamped holes required in seismic exploration. Freezing resistance. Most gelatin dynamites are low-freezing and may be used the year round throughout the United States. For severe cold weather a special low-freezing grade is available. Safety is one of the prime considerations in any application of explosives. The straight nitroglycerine dynamites are least perfect in this respect; they are too sensitive to shock and friction. Gelatins and ammonia dynamites rank very well. Low-density explosives, because of built-in cushioning effects, are the safest but unsuited for geophysical applications on account of their lack of consistency and low water resistance. Safety of explosives is determined at the factory by impact testers or by dropping an iron ball a distance of about 10 feet on a square section of powder resting on a steel surface. Cuap. 9] SEISMIC METHODS 487 It is unfortunately true for much of the seismic work that familiarity breeds contempt. The most frequent offense is the storing or transporting of blasting caps with the dynamite, despite repeated warnings by powder companies. Accidents have happened in seismic work. Although remark- ably few in number, they were probably more frequent in the days of re- fraction shooting, owing to the greater quantities of explosives and greater distances involved. Considerable progress has been made in recent years in solving the prob- lem of storing explosives for seismic parties. Portable magazines have been constructed. Two types are available, one on a two- and the other on a four-wheel chassis. The body is electrically welded steel of a capacity of about one ton. The housing is well ventilated, protected by locks _ against theft, and coated with aluminum paint (see Fig. 9-24). Since it is illegal to carry dynamite in a trailer or in a car towing a trailer, the dyna- mite may be transported in one vehi- cle, the trailer towed by another, and the dynamite transferred on location. Separate steel boxes for caps are also available. These may be chained to a tree in the field. Inflammability. Straight nitrogly- cerine dynamites are most easily ignited, but all other grades are of low inflammability. Explosives should be well protected against fire. Experience collected with various types of explosives in seismic work in this country for over twelve years indi- cates that the 60 per cent ammonia gelatins, especially the high-velocity types developed for seismic applica- tions, are the most satisfactory. Dynamites for seismic work are manu- factured by the Du Pont Powder Company, the Hercules Powder Com- pany, and the Atlas Powder Company. The most popular sizes are: $-pound sticks, 13 x 8 inches; 1-pound sticks, 2 x 6 inches; 23-pound sticks, 2 x 16 inches; 5-pound sticks, 3 x 12 inches; and 70-pound sticks, 8 x 24 inches (for swamp work). For setting off the charge, electric blasting caps are used exclusively (Fig. 9-25). These consist of a metal container, two insulated leg wires sealed with a waterproof compound and with sulfur on top, a pressed charge at the lower end of the cap, and a primer charge at the ends of the leg wires where they are connected by a bridge wire. The fusion of this wire detonates the cap. The bridge wire is made of an 80-20 platinum-iridium alloy and is 0.00125 inch in diameter. The priming charge surrounding Texas Body and Trailer Co. Fia. 9-24. Portable dynamite magazine. 488 SEISMIC METHODS [CHar. 9 Bridge Wire Fig. 9-25. Cross section of Hercules electric blasting cap. a second. Ordinary caps are unsuited for this purpose. As shown in Fig. 9-26, the delay for low currents is great. For high currents two breaks oc- cur—one when the bridge wire fuses and the next when the cap fires. In caps especially developed for seismic applica- tions (Du Pont ‘SSS’’) not only is the time difference beween bridge break and deto- nation eliminated but the fir- ing delay is reduced consider- ably. This type of cap can be fired by any current greater the bridge wire is usually mercury ful- minate; in the Du Pont “SS” caps it is fulminate chlorate. Instead of hav- ing a loose charge around the bridge wire, the Atlas caps have a bead in the form of a matchhead. Caps are usually protected by a shunt clip against accidental discharge due to static or other sources of electricity. This clip is removed immediately before firing. The time characteristics of electric blasting caps are of great importance in seismic work. Connected to the blasting cap is a circuit for transmit- ting the instant of the explosion to the seismic record. With the introduc- tion of the reflection method, the re- quirements of time accuracy went up considerably, for the time of explosion must be transferred to the record with an accuracy of 1 to 2 thousandths of Fig. 9-26. Firing current vs. firing time for Du Pont seismograph blasting caps (after Burrows). 1 is ‘SSS’ bridge break and total cap lag; 2A, ‘‘SS”’ bridge break; 2B, ‘‘SS’’ total cap lag. than 2 amperes. At 3 amperes the firing time is about 0.003 second + 0.0003. Batteries or blasting machines may be used for firing electric blasting caps, the latter being preferable from the point of view of safety. A 50-cap blasting machine furnishes about a 300-volt peak e.m-f. Cuap. 9] SEISMIC METHODS 489 When dynamite is primed with an electric blasting cap, the latter should be so fastened with its lead wires around the charge that the cap does not pull out when the charge is lowered into a hole. Before shooting, the firing circuit should be tested for resistance to be sure that the current is passing through the blasting cap and through all parts of the line. For this purpose the powder companies furnish test instruments consisting of an ohmmeter and a silver chloride battery which supplies less current than is required to blow up a cap. The resistance of the caps plus the resistance of the leads should be calculated and compared with the results of the test. Both short circuits or high resistance breaks are equally objectionable. 2. Placement of charges. In both refraction and reflection work it is necessary to place the charges in the surface in such a manner that maxi- mum energy transfer from the explosive to the ground is obtained. The amount of energy released by the explosion itself is appreciable. It has been estimated” that the temperature of the gases liberated by it is of the order of 3000° C., and that pressures of about 50,000 atmospheres (or about 700,000 pounds per square inch) are produced by an explosion of 60 per cent dynamite. However, very little of this energy is likely to be transmitted to the ground. If the charge were placed on the surface without confinement, not only would its rate of detonation be low (unless a high velocity powder is used) but most of the energy would probably be converted into a compressional air wave. Hubert, as early as 1924, dem- onstrated experimentally that the effect of a buried charge may be from 50 to 100 times greater than the effect of a surface charge. Even then, most of the energy is probably expended in enlarging the hole, in crushing the rock, in moving out water and mud, and in heat. Comparatively little is converted into elastic wave energy. Charges should be placed as deep as time, terrain, and cost permit, although it may happen that deeper layers have poorer transmission characteristics than do more shallow layers. Firm shales or water-soaked beds are the most effective carriers of seismic energy. Reflection shooting has made it a fairly general practice to place the charge at the depth of the ground-water level if it is not too deep. In long-range refraction shooting, usually a hole 4, 5, or 6 inches in diameter is drilled to a depth of from 12 to 25 feet, and a cavity is blown at the bottom with 4 to 8 pounds of dynamite. The entire charge is then placed in the cavity and the hole is tamped with dirt and water. The large cartridges 8 inches by 24 inches mentioned before are applied in marsh work and are forced down with a wooden tamper as far as they will go. In open water the charges are sacked and primed, and the bags are lashed together and tossed over- 25 H. KE. Nash and J. M. Martin, Geophysics, 1(2), 239-251 (June, 1936). 490 SEISMIC METHODS [CHap. 9 board at the desired location. Reflection shot holes are generally of small diameter, and the primed charge is pushed down with a tamping stick con- sisting of several sections connected by hook joints. Several sticks may George E. Failing Supply Co. Fig. 9-27. Failing seismic shot-hole drill; view of hydraulic. be taped to a piece of lath, or they may be placed in a tin torpedo. Nitra- mon cans are loaded with a spoon attached to the end of the loading pole. Shot holes are drilled in various ways, depending upon conditions. In easy drilling soil, the use of hand augers is quite feasible, particularly if Cuap. 9] SEISMIC METHODS 491 local labor is cheap. In most cases truck-mounted rotary drilling machines are used (Figs. 9-27 and 9-28). In soft ground holes may be ‘‘washed down” by the use of centrifugal pumps driven by gasoline engines (Fig. George E. Failing Supply Co. Fig. 9-28. Failing seismic shot-hole drill; view of entire unit. 9-29). Hole caving may be prevented by the use of Aquagel or lime, or by the use of casing” which can usually be recovered and used again. % A light-weight casing, made of piastic, has recently been put on the market. 492 SEISMIC METHODS [Cuap. 9 Shot holes are tamped with water. Most reflection parties have a water truck following the drilling truck. Drilling costs may range from 25 cents to over a dollar per foot, depending upon conditions. Seismic-hole drilling may be contracted at $1000 to $1500 per month. Charges are generally fired from a shooting truck set up as close to the shot point as practicable. Swivel— ne ae LZ pd Foot valve Sto? Hole Fig. 9-29. Evinrude centrifugal pump for drilling shot holes in swamps. In earlier refraction shooting Ground Auphiude some companies fired charges by radio from great distances but this practice is now aban- doned. It has been demonstrated that no changes in travel times occur when _ charges _are <0 Gad aan leno ae changed as much as ten times * Grams Charge in energy, that is, in quantity Fig. 9-30. Variation of amplitude with charge or in strength. As shown in (after Rixman). (1) Shots fired in dry sand; (2) : an 27 . shots fired in moist sand; », ground amplitude Fig. 9-30," the amplitudes ji) icrons. generally increase in propor- tion to the square root of the charge. 3. Energy transmission and absorption. It is difficult to determine accurately the relation between distance and record amplitude, because such measurements make it necessary to move either shot points or ob- servation points. If the shot point is moved, the energy transferred to the ground changes with local conditions at the shot point. If the re- 27 F, Rixmann, Zeit. Geophys., 11(4/5), 197-207 (1935). Cuap. 9] SEISMIC METHODS 493 ceivers are moved, the recorded energy varies with the so-called ground factor, that is, with the dynamic response conditions of the surface strata. Different propagation paths of refracted, reflected, and surface waves further complicate the problem. In refraction work the amount of dynamite required increases with dis- tance, probably in linear relation. In reflection shooting a relation be- tween charge and depth is hardly recognized, since the recorded ampli- tudes are predominantly dependent on transmission conditions of surface beds at the shot point. The curves in Fig. 9-31 have been plotted from data published by Barsch and Reich for a number of refraction traverses. 60 40 nen Z| 40 S fool aes? H ae ) eae ei wt s oe eee <= ee io eras 10 1000 2000 5000 4000 5000 Distance in meters Fig. 9-31. Dynamite charge required to produce legible impulse, as a function of distance (compiled from data by Barsch and Reich). P, S-H, and¢*D indicate localities. They indicate that the amount of dynamite required varies approximately in direct proportion to distance. 4. Transmission of shot instant. The accurate transmission, from the shot point to the receiver, of the instant of the explosion is of importance, since virtually all interpretation methods are based on determination of travel times. In refraction shooting the accuracy in time transmission varies from 3p of a second for short distances to several hundredths of a second for great distances, in reflection work it is of the order of zp of a second. The instant of the explosion may be determined (a) by its direct effects (sound, light, or temperature), or (b) by an indirect effect (electrical current or radiation) released by the explosion. 494 SEISMIC METHODS [CHap. 9 The instant of explosion may be computed from the time of arrival of the sound wave, taking into account the velocity of sound, barometric pressure and temperature, wind direction and velocity, and the distance of seismographs from the firing point. Application of this method de- creased when charges were buried at greater depth, but it was later revived for the purpose of determining the distance between firing point and receiver in difficult terrain. In this procedure a ‘‘sound” charge is placed on the ground above the buried main charge and a blastophone is used for recording the sound waves. The use of the light transmitted by the explosion was mentioned by L. Mintrop in one of his patents. The possi- bilities of recording an explosion through its heat radiation have never been investigated. In the transmission of the shot instant by wire, a contact in an electrical circuit is made or broken at the instant of the explosion. Double wire or ground return may be used. The indicating devices are electromagnets with mirror armatures, telephone receivers or loudspeaker elements with mirrors attached to their diaphragms, oscillographs, string gal- vanometers, and the like. These will be dis- snap spring cussed in more detail in the article on radio transmission. The transmission circuit (1) may be broken at the instant of firing (a) by epi ae wrapping it around the charge, (b) by a series per heels Peeeaie, Rial cap, or (c) by a relay in the firing circuit; (2) mission. it may also be closed by a relay, actuated (a) by the firing circuit or (b). by a series cap; or (3) the transmission circuit may be coupled directly to the firing cir- cuit by (a) a resistor or (b) a transformer. Wrapping the transmission line around the charge has the disadvantage of placing four lines in the shot hole. A series cap is more convenient for breaking the line. For closing the circuit by a series cap, the firing relay shown in Fig. 9-32 has been used in connection with refraction shot-instant transmission. Two field phones are usually connected to the shot-instant transmission line as shown in Fig. 9-33. The first arrangement is actually a three-line circuit. Communication is not interrupted when the shot- instant circuit is broken; the phone current passes through the indicator, which is avoided in the second arrangement. However, the use of a single line requires switching from communication to shot transmission. Various arrangements are applied (particularly in reflection work) to couple the firing line directly to the transmission line. A small amount of current, not enough to set off the cap but sufficient to attract the armature of the indicator, may be passed from a battery through the aS cap American Askania Corp. Cuap. 9] SEISMIC METHODS 495 circuit before firing. At the instant of firing, the circuit is broken and the armature released. Instead of feeding directly into the transmission line, the firing line may be coupled to it preferably by a transformer, or by a indicator Pa Parsw mua enn ustolkenitess Gun. Seal Or SOrles phone aoe a Fig. 9-33. Arrangements for shot-instant transmission by circuits separate from firing line. LE ERAT RT SORE TS Sy A ALN Re ate Amplifier oulput tL. GZS Fig. 9-34. Arrangements for shot-instant transmission over single and double communication lines from firing circuit. resistor. This method is the most prevalent. Fig. 9-34 shows three varieties. A transformer is connected in parallel to the firing circuit in such a manner that a portion of the firing circuit passes through its primary. 496 SEISMIC METHODS [Cuap. 9 In Fig. 9-34a the phones are in parallel with the secondary of this trans- former; in b and c the phones (or the speaker input transformers) are in series with it. In all cases the regular seismograph galvanometer is used for the time break, and the output of the shot-transmission transformer is either in series (a and b) or in parallel (c) with the amplifier output transformer. Arrangement c differs from b by the use of microphones and speakers, which makes for more convenient operation in a recording truck. Wire transmission of the shot instant is applied in short-range refraction and in most reflection work. In all long-range refraction work and for reflection shooting in areas where distance, type of country (swamps), or topography make laying of lines impracticable, radio is used. Trans- mitters vary from about 40 to 200 meters?” in wave length, and from 0.2 to 50 watts in power, which must be great enough to overcome static and to actuate the type of indicator used. Their range may extend to 150 miles or more. Fig. 9-35 shows a portable transmitting and re- ceiving unit. The transfer of the shot instant to the transmitter is gener- ally accomplished by making or breaking the plate circuit. For breaking it, the B battery lead is shot apart; for connecting it, the firing relay shown in Fig. 9-32 is used. Often the transmitter sends some sort of a signal (produced by buzzer or tuning fork) which is either turned off or on by the shot. On the receiving end the signals are picked up as sound and recorded. A great variety of devices are available for recording. In long-range radio time-signal transmission (deep refraction and pendulum surveys) relays are sometimes applied in connection with less sensitive and, there- fore, more rugged indicating devices. These may be mechanical relays or gas-filled tubes (grid-glow tube or thyratron). In the majority of cases relays are avoided, and indicators of special design or oscillograph galva- nometers are applied. A simple recording device may be made from a phone receiver by at- taching a mirror to the diaphragm and placing the receiver behind a lens of the same focal length as that used in the (mechanical) seismograph. The receiver is then set up on a stand next to the seismograph. A more effective recorder is made from a magnetic speaker by removing the diaphragm and coupling the driving pin to a light spring fitted with a mirror, or to a mirror suspended on a short platinum-iridium torsion wire. In both cases suitable damping should be used. In refraction work the Askania mirror device has been widely applied (see Fig. 7-24). All kinds of oscillographs, vibration galvanometers, and string gal- 2a In this country, the following frequencies have been allotted by the F. C. C. to geophysical work: 1602, 1628, 1652, 1676, and 1700 kilocycles. Cuap. 9] SEISMIC METHODS 497 vanometers are extensively employed.” ‘They are generally coupled to the receiver by a suitable step-down transformer; the regular seismic oscillographs (coil galvanometers or string galvanometers) may be used when a separate indicator is undesirable. In that case the output trans- former of the radio receiver is connected in series or in parallel to the secondary of the output transformer of the seismic amplifier. A disad- vantage of all oscillographs and mirror devices is their inertia, which re- quires damping. This is avoided in the glow-tube oscillograph shown in Fig. 7-25. The latter ignites with about 2.10 * amperes for optimum plate voltage. Its cathode is a hollow slotted cylinder whose end surrounds B+ 7 = 250 volts 8+ *2 = 300 volts ar 5 te be (en sta ToFil Bet. 1e ee To 8+*2 To B+ */ Harvey Radio Laboratories, Inc. Fig. 9-35. Radio transceiver. the anode. The current controls the length of the glow in the slot. This glow is projected on the photographic paper. 5. Review of seismic methods (fan shooting, refraction, reflection). All seismic prospecting methods have in common the generation of an in- stantaneous shock and the measurement of resultant surface vibrations at one or more distant points. The physical parameters which may be deter- mined for any vibratory motion are (1) frequency; (2) intensity or ampli- tude; (3) velocity and travel time. Practical experience has shown that the first two parameters are too complex to be used for interpretations in 28 The regular seismic oscillographs are discussed on pp. 552; 598-601. 498 SEISMIC METHODS [Cuap. 9 terms of depth. However, they enter indirectly into the interpretation of a seismogram, since impulses due to any new phase are characterized by a change in both frequency and intensity. The only wave parameter employed for depth calculations in present practice is the time interval elapsed between the instant of the explosion and the arrival of the first or later impulses. According to the type of wave used and the manner in which travel times are observed and analyzed, the following seismic meth- ods are distinguished: (1) fan shooting, (2) refraction, and (3) reflection. The objective of the first method is to determine whether there is an intervening medium of different velocity between shot point and receiving points. Fan shooting is a reconnaissance method, capable of covering a large area in a comparatively short time. Indications obtained by it may be detailed by the refraction or reflection methods. In many ways the fan shooting method is comparable to resistivity mapping of electrical prospecting. When distances between receivers and shot are kept fairly constant, the depth penetration also remains about the same. In con- trast to the fan shooting method, refraction J reflection methods in- volve absolute determinations of depths to geologic formations. In the refraction method, this determination involves an observation of the varia- tion of travel time with interval between shot point and receiver. Hence, it is comparable with the resistivity-sounding method of electrical prospecting. While in fan and refraction shooting primarily the first impulses from high-speed beds within the range of the shot distance are evaluated, the reflection method is based on the determination of travel times of impulses arriving subsequently in the seismogram. The interval between shot and receiving points is no longer a factor controlling depth penetration. Were it not for ray curvature and absorption it would be possible to penetrate to any depth with any given spread. This method can be used for both reconnaissance and detail. However, because of difficulties in correlating records through large distances, its main application is to detailed survey- ing. In refraction shooting, the distance between shot and receiving points is roughly a multiple of the depth penetration (generally from 3 to 5); in reflection shooting, it is a fraction thereof (from 75 to 3). To obtain depth in refraction shooting, the travel time must be deter- mined as a function of distance. Hence, observations in a number of distances are required. In reflection shooting, one distance would the- oretically be sufficient if the velocity is known. In practice, however, more distances are necessary, since it is not possible to differentiate be- tween a refracted and a reflected impulse in a single record. In field application the distinction between the three seismic methods is not so sharp as it may appear from the above description. To calibrate Cuap. 9] SEISMIC METHODS 499 the time scale in fan shooting in terms of normal geologic depth-velocity sequence, a refraction profile is first shot. There are combinations of fan and refraction shooting in which absolute instead of relative depths are obtained; refraction profiles may be tied in with reflection traverses to obtain average velocities to reflecting beds. Finally, refraction shooting for weathered layer corrections is part of everyday reflection practice. B. Fan-SHootine Mrruop 1. In oil exploration the fan-shooting method was applied extensively on the Gulf coast for the location of salt domes from 1924 to 1929, which = va Fic. 9-36. Preliminary profile and fan layouts (after Barton). are ideally suited for this work, since their velocity differs considerably from that of the surrounding formations. The area to be prospected is covered by a series of overlapping fans (see Fig. 9-36). Receivers are grouped, by repeated setups, on the circumference of a circle about the shot point, at distances varying from four to eight miles. In a new area a profile is first shot to determine the normal sequence of beds, that: is, the “normal” travel-time curve (see Fig. 9-37, and profile extending north from fan shot point A in Fig. 9-36). Travel times observed at the fan 500 SEISMIC METHODS [Cuap. 9 10000 20000 Feet Fic. 9-37. Fan times plotted on preliminary travel-time curve (after Barton). FMS. GMP LE EW —$ s0e— a 1 2 Miles MOSS BLUFF DOME Fic. 9-38. Refraction fans and travel-time anomalies (‘‘accelerations’’) at Moss Bluff salt dome (after Eby and Clark). stations are then compared with the corresponding times of the standard curve for the same distance. Fig. 9-37 shows such fan times plotted on Cuap. 9] SEISMIC METHODS 501 the standard travel-time curve, indicating that there are no media of anomalous velocities within the range of the fan. Time anomalies are plotted for each fan as “accelerations” (in fractions of seconds). Fig. 9-38 shows such fan accelerations for the Moss Bluff salt dome. An analysis of the length of the acceleration vectors makes it possible to determine approximately the location of the dome. The corresponding travel-time curve for a salt dome is given in Fig. 9-39. After a dome has been located by fan shooting, the company doing the work usually blocks Salt Dome Fig. 9-39. Travel-time curve across salt dome (adapted from Barton). the prospect as quietly as possible and then returns to the area later to detail the indication by refraction profiling, reflection shooting, or torsion balance to determine the shape of the cap and the attitude of beds above and around the dome. The fan-shooting method has also been applied in the mapping of anticlines” (see pages 547-548). 2. In mining exploration the fan-shooting method can be used for the location of gold-bearing placer gravel channels and similar problems. Figure 9-40 shows a fan layout as applied in prospecting for gold-bearing 29 J. H. Jones, World Petrol. Congr. B.I., 169-173 (London, 1934). 902 SEISMIC METHODS [Cuar. 9 leads. The receivers are placed at the ends of radial lines at distances of 1000 to 2000 feet. The location of the lead is given by the maximum travel time, and this point is then made the vertex for the next fan. The position of the edge of the channel, as well as the channel depth, may be Travel Time Mmlliseconde 500 300 200 200 100 100 0 0 1000 2000 3000 000 500 0000 7000 2000 3000 tt Alluviel 6old Channel See Spgs e ed OS STIS IIT IF TIT FIT ie ET FS . 77, > 1; (branite) Bedrock 4, Fig. 9-41. Travel-time curves on two gold-bearing alluvial channels in the Gulgong gold field, New South Wales (after Edge and Laby). detailed by refraction profiles at right angles to and parallel with the strike of the leads. Fig. 9-41 shows up- and down-lead travel-time curves (to determine dip of bedrock surface, see page 525). The depth of the chan- nel is roughly proportional to the ordinate of the break in the travel-time curve. Cuap. 9} SEISMIC METHODS 503 3. Fan-shooting equipment. Equipment and instruments used in fan shooting depend to some extent on the purpose of the survey. Fan-shoot- | ing equipment for oil exploration is more elaborate than that employed in mining and engineering applications, since the distances between shot point and receiving points and the distances between individual fan sta- ‘tions are much greater. For this reason, the shooting technique also differs. In oil exploration, where large charges are required for fans three to seven miles in length, a hole is drilled first to a depth of 20 to 25 feet; a large cavity is blown out at the bottom of the hole, and the main charge is placed in it. A surface charge is hooked in with the main charge to transmit the sound of the explosion. The two charges are then fired simultaneously from a shooting truck which is set up at a safe distance and is equipped with a radio transmitter to relay the instant of firing to the receiving points. The latter are individually equipped with either photographically recording mechanical seismographs or with electrical detectors connected to a three- to four-stage amplifier and oscillograph. The recording camera often contains another oscillograph element for the recording of the sound of the explosion, which is received by an elec- trical microphone (blastophone). A third element may be used to record the shot-instant signal picked up by the radio receiver, or the shot instant may be recorded on the seismic detector trace. The sound record serves to calculate the distance between shot point and receiving point. Since wind direction, velocity, air temperature, and barometric pressure must be known for an accurate evaluation of the record, the receiving units are usually equipped with meteorological apparatus. Mechanical seismo- graphs are set up in small tents, and electrical detectors are buried in auger holes several feet deep. The radio receivers are equipped with antennas strung out on bamboo poles, one on the recording truck and the other set up some distance from it. The receiving apparatuses with seismic, mete- orological, and radio accessories are carried in recording trucks, of which there are usually three to six to each fan party. These operate simul- taneously in fan arrangement for one shot and are then moved to the next portion of the fan, the shot being repeated at, or very close to, the original shot location. At the present time the fan-shooting technique in oil ex- ploration is more or less past history in this country, but it is still being applied in foreign oil exploration. In mining and in engineering applications the dimensions of the fans are small, and therefore multi-channel electrical equipment with a com- mon recording element is much preferred. Four to twelve electrical de- tectors are connected to a recording truck, recording trailer, or recording tent, which is set up approximately in the middle of the arc of the fan. At this central recording point are the amplifiers and the recording camera 504 SEISMIC METHODS [CHap. 9 which contains as many galvanometer elements as there are channels. Communication with the shot point is generally maintained by wire and the same wire is used for the transmission of the shot instant. An ap- paratus that is adapted to extreme requirements of portability and does not necessitate the use of a truck or tent is illustrated in Fig. 9-114. C. Rerraction METHODS 1. General. The travel of seismic waves in the earth is controlled by the same laws as is the propagation of light rays. Seismic waves are re- fracted and reflected on any interface at which there is a change in veloc- ity. Therefore, a deviation from normal ttavel time is observed when media of different velocities occur below. When the variation of travel time with distance has been determined, depths and nature of the refracting beds may be deduced from the travel-time curves. If the velocity within a given layer is constant, the seismic rays may be considered straight. The theory of wave propagation is based on Snell’s law of refraction and the principle of Fermat which states that seismic energy follows that path which enables it to travel from the shot point to the receiving point in a minimum of time. In refraction shooting, a charge is placed at one location and a number of seismographs are set up in a straight line, preferably at equal intervals. Profiles may be laid out in the direction of the strike, at right angles thereto, or in both directions. For dipping formations, profiles are shot both up slope and down slope. Depth calculations are based on a time-impulse analysis of the seismogram. Impulses are located which correspond to the arrival of different types of waves; their arrival time is measured from the instant of the shot. In practice, only impulses of longitudinal waves are used. ‘The first impulses or ‘‘breaks’’ are due to the deepest high-speed bed within range. If later impulses (due to shallower beds of lower velocity) are noticed, they may also be timed. However, depth calcula- tions may be based on first impulses only. Travel times are plotted against the distances of the various receiving stations from the shot point. Thus, the travel-time curve is obtained. It consists of one line if only first impulses have been plotted, but it may have several branches if later impulses have been utilized. If the travel time curve is straight and has essentially the same slope for all distances, no higher-speed beds have been reached. When breaks (changes of angles) occur, they may be due to a variety of conditions. Several simple types are discussed below. 2. Refraction equipment. Seismic refraction equipment is similar to and in many cases identical in general design with fan-shooting equip- ment, described on the preceding page. However, in refraction shooting there is greater opportunity to use multielement equipment with a com- Cuap. 9] SEISMIC METHODS 505 mon recording point. In oil exploration there are quite a number of prob- lems which can be successfully solved by refraction profiles of moderate detector intervals. Whereas the detector interval in a four- to six-mile fan is of the order of a mile, a refraction profile shot under similar circum- stances would utilize detector spacings of the order of 1000 feet. In mining applications, such as mapping of the bedrock surface on placer sites, the detector spacing would be of the order of 25 to 100 feet. In engineering work the detector interval depends largely on the problem and would vary between 5 and 25 to 50 feet. In the early days of refraction shooting, mechanical seismographs with individual setups, such as the Mintrop and the Schweydar seismographs (page 608), were widely used. These were soon superseded by electrical seismographs, such as those described in connection with the fan-shooting equipment for individual setups, and later by multichannel equipment with central-point recording. Reflec- tion seismograph equipment is well suited for refraction applications; de- tails are discussed on pp. 551-56. As a matter of fact, reflection equipment is used for refraction work in everyday reflection routine for the determination of the thickness of and the time delay in the weathered layer. A portable refraction apparatus suited particu- Wh Wy yy, larly for shallow engineering and min- Fia. 9-42. Refraction travel-time ing applications is illustrated in Fig. curves on vertical boundary. 9-114a. 3. Travel-time curve for vertical boundary. In Fig. 9-42 let v, = 2000 m per sec. and ve = 4000 m per sec. Assume that the shot point is at 0 and that detectors are set up at the points 1 to 5 at 400-m intervals. The ex- plosion wave will reach point 1, 0.2 sec. after the shot has been fired, point 2 in 0.4 sec., and point 3 in 0.6 sec., point 4 in 0.7 sec., point 5 in 0.8 sec., point 6 in 0.9 sec., and so on. Plotting these times against distance gives a curve with a break above the contact. Since a travel-time curve of the same shape is obtained also for a horizontal layer, another shot may be fired some distance away from the first shot point. In case of a vertical fault at the surface as assumed here, the position of the break remains the same. If a horizontal boundary occurs at depth, the distance of the break from the shot point remains unchanged. The slopes of the two parts of the travel-time curve indicate the respective velocities below: cotan a = 5 = Vi} cotan 6 = T= we. 506 SEISMIC METHODS [Cuap. 9 4. Single horizontal layer. Equations for this case are obtained by considering the possible longitudinal wave paths through two layers. When a charge is fired at A, waves radiate in all directions. For the wave traveling horizontally to location D, the time is s i= a (9-42) (see Fig. 9-43), and cotan a = ds/dt; = v,. To find the path of the wave which reaches the receiver through the lower medium, consider the rays impinging on the boundary. If an incident ray subtends the angle ¢ with the normal to the boundary and the refracted ray subtends the angle y, then, according to Snell’s law, sin g/sin Y = q = vi/Ve, where q = index of refraction. For a given index of refraction there occurs an angle g, for which sin y = 1; that is, the refracted beam travels along the boundary surface. If ¢ becomes greater than this “critical” Tia -9'43 ° Chitiealsrayspathe! angle 7, total reflection takes place. single-layer case. Hence, sin 7 = vi/ve = q. Evidently, A 3 Fic. 9-44. Wave fronts in upper and lower layer. the only ray which can reach the receiver by refraction will travel hori- zontally on the boundary of the lower medium. It strikes the boundary at the angle of total reflection and leaves it at the same angle. This statement. involves the application of Huygen’s principle, since any point of the underlayer wave may be considered a source of new waves. While this wave proceeds with the velocity of the lower layer, impulses are continually sent upward into the upper medium, where they propagate with the velocity of the latter. In Fig. 9-44 locations 1, 2, and C are considered such source points. Their distance is given by the product v,-, with t as an arbitrary time unit. The “wave fronts” in the lower layer will occupy these positions in successive equal intervals of time. Similar wave fronts may then be drawn for the wave propagating from Cuap. 9] SEISMIC METHODS 507 points 1, 2, and so on, into the upper medium, their spacing for the same time intervals being v,-t. Since in the schematic of Fig. 9-44 the velocity in the upper medium was assumed to be half that in the lower medium, the spacing of the fronts in the lower medium is twice that in the upper. By joining points reached by wave fronts at the same instant, one ob- tains the front BC in the upper medium, which subtends the angle 7 with the boundary of the lower layer. Schmidt” has coined the expression “traveling reflection” for this phenomenon. He showed that it is analo- gous to the bow wave which appears when a bullet travels with a velocity greater than that of sound in air (see Fig. 9-45). While the bullet is traveling with the velocity v2, a compressional wave is produced around the front of the bullet which propagates with the velocity v; (sound in air). Hence, the angle of the bow wave with the path of the bullet is given by sin 1 = vi/ve. This wave does not occur if the bullet (or any other com- pressional impulse) travels with the velocity of sound in air or with less velocity. In the propagation of re- fraction waves, an analogous phe- nomenon occurs. In the lower me- dium the impulses travel with the velocity of that medium, and a bow wave can not occur. It appears, however, in the upper medium, for its velocity is less than the velocity of the lower medium. Fig. 9-45. Bow wave of bullet (adapted In Fig. 9-43, let 4 ABB’ = % from O. V. Schmidt). CCD: =4, AD ='s, B’B = C'C = d, AB’ = C’D = dtani and AB = CD = d/cosi. Then the travel time for the wave traveling the path ABCD is t = 2(AB)/v: + BC/v2; BC = s — 2d tan 2; therefore, te = — + — cost. (9-43) Differentiation of this equation gives ds/dtp = v2 = cotan 6. Without physical contact with the lower layer it is thus possible to obtain the elastic wave velocity in the layer from the slope of the travel-time curve. Near the shot point the wave traveling directly from A to D arrives ahead of the underlayer wave; beginning with the ‘‘critical” distance z, it arrives later than the underlayer wave. A break occurs in the travel-time curve at the distance x, that is, for the simultaneous arrival of both waves. By #0 O. V. Schmidt, Zeit. Geophys., 12(5/6), 199-205 (1936). 508 SEISMIC METHODS [Cuap. 9 equating (9-42) and (9-43), substituting z for s, and multiplying both sides by v;/cos 2, pe x Vo x Ve — V1 _ = — d = —e = ° — 2\ cosz 2 Ve + vi eae ee) pail Vo — Vi - where C, = is a constant for any area as long as overburden 2 Ve + Vi and underlayer velocities remain constant. A number of travel-time Asmari Limestone Fig. 9-46. Strike travel-time curve on anticline of Masjid-I-Suleiman, Persia (after Rankine). curves for a single horizontal bed of varying thickness are given in Fig. 9-41. Fig. 9-46 is a good example of a depth determination in the single-layer case (limestone under shale on crest of anticline). From eq. (9-44) it is seen that the depth is always less than z/2. The break in the travel-time curve occurs at distances at least twice the depth when the velocity contrast is great, but the break moves further out from the shot point as the contrast is reduced. If q is refractive index and r its reciprocal (ratio of velocity in lower and upper medium), red 4/ Rite aadwiietiod 4/ oe a (9-445) r 1 1—q 31 Examples of depth calculations are given on p. 510. Cuap. 9] SEISMIC METHODS 509 In another method of depth computation, the second part of the travel- time curve is extended to the intersection with the abscissa, obtaining the distance D. Then tan 7. (9-44c) ao 3-va-tan i a ee (9-44d) A fourth method of depth calculation is based on the time ¢t, of the intercept: _ Witz V2 — Vi i= 9 \/ yeas (9-44e) The determination of depth is as accurate as the measurement of dis- tance between shot point and receiver, other things being equal. It de- pends, further, on the relief (ac- curacy of elevation correction), on the accuracy of timing of the im- pulses, and on the difference in velocities. Other refraction meth- ods for the two-layer case, using different interpretation methods and different field technique, are Fia. 9-47. Wave paths, two-layer case. discussed on pages 533 and 546. 5. Two horizontal layers. In the single-layer case impulses past the first break in the travel-time curve arrive by the path AGHF (see Fig. 9-47). If a third layer is within range, these will be overtaken by waves traveling along the path ABCDEF, and the travel-time curve will now have two breaks. Let the velocities of the three media be v, , Ve, and v3, and the respective depths of their lower surfaces d; and d;. Then sin 8 = v2/Vs; , since the angle at C is 90°. For the remainder of the path in the upper layer, sin a/sin 8B = vi/v2. Substituting sin 8, sin a = vi/V;. In the expression for the underlayer travel time, (9-43), the first term represents the underlayer effect and the second that of the overburden. By analogy, the time for the path ABCDEF is composed of one under- layer time and two overburden times, so that 2(de — di) Ve cos B + th COS a. (9-45a) 1 § k= d V3 Vv The second part of the travel-time curve gives the velocity through the second layer, and the third part gives that through the third layer. By 510 SEISMIC METHODS [CHap. 9 differentiation of eq. (9-45a), tan y = dt3;/ds = 1/v3;. Neither the first nor the second layer is effective after the break xz is passed. For deter- mining the depth dz, let ff = ts. By equating eqs. (9-42) and (9-45a), substituting 2x2 for s, and proceeding as before, “2 = 2 1 ae fi sh 4 / Oo al afi aU ant GonG (cos 7 — cos -)| =d,. (9-45b) All data for the computation of the depth of the lower surface of the second layer are obtainable from the travel-time curve, since sin 7 = v1/Ve , sin 6 = V2/v3, and sin a = v;/v;. The depth to the bottom of the second layer may also be calculated by extending the v; and v; portions of the travel-time curve to the intersection at the abscissa 213 (Fig. 9-48). Then™ 213(1 — sin a) — 2d; cos a (9-45c) Oe lie 2 sin 2 cos B Another convenient depth-calculation method uses the time obtained on the ordinate by extending back the third part of the travel-time curve. Then from eq. (9-45a), with T; = t; for s = 0 and he for d2 — d,, i = cos B + % “COs a. (9-45d) As an example of depth calculations in the single- and two-layer case, the curves in Fig. 9-48 furnish: 21(= 212) = 1000 m; x3(= x2) = 3000 m; tig = 1750 m; vi = 1000 m-sec '; ve = 2000 m-sec “1, ; v3 = 5000 m-sec = Hence, sin a = vi/v3 = 11.5°; ~~ 6 = 1¥e/¥ar—i2otoe nine = Vy Vor poe _ (1 — smz) | 500-0.5 _ 2 cos 2 0.866 X2 V3 — Ve cos 2 — COS a dg —-di = = + d, ———_—_ 2 V3 + Ve sin 2 cos B ie 5000 — 2000 0.866 — 0.979 _ oe a 9000.1 05.0916 Also, X13(1 — sin a) — 2d; cos-a 2 sin z cos B dg — di = _ 1750-0.8 — 578-0.979 0.916 = OLE 32 Schmidt, op. cit., 7(1/2), 37-56 (1931). Cuap. 9] SEISMIC METHODS 511 Travel Time 1000 2000 3000 4000 Fic. 9-48. Depth calculation of two layers from intercept distances (after O. v. Schmidt). 6. Three horizontal layers. The seismic ray follows the path ABCDEFGH; the ve- locities are Vi, Ve, V3, W4; the angles at the formation boundaries are e¢, 6, and Fig. 9-49. Wave paths, three-layer case. y as shown in Fig. 9-49 in which the two- and three- layer paths have been indicated for comparison. The angle at D is 90°; hence, sin y = vs/vs. Furthermore, sin 8 = sin 6/sin y = V2/V3 and sin 6 = vo/v,. Also, sin? = sin e/sin 6 = vi/vVe and sin e = vi/W%. The travel time j= 2 4 Ads — ) On, bp aE) ea €. (9-46a) V4 V3 Vo V1 The fourth part of the travel-time curve corresponds only to the velocity in the fourth layer, since dt,/ds = 1/v,. For the simultaneous arrival 512 SEISMIC METHODS [Cuap. 9 of the waves with the travel times ¢; and t,, a break with the abscissa z3 occurs, and the depth d; may be computed as before: ah WA oan Uy? da rae (cos B — cos 6) + io (cos a — COS e) 2 vitvs sinfcosy sin a COs y +d2=d3. (9-46b) CO 300500 700 1500 7800 3000 3500 4400 4900 5400 Oistance - feet TRY 1600 & ELSES TI pea fa 4900 g Calculated Section, /gneous rock V=7350 at ft. sec” % 1200' “gneous material Basal ? Fic. 9-50. Refraction profile, calculated section, and results of drilling (southern California). (Adapted from F. Rieber.) Again a more convenient method for depth calculation is the use of the travel time corresponding to the ordinate intercept. Then, from eq. (9-46a), with s = 0, d; — dz = he, and so on, a ya + 2 cos 8 che a (9-46c) V3 Ve Vi Fig. 9-50 gives an example of a travel-time curve in the three-layer case, shot in one direction only. This profile was made in southern Cali- fornia. The sedimentary section is probably Pico formation with sands Cuap. 9] _ SEISMIC METHODS 513 and shales of increasing velocity, and the lowest layer is igneous material, probably basalt and basaltic agglomerates. The depth determination based on the travel-time curve gives 1200 feet for this igneous material; a well drilled a mile away from the profile encountered it at 1140 feet. 7. Multilayer case. If d, is the depth to the lower surface of an nt layer, hy = d, — d,y_1 its thickness, v, its velocity, and a a refraction angle, then the travel time corresponding to the next (n + 1) layer is at the distance s: tee a 31.9) yy Ga URS bee Qn. (9-47a) Vn+1 1 V; n For depth calculations it is more convenient to use eq. (9-47a), as applied to the intercept travel time on the ordinate instead of the distance (z) intercepts. Hence, with 7 as (ordinate) travel time for x = 0: Te = 2 >; 2 COS ay. (9-47) 1 n Likewise convenient for depth calculations is the use of travel times corresponding to the distance intercepts z,. Substituting z, for s and solving for the thickness of the deepest layer, ha . Ly a hy 2— COS tg = O41 — | — +2 SS — COS ay }, (9-47c) Vo Vn+1 k=1 VE where 7, is the critical angle in the nth layer. By comparison with eqs. (9-43), (9-45a), and (9-46a), this is seen to give for the successive thicknesses: 1 . Z1 = COS) 21) = le a 5 1 V2 HD) 2hi — COS 22 = fs — |— + — cosa, V3 2hs 6 v3 2hi 2 — COS 23 = 4 — | — + — COS a1 + — COS a), V3 V4 Vi 2 and so on. Application of these formulas to depth calculations of five layers is shown in Fig. 9-51 and the schematic on page 515. Results of a seven-mile shot are shown there, evaluated in the form of velocities, intercept distances, and travel times corresponding to them. These data are entered in columns H, 111,andi1v. Nextis the calculation of all angles of total refraction 7, in columns v through vi. Similarly, the refraction angles a, (k varies from 0 to n — 1) are calculated in columns vim through x. The procedure is seen to be in accordance with formulas preceding (9-45a) 514 SEISMIC METHODS . [CHap. 9 and (9-46a). Next follows the ratio z/v, and in column x11 is given the time spent in all layers above the n‘*. For successive layers column x11 is obtained by multiplying the 2h/v values in column xv by the cosine values in column 1x. Column xim is the sum of x1 and xu, and xm in turn is deducted from 11, giving 2h/v cos 7 in column x1v, which is divided by cos 7, of column vi. Thus, the thickness (xv1) and the total depths (xvi1) are obtained. 20 10 Tay US ba StL eee Us Jt Wee 1G000 20,000 30,000 Fia. 9-51. Multiple layer travel-time curve. 8. Vertical steps and domes. ‘Travel-time curves obtained on faults, terraces, buried escarpments, salt domes, and igneous intrusions often approach the simple cases discussed in the following section. Contrary to conditions treated previously, formations are not continuous in hori- zontal direction or are not parallel with the surface for the entire length of the profile. Hence, additional unknowns enter. These can be deter- mined by taking two profiles in opposite directions or by shooting at two shot points at different distances from the detector spread. In the fol- lowing discussion the direction of shooting is assumed to be at right angles to the strike; however, the same problems may also be handled by shopting parallel with the stnikee: m LA 1+Uq UA #20 800 —. 2+ — } — 1+) = % soo — Z "y phe °r Sy IIAX IAX AX AIX IlIx IIX Ix xX XI IIIA IIA IA A AI III II £6220 {98h |S199°0) ~ 24/%A : : ; 029¢°0 ; LoS | Z88°0| ~ 24/8 : : : 4 3 ZEFOL| EFEZ ||/L6ZF 0 ZL '0 180¢°€ °862°0 181% ‘2.62 | ££8°0| ~ %A/*A 1608S |S9TS*O1Z9SS O}|002 ‘ET/000 ‘SEi0ez'€ G6LT'O 198% | LI6'O) ~ 2A/tA Z61S'0 ¥o0F | 1920) ~ 24/80 2 2 ~~ [A /%. ‘ ‘ a 68FZ | 264% ||ZOTF'0 102'0 810g 8182°0 rr0's| (oFE | BBO, ~ *A/*A\ || > Tg lovee-olgezg-oll000‘ztlo00‘szi6iz'¢ | $21°0 8oLZ | $88°0| ~ 24/ta 90920 1S00P | 092°0| ~ *A/*A Z66P | 8ZOE |/1Z89°0 6cF'0 7860'S 199° LoL’ |96L9' 0|00FL‘ 0)|088‘8 |000‘ozlZS¢"z 96910 1GoOE | OF8°O) ~ *A/TA FO6I | SEET |lOEFe'O POLO L8F'T LGET‘0 TS8'T!| ,2.9F 9269°0) ~ *4/'A |) ,Fo19 |Z8LF OlE8Z8'0/008‘Z |000‘ZI|TS9° T (*XI X TAX) en - a G°9Z9 |S°9Z9 || 961°0 ZITO 8ZIS'0; sais‘o ToS | ZLS°0/0Z8" O}|00F‘9 |000'F |Sz9°0 u u x I+u | I+ T+t,q |] (3003 ut)| (geo uw) Up Uy = Uy goo = Zz 1x -+ 1x ” s00 a Zz ae Yo | Aw 600 = uy, T goo oe U, U, I+, 515 516 SEISMIC METHODS [CHap. 9 In the simple case illustrated in Fig. 9-52,” the first part of the curve is given by ¢, = s/vi. Then follows, past the intercept x,, the travel time f2 for a single horizontal layer. This is s/ve + 2d/v, cos7. Beyond the edge of the step the rays travel through the low-velocity medium only. Their path becomes increasingly horizontal with increasing distance so % * $000 msec” Fig. 9-52. Travel-time curve for deep- Fic. 9-53. Reverse travel-time curve for seated fault block. deep-seated fault block. that the travel-time curve past x2 rapidly approaches the slope corre- sponding to the overburden velocity v:;. Then the travel time d e—dtant , ~V/d?+(s — e)? Pinyin pee! Vi COS 7 Ve vi or Pye Sa COS SH gL Nets eal (9-48a) Ve Vi Vi For greater distances the last term approaches s — e/v; , so that ds/dt; = vi. The distance of the scarp from the shot point is given by e€ = 22 — d tan?; (9-48b) d is calculated from 2, and ¢ follows from vi and v2. This formula will give only an approximate value, for zz cannot be acourately determined. 33 Travel-time curves in these figures were calculated for long-range shots to determine regional basement structure. Cuap. 9] SEISMIC METHODS 517 If the same profile is shot in the opposite direction, a travel-time curve identical with the one for a single horizontal layer, but with increased intercept distance, is obtained (Fig. 9-53). Hence, its interpretation alone would give too great a depth unless the same profile is shot in the opposite direction. Together, both travel-time curves furnish an accurate SEC. Pa 08 2a 40 i ee a a see 06 fo A WY Ca *& 04 é « 02 as Fic. 9-54. Travel-time curve, Marafael, Venezuela (adapted from O. v. Schmidt). value for the location of the vertical face. If, from the up-scarp time d Sie NN Met Vi : Vi COS 2 Ve ts the 4 down-scarp time for the same distance, 2d pe teyettenls V1 COS 2 Ve : is deducted, one obtains for e Bie vilts = te) + d cos 2 (9-48c) 2 ee — sin2z e where e’ is the approximate distance of the scarp from the shot point calcu- lated from eq. (9-48b). 518 SEISMIC METHODS [CHap. 9 Combination of two travel-time curves, as in Figs. 9-52 and 9-53, gives the curve for a salt dome or intrusion with vertical flanks (see Fig. 9-39). Salt Dome Fic. 9-55. Travel-time curve across salt dome (after Rankine). 15 sec. \ Asmari Limestone \ ‘ Fic. 9-56. Refraction profile across strike of Masjid-I-Suleiman anticline, Persia (after Rankine). In some cases the assumption of a homogeneous overburden, as made here, does not furnish the actual travel times accurately enough. Then an assumption of a uniform increase of velocity with depth is required or Cuap. 9] SEISMIC METHODS 519 the section is split up into individ- ual layers as. discussed in the preceding chapter. Data _pertain- ing to the normal section may be obtained from off-dome travel- time curves.” Figs. 9-54, 9-55, and 9-56 are examples of the problem treated here, shooting downward from a faulted block, from the edge of a salt dome, and from a limestone ridge. When faults, scarps, terraces, and the like, have shapes indicated in Figs. 9-57 and 9-58, additional branches appear at the end of the travel-time curve because the faulted- Fic. 9-57. Travel-time curve for deep- down portions of the high-speed peated ce carnmeny: media are within range. Down scarp, the last part of the travel-time curve is given by 1 SPIO ge , 2S ea Hk oper fe MN Vi COs 2 Ve gC Car 0 2 If the displacement of the fault is small, the sloping path from the point of incidence to the bottom of the scarp may be assumed to be equal to the horizontal path along its surface, so that _ 2d) cos 2 Vi dS uglelamoa)iC08 2 (9-490) Vo Vi ta By differentiation it follows that this part of the travel-time curve has the same slope as the second part. By subtracting t from 4; we obtain At (see Fig. 9-57), which gives the height (d. — d;) of the scarp: dz — dy = Atv, cos 1. (9-49c) In the reverse direction of shooting, the rays emerging from the top surface on the right are no longer parallel because of the different angles of incidence from below. This causes a deviation of the last part (ts) of 347. Roman, A.I.M.E. Geophys. Pros., 493 (1934). 520 SEISMIC METHODS [Cuap. 9 the travel-time curve from a straight line. Where it is nearly enough parallel with 2, --~ the tf curve, the time differ- b-% : it ence At may be determined 8 oe and is again approximately proportional to the displace- ment dz — d,. Fig. 9-59 is an example of the determina- tion of depth of overburden and displacement of a fault at the same time. The first part of the profiles shown are at right angles to a fault, and the second part (profile D) is in the strike of a fault, which had been located by torsion Fig. 9-58. Reverse travel-time curve for deep- balance observations and by Seated cocar pment wells. Faults are of commer- cial importance in this area, as the occurrence of hematite ore in the lime- stone is associated with the faults. In this case the seismic problem was 10 £0 TEE tz IIIA & O.t3 s&. 0.42 We 5650 ti-sec! Wye 5850 %= 16400 : 1 West D (strike prot} North South B Orilled depth 257° 2000' 1000' _y) cale. 245° "HEE 2+ oe Olactal Sands € Clays oi et ed Pe a : Ci Me ea aera 205, 16. Ree a Sa cel Sa Si RFS ae Pres fea > & —Mew Ke andstone— = = as) Be ae BI ee aI Rae we ee ea asa] Se eS ee ee Carboniferous | | Pay eae ie ee) RY d yas amas ee ry Limestone a eae ae oe rc ee a a Fig. 9-59. Seismic refraction profiles, hematite district, Millom, Cumberland, England (after Shaw). Cuap. 9] SEISMIC METHODS 521 comparatively simple, inasmuch as the velocity in the red sandstone was almost identical with the velocity in the overburden. The profile shot down the fault from A is almost the same as the ideal profile of Fig. 9-57. However, in the second part of the travel-time curve the velocity is not a true but an apparent velocity, since the profile is shot down the dip. Therefore, the velocity in the last part of the travel-time curve does not coincide with that in the second part. Furthermore, the third part of the curve is not curved as required by the theory but is straight. B and C represent the up-fault and also the up-dip profiles, as far as the boundary between overburden and limestone to the east of the fault is concerned. This explains the negative apparent velocity in profile C, second part of the curve. Profile D was shot in the strike, along the line / ed uy u (her) M7 ie % = Bu ed Ne Y 7 ypdlip (44) hor- G% 2 2 downdp(«d) Fig. 9-60. Schematic up- and down-dip travel-time curves. indicated in the figure. The travel-time curve is that of a single layer; the calculated depth was 245 feet, the actual depth 257feet. Considering that the dip is 10° and that the depth calculated from the refraction profile is the oblique depth, the diserepancy of 12 feet is reduced to 8 feet. 9. Single dipping layer. In the cases previously considered, the travel- time curves gave, with a few exceptions, the true velocities of the sub- surface formations. For dipping layers this is no longer true; the slope of the travel-time curve depends upon the dip. Hence, it no longer repre- sents the true underlayer velocity but an apparent velocity which depends on both the dip and the velocity ratio. As seen in Fig. 9-60, the first part of the travel-time curve always corresponds to v,. If the bed dips away from the origin, the seismic ray travels a greater distance through the upper medium. This results in increased travel time, decreased ap- 522 SEISMIC METHODS [CHaP. 9 parent velocity veq, and increased intercept distance zz. When the stratum dips up from the origin, the ray travels a greater distance through the lower high-speed medium. Travel times are reduced; the apparent velocity (vV2,) is greater than in the case of a horizontal bed and the inter- cept distance (x,) is less. The apparent velocity depends upon both dip and velocity ratio. One profile is not sufficient to determine velocities and dip. Hence, shots are fired at two points on one side of the spread, or else the direction of shooting is reversed and profiles are shot up dip and down dip. This may be accomplished by two shot points on either end of the profile, or by one shot point in the center of two receiver spreads, the former being the preferred procedure. In Fig. 9-61 let ¢ be the dip, H the depth vertically below the shot point, and h the depth below the receiving point. Depths normal to the stratum are Z and z. The profile is assumed to be at right angles to the Fig. 9-61. Refraction path in dip shooting. strike, that is, in the direction of maximum dip. The first part of the travel-time curve is given by t; = s/v,. For the second part the time for the path ABCD = t = (AB + CD)/v + BC/v. Since AB = Z/cos i, DC = z/cos 1, AD = s, FE = ID = s cosy, AI = ssing = Z — 2, FB = Z tani, CE = z tani, and BC = ID — FB — CE, Aah ee it tated, (9-50a) Vi Vo te = For the up-dip case, substitute for z: Z — s sin ¢, and sin 2/v; for 1/v2 ; then goin OD yap 8 ia (et ey (9-50) V1 Vi If for the down-dip case Z = z + s sin g, _ 22 cos2 tai a = sin (i + ¢). (9-50c) Cuap. 9] SEISMIC METHODS 523 Since Z = H cosy andz = hcos¢, ete 2H cos ¢ cos 2 i pe Gen Vi Vi and (9-51) hit 2H cos ¢ cos 2 tie Se Gee Vi V1 The apparent velocities for the up- and down-dip cases are obtained by differentiation of eq. (9-51): AO res vs ju v1 eS Wouter G25 and Voa Gale) (9-52) Hence, eqs. (9-51) become bh, < 2H eosycost , 8 i Vi Vou | and (9-53a) 2H cos ¢ cos 12 8 CES ————— a5 Vi Vod The true underlayer velocity is not the arithmetic mean of the two apparent velocities. From eq. (9-52) Vu-Va Vu =F Va ; The true velocity has the same relation to the up-dip and down-dip velocities as a resultant resistance has to its component resistances in parallel. In the example of Fig. 9-63 (where vo, = 6190 and vay = 2790), the above formula gives v2 = 3795, whereas the arithmetic mean is 4490. From eq. (9-52) the critical angle 7 and the dip are calculated as follows: ESTA SET NAT x (sin —-+sin %) Vou Vod pei NAT Sew Al 3 (sin — — sin =), Vod Vou ) and the true underlayer velocity is obtained from v2 = v;/sin?. Fig. 9-62 shows apparent up- and down-dip velocities for dip angles up to +40° and for velocity ratios of four (¢ = 15°) and two (¢ = 30°). The variation is small down dip. On shooting up dip, the velocities change rapidly when the dip angle approaches the critical angle, and they become plus and v, = 2cos¢- (9-53) >. I (9-54) 7) 524 SEISMIC METHODS [CHap. 9 minus infinite in this range and negative after dip angles pass the critical range. The lower layer is not detectable if 2 + ¢ exceeds 90°; the ray emerging from it does not return to the surface. The depths of an inclined layer under either shot point may be deter- mined from the overburden velocity, the up- and down-dip velocity, and the distances of the intercepts from the shot points. For the two direc- tions of shooting, two intercepts are observed, 2, and zz. As at the inter- cept, ti = tox = ta and t, = x/v,, we have, from eq. (9-51), Hy tg BUM O) ad hy % xg. ee Ean 2 COS ¢ COS 2 2 COS ~ COS 4 f (9-55a) where H, is the depth vertically under the shot point when shooting up dip, - = ---" Youn “a ra 16° 6 Sowndip —-g — (2) 4%. (Ham. tw 4 Set Oe & %, (Bam. w #22 Fia. 9-62. Apparent velocities for up- and down-dip angles from 0° to 40° (after Meisser). and ha is the depth under the shot point when shooting down dip. By substitution of (9-52), ae Fel i _ 2 cos ¢ cos2 Vou and (9-55b) oe pute (1 a a 2 cos ~ cos2 Vea Calculation of depth proceeds, therefore, in the following order: (1) plot travel-time curves; (2) determine Veq and vz, ; (3) determine z, and 2q ; Cuap. 9] SEISMIC METHODS 525 (4) compute z + 9, 7 — ¢, 2, and ¢; (5) compute v2 ; (6) compute H and h; check result with s and ¢. Fig. 9-63 illustrates steps 1 to 3 in the evaluation of two travel-time curves. Bystep 4, sin (¢ — v) = $$$ = 0.259;7 — 9 = 15°;sin (¢ + ¢) = 930 = 0.574; 7 + ¢ = 35°; 7 = 25°39 = 10°. ve = vi/sing = 289° = 3790; H = 235 (1 — 0.259) /2-0.985-0.906 = 97.5m;h = 150(1 — 0.574) / 1.97-0.906 = 35.9 m; s = 350 m; (A — h)/s = tan g; $&¢ = tan 10°. Determination of dip and depth of dipping layers does not necessarily erequire reversal of direction of shooting. Shots may be fired at two points on the same side of the receiver spread. Shooting down dip, we find that the second part of the travel-time curve is the apparent velocity Vag ; +6190 shy Fig. 9-63. Dip and depth calculation from up- and down-dip refraction profiles. shooting up dip it is ve, as before. The intercept of ta with t; moves up when shooting down dip, whereas it moves down when shooting up dip. Depths h and H may be determined from extended ordinate intercept times.” The relations derived in this section hold only if profiles are shot down or up the total dip, that is, at right angles to the strike. If profiles are not shot in this direction, only an apparent dip in the direction of the profile is obtained. In Fig. 9-640” the plane AFED is the same as that represented in Fig. 9-61. When this plane is rotated about the shot point A in the direction AD’, the rays still travel in a plane at right angles to the dipping bed, AFE’D’, whose apparent dip is ®. If the azimuth of 35 For formulas, see B. Gutenberg, Lehrb. Geophys., 3, p. 599. 36 F. Gassmann, Beitr. ahgew. Geophys., 4(3), 358-363 (1934). 526 SEISMIC METHODS [CHap. 9 the profile AD’ is a (from the direction of maximum dip) the relation of apparent and true dip is given by sin ® = sin ¢ Cos a. (9-56a) The azimuth a may be determined by shooting two profiles each, up and down dip, at right angles to one another (Fig. 9-64b), which give Fic. 9-64a. Relation of apparent dip, true dip, and azimuth (adapted from Gassmann). four apparent velocities or two groups of up- and down- 7; dip velocities: / Vi y= 6 a0b Sig 8s el ey | eae) where k = 1, 2, 3, 4. The travel-time curves obtained in this case are indicated in Fig. 9-64c, and the azimuth of dip with respect to profile 1 is ourection v_v, Vv, ees ss of dip 13.2 =tana. (9-56c) Wao Va = Vi Fic. 9-64b. Two profiles for strike and dip : determination (adapted from Gassmann). If the apparent angle of dip ®,_;is measured in profile 1-3 and the angle @4. in profile 4-2 by using the relations given in eq. (9-54), then from (9-56a): SUBD Es) Le eee (9-564) sin @)-3 Cuap. 9] SEISMIC METHODS 527 The true dip is then calculated from eq. (9-56a). With the above formulas, relations may readily be set down for two profiles making an arbitrary angle with each other. 10. Two dipping layers. Travel times for two inclined layers are derived in the same manner as for the single inclined layer and the double horizontal layer.” Thicknesses of layers below the origin will be designated by H for up-dip shoot- ing and by h for down-dip shooting. A profile shot up dip in reference to the 5 upper formation boundary ma down Hae reference to the aia Mia: 0 Gio Trae) Himes ferive profiles as in Fig. 9-646 (adapted In order to avoid ambiguity, the direc- from Gassmann). Fic. 9-65. Ray paths in two dipping layers. tion of shooting will be referred to the upper boundary. With the nota- tions of Fig. 9-65, OO cele We ale Vi sina sinB eae Vi Sin %2 = —; SIN} 71 =-; —— = —. =sny=—-; V3 Vo siny sin 6 V2 Y=t+(Ww—e¢) and 6=x%— (Wy —g). Therefore, sin 6 = sin [2% — (W — ¢)] = pu S1n 2 (9-57a) siny = sin[z + (Y — »)] = 2 ‘ sin 1, 37 For details see Schmidt, op. cit., 7(1/2), 37-56 (1931). 528 SEISMIC METHODS [CHap. 9 The travel times are: (a) For up-dip shooting: eS = {ss sin (8 — ¢) + Hi,[cos (a + ¢) + cos (6 — ¢)] + He,-2 sin 2 cos 72 cos y} (b) For down-dip shooting: (9-570) tsa = 2 {sa sin (2 + ¢) + Mnaleos (a + ¢) + cos (8 — ¢)] 1 + heq-2 sin 7; COs 22 cos py} and the apparent velocities are: ot dd basin (Glaake) (9-57c) ds Vi V34 = 7 dig cinco): Depths may be calculated from intercepts x; and 22 (X12, 223) in the up-dip and down-dip profile. As the relations for x12, and x12q have been given before eq. (9-55), it is assumed that H,, hi, and gare known. For the computation of Hz and hz use is made of the intercepts 223, and 23 ; or the first and third parts of the travel-time curve may be extended to the intermediate intercepts 213, and 2334. Then the depths follow from: (a) The 2x13 intercepts: _ %su[1 — sin (6 — ¢)] — Huleos (« + ¢) + cos (6 — ¢)] 2 SiN 21 COS 22 cos p and (9-58a) pe tizall — sin (a + ¢)] — hialcos (a + ¢) + cos (B — ¢)] = 2 Sin 21 COS 22 cos W Aw (b) The 223 intercepts: _ asu{sin (1 — ¢) — sin (6 — ¢)] — Hiulcos (a + ¢) + cos (6 — ¢)] 2 SIN 21 COS 22 Cos p Aw Hy,2 cos 7; Cos ¢ 2 sin 21 COS 22 cos p ho, = 2udlsin Gi + 9) — sin (a + ¢)] — Mraleos (a + ¢) + cos (6 — ¢)] = 2 sin 21 COS 22 COs W hig2 Cos 2; COS ¢ 2 sin 7; COS 12 cos wy’ Coes) Cuap. 9] SEISMIC METHODS 529 where the substitutions may be made, PaanG 7) ine — ol = ravi .s =| Vou V3u and (9-58c) TeaalSin (a + ¢) — sin (a + ¢)] = rae-vs| 2 Sag =|) Voda V3d Computation proceeds in the following steps: (1) Compute 7, and ¢ from formulas (9-54). (2) Determine v2 = vi/sin i. (3) Calculate Mi and 1 \ \ ' ' a 1 \ 1 \ \ ' ' ' | s = Fig. 9-66. Travel-time curves for two layers of same dip direction (after O. v. Schmidt). h; from eq. (9-55). (4) Find angles a and 6 from apparent velocities V3. and V3¢ (formulas [9-57c]). (5) Compute 7 and (W — g) from (9-57a). (6) Find y from (WW — ¢) andg. (7) Calculate v3 = ve/sin 72. (8) Find H2, and (9) he from (9-58). Two examples are given below, one for boundaries of the same dip direction, the other for boundaries of opposite dips. The corresponding travel-time curves are shown in Figs. 9-66 and 9-67 and furnish the following numerical values: 530 SEISMIC METHODS [CHap. 9 (Fig. 9-66, AB = 2200 m) Up-Dip PROFILE Down-Dir PROFILE v», = 1800 m-sec~ v: = 1800 m-sec vo, = 3415 m-sec * Voq = 2700 m-sec — v3, = 6530 m-sec Vza = 3495 m-sec * 119 = 845 m Lisa = 2h rel 1 ee risa = 677 eT frome The calculation proceeds as follows: (1) = = [sin i — ¢] = = = 0.527 = sin 31° 50'}¢ = 5° = = [sin i, + ¢] = a = 0.667 = sin 41° 50’| 4, = 36° 50’ (2) ve = a5 = = = 3000 m-sec @ ee eenoee 1 Oa ale i = mone 208-00 (4) = = sin (6—y¢) = a = 0.2756 = sin 16°|6 = 21° = = sin(a +) = = = 0.5150 = sin 31°|a = 26° (5) me i etd bie Scao Nic ee = 0.729 = isin 46°50’ sala pod ce era ee ese a = 0.598 = sin 36°50’; i: = 41°50’ (6) v = 10° (7) ¥a)= Nag COU 4500 m-sec Cuap. 9] SEISMIC METHODS 531 tisull — sin (8 — ¢)] — Hilcos (a + ¢) + cos (6 — ¢)] 2 sin 21 COS 72 cos 2 sin 72 Cos 72 cos W = 2-0.6-0.745-0.985 = 0.881 cos + ¢) + cos (6 — ¢) = 0.961 + 0.857 = 1.818 (8) H= AH, = [1174(1 — 0.2756) — 250-1.818] = 450m 0. ae tizall — sin (a + ¢)] — Mialcos (a + ¢) + cos (6 — ¢)] 2 sin 21 COS 72 cos W (9) hea = [677(1 — 0.515) — 57,5-1.818] = 252 m 20. a Fig. 9-67. Travel-time curves for two layers of opposite dip direction (after O. v. Schmidt). For the second example, Fig. 9-67 furnishes the following data: (Fig. 9-67, AB = 2500 m) Up-Dip PROFILE Down-Dire PROFILE vi = 1800 m-sec vi = 1800 m-sec* Vo. = 3230 m-sec ? Voq = 2805 m-sec~ Vi. = 4370 m-sec ! Vsq = 4710 m-sec * 532 SEISMIC METHODS [Cuap. 9 Zz, = 1006 m tsa = 1085 Z| Xo3n = 1325 m> from A Xexqa = 1890 m;from B TM12u = 890 m L104 = 525 a In the calculation, steps 1 to 3 are carried out as before and give: y = 3°: 1 = 36°50’: v, = 3000 m-sec> Hy, = 250m; fia 19m. Vi Co Ws a ito 1800 ei Bs isue onn,. Bs. enn: (4) cone sin (8 — ¢) = 4370 ~ 0.412 = sin 24°20’; B = 27°20 Viena he 1800 ra) reso AGYR., 5 oan? i o sin (a + y) = 4700 = 0.383 = sin 22°30’; a = 19°30 (ay) rhs oy) Se ey ain BEET” sin 21 0.6 say = sin [t2 — (W — ¢)] = One 0.764 = sin 49°50’ sin 24 0.6 vy—¢ = —8°; t% = 41°50’ (6) y= -5 te V2 Ls 3000 a =| (7) v3 = sin io a 0.666 = 4500 m-sec (8a) Hy = 2i3u(1 — sin (8 — y)] — Hilcos (« + ¢) + cos (6 — ¢)] ‘ 2 sin 21 COS 72 COS P 2 sin 2; COS 22 cos YW = 0.891 cos (a + ¢) + cos (8 — ¢) = 1.835 ~ Hy = pea [1006.0.588 — 458] = 150m (Gb) Hes 293, [sin (11 — ¢) — sin (8 — ¢)]— Hiu[cos (a + ¢) + cos (6 — ¢)] 2 SiN 21 COS 22 Cos + Hy,-2 cos 1, cos ~ 2 SiN 1; COS 72 Cos 1 = 0801 [1325-0.145 — 458 + 250.2-0.8-0.997] = 149 m. Cuap. 9] SEISMIC METHODS 533 This checks results obtained with different (23,,) intercept. _ 2yall — sin (a + ¢)] — malcos (a + ¢) + cos (6 — ¢)] (9) hea = — 2 SiN 21 COS 22 Cos Y — 1085[1 — 0.383] — 119-1.835 _ For the calculation of depth and dip of several layers it is noted that the travel-time formulas given here for two inclined beds may be written in the same form as those used for depth calculation of horizontal layers. For example, for a single dipping layer the up-dip travel time may be written fens =e UCU IN it. Vou Similarly, for two layers h 2h : in = = + + = [eos (aw + v) + cos (8 — ¢)] + OS 08 ts which for g = 0 takes the form previously used for depth calculation of three layers: Zhe : 24 * cos a, + — COS 72, and so on. 2 10. Variants of as, method using different interpretation procedures. The interpretation theory discussed in the preceding sections is based on the assumption that the seismic rays propagate in individual media of constant velocity along straight lines and are refracted in accordance with Snell’s law. In addition to the above, there are other interpretation pro- cedures. One uses curved rays resulting from a uniform increase in ve- locity with depth. Another applies a graphical method involving the pattern of the wave fronts of seismic impulses at progressive time inter- vals. A third method abandons the assumption of refraction according to Snell’s law and operates with vertical incidence upon the underlayer. (a) Vertical-ray interpretation. This method arose from observations of angles of emergence with a two-component seismometer, which indicated nearly vertical angles close to the origin and led the earlier experimenters to conclude that Fermat’s principle did not hold in all cases. It is now known that their results were due to the existence of the weathered layer which causes the emerging ray to be deflected into a practically vertical direction. Nevertheless, vertical-ray theory has a practical application as a simplification of refraction theory where considerable contrast between 534 SEISMIC METHODS [CuaP. 9 formation members exists and where, therefore, the oblique overburden path does not differ sufficiently from the vertical path. In weathered- layer procedure in reflection shooting, interpretation is based almost ex- clusively on vertical-ray propagation. The following paragraphs contain derivations of vertical-ray formulas for the single and double horizontal layer, and for the single and double inclined layer. In the case of a single horizontal layer, the wave is assumed to travel vertically to the lower layer, to travel along the interface with the velocity of the lower layer, and to come up vertically. Hence, tg = 2d/v1 + s/Ve, 20 10 0 0 20 50 40 50 60 70 60 UDR Fic. 9-68. Error of vertical-ray calculation as a function of velocity ratio. so that the slope of the second part of the travel-time curve ds/dt: = Ve. For the intercept, s = 2, so that BAW (re RecN Wr ela Qi Teg u = 5 ( sin 7) (1 ) 7 (9-59a) whereas the application of Fermat’s principle gives Mee — sin 2) : 2 COs 2 ) which for an angle 7 of 30° is dpermat = Gvert,-1.15. With d, as depth determined by the refraction interpretation and d, as depth from vertical- ray interpretation, the error (d, — d,)/d} = 1 — cos7. Fig. 9-68 shows this error as a function of the velocity ratio vi/Ve . Cuap. 9] SEISMIC METHODS 535 In the case of the double horizontal layer we have for the intercept 223 : Qd1/V1 + 203/V2 = 2di/vi + 2(d2 — d:)/V2 + 223/Vv3, which leads to i ee = (1 He i (9-59b) 2 V3 For the refraction path the corresponding depth = (: ow ) cos 7 Cos 3 es a ds = di + Patents eh ae di . ° 2 COS 22 sin 2; cos 8 ) that is, the simple cosine ratio previously mentioned applies here only to the first term. The error increases as more layers and less velocity con- trast are involved. In the case of a dipping layer the underlayer travel time for vertical propagation is given by where the symbols have the same meaning as in formula (9-50a). Sub- stituting e = scosy, Z = H cosg,z = hcosg, a = (Hy COS gY — S, Sin ¢) +e 2 i = = (2ha cos yg + sasin yg) + — a wont a 2 By differentiation, diy _- sing , cosg_ iL ds Vi V2 Vou and dteg _ sine cosy _ 1 ds Vi Vo Voa’ so that r (1 -") ra(1 - *) TE i gc LANES canes i ei en Ny (9-59c) 2 cos ¢ 2 cos ¢ These relations differ again by the factor cos 7 from those previously given for the depths calculated for the refraction path. If in the case of the double inclined layer Z, and z, are the depths 536 SEISMIC METHODS [Cuap. 9 normal to the interface between the two upper formations, and Z, and 2, the thicknesses of the second formation (normal to the interface between the second and third formation), _ 2%y Pu su 22; , 223 | Sa eh Commu Ns = hence, Zi, = a (2 = 2) and 24 = =“ 3 (2 +h _ (9-59d) (b) Wave-front diagrams. In addition to the analytical methods dis- cussed in the preceding paragraphs, graphical methods may be employed in the solution of travel-time problems. They involve the construction of “‘wave-front diagrams’? which have the advantage that the advance- ment of the seismic wave through geologic formations, both simple and complex, may be more readily visualized. Their principal application is in indirect interpretation. From a preliminary evaluation of a travel- time curve, an approximate geologic profile may be constructed. Then the wave-front diagrams are drawn; travel times obtained from them are compared with the field data; and the geologic section is changed until complete agreement is obtained. Their construction has been described by Thornburg™ and E. A. Ansel.” A wave front ‘is defined as the surface which a given phase of a seismic impulse occupies at any particular time. A wave-front diagram is a graph showing a number of such surfaces for many successive instants which for convenience are chosen a given constant time-interval apart. In an in- finite isotropic medium the wave fronts are spherical shells; their inter- section with a vertical plane is represented by circles; their spacing is proportional to the velocity. If the time between consecutive wave fronts is At, the spacing is As = v- At. However, wave fronts are circular only in such portions of a layer in which the propagation is not disturbed by an adjacent formation (see Fig. 9-69). The construction of wave-front diagrams for several layers proceeds as follows: Draw a series of concentric circles about the shot point in the upper layer, and calculate their spacing from the above equation. Draw the angles of incidence on the formation boundaries involved (critical and refraction angles). The point of incidence of the critical ray on the first boundary is then determined; wave fronts in the lower layer are drawn about this secondary shot point, their spacing being proportional to the 38 A.A.P.G. Bull., 14(2), 185-200 (Feb., 1930). 39 Gerl. Beit., Erg. Hefte, 1(2), 117-136 (1930). Cnap. 9] SEISMIC METHODS 537 velocity in the lower layer. The underlayer fronts are advanced farther than the corresponding overburden fronts. Since there can be no dis- continuities, the lower wave front has to be connected to the corresponding Contact curve WETS ZI USN\N G vie ee | Fic. 9-69. Travel-time curve and corresponding wave fronts in three horizontal layers (adapted from Thornburg). upper front. This is done by drawing lines through the upper points of the underlayer wave front normal to the critical angle of the emerging ray to intersection with the corresponding wave front in the upper medium. As seen from Fig. 9-69, a straight wave front (contact front) results, 538 SEISMIC METHODS [CHaP. 9 which moves upward along the contact curve (a parabola) and reaches the surface at the point of the intercept in the travel-time curve. In a two- layer problem, the angle of incidence on the first and the critical angle 72 on the second interface are determined. Wave fronts in the second layer are completed; the point of incidence on the third layer is determined; and wave fronts in it are drawn with a spacing corresponding to the ve- locity in the third layer. Connections with the wave fronts in the second layer are made again as before, the second contact front being parallel with the angle of incidence on the third layer (see Fig. 9-69). With in- creasing distance from the shot point, only contact fronts will be present in the upper layers. With a wave-front diagram, a depth determination would proceed as follows in the case of one layer: (1) Draw circles with interval v, At about surface shot point. (2) Locate intercept distance. (3) Lay: off the angle z from the surface; ‘draw a line through the point of intercept; and draw Fic. 9-70. Wave fronts, dipping layer (after Ansel). parallel lines thereto with a spacing of v,A¢ (spacing in horizontal direc- tion, vet). (4) Find intersection with v,At curves and draw contact curve. (5) Determine depth by intersection of ray (90 — 7) from shot point and contact curve. For two horizontal layers the procedure begins with the location of the second intercepts after the above steps have been followed and the first interface has been constructed. Then the break 223 is lowered down to this interface by using the refraction angles a. Hence, a sec- ondary shot point is established on the interface. From then on the problem is treated like the single-layer problem. To obtain depths below shot points and dips of inclined layers, the direction of dip is first established from an inspection of velocities and intercepts. Then the construction proceeds as follows: (1) Draw circles at intervals As about shot points S 1 and S 2 (Fig. 9-70). (2) Locate breaks in travel-time curve. (3) Determine angles 7 + ¢ andi — g from sin (¢ — ¢) = V;/Vo, and sin (¢ + ¢) = vi/Vea. (4) Lay off angles (¢ + ¢) from the down-dip and angles (¢ — g) at the up-dip shot points, with a spacing (at right angles to the wave front) of As,. (5) Locate inter- sections of these parallel lines with upper layer wave fronts, thus obtaining Cuap. 9] SEISMIC METHODS 539 points 1, 2, 3, 4, and so on, on the left and corresponding points on the right (see Fig. 9-70). (6) Draw contact curves on both sides. (7) Draw a tangent to the two contact curves, obtaining depth and dip of stratum. (8) The dip of the lower layer is given by the diagonal of the parallelogram formed by intersection of the two underlayer wave fronts. (9) The ve- locity and spacing of wave fronts in the lower layer is given by the length of this diagonal. The case of three inclined layers is treated in a similar manner. As before, the essential point is to lower the surface shot points and 23 inter- cepts to the first formation boundary. A secondary shot point below S is given by the angle a, which follows from sin (a + ¢) = V:i/V¥3 down - Fic. 9-71. Wave fronts, inclined terrace (after Ansel). Wave fronts are drawn about this point with the spacing As., corre- sponding to the velocity ve previously determined. The location of the secondary shot point on the other side is given by the angle of emergence 6 which follows from sin (8 — ¢) = vVi/V3 up . After the shot point has been projected on the lower layer, wave fronts are drawn about it with the spacing As.. After secondary shot points and secondary breaks have been established on the first interface, the construction proceeds as before. Wave fronts of the second contact wave are constructed by drawing parallel lines from the secondary breaks down to intersect with the wave fronts with the velocity ve. The inclination of the wave front of the second contact wave is given by the angles ¢2 — (¥ — ¢) and % + (¥ — ¢) (see formula [9-57a]). Contact curves are constructed from the points 540 SEISMIC METHODS [Cuap. 9 of intersection with the v. fronts. The second interface is tangent to these two contact curves. Wave-front interpretation may be used not only for an analysis of simple travel-time curves but also for more complicated types of struc- tures, such as faulted strata, salt domes, and the like. A number of examples of the application of wave-front methods to such types of strue- tures may be found in Thornburgh’s and Ansel’s articles previously re- ferred to. Fig. 9-71 illustrates travel-time analysis by wave fronts for a sloping terrace. t Fig. 9-72a. Curved-ray paths. (c) Curved-ray interpretation. While vertical-ray and wave-front inter- pretations are a matter of preference over standard refraction methods, curved-ray interpretation becomes a necessity where the overburden por- tion of a travel-time curve is not straight. This curvature may also occur on later portions of travel-time curves. However, its presence in the first layer is the predominant condition. Curved rays occur in thick sections of sedimentary beds over basement rocks and in surface-weathered layers above more consolidated formations. In each case, the type of travel- time curve obtained and the interpretation problem resulting therefrom are identical. The mathematical theory has been treated by several authors.” 5 40. B. Slichter, Physics, 3(6), 273-295 (Dec., 1982). H.M. Rutherford, Amer. Geophys. Union Trans. 1933 (Seism), 289-303; Soc. Petrol. Geophys. Trans., V, Cuap. 9] SEISMIC METHODS 541 In the following analysis it is assumed (see Fig. 9—72a) that the velocity increases linearly from vo at the surface to vi at the bottom of the top layer, changes abruptly to v2, and remains constant in the second layer. Then the upper velocity as function of depth is Vv, = Vo + kh. (9-60) In the upper layer the rays travel in circular paths; their radius of curvature depends on the vertical velocity increase k. The locus for the centers of curvature is a plane whose distance from the surface is given by 2 ines ee The travel-time curve is no longer straight and the surface velocity is not constant. By differentiation with respect to distance, an ‘‘apparent” velocity is obtained (eq. [9-62]). For an arbitrary number i of thin parallel horizontal beds, the paths for the incident and emerging rays are identical in the same stratum. The horizontal displacement of the ray due to refraction is (9-60b) i=n c=2 >> h, tan ai, (9-614) i=1 since in each bed the distance is decreased by the amount h; tana;. The travel time for the downward and upward (curved) paths is therefore t=2 9-61b i=1 Vi COS ai’ ( ) where hy/cos a; represents the oblique I aims path within each layer. According to | H Snell’s law, sin o;/sin oj+1 = V;/Viti OF sin ai/¥j = sin aj4i/Vi41 = constant = C for each ray. Since sin a/v = pt s : ana Vo sin %/Vo (where % is the angle of emergence as indicated in Fig. 9-72b, EN eg and vo is the surface velocity), the py4 9-79. Apareritendiate constant C may be determined at the velocity. surface by graphical differentiation of the travel-time curve. If v is the apparent velocity, it is seen from the figure that sin 7% = v/v; therefore, sin a Vv =C= (9-62) PB/p, v:/Ve is Vi/Kp, or p = Vo/k. The travel time of the trajectory ABCE is tas + tac + tcz, where tas = 8&8 ten = [ ds/v. The value of s is pgi and g is a — y;p and a are given 0 Cuap. 9] SEISMIC METHODS 543 by the expressions in the preceding paragraph. Sin y = wW)/Kp = (v — kh) /kp. Hence, sin g = v/pk and s = p arc sin v/pk. ‘Therefore, pdv sa dv V pk a Vv k 1 v ae ak CAV AS PREM Coes | / ds) — (9-644) BIRR AAADRA YAY WONT 8 a Xx \ Fig. 9-72c. Depth determination in curved-ray method. ‘t cf ky ye 1- = a i ) oe (2) |. re The travel time in the underlayer is given by tac = (D — 2a)/ve, where oo v2/k[-V 1 — (¥/ve)) — eee (vi/v2)’]. Therefore, the total time h = * [eos h* (vs /vo) — cosh (v2/vi)] +2 — 2 V1 = (w/v) — V1 = (wi/¥0) 544 or SEISMIC METHODS [CHap. 9 tg = 2 {foo h (vo/vo) — V1 — (vo/ve)"] — [eos h™ (ve/v,) — V1 — w/w") + =. (9-65) If we let f(r) = cosh” (1/r) > V1 —1’, withr = w/ve andr’ = v;/Vve, respectively, eq. (9-65) becomes Din? ; h = yt RU) — fe ie (9-662) Fig. 9-73a shows the variation of r with f(r) and is valid for any condi- tions. If f(r) = [fvo/vs) — f(vi/ve)] = TP, se se ea ae da ee HSER a es a ce i a Ea a dG) Fd a a PS a a Fe a as Fa Pe TG Fa ie Ne ite AAV IE eo] EIS eli oe Na aaa a O Of 02 03 Od 05 06 07 06 09 1 fr Fig. 9-73a. Graph of f(r) for curved-ray inter- pretation. (9-66b) then p Spe =. (9-66c) The application of these re- lations is as follows: Assume k to have been determined from the first part of the travel-time curve, as shown in Table 57-A. If, further, v2 has been measured in the second part of the travel curve (past the 3000-m inter- cept in the example), the value of the time function T may be calculated from form- ula (9-660) for various depths (and therefore for various values of v,). In this manner a curve T = f(h) is obtained, as shown in Fig. 9-736. For the depth determination, T is calculated from the travel- time curve by subtracting, in accordance with formula (9-66c), the value of D/ve for each distance as shown in the last set of columns in Table [ES Ee Tt TIt'T CITT Tilt Ur GLET 62I'T 896°0 908°0 cr9°0 cA mooudag OL HIdaq ” OFZ °S 0002 ” 610°% 0009 ” 8161 000¢ 0029 = *Al| 9CL°T = *7) 000K = @ Vv Z6F | 669'0 IF€ 98°O | LOTT | LEL°0 || ,LE.€S | S080 | ELIZ S6¢°T 0008 Gece | céL°0 6&2 98°0 | OOF'T | FI9'O || ,9%8E | ZS8°0 | E02 TSe"T 00S2 6°18 | TLL°0 641 98°0 | OSL°T | T6F°0 || 09.89 | 268°0 | OS6T OOT*T 0002 8&1 | 908°0 801 98°0 | €€€°% | 69E°0 |} ,9F.69 | 886°0 | S98T 8£8°0 00ST 9°09 | S€8°0 | 9°0¢ 98°0 | 00S°€ | 9FZ°0 || ,ZT.9L | TL6°0 | ZO8T G9S°0 000T €°cT | €S8°0 | T&T 98°0 | 000°Z | €2I°0 || .69.28 | 266°0 |} E€9ZT 982° 0 00¢ ({-"008" UI OST 0 0 = 04) = ome, | Samer a a 0 oe ¥ (UIs — [)oa H= | i . 0 UB}00 04 m a» as snes a ~B1}0U0g 0A = on Naaqungugag ASV@UONT SIONY ‘NOILVULGNG YG HLdaq ALIOOTE A TOILET A GONGDUANGY tALIOOIN A INDUVddy VIVG QaAuaSAO GAWNO ANIL-THAVUL WOW HLIdAd MOOUdHA CNV ‘NOILVULANAd HLdad ‘ASVAMYONI ALIOOTAA TVOLLUGA ‘ATONV FONADUAWA JO NOLLVINOTVO V-lg¢ GIavV yi, 545 546 SEISMIC METHODS [Cuap. 9 57-A. This gives, for each distance, a constant value of T, from which, in turn, follows the depth by applying the graph of Fig. 9-73b. If, in the example, a uniform velocity (of 1881 m-sec) were taken to the 3000-m intercept, the depth would be 1097 m instead of 1375 m. 11. Variants of refraction method using different field technique. ‘The methods discussed in the following paragraphs employ such modifications of refraction technique as afford short cuts in the more elaborate methods of depth calculation. These methods are (1) the arc method of structure mapping, and (2) the method of differences (ABC system). They involve a more direct determination of time differences which are evaluated in terms of overburden thickness. 20 18 ola eee 16 CCR fel ea Pele eel Aol al Ae uae aaneeee ace 02 Yl ee ea a9 Q2 04 06 06 10 12 14 16 16 20 22 24 26 26 30 32 94 Depth in km (h) Fig. 9-73b. Graph of 7T'(h) for depth interpretation (basement rocks). (a) Arc method of structure mapping. In this method time differences of fans are correlated with refraction profiles connecting the fan shot points. Thus, a time-contour map of subsurface high-speed beds is ob- tained and converted to a depth-contour map. The method is applicable to low-dip structures only.” The shot points are generally laid out along the strike in a longitudinal traverse (Fig. 9-74a), and reception points are arranged in overlapping fans on the circumference of circles about these shot points (tangential profiles, Fig. 9-74b). Time differences are calcu- lated, as shown below, and plotted for both profiles. With a suitable scale the time curve will indicate the profile of high-speed formations. Depth calculations are based on simplifications of formulas previously derived. If in eq. (9-50a) the substitution 1/v; = 1/ve sin 7 is introduced, 41 Jones, op. cit., 169-173 (1933). Cuap. 9] SEISMIC METHODS 547 the travel time tf = Z cotan i/v2 + s cos g/v2 + z cotan i/ve2 ; with Co = Z cotan 2/v2 as shot point constant, C’ = cotan 7/v2 as depth point constant, h= C+“! 4 c% (9-67a) 2 Travel Time seconds — OF feet Fig. 9-74. (a) Longitudinal, and (6) transverse profiles, with travel times and lime- stone profile (arc method). (After Jones.) Since cos gy 1 for small dips, the depth at any point 1 s which, strictly speaking, is depth normal to formation but for small dips may be taken as vertical depth. With t’ = t — s/ve, eq. (9-67b) may be written z= 5, (t' — CQ) (9-67c) 548 SEISMIC METHODS [CHap. 9 The constants C’ and Cy are obtained from refraction profiles shot at the starting point in two directions. It remains necessary to reduce all shot points to one datum, that is, to eliminate differences in their shot- point constants by referring all times to the Cy of a reference point. If at a reception point common to two overlapping fans a difference in time of to: — tog corresponds to shots from two different points, their difference in shot-point constant is Cn = Cn = tr — te. (9-67d) Adjusted times are plotted against the location of depth points; points with equal time differences are connected by isochrons which, barring velocity variations and steep dips, give a true picture of the depth con- tours of the structure. (b) Method of differences (ABC system). ‘This method has been applied” by the Imperial Geophysical Experimental Survey for the determination of irregular bedrock surface in gold placer channels and is in widespread use in reflection shooting for calculating the delay in the weathered layer. It consists of shooting at A (Fig. 9-75) and receiving at B and C, then 2 Aa c O———— 30’ ———- © © 0 o—/f/—+o Detect Ist Shot Heber Rs 2nd Shot Fig. 9-75. ABC system (method of differences). shooting at C and receiving at B. This gives the depth under B where one or several receivers may be set up. One receiver is sufficient at A or C. Since in placer and weathered-layer problems, the velocity contrast 42 A.B. Edge and T. H. Laby, Principles and Practice of Geophysical Prospecting, pp. 339-341, Macmillan (1931). Cuap. 9] SEISMIC METHODS 549 is great, vertical ray propagation may be assumed so that the travel times are: (1) at B, shooting from A: ts. = ch + 1 4 & Vi Vo Vi (2) at B, shooting from C: tsc = ds + s 1 de Vi Vo Vi (3) at C, shooting from A: tca = dy ai $1 + 82 ue ds Vi Vo Vi Adding the first two equations and subtracting the third, we get tea + tac — toa 9 “Vy = de ° (9-68) The overburden velocity v; is determined from short-range profiles or (for deep reflection shots) by providing a shot-hole receiver at A. In reflection-correlation shooting, the shot at A is a regular reflection shot with five receivers set up near B and one receiver at C. This receiver is then removed and the second shot placed as shown. In continuous pro- filing, the reverse reflection shot automaticaliy performs the function of the weathering shot from C. D. REFLECTION METHODS 1. General Problems. Reflection methods differ from refraction pro- cedures in that not the first impulses but later impulses are utilized for the depth calculations. Hence, a principal problem in reflection shooting is to separate reflected impulses from all others of a different character, that is, not only from the first high-speed refraction impulses but also from low-speed surface waves and other refraction impulses arriving after the first impulses. A separation is possible (a) in regard to time, and (b) in regard to amplitude. In the design and arrangement of detectors, as well as in field technique, various measures are taken to accomplish this. A universally adopted means for time separation of impulses following in rapid succession is high paper speed (10 to 15 in. sec. ’) and near- critical damping of overall channel response. A record taken with an underdamped receiver at refraction-record speed would scarcely show any reflections. An overlap of interfering impulses with reflections may often be eliminated by changing the distance of the entire spread from the shot point. The principal means of segregating refractions from reflections is the use of a multiplicity of receivers (six, eight, or twelve). Interfering impulses (such as refractions or surface waves) will arrive at each receiver 550 SEISMIC METHODS [CHap. 9 in proportion to the speed of their respective media, whereas the reflected waves (because of their almost vertical incidence) arrive virtually at the same time and have therefore a high apparent velocity. When multiple receivers are connected in series groups, there is an addi- tional possibility of eliminating refractions and reinforcing reflections. In the example illustrated in Fig. 9-76, eight seismometers, connected to- gether, are set up at distances varying from 1000 to 1100 feet from the shot point. When a refleetion of 40-cycle frequency with an apparent velocity of 100,000 feet per second strikes the group of receivers, the im- pulses are virtually in phase and hence reinforced. Conversely, when a Spread s00ft Spread 100 ft Spread 300 ft Interval $ A=#5 / seit Mi Reflection wave Beflection wave Summation Summation ‘Ground wave summation v= 2000 ft-sec? V=10°ftsec’ f= dOcps| 0=75 x10 thsec” fds A= 100 ft f=20 cps Average velocity 8000 ft sec? Hor retl. bed at b000Tt Fia. 9-76. Wave summation in series detectors (after McDermott). refraction, surface, or “ground roll”? wave passes the receivers, the velocity is so low (2000 ft. sec.’ in the example) that the phase difference between each receiver is 1/140 sec., and cancellation occurs except for the beginning and end of the ground wave. The peaks shown in the figure are not serious, as they are much smaller than the amplitude of the reinforced reflected wave. A decrease in the amplitude of interfering impulses is often made pos- sible by judicious placement of shots and selection of charges. By placing them under the unconsolidated weathered layer, the amplitude of the surface waves at the end of the seismogram (ground roll) is reduced, and Cuap. 9] SEISMIC METHODS 551 better confinement is obtained. Sometimes the reflection amplitude can be increased, compared with the refraction amplitude, by firing simul- taneously two charges one below the other. As the reflected energy comes vertically from below, vertical type seismographs are used. How- ever, this does not minimize refraction impulses, since they likewise come in from an almost vertical direction, nor does it reduce the ground roll (Rayleigh?) waves, since they too possess a strong vertical component. However, if there is a difference in the frequency of undesirable impulses and the frequency of reflected waves, the former may be eliminated or reduced by selective response characteristics of the channels or portions thereof (filters). The first high-speed impulses are generally reduced in amplitude by automatic, semiautomatic, or manually operated volume controls. Finally, a field technique combining suitable drilling depths, charges, and shot distances is the most effective means of obtaining distinct reflection records. Under favorable surface conditions there is virtually no limit to the possibilities of the reflection method in sedimentary areas of low dip. The range for which it is commonly used extends from 2000 to 10,000 feet; the extremes are 300 feet and about 30,000 feet. Depth penetration is not controlled by the dimensions of the effective beds. Other advantages are small charges, accuracy of depth determinations (0.2 to 0.5 per cent of depth), completeness with which depth information can be obtained with- out complicated calculations, freedom from terrain effects, and the fact that depth data may be obtained for more than one layer with undimin- ished accuracy. This is of importance to the geologist, since it makes possible the determination of the displacement of the axes of folds with an increase in depth, the mapping of variations in formation thicknesses, and the determination of the existence and extent of unconformities. 2. Instruments.“ Three primary and two secondary devices are the fundamental constituents of a reflection instrument: (a) an electrical detector (phone), (b) an amplifier, (c) a recording device, (d) time-marking mechanism, and (e) shot-instant transmission system. (a) Detector. The function of the detector is to convert the mechanical ground vibrations into fluctuations of electrical current which are amplified and reconverted into mechanical (rotational) motions of a recording gal- vanometer. All types of electrical detectors are similar to microphones in construction. The inductive type is comparable to the coil microphone, 43 See footnote, p. 451 44 References to the literature on this subject are given in C. A. Heiland, ‘‘Instru- ment Problems in Reflection Seismology,’ A.I.M.E. Geophys. Pros., 411-454 (1934). This section gives only a general description of reflection instruments; theory is discussed in section IV. 552 SEISMIC METHODS [CuaP. 9 the reluctance type is similar to phonograph pickup, the capacitive detector is built in the same manner as a condenser microphone, and the pressure detector follows the design of the carbon microphone, or that of the crystal microphone. All electrical pickups have in common a spring- suspended mass whose motion relative to the instrument frame is converted into electrical impulses by some sort of transducer. The two component parts of the transducer are attached to the seismograph mass and to the frame. In the inductive detector, the transducer is a coil moving in a magnetic field (see Figs. 9-113a and 9-113b). In the reluctance detectors (Fig. 9-115), the transducers consist of iron armatures surrounded by coils and placed close to the poles of a permanent magnet or magnets which usually act as the detector mass. In the capacitive type of seismograph (Fig. 9-116), the transducer is a condenser; the mass is mounted close to a stationary plate so that the two together act as a variable condenser. In the piezoelectric detector (Fig. 9-118), the seismograph mass rests on a stack of quartz plates or a rochelle salt crystal. (b) Amplifier. Virtually all reflection equipment employs, between seismograph and recording device, amplifiers of widely varying construc- tion. At present the preference seems to be for the resistance-coupled type, usually of three stages. The following features are common to most amplifiers: filter systems, input and output transformers for matching the impedance of the pickup and of the indicating device, battery operation, gain and filter controls, A.V.C. systems, and separate volume expanders (companders). A scheme of a seismic amplifier (without A.V.C.) is given in Fig. 9-77. (c) Recorder. The recorder is a combination of recording camera and a bank of galvanometers which may be of the coil, bifilar oscillograph, or string type. The coil galvanometers are modified d’Arsonvals with torsion wire or ribbon instead of jewel suspension and short natural period. Therefore, they are really damped vibration galvanometers, with oil or electromagnetic damping. Bifilar oscillographs are less. frequently employed than are coil galvanometers. They combine the advantages of high sensitivity with high natural frequency, but greater care has to be devoted to the design of a good optical system. String galvanometers (harp of strings in a magnetic field) share most of the ad- vantages of the oscillograph but have the drawback of shadow photography (which is somewhat tiring for office work on the records), low sensitivity, and possibility of tangling of the strings. (d) Time Marking. Since for the timing of reflection impulses an ac- curacy of the order of one one-thousandth of a second is required, it has become general practice to project time lines at one-hundredth of a second intervals on the paper and interpolate to an accuracy of one-tenth line. ‘snqzeivdde uoljoaper D1uIslos JUSWUOTO-9AJOM} B JO WIBIZVIP SULLA O1YeuIaYOS pegiduig “27-6 ‘OTT ® = sauoyg 9 4H 3 K vous sau0ug 9 ssaiiduWy @o SIINIIWY 9g uoynrUNUW0) §4af{00YC r | re alg ¥104 burny {x Sdwo7 x sense any | wouomunuWoy §40j04200 psawn7 553 [CHap. 9 SEISMIC METHODS 554 Se Se ae a etland Research Corp. A in record ing truck. tus ion appara ic refiect 1sm. ° -element se Twelve 9-78. Fie - Cuap. 9] SEISMIC METHODS 555 One method employs a hundred-cycle tuning fork which drives a syn- chronous motor whose shaft carries a wheel with ten spokes, one spoke being heavier to mark tenths of seconds.“* This arrangement is used for shadow photography with string galvanometers. For black on white records the spoked wheel is replaced by a disk with the same number of slots.” In another arrangement, the prongs of a fifty-cycle tuning fork are provided with slotted diaphragms to project the slot opening every hundredth of a second directly upon the paper.” Lastly, vibrating reed timers of fifty-cycle frequency are used, driven by vacuum tube oscillators or tuning forks. (e) Shot-instant transmission is accomplished by wire or radio. The shot-instant line also serves for communication with the shot point. In Heiland Research Corp. Fig. 9-79. Seismic recording truck with detector case and reels. most reflection equipment the shot instant is recorded on one of the galvanometers as previously described. A second galvanometer may be used to indicate the vertical (or up-hole) time recorded by a shot point detector. In Fig. 9-77 a schematic and greatly simplified wiring diagram for a twelve-channel seismic apparatus is given, including twelve regular reluc- tance detectors, one shot-point detector, twelve amplifiers, a twelve-gal- vanometer camera, synchronous timing arrangement, two-way communica- 44a See records Nos. 1 and 2 of Fig. 9-91a. 46 See records Nos. 4 to 8 of Fig. 9-91b and c. 46 See record No. 3 of Fig. 9-91a with 1/200 sec. time lines from 100 cycle fork. « 556 SEISMIC METHODS [CHap. 9 tion system between shot point and receiving point, and arrangements for transmission of the instant of the shot and the vertical time break. Figs. 9-78 and 9-79 show the interior and exterior of a recording truck for such equipment, with six amplifiers on each side, switch panel and camera be- tween them, communication system on upper left, compander unit in upper center, tuning fork arrangement at upper right. Developing cans are in the rear of the recording compartment within easy reach of the operator, whose position is in a swivel chair in front of the equipment. Fig. 9-80 illustrates a portable six-channel apparatus. Hetland Research Corp. Fic. 9-80. Portable seismic reflection equipment. Upper row: two amplifier boxes, each with three amplifiers; camera between them. Lower row (left to right): communication unit, detectors, timing system. 3. Travel-time relations. Simple travel-time relations are readily calcu- lated on the assumption that the reflections originate on plane horizontal or inclined surfaces. A further simplification may be introduced by as- suming that the rays are straight. Experience indicates that in many cases the curved path may be replaced by the straight path. Another simplification results from a substitution of the straight for the complex path. The latter has offsets due to refractions in reflecting beds higher up in the section. (a) Horizontal layer. In Fig. 9-81a, let SR = x, which is the dis- Cras g] SEISMIC METHODS 557 tance between the shot point S and any receptor RF at the surface, d be the depth, and v; the velocity in the section above the reflecting bed. Then the reflection travel time is t, = Ve + 4d?. (9-69a) 1 If x is small compared with d (vertical shooting), 2d et (9-69b) ty = The travel-time curve represented by eq. (9-69a) is shown in Fig. 9-81b, together with the corresponding travel-time curve for the refracted wave. The reflection-time curve is a hyperbola and is almost horizontal for steep angles of incidence (vertical shooting). For larger distances it rises rapidly b— 4 + S NY % Fie. 9-8la. Reflection path. reflection travel-time curves. Fic. 9-816. Relation of refraction and until it approaches asymptotically a straight line representing the over- burden velocity. If the second part of the refraction travel-time curve is extended toward the shot point, it will be tangent to the reflection travel- time curve at a point corresponding to the critical ray (that is, for which the path in the lower medium is zero). The reflection-time gradient de- pends on distance as shown by differentiation of eq. (9-69a): ee EE ee Wig O80). (9-70) dx w/z? + 402 vit It is often convenient to calculate travel times for vertical incidence and to apply a correction expressed by the ratio of depth and shot distance, R = d/z, so that ed x \? ic ale 83 be a 1+ (5) or t= 4/1 t (sh). (9-71a) 558 SEISMIC METHODS [CHap. 9 ie 2d\?2 “ aE y/rs (74), (9-71b) Also, Sa eA ee RE ee See RO ns eA ONS GEES OCS NG = (Lee NIN ISON © CONN » COPS 8 Tes ra Sa SS a Sa OR EA co Rae CSN TTS ON TI AS SR Sat SRR (ee GEE a Ura (ed i) COR Cd SN By mariah taal RN i PLCECCERSISE on ae CCST <0 BBE Em PN es eR aa aH HSS i a BSS ASEL i 100 CAAT SSI Patio of Depth to Spread Fia. 9-82. Time gradient of reflection from horizontal bed. Another correction method is based on an expansion of the second expression in eq. (9-72) into a binomial series. Consideration of only the first two terms gives 1 x — 1 iii iar f re =) so that, with ¢t, as vertical time, a= 5Vi (ty = At), where At = x? /2Qvit. © AVAVAVAVAYA'S GPA Ea IBA NE ance eaaaaeenistilll VITALLY) (A GATT IE LA AAAAAAY AUN VIAAALL AA AAT LAAN VV VV TAT Sar esUnREENMUlliE VIAALV YA ATLL RARSRSB 030 Sec. RAR NNNNNNES HUA VAR AN SKA AAA A AVAAAY TT MAR AN AAI 220 CITA ANNALLE NYYCK AAS CLL é \NS ZANE N IN UK ARIA \7 DS4SEi ABB AR ATA TAA YAN A AY we LAV AYN WAAAY TRLRYARY WI LANA VA WIAA TATA 7 LIA A TA TA Zee TT ET TY t= 00 Fig. 9-83. Reduction chart to vertical time (after Pirson). NSS BSUHS 2i BGA. VIZ 73 AV, | YT Al Q4 sec. AVGAiBa Z a Z| Ba a EJ nea = eee ACNCCN soe ENCED TP NT aLEING ASRS SSSR y AE PERCU NTE INST NGI TEN TINT GEN GEN TERT NIN NWAS VND SNNRNABNAUNENGNENENERE NCEE TONGUE TING a AVA iA VIAL | TA TA el i) B | B | S ABIDE |_| 4 a zB a = a7 fl 06 IAA 17 Ci GOGIOO) 407 7) VA a NNINAY NAGBw CCNA SOIT PARSER ACATAT PLE AKAROA AASB AR ALL a NS UNO ANDY PT TT UINANAAAAAANAAKRARARAANATYA SY RNA HL ASRS NNEC AAA ALT TT TT INARAAAAAAAAANATVAATIVAARAY AYR RATATAT CAAA AM SARA AIDC SCA ia i a pe NKIAAARKAAAA KAA AAA AAA OAT PATA TG RAE EARS A AARARRER A ARLARAAES PT AANAAISAAR AAA RODE CUNNA DEN UNS ARRAS STAR SNAICC HARAINNI RAIA A IAA AAA ANINCINS ATIVAN USTONIAT NAVAN NAAR NITY PASSA ARRAN E R \ io | \ iN Yh 4 WAY WAU ATAU QURTATTAN TWN WL WAUAVINUE WILE ECEEE ANNA SORES BRRRRAUNANANVUNVERNRRARR RAR SUITAR SSSSSSNAUAUAUNCUUERUUUC ESS ULLTLIO fuss (ae LTT AAR EANALAEEER EEN 559 560 SEISMIC METHODS [CHap. 9 Fig. 9-83 shows two charts for the calculation of this correction. For any velocity between 6000 and 15,000 feet (ordinate) and any mean re- flection time between 0.3 and 1.4 seconds (abscissa), the first chart gives the denominator of the above equation, or the factor a = 2vt-10°. This factor is the ordinate in the second chart on the right. By intersec- tion with the spread distance x (from shot point to center detector), the time correction At is located on the abscissa. Thus, this chart carries out the operation x”-10-°/a. In summary, the following expressions are available for depth calcula- tion from reflection, assuming straight paths: (general formula) d = }/v?? — ‘ P ; 1 xz \2 (in terms of vertical time) d = =vit, / Ths 4) 2 (9-72) = dvi (tp ray At) (vertical shooting) d = ivity. T2tKt In eqs. (9-72) the speed of the overburden is as- 4 Sh BeRO se yee rs sumed to be constant; in practice, an average veloc- a ity Va is substituted for vi. For reflections from differ- 08 ent depths, different aver- age velocities are generally 06 used. Eqs. (9-72) may be modified for curved ray travel-time curves for (1) a linear, and (2) an expon- Ting eeeeeiee eR Oe : ential velocity increase. 1G. 9-84. Relative reflection travel time, in a : : ; medium of continuous linear velocity increase For a linear ei ever (after Slotnick). by the relation v, = Vo + kh (h = depth), the travel Wy, paths, that is, when there is a variation of the aver- age velocity with depth. 02 Slotnick” has calculated the a2 a4 ropa’ AGE! LGR Bae time at the distance z is 47 Loc. cit. Cuap. 9] SEISMIC METHODS 561 or aia : _, kx iw i inh By," (9-73a) By introducing the following dimensionless quantities: ¢ = kt/2; 6 = kx /2vo ; v = (vo + kh)/vo = vi/Vo, the travel time may be written 2 < = COS yee (9-73b) es Reflection F A a OE ae See Ogee Fig. 9-85. Reflection travel-time curves for three ere A graph of reflection travel-time curves for a linear increase of velocity with depth is shown in Fig. 9-84. Fig. 9-85 gives travel-time curves for three reflections originating in a Cretaceous section in Canada. These curves become flatter with depth, which is caused by both the increase in depth and the increase in average velocity with depth. 562 SEISMIC METHODS [Cuap. 9 (b) Dipping bed. Since in Fig. 9-86 the path I’R from the image of the shot point may be substituted for the path to and from the reflection point C on a horizontal bed, it follows that the down-dip travel time for a dipping bed may be written viz = IR. (9-74) If tg is varied and x is varied, viz = IR, , vig = IR. , viz’ = IR; , and so on. These relations may be solved of r graphically for the point J by drawing Fic. 9-86. Reflection wave path for circles with radii Vin about the her dipping bed. celving points which intersect in I. Increased accuracy is obtained by using two sets of receiving points on either side of the shot point. Analytic- ally, the following relations follow from Fig. 9-86: (Down Dip) TR? =DF + DR’: |. DR = cieosies IR = via; DS = xrsing; DI = 2z + DS: hence, vi; = 4¢ + 4ersing + x. (9-75a) (Up Dip) (for the same distance 2): vi, = 4 — 4ersing +2. (9-75b) Subtracting the up-dip from the down-dip time (for the same shot distances), 2/42 2 V (ta — tu) = sin ¢, (9-75c) 82x and adding, waa ee Vas aN 3 = Zz. Hence, up- and down-dip times furnish both depth (normal to the bed) and dip, so that the depth d vertically below the shot point becomes (9-75d) Pg Le (9-75e) COs y Cuap. 9] SEISMIC METHODS 563 With the ratio R = z/z, formulas (9-75a) and (9-75b) may be written: Ve = \/(QR) + Wisin o + 1 (9-762) ™ = VQ@R} — Resin g + 1. (9-760) The depth under the down-dip shot point is approximately equal to the arithmetic mean of the down-dip and up-dip travel times, multiplied by one-half the velocity. Eqs. (9-75) hold only for equal distances on opposite sides of the shot point. For different distances xq (down-dip) and x, (up-dip), we have vt; = 42? + 4erasin ¢ + 23 Qe 2 : 2 vit, = 42 — 4ex,sing + 2,1, so that Mi atte ta Ll y ( ‘Te te ) 2 Ta = sing (9-77a) and ViGity + bute) — Buta — Tuma _ 2 (9-770) 4(ta + Xu) Tein If dips are determined in two or more distances on the same side of the shot point, vii = 42 + 4en sing +c} Vv ty = 42? + 4zm sin » + 23, or 2742 2 2 2 iy i ety Sai ks — Ae ers en ye oa mee and V (tia, — tar) — wee, + rae _ 2, (9-77) 4(x2 — 21) ifr. > ri andl, > t;. In eqs. (9-77a) and (9-77c), an approximate value for z calculated under the assumption of horizontal bedding gives sufficient accuracy for small dips. Formula (9—-77c) may be written ae <5 ap el Hp De NTID ee iy Dew 2 564 SEISMIC METHODS [CHap. 9 or Wie aAtny al sin g = eer age — gy 1tm, (9-78a) where ¢t,, is the mean time in the mean distance xm. In this equation the depth z (normal to the bed) appears. It may be obtained from eq. (9-77d) with its correct value or be calculated from the mean time under the assumption of horizontal bedding. For many dip calculations, other approximations are satisfactory. One of these is to draw a travel-time curve and to extend it toward the shot point. If the shot-point travel time thus obtained is f) = 2z/v, eq. (9-78a) becomes tine eee (9-78b) In further approximation, let 22 = JR = vt, (Fig. 9-86). Then (9-78a) becomes : At lis j in BIRO oe Visine a as (9-78c) Finally, the last term of this expression may be dropped so that ; At SOR A Aa (approx.). (9-78d) Since At/Azx is equal to the reciprocal of the apparent velocity, eq. (9-78d) is identical with eq. (9-62), and the angle of incidence at the surface, % (at R in Fig. 9-86), is assumed to be equal to the angle of dip. For vertical incidence upon the bed (distances close to shot point) formula (978d) is rigorous. The apparent up-dip and down-dip velocities of reflection impulses may be obtained from a differentiation of the up-dip and down-dip travel times given by eqs. (9-75a) and (9-75b), so that the down-dip gradient (D.G.) is given by lah. 2z sin g + 2a dig VV 42? + 4zrqsin g + 23 and the up-dip gradient (U.G.) is dty —2z sing + ty = * £ UG. 9-79b ate vvV/ 42? — 4zz, sing + 22, =DG., (9-79a) Hence, dtg 2Qzsing + 2a dty —2z sin g + tz ee => ° 9-79 Cuap. 9] SEISMIC METHODS 565 These relations are identical with eq. (9-78a). They may be applied in various ways. Fora given set of conditions (in an area where the velocity is known and the distance between center of spread and shot point are kept constant), diagrams such as shown in Fig. 9-87 may be prepared, showing, in vertical section, intersecting lines of equal gradient and equal time to center of spread. After the time gradient, or step-out time, has been measured, the point corresponding to these values is located in the diagram, which gives the depth of the reflection point. By connecting Fig. 9-87. Graph for determining depth and dip from total time and step-out time (after Pirson). this point with the shot point and drawing a perpendicular, the dip is ob- tained. A vertical change of velocity may be incorporated in the diagram. Eqs. (9-79c) may also be utilized for direct dip-calculations. By sub- tracting the two equations, CDW Che eee DE AD) ee eal 4z in which the last part of the numerator becomes 0 when equal distances on either side of the shot point are used. Eqs. (9-79a) and (9-79b) are, in = sin ¢, (9-79d) 566 SEISMIC METHODS [Cuap. 9 terms of ratios R = 2/z, DG. = 2Ra sin g + 1 “iT wa AOR the sin eet and (9-79e) UG = —R, sing + l ~ ya/(2R,)? — 4B, sing + 1° Time Gradient for 00tt (at vy, = 10000 fsec™') in milliseconds Ce CT ia” hanna e/a Zz. oblique depth x distance VAR Wt | it tts "aaa eo Ra Fic. 9-88. Time gradients for dipping bed. gs ‘ee With these equations the diagram shown in Fig. 9-88 has been con- structed. For high ratios of z/x the gradients become negative for com- paratively small dip angles, that is, the reflection impulses travel back- ward in the seismogram. For low angles of dip, travel times of dipping beds are virtually identical with those from horizontal beds; dip shooting becomes applicable if dips exceed about 100 feet to the mile. However, as a means of checking correlations, it is used with lesser angles of dip. Cuap. 9] SEISMIC METHODS 567 Ail formulas derived above for dipping beds imply that the tra- verse is shot up or down in the direction of maximum dip. If the traverse makes the angle a with the direction of dip, the true dip ¢ follows from the “apparent’’ dip ®, as determined along the tra- verse, from sin ® COs a = sing. [see 9-56a] Directions of strike and of total dip may be determined in two re- flection profiles at right angles to each other; if the apparent dip Fia. 9-89. Location of shot-point image angles are ® and @®’, sin ®’/sin from three travel times. ® = tana. Another method® of determining both dip and strike consists of locating the image of the shot point in three profiles at right angles to one another. At three points of equal distance c from the shot point (see Fig. 9-89) the travel times ¢, , ft, and ts are given by vi=(e—c)+y¥+D x + (y—c) + D vi = (e+e) +7 + D’, where xz, y, and D are the coordinates of the image point. Then 2,2 Vio 2 = i (2 — #2) (identical with [9-75c]) 2 — y= +) ae Deve y= Good. | The coordinates of the reflecting point are 2/2, y/2, and D/2; the dip is given by tang = ~/z? + y2/D, and the strike by tan a = y/z. The dip-shooting method does not give small dips accurately. This is because of the inherent failure of the travel-time curve to respond to small 48S. J. Pirson, Oil Weekly, April 26, 1937. 568 SEISMIC METHODS [CHap. 9 dip angles and errors introduced in the records by surface geological “step outs.’”’ The accuracy is probably not greater than 1° or 2°. It can be increased by reducing the station interval, by surveying closed loops, and by adjusting the errors of closure. The most favorable range is from 5° to 30°; in exceptional cases dips of as much as 55° have been recorded. 4. Average velocity determination. Notwithstanding the frequent curva- ture of reflection rays, the assumption of uniform or average velocities to the reflecting bed or beds is generally satisfactory. In the absence of average velocity data, reflection maps may be contoured in reduced time units. In areas where changes of the character of sediments occur, it may be necessary to introduce an average velocity as a function of the geographic coordinates. One or more of the following procedures may be used for the determination of average velocities: (a) Calculation from known depth. Where the geological section js clearly defined so that there is no doubt about the nature and depth of the reflecting formation, a profile is shot near a well and the average velocity is calculated from ri, 2d a \? a eat 4/i +(e): a (b) Well shooting. A well detector is lowered to various depths and a number of shots are fired at the surface. Usually the distance of the shot locations from the well is made equal to one-half the shot-receptor distance used in the survey, in order to obtain as nearly as possible the velocity along the actual wave path. Well detectors are long seismometers of small diameter, corresponding in design to that of the regular pickups; they have the shape of torpedoes and are well protected against water, mud, and the like. They are lowered on strong steel cables. Average velocities are calculated by dividing the paths from shot point to detector by the respective trave] times. Recording of shot instant and accurate time marks are required as in ordinary reflection work. The method is laborious but in most general use at this time. (c) Calculation from refraction profiles. When the thicknesses d, and the velocities v, of the strata composing the geologic column are known from refraction profiles, the average velocity to the depth z in the column is (9-81b) This method is not particularly accurate, nor is it generally advisable to shoot refraction profiles in an area to obtain average velocity data. Cuap. 9] SEISMIC METHODS 569 (d) Calculation from surface profiles. Since the travel-time equation contains two unknowns-—depth and average velocity—a minimum of two equations must be set up to determine both velocity and depth by record- ing times in at least two-distances. Thus (for horizontal beds) 2 2 Vo = 4/ = a a (9-81c) Dine In practice many distances are required to give accurate values. Squares of travel times are plotted against squares of the distances. For a reliable determination the curve must be a straight line. The cotangent of its angle a with the abscissa is the square of the average velocity. By dif- ferentiating in the travel-time formula (vf? = 2’ + 4d’), the square of travel time with respect to the square of the distance, we have d(t’) /d(z”) = 1/v’ or Vv’ = cotan a. Since ? = 2’/v’ + 4d’/v’, the velocity squared is the ratio of distance squared divided by times squared. The ordinate at zero distance is 4d’/v’. For this calculation travel times have to be cor- rected for weathered layer and elevations; they should also be reduced to regional datum. When the reflecting beds are inclined, it is necessary to shoot an average velocity profile in two directions. In this case the curve representing the squares of travel times as function of the squares of distances is no longer a straight line. Its direction of curvature depends upon whether the profile is shot up dip or down dip. From formulas (9-75a) and (9-75b) we obtain by differentiation Bed a) Tal 23. (down dip) tan ag = ia) Thea (1 + = sin e) (2) (9-81d) : OAC an | Layee. (up dip) tan ay = ia) ¥ ¢ a sin °), which indicates that the curvature decreases with distance; that is, the time- squared distance-squared curves approach true velocities farthest out from the shot point. The arithmetic mean of two tangents to the curve at identical up- and down-dip distances gives the true velocity to the depth under the shot point: tana, + tanag_ 1 5. Field practice. (a) General procedure. In a new area where neither transmission characteristics of the near-surface beds nor the subsurface section is known, the most suitable shot depth and arrangement of re- eeivers (shot distance and receiver interval) must be determined by experi- 570 SEISMIC METHODS [Cuap. 9 ment. The best procedure is to select a favorable location (see paragraph c below), to drill a hole 25 to 50 feet deep, and to select, from inspection of the well samples, a firm or moist formation for placing the shot. Shots are fired with gradually increased charges and records are taken at 100- to 200-foot intervals, beginning as closely to the shot point as possible. These may be utilized later for average velocity calculations if desired. The distance most favorable for the desired reflections is then selected. Quality of reception may be improved by suitable adjustment of filters, and the like. From the records and from geologic considerations the observer will decide whether dip shooting or continuous profiling may be necessary. Surface geology data will determine the weathered-layer procedure. (b) Types of shooting. When reflecting beds are consistent and of low dip so that no correlation difficulties are experienced, the normal setup with receptor spread to one side of the shot point is used (correlation shoot- ing). Shot distances vary from 200 to 2000 feet to the middle receiver and re- ceiver intervals from 20 to 100 feet. If reflecting beds are not consistent or if cor- relation difficulties arise from other sources, con- tinuous profiles are shot.” This is a variation of dip shooting. When the spread has been shot in the for- Fie. 9-90. Arrangement for continuous profiling. ward direction, the shot point is moved to the loca- tion previously occupied by the last receiver. From this point the first spread is shot in reverse and the next spread in forward direction (Fig. 9-90). Since the paths from I to 6 and from II back to I are identical, the travel times are identical and the two records may be tied in. Within the setup shown in the figure, the reflection points are continuous. The “holes” left under the shot points between successive profiles may be avoided by using more overlap. Receivers are evenly spaced between shot points, generally at 100 to 150 feet. Dip shooting is applied when there is noticeable dip and when reflecting beds are not consistent, so that presence or absence of structure may be 49. J. Pirson, A.I.M.E. Tech. Publ. No. 833, 1937. Cuap. 9] SEISMIC METHODS 571 established by correlating dips between stations. The following proce- dures may be followed: (1) shoot twice in the same hole and move the recelvers over; (2) leave receivers in place and shoot from both sides of the spread; (3) shoot once in one hole, and use half of the receivers on one side of the shot point, and the other half on the other side; (4) shoot with receivers to one side and determine dip by absolute times and time gradient. These procedures may be applied’ in two profiles at right angles to each other to determine strike. Structural mapping by small dip angles should be done in closed loops, since the depth errors of closure are considerable and must be distributed by suitable adjustment. Shot distance and receiver interval vary as in correlation shooting. (c) Shot placement, surveying, drilling. Reflection locations should be selected from the point of view of good energy transmission, ease of drilling, and minimum variation of elevation and surface geology along receiver spread. Low places are generally preferred, since water-bearing beds occur closer to the surface. In many eases the selection of reflection loca- tions is a matter of compromise between the above factors. Elevation of shot-point and receiver locations must be determined with an accuracy of about one foot. When dip profiles are shot in more than one direction to determine strike, the direction of the profiles must be recorded. Holes may be drilled with hand augers in favorable locations or when speed is not an important consideration. However, the more general prac- tice is to use rotary drilling rigs mounted on trucks, as previously de- seribed (page 491). In clay, marl, and other soil which is easy to drill, two crews can make as much as 500 to 600 feet of hole a day. For hard formations, coarse gravel, boulder clay, and the like, spudders are used. Caving of shot holes is overcome by the use of “Aquagel,” or lime, or by setting casing. In soft marsh ground, holes are washed down with a high pressure pump operated from a small gasoline engine (see Fig. 9-29). Charges may vary from a single cap to 10 pounds of dynamite. Sixty per cent special gelatin dynamite and Nitramon is most frequently used. Charges are forced down the hole by rods consisting of several sections provided with junctions so made that they do not come apart when lowered into the hole but may be dissembled readily when pulled out. Holes are generally tamped with water; in exceptional cases, with mud. For this purpose a water tank is carried on the shooter’s truck. (d) Weathered-layer technique. A near-surface ‘‘weathered” or ‘‘cor- rection” zone with a considerable reduction in velocity occurs in every area. As this layer is not likely to be identical at all stations it has become general practice to correct for the delay of the reflected wave in this layer. As it has, furthermore, very poor transmission characteristics, shots are placed below it or at least near its lower surface. The extensiveness of the weathered-layer correction is usually a com- . td 1-"998- "93 0006 'd 1-"998- "93 0008 “1 “43 CSTS “YS 8h8S aa 9 CO 8 Co Geli 68 1— 9298-°9} 0008 UL ung peoidg unzeq 0%} p-a 4a § = p 7 °HXOD 7 ‘OUI XLDOTAA Be Rico | SNOLLAUOD NOILVTAUHOO ‘NOILVINOTVO NOILOATAAY PA PA "p) =P U = dats Cp Lic! at FOLK G'S = PI a -a='s Z6'F = Cs) + 4) j— 008 “yy O00L = PA ay 0= * = SAS ore = 47 "008 “25 1999 = FA 17098 “9 006Z = "A = 5 "??—'"M ‘9389 ="M = "AX PA | J = Sigg Se . . . . . nm — Vv - = > } aq—‘m — ‘a Go" Ls G8°9Z G0°9¢ 0€ SZ Go FZ } } 0Z=64 82S = UBIUI *M = Ta x OF = 4) A (4 + 002 7) ZA Cs) = Ueour ¢9'T S8'T G0°% a! $81 a= o> ONS 002 ee Ls lt g Lg 9 — wing Oe ea @ SE 9 SE 0°9€ “GE 9°SE ung O'G = ‘1109 0029 61s.= "3 G 66 L8G T° 8% : ¥ ‘9% 4] 0% = TO+ = ‘1100 0°9 6°9 6°L 6 “1109 4%] ‘43. 8¢ = (‘p) yydeq youg 43% = 5p 6°¢ 8°9 SL T'6 "sqo % ‘43 OHESS = ("H) “APTA IOUS L'cozs ae e122 g-0128 9°6029 ¥'s9z9 "45 B°heS eNOILVAGIGE "93 0S61 “93 0O6T 93 OS8I "33 OSLT “93 002 SHONVISIG NOILOHYYOO WOALVdC GNV DONIQVHHLVEM AO NOILVINOTVO MS§ :NOMoguiq M 6G 4 Stl = .b 9 :NOILOAG 1ajuay |] :NOILISOg u[ooury :ALNOOD OpBI0[OD :ALVLG Vor :‘ON LNIOg LOHg 6861 ‘8 ABI :aLvd osny :AGAUAG 572 573 Seismic reflection records. Fig. 9-9la. } ( ul l prabasdad aniapiayt ae an. ] 7 2 0 a Se 574 | PUORD AL ANGOOHNORADURAGURODUANNUODUBOLEY Uh TT GUDROOURDORORGUADOUANODEDUREED ODOOONEL ET UURRRDDGUUOOUUAUERNDODY: (5) | | Heiland Research Corp. flection records (continued). ismic re Fia. 9-91b. “409 yolvaeay punpa H ‘(PapN7IUOI) SPIOIIA UOIZPIOBal oNUsIag *9ITG-G ‘OI | Il PTW ALUMI tM AA FLREUE ERAGE te ei © FUER ETN NMA \ | | CHNNUOORUAOLONL | AU r HNEACDENDL)A)e) AH} ERNE OM SoU | WUE Sr a ee le aA AGAMA NAV GAMMA Mu TWN Vy TMM UY ! HUNNNUUAUUUAHAAAUUTE | | \ \ Tumuli hf AAV VIANA iit Hl eee Rene ranma ee, are NANA Wy yl HYVER ENA TH iN} LT TTaGAO AGAMMRUNNOLORTNAS GFLOS CIMT AH ACH (9 576 SEISMIC METHODS [CHap. 9 promise between accuracy and time available to obtain the correction data in the field. The accuracy need be no greater than that for depth deter- mination. The time required to obtain weathered-layer data in the field depends on the lateral consistency of the layer. Four possibilities exist: (1) conditions may be the same in the entire area; (2) conditions may be the same at the shot and receiving points but vary throughout the area; (3) conditions may differ on shot and receiving points but be the same at the individual receiving locations; (4) conditions may be different at the shot point and differ at the receiving locations. The first condition prevails in some limited areas so that the correction may be determined once and for all by vertical-time or refraction methods. Assumption of the second condition furnishes sufficjent accuracy in many cases. ‘The weathered-layer delay is then most conveniently determined by measuring the vertical-time interval at the shot point with a shot-point detector and correcting to shot level. In the third case (different condi- tions at shot point and receiving points) the vertical time is measured at the shot point, and a refraction profile is shot at the receptor spread. Finally, when conditions are different at the individual receiving stations, the vertical time is again determined at the shot point and the time delay for each receiver is established by the method of differences (ABC system). This is the procedure in most prevalent use. Further details are given in the calculation records (Table 58). The vertical-time phone is usually connected by a separate line to the truck and recorded on the fifth or elev- enth trace. A correction to regional datum, from which the average veloc- ity is reckoned, is generally added to the weathering correction. 6. Calculation, interpretation. Reflections are not very difficult to spot even in a fair seismogram. They appear with a marked change in ampli- tude, consist of one to three or four waves (generally with declining ampli- tude), and reveal themselves primarily by their almost simultaneous ap- pearance on all traces (except when strong dips are present) (see Fig. 9-91). A reflection may be recognized by comparing its time-distance gradient with that of the first impulses. A graphical analysis of records taken in an entirely new area by travel-time curves will identify reflections with certainty, besides offering the advantage of a determination of their average velocity. After reflections have been identified, they are timed, using the trough of the first wave. The mean time, referred to the center of the spread, is entered in the calculation form. In dip shooting, times are read for the closest and the farthest detector. The recorded times are then corrected for weathering to datum and for spread, as described below. Some reflections may not show very distinct first troughs. In case of doubt, two and sometimes three troughs or “phases” are timed (see Fig. 9-92). Depth errors may readily be committed unless the correct phases Cuap. 9] SEISMIC METHODS 5770 are correlated from point to point. For preliminary depth calculations an average velocity may be assumed or be determined from surface profiles. However, for most areas accurate values derived from well shooting are now available. © definite phase © semi-definite phase © indefinite phase Fig. 9-92. Reflection correlation (phase) logs. Records are generally calculated in the field office; some companies make it a practice to send duplicate records to headquarters. The field crew keeps the following records and turns them in to the field office at the end of the day’s work: (a) Driller’s notes, containing data on location of shot holes, formations encountered, depth of hole, depth of casing, and 578 SEISMIC METHODS [Cuap. 9 soon. (b) Surveyor’s notes, giving locations and elevations of shot holes and receivers, direction of shooting, and the like. (c) Observer’s notes, consisting of a schedule of records taken, charges and shot depth, distances of receivers, and data pertaining to instrument control and filter settings. Calculation forms used in the office for the evaluation of seismic records vary greatly in arrangement, depending on company procedure and prefer- ence. The form given in Table 58 will be found to be flexible enough to cover most weathering and reflection procedures which are likely to be applied in practice. It contains, in the upper portion, general data on location of shot point and receivers. In the lower part follows a form for calculation of weathering correction by the ABC method. Distances and elevations of receivers are entered first. Of the three main columns, the left pertains to the shot point and a location 200 feet away from it, which is intended to give the depth of weathering W, under the shot point. In it are entered shot elevation #, , shot depth d, , vertical time ¢, and time to the 200-foot detector to corrected for elevation. Depth to weathering at the shot point is obtained by adding the 200-foot time to the vertical time, subtracting the horizontal time ¢, , dividing by 2, and multiplying by the overburden velocity v, calculated from shot depth and vertical time (d;./ty = Vi). The result will indicate whether the shot is located above or below the weathered layer, and the correction tj = (W, — d;)/v: is applied accord- ingly. Added to it is a correction to datum ta calculated with an (average) velocity vz of the high-speed bed under the weathered layer. In the mid- dle row of columns are entered the times ts from the reverse weathering shot which are then corrected for shot depth ds/v,. Next follow the times t, of the first breaks from the reflection record. They are added; the time t to the sixth receiver (set out as shown in Fig. 9-75) is sub- tracted; the result (2¢,) is divided by 2; and weathering W, under each receiver is calculated by multiplication with the overburden velocity. As shown in the form, it is usually sufficient to average the times and calculate a mean weathering depth. Subtracting the weathering times #, from the forward times é, gives accurate times corresponding to the advance of the wave in the high-speed bed underlying the weathered layer. From this, an accurate value for its velocity v2 may be obtained. An average value va (usually close to v2) determined from refraction profiles or well shooting is used for the calculation of ég in the first, and of t, = (Z, — W, — D)/vain the last column for reduction to datum. The total correction (t, + to + t: + ta) is entered in the reflection calculation form and added to the spread correction. In correlation shooting, times corresponding to the various reflections and their phases are entered and corrected, and depths are calculated for Cuap. 9) SEISMIC METHODS 579 vertical incidence and converted to elevations above sea level. For dip shooting, this form is modified for the calculation of depths and dip from mean times and time gradients (corrected for weathering and to datum). In correlation shooting, stations are arranged on profiles and cross traverses so that an interlocking pattern is formed. Reflection impulses may be entered by appropriate symbols in the reflection log for each sta- tion and may be connected in much the same manner as key beds of ad- jacent well logs (see Fig. 9-92). In dip shooting, dips may be indicated by a short bar at the reflection depths and correlation may be made on a “phantom”’ horizon or horizons (see Fig. 9-93). Depth determinations made on this basis are not very reliable, but errors are reduced by con- ducting the survey in a closed loop and distributing the errors graphically or by calculation. Fig. 9-93. Dip profile across deep-seated salt dome in southern Louisiana (after Goldstone). IV. ELEMENTARY THEORY AND DESCRIPTION OF SEISMOGRAPHS A. CLASSIFICATION Seismographs may be classified according to component recorded or according to application. The first division is customary in station seis- mology. ‘There we speak of horizontal, vertical, and universal seismo- graphs. Fig. 9-94 shows a number of horizontal seismographs in diagram- matic form. ‘The oldest type is probably the simple pendulum (1). The pendulums in 2, 3, and 4 follow the “swinging door’ principle. The Wiechert astatic pendulum (5) is used in most seismological observatories of the world. The torsion seismometer (6) has been installed in many U.S. Coast and Geodetic Survey and Carnegie Institution observatories. The construction of Nos. 7 and 8 is applied in vibrographs and prospecting seismographs. 580 Fig. (schematic): Paschwitz, (3) Zoellner, (4) Milne; (5) 9-94. Horizontal seismographs (1) Ewing, (2) Rebeur- Wiechert-astatic, (6) Wood-Anderson, (7) Galitzin, (8) Schweydar. According to application, seismo- meters may be divided into (1) station seismographs, (2) vibro- graphs, and (3) prospecting seis- mographs. These differ in respect to mass, magnification, natural frequency, and method of record- ing, as shown in Table 59. B. ELEMENTARY THEORY 1. Geometric and physical char- acteristics of sersmometers. Assume a simple pendulum seismograph, as shown in Fig. 9-96, its mass m being suspended at a distance l’ from the axis. Attached to it is a magnifying lever whose equiv- alent length is J — Il’. According to the well-known theory of the mathematical pendulum, SEISMIC METHODS [CHap, 9 Of the vertical seismographs (Fig. 9-95) the simplest consists of a mass suspended from a coil spring (1). The three seismometers in 2, 3, and 4 use levers with coil springs; the pallograph (4) is employed for the measurement of ship vibrations. The designs in 2, 5, 6, 7, and 8 are used in seismic prospecting de- tectors.” Universal seismographs for the recording of all ground com- ponents have been made by com- bining the coil type (Fig. 9-95, 1) with the Ewing pendulum (Fig. 9-94,1). This is known as the De Quervain universal seismograph. They have not found application as prospecting detectors. Fig. 9-95. Vertical seismographs (sche- matic): (1) coil spring, (2) Gray spring- lever, .(3) Tanakadate, (4) pallograph, (5) dual spring, (6) geophone, (7) combina- tion of (1) and (5), (8) Vicentini. 50 Vertical seismographs, particu- larly the astatic types, are also em- ployed as gravimeters (see pp. 125, 126, 132, and 134). Cuap. 9] SEISMIC METHODS 581 2n 3 g (=) iii l”’ (9-82a) where 7% is the natural period of the pendulum, g is gravity, l’ is pendulum length, and J is indicator length. If b is the deflection of the mass from TABLE 59 TYPE Mass | MAanrrt- NATURAL RecorDING METHOD CATION FREQUENCY Station seismograph........ large small | low mostly mechanical; some optical and electrical ANOMOCT APN 2.0.0.2 cee eae e ake small | small | high mostly optical Prospecting seismograph...| small | large | intermediate | mostly electrical and high its rest position and a the corresponding ampli- tude of the pointer, the indicator or static mag- nification is yo ied, (9-82b) If the suspension point of a seismograph is dis- placed rapidly, the ground displacement is recorded with the magnification V in opposite direction, and the negative indicator magnification gives the 4, 9-96. Seismometer pendulum displacement for rapid ground move- as a pendulum. ments. In the corresponding physical pendulum the period is proportional to the distance of the center of oscillation from the axis of rotation. The reduced or equivalent pendulum length is given by 2 — = i (9-82c) Tv Substituting, in eq. (9-82c), wo for 27r/T,, where w is the angular frequency of the seismograph, hereafter briefly referred to as natural frequency, (wo = 27fo, see eq. [9-18a]), 2 g 8 where s is the distance of the center of gravity from the axis of rotation and K the moment of inertia about the same axis. For any type of spring seismograph, (9-82d) (9-83) 582 SEISMIC METHODS [CHap. 9 where ¢ is a spring constant and is equal to the ratio of force and spring elongation d (see page 591). 2. Undamped free oscillations. In an undamped seismograph, as in a mathematical pendulum (see page 97), the condition of equilibrium of restoring and inertia forces is expressed by mg sin ¢ + ml (d’¢/dt’) = 0 (see Fig. 9-96), so that in abbreviated differential notation after dividing by ml, and letting sin g = ¢, eo 7 o= 0: (9-842) Substituting a = Jy (Fig. 9-96, where a is the recorded amplitude) and utilizing eq. (9-82d), we have dé + wa = 0, (9-84b) whose solution is a = Ap sin(wot + ¥) = Ao sin a(t + b), (9-84c) which is identical in form with eq. 9-19 given on page 449. _ 3. Free oscillations with friction. Actually the last equation does not express completely the motion of the seismograph. Its amplitude de- creases with time, since the kinetic energy is consumed and converted into heat. This transformation acts as a brake on the amplitude. The manner in which the amplitude decreases is dependent on the type of braking resistance, of which the following are the more important types: (1) Coulomb’s friction, constant during the entire motion, (2) velocity damp- ing, which is proportional to the velocity of motion, and (3) velocity- square damping, proportional to the square of the velocity of motion. Only the first and second will be discussed here. Details on the theory of velocity-square damping may be obtained from the literature.” In early seismograph construction, attempts were made to reduce the natural movement by excessive friction. However, this makes the seis- mograph inoperative for accelerations equal to or less than the frictional force. It does not return to its zero position, while with velocity damping it always returns. Although friction is undesirable in a seismograph, it is never possible to avoid it altogether, since there is a certain amount of friction in the sus- pension springs, electrical wires, and the like. The type of record obtained with a seismograph under the influence of friction only is shown in Fig. 9-97. A line connecting the peaks is straight, while for a damped seis- 517, S. Jacobsen, Seis. Soc. Amer. Bull., 20(8), 160-195 (Sept., 1930); B. Hague, Alternating Current Bridge Methods (section on oscillographs), London (Pitman & Sons), 1930. mn CuHap. 9] SEISMIC METHODS 583 mograph it is an exponential. The effect of friction may be distinguished from damping by measuring both ratios and differences of successive amplitudes. In a damped curve the ratio is constant (corresponding to a geometric progression), while in a friction curve the difference is constant (representing an arithmetic progression). The vector figure of amplitude progression is an Archimedian spiral for friction and a logarithmic spiral for damping. As shown in Fig. 9-97, equiphase amplitudes lose the amount 4f within one period so that a; = a, — 4f. Since deflection is force divided by spring constant, the loss of deflection f due to the frictional force is equal to m’g¢/c, with ¢ as Coulomb’s friction factor and m’ the ‘‘equivalent”’ mass of the seismograph. The period of a seismograph with friction is the same as the period of a seismograph without friction. Fig. 9-97. Seismograph oscillations under influence of friction. 4. Free oscillations with damping. The type of amplitude decay just discussed may be said to be due to exterior friction. Conversely, interior friction (as in liquids) produces damping in proportion to the first or second power of the velocity of motion. In velocity damping, the closest approach to a correct reproduction of actual ground motion is obtained. Three types of damping are employed in seismic detectors: (1) air, (2) oil, and (3) electromagnetic damping. Air damping is effective only if the mass of the seismograph is small” and the frequency low. Hence, it has found application in condenser- microphone detectors and in some inductive geophones with very light coils. Ozl damping is most frequently employed. In mechanical seis- 52 These statements refer to seismic detectors. Air damping can be effective in station seisrnographs (Wiechert) when used at the end of levers which, however, are usually undesirable on detectors. 584 SEISMIC METHODS [CHap. 9 mographs a vane may be attached to the end of the magnification cone to be free to move in an oil cup; or a series of vanes may be fastened to the mass directly, arranged between partitions in an oil container. In elec- trical detectors the receiver cases are generally filled to a level which gives the desired amount of damping. It is preferable to use mineral oils of low temperature coefficient of viscosity (Nujol or automobile oils of vari- ous §.A.E. ratings). Electromagnetic damping is most satisfactory from the point cf view of design, clean operation, and independence cf temperature. It is most effective in detectors of low natural frequency and light mass. In a Galitzin type seismometer a copper plate at the end of the coil-carrying lever moves between two permanent.magnets whose spacing can be ad- justed to obtain the desired damping rate. In the Wood-Anderson torsion seismometer the mass moves between the poles of a permanent magnet. In the Wenner seismometer pickups and galvanometer coils are of comparable mass and damp one another; the damping rate may be regulated by a shunt across the line. With an amplifier between pickup and galvanometer the primary of the input transformer produces damping. Additional damping may be produced by short-circuited turns or coil frames of conductive material. If p is defined as damping resistance, or damping force on mass of unit velocity, the damping acceleration equals pa/m, and a+Patwa=0. (9-852) Substituting a damping constant « = 3p/m (which has the dimension of a fréquency), d+ 2d + aa = 0, (9-85b) whose solution a = By-e"!’ + Cy-e™', or a = By-enle-V e254] 4+ Cy elet Ve? 02) (9-85c) If « > wo , the exponent is negative, the motion overaperiodic, the damping overcritical, and the mass creeps back to the zero position. If « = w, the mass returns to zero without overswing, and the motion is aperiodic (critical damping). If ¢ < w, the mass oscillates about the zero position with declining amplitudes. This is referred to as damped free oscillation, comprising damping rates between zero and critical. In this case, the term Ve — w? becomes j+/w? — &, so that by the use of Moivre’s theorem a = Be “-sin V/wt — &t + Cove “-cos Vw? — &t (9-86a) Comparing this with eq. (9-18a), we see that +~/w? — & represents the natural frequency reduced by damping. Hence, Cuap. 9] SEISMIC METHODS 585 wa = Vw — 2, (9-86b) the damped natural frequency, is always less than the undamped frequency, and approaches zero for critical damping. With (9-86b), eq. (9-86a) may be written isi EB lh C a=A.e“ E sin wa-t + A °° wut, which by substitution of B/A = cos y and C/A = sin » becomes a = A-e “‘sin(wat + y) (9-86c) and is represented in time-amplitude and vectorial form in Fig. 9-98. The peak amplitudes decrease in geometric progression. A line connecting them is an exponential, since the amplitude at the time tis A, = Ay-e Fig. 9-98. Oscillation of damped seismograph. Thus, the ratio r of two equiphase peak amplitudes within one period A a A;-e * A; is, Aiea etter) s Hence, r =e"! = e/a (9-87a) where r is the damping ratio and fa = 1/Ta is the damped frequency. In logarithmic form PAs f — log. r = log. 2 el g = AN. (9-87b) 3 A € fa with A, as the natural logarithmic decrement. In highly damped seismographs it is difficult to measure accurately the amplitude ratios for one complete period. More suitable is the deter- mination of the overshoot, which is the (reciprocal) damping ratio referred to successive amplitudes within one-half of a period. It is expressed as the overswing AA in terms of the original amplitude A so that AA = Ay-e “ec”. (9-87c) Another characteristic of damping is the relaxation time (Fig. 9-98), that is, the time which elapses until the amplitude has declined to 1/e of its initial amount: 586 SEISMIC METHODS [CHap. 9 bide we De. als Seer eye loget = =. (9 87d) In seismograph calibration it is convenient to use the relative damping n, Which is the ratio of damping constant and natural frequency w and varies therefore from 0 for no damping to 1 for critical damping. Hence, coe Ja gaa (9-87e) wo fo In Galitzin’s publications a damping factor y is used. This is equal to the ratio of damped and undamped frequency: pie elo iam | (9-87f) 5. Forced oscillations; steady state conditions. Generally the ground continues to move after the seismograph motion has started. The two motions will be superimposed on each other. Expressions may be derived for the resultant “forced”’ oscillations, provided that certain simplifications are introduced. Replacing the 0 on the right side of eq. (9-84b) by a term containing the acceleration <¢ of the point of suspension, d+wa = — VE. (9-88a) It is seen that a seismograph can be made to record the ground motion perfectly if the pointer acceleration equals magnified ground acceleration, that is, if d = — V%. This condition can exist only if w) = 0 and if the seismograph has an infinitely long period, that is, if it is astatized. Ac- tually zero frequency is mechanically impossible; however, the lower the natural frequency, the more the second time derivative of the recorded amplitude will correspond to the ground acceleration. The seismograph is essentially a displacement recorder. Conversely, if a seismograph is made with a natural frequency much higher than that of the ground motion, @ is negligible compared with wa and eq. (9-88a) becomes a = (—V/w5)#. It is seen that the recorded amplitude is proportional to the ground accelerations and that, therefore, the seismograph is an acceler- ometer. However, the ground accelerations are recorded with a reduced magnification (V/w0). A definite solution of eq. (9-88a) can be given if a time function of z is introduced, the simplest assumption being a continuous harmonic function. Hence, if x = X sin wi (where X is the maximum amplitude and w is ground frequency), ¢@ = —Xw’ sin wt, and eq. (9-88a) becomes ad + wa = VXw' sin at, (9-88b) Cuap. 9} SEISMIC METHODS 587 whose solution 2 4 a= Vio sin wt = mi 2. (9-88c) we — w? we — w? Substituting the dynamic magnification W for the ratio a/z, and the “tuning factor” n for the ratio w/w», 2 n WwW =V-.- gale (9-88d) If w = w , resonance occurs; W = ~; and, theoretically, infinite ampli- tudes are obtained. In practice they do not occur because of a certain amount of friction or damping which is always present. If w > w, W = —V; the dynamic magnification is equal to the negative static magnification; and very rapid ground motions are recorded with the indi- cator magnification. Ifw< ¢ + 90°). (9-92a) With T as a transmission constant equal to —H,/C (where C is a factor introduced by short circuiting the detector through the primary of an impedance matching transformer), the peak e.m.f. = EH, is Va" TX whi A erm ETT (9-92b) En Cuap. 9] SEISMIC METHODS 595 If the detector is coupled directly to a galvanometer; if the total im- pedance of detector, external circuit, and galvanometer is Z; and if U = — H.l/Z is a galvanometer transmission constant; the peak value of the current is i Vu'VX VAC Te Ae An electromagnetic seismograph equipped with a coil transducer is known as an inductive detector. If the coil is replaced by an iron armature separated by an air gap from a magnet provided with coils (telephone receiver), the seismograph becomes a reluctance detector or, more specifi- cally, an unbalanced reluctance detector. A station seismometer of this kind has been developed by Benioff.” A more advantageous design is afforded by a balanced reluctance detector which is so arranged that the pull of a magnet on two armatures, or the pull of two magnets on one armature, is balanced. The Baldwin telephone receiver, most phono- graph pickups, and the seismic detectors shown in Figs. 9-115a and 9-115b are examples of bal- anced receivers. Although fundamentally the theory of these receivers is the same as that of the inductive detector as far as voltage output in proportion to the velocity of ground motion is concerned, a modification is introduced because of the de- pendence of the natur&’l frequency on the mag- netic field. The force of attraction of the magnet on the armature F’ opposes the elastic- restoring force F = cd (c = spring constant, d = deflection). The magnetic force is a func- tion of the field in the air gaps; the field, in turn, is equal to magnetomotive force over reluc- Coimim 4 tance. If, in the schematic reluctance detector shown in Fig. 9-103, M is the m.m.f. of each ee Bone ae magnet, the upper field for two gaps in series tector. is H, = M/2(a — d) and the lower Hp = M/2(a + d), where a is the normal gap and d the displacement from its position. If S is the section of the magnet, the force Im (9-92c) ES Sis g SM’. ad ee = Tt Ty SCE ENO i ST tet) rg Geen Ne ee Neglecting in the denominator d’ against a’, the force F’ = SM’d/4na’. Since, in the position of equilibrium, cd — F’ = O, we have 57 Loc. cit. 596 SEISMIC METHODS [Cuap. 9 d(c — SM’/4ra’) = 0, from which it is seen that the second term repre- sents a negative spring constant, also called negative stiffness: SM’ ne 47a?” (9-93b) The presence of the magnetic field reduces the elastic spring constant and, therefore, the natural frequency is 2 wo = // mC ise SM ; (9-938c) m 42ma? When the armature or magnet alee moves, the flux 6 = SH changes, since the gap width and hence the reluctance increases or decreases, respectively. In a balanced de- tector the two armatures are so wound that opposite flux changes above and below produce an e.m.f. in the same direction. The flux through the upper two gaps (disre- garding the deflection d) is SM/a. The same flux passes through the lower gaps, so that 6 = 2SM/a. If N is the total number of turns on the two armatures, the induced emf. He ao od es so that 2 4 6 8mm dt da dt Fie, 9-104. Voltage output of experi- mental reluctance detector as a function E=—-— 2NSM da of gap length. . a dt 10 (9-94a) By substitution of the time derivative of the steady state term in eq. (9-89d), 3 E=-— AS : Vo sin (. + 5 + e) f (9-94b) My VAC Be aay The voltage output increases, therefore, in inverse proportion to the square of the gap width which is verified by the experiment represented in Fig. 9-104. Analysis of this curve gives 94-dnm” millivolts for the e.m.f. in this case. The deviation from the exponent —2 is probably caused by the fact that in eq. (9-946) the variation of wo with gap width Cuap. 9] SEISMIC METHODS 597 is not considered. Fig. 9-105 shows the response curve of various com- mercial reluctance detectors and one inductive detector in terms of voltage developed on the first amplifier grids for ground motions of 14 amplitude. 100 millivolts per micron pi t= Frequency | 20 40 60 60 Fig. 9-105. Voltage at grid of first amplifier tube in millivolts per micron ground motion (through impedance matching transformer) of some commercial reflection detectors. R, reluctance detectors; Jo, inductive detector, oil damped; J, induetive detector, electromagnetically damped. The difference in the response curves N and S is due to the fact that S is adjusted to a low and WN to a high natural frequency. 2. Amplifier. A specific solution for the response of an amplifier is difficult to give because of the complexity and variety of the individual circuits employed. As a rule, detector and galvanometer are coupled to 598 SEISMIC METHODS [CHap. 9 the amplifier by transformers which are inefficient in the range from 0 to 20 cycles. Therefore, the response of a seismograph amplifier rises with frequency in this range. Depending on interstage coupling, some ampli- fiers have an essentially straight response, others keep rising in the range up to a hundred cycles, and still others are peaked. Peaking may be accomplished by filters or by resonant circuits. In view of these differ- ences a general and approximate solution only may be given. The re- sponse may be considered equivalent to one obtainable by assuming a definite damping factor and a natural frequency approximately equal to the peak frequency. In the steady state the general equation for the amplitude of a force- coupled system is = 1 Nie ~ ae + 40 Y = Y sin (wt — ¢), (9-95) where V, is the equivalent magnification or gain of the amplifier, w, its equivalent natural frequency, €. the equivalent damping, y the output (current), and Y the peak value of the input voltage. As is shown below, the above expression fits the experimental results, although its simplified form is equivalent to disregarding the action of input and output devices. 3. Galvanometer. Three types of galvanometers (Fig. 9-106) may be employed in seismic recording channels: (a) oscillographs, (b) coil galva- nometers, and (c) string galvanometers. All have in common a magnetic field and a current-carrying conductor in this field. In a string gal- vanometer only one conductor is present; its motion in respect to the lines of force is transverse. In coil galvanometers and oscillographs, two conductors are traversed by currents in opposite directions so that a rota- tional motion results. In an oscillograph, assume a bifilar loop to be suspended in an air gap of the length L of a magnet with the field strength H,. The distance of the wires or ribbons is 2d; its plane of rest is parallel with the lines of force; 7 is the equivalent torsional coefficient of the suspension; K the moment of inertia of the wires inclusive of that of the mirror; and ¢ the deflection. Then the equation of motion for free oscillation is Kg + rg = 0. For the deflection ¢ produced by a current J, the torque is —2H,/Ld cosy. Since 2Ld is the area S of the loop between the pole pieces, the current torque is —H,SJ cos ¢. In the equilibrium position this is balanced by the elastic torque of the suspension TY, so that for ‘static deflections te = HSI cos gy. For small angles cos g = 1, so that the equilibrium of elec- trical, elastic, and inertia forces in the state of oscillation is given by Ke + te = HSI. (9-962) Cuap. 9] SEISMIC METHODS 599 Cambridge Instrument Co. Fic. 9-106a. Multiple string galvanometer in camera. L, Lamp; S, string harp; M, synchronous timer motor; P, prism; F, fork. Heiland Research Corp. Fig. 9-1066. Multiple-coil galvanometer (four channel) in camera. (A twelve- element camera is shown in the center of Fig. 9-78.) This holds for undamped oscillations. Damping in galvanometers is composed of electromagnetic and viscosity (air or oil) damping. The former results from a counter e.m.f. set up in the coil by its motion when 600 SEISMIC METHODS [CHap. 9 it is connected to a load. This load may be the seismograph coil or the transformer secondary in the output stage of an amplifier. The counter e.m.f. ZH, = HS¢, where ¢ is the velocity of motion. The current resulting from it is, for pure D.C. resistances in the circuit, J. = coe? where R is the resistance of the external circuit and R’ the oscillograph resist- ance. Since the torque of a current, J, passing through the loop, is HS/, 2 2 the torque due to the counter e.m.f. is or d.-¢, with d, as the Say R + R’ Y) electromagnetic damping factor. To this may be added a damping factor d,, resulting from mechanical damping (oil or the like), and their sum d. + d, may be combined into a resultant galvanometer damping factor d,. Then eq. (9-96a) is Ke + do + re = H,SJ. Dividing by K, and letting d,/K = 2e, (the damping constant of the galvanometer) and +/K = w, (the square of the natural frequency of the galvanometer), we get HS K This may be converted into record amplitudes b by letting b = 29D, with D as focal length of the lens in front of the oscillograph mirror: 2DH,S K For a coil galvanometer the right side of the last equation is multiplied by N, , the number of turns in the galvanometer coil, so that _ 2DH,-S-N, K In a string galvanometer a wire or “harp” of wires of the free length 1 is suspended between pole pieces of the length L in a field of the strength H,. The natural frequency of a string (fundamental) is given by gee ad’ where a is its sectional area, P the tension, and 6 the density. The free oscillation with combined air and electromagnetic damping and with m as mass of the string is then b + 2¢,-6 + wb = 0, e+ 2,-o+ 059 = i (9-96b) b + 2,6 + w,-b = ie (9-96c) b + 2€,-6 + wi -b i (9-964) where b is the deflection corresponding to a current J as viewed under a microscope of the magnification M, so that b = HLIM. Hence, the gal- Cuap. 9] SEISMIC METHODS 601 vanometer equation corresponding to (9-96d) is b+ 266 + usd = MOY. (9-96e) Eqs. (9-96c, d, and e) may be written in the same general form by denoting the factor of J on the right side as galvanometric magnification factor (static or D.C. sensitivity) V, , divided by K: Vo R The solution of this equation for a current of the peak value J, and the frequency w is b+ 26,6 +b = 6 (9-97) pee Maina ee (wt + oy), b=Ce “sin (wat + ¥,) + ; : K V (co? ee dew” (9-97b) where wa, is the damped frequency of the galvanometer, y, the initial phase angle, and gy, the phase shift between galvanometer record and im- pressed current. Galvanometer response curves for steady state conditions (second term in eq. [9-97b]) are shown in Fig. 9-107 for various damping rates. It is noted that these curves show the opposite behavior compared with the response of a seismograph. While the dynamic magnification of the latter increases to the static level for tuning factors greater than 1, the dynamic response of the former decreases for tuning factors greater than 1 below the (D.C.) static sensitivity. In a seismograph response curve, the resonance frequencies move toward greater tuning factors with increased damping. In a galvanometer response curve they move toward smaller tuning factors. The resonance frequency of a galvanometer is Org = Mia — 2. Fig. 9-108 shows response curves of a number of commercial seismo- graph galvanometers. 4. Over-all response. To obtain the over-all response of a recording channel, that is, the galvanometer deflection for a ground impulse of given amplitude and frequency, the dynamic responses of detector, amplifier, and galvanometer are combined. A similar problem arises in station seis- mology. Various authors have discussed the reaction of a galvanometer coupled directly to a seismograph. Two extreme cases exist: (1) the seismograph mass is large and the galvanometer mass small, so that the seismograph is essentially the driving and the galvanometer the driven unit, with no energy going back into the seismograph from the galvanome- ter; (2) seismograph and galvanometer masses are comparable, so that they 602 SEISMIC METHODS [CHaP. 9 represent a coupled system with comparable merits of its members. The latter leads to fairly complex equations, discussed by Wenner” and Schmerwitz.” ; The first case, involving an energy transfer in one direction only, has been calculated by Galitzin. When an amplifier representing a unilateral impedance is employed between seismograph and galvanometer, Galitzin’s 3.0 Fig. 9-107. Frequency response of galvanometer, as a function of tuning factor and relative damping. solution is applicable, provided that the amplifier action is equivalent to that of a system with simple static magnification. Combining eq. (9-97a) with eq. (9-92c) and lumping all constants, so that V,-V-U/K = C, we obtain Cw’ X V (w? = oy + Sew of which the steady state solution is C w : bi : . Xwsin (wt +90°+¢+¢,). V (we —w) +4 V/ (ui So) deo. i‘ b + 2e,6 + wb = ; sin (wt + 90° + ¢), (9-98a) 58 F. Wenner, loc. cit. 59 G. Schmerwitz, Zeit. Geophys., 12(5/6), 206-220 (1936). Cuap. 9] SEISMIC METHODS 603 Stale Deflection, miltimefers per 10°* amperes Long permanent magnet bifilar oscillograph 20 15 Short permanent magnet bifilar oscillograph =——_——_— ~~ 10 Flectromagnetically domped coil galvanometer Multi-element bil damped coil * string galvanometer A cadena al acess Ne (Sr (magnihed 10 times os ess =" < oi 7 ae SAS tees a | 50 100 1 x6 es Fic. 9-108. Response of various commercial reflection galvanometers. Hence, the over-all dynamic magnification W, of a galvanometer for ground motions of the peak amplitude X, when coupled directly to a seismometer, may be written in terms of their respective dynamic magnifications: W;=W,-W:z- a (9-98b) K Expressions for special cases of over-all magnifications are of interest. When both seismometer and galvanometer are critically damped, the 604 SEISMIC METHODS [Cuap. 9 damped frequency factors (in the denominator of eq. [9-98a]) are 1 (fe) = w; rey and = (fa) = or 1 1 CAS eae ie eee where 7, is the tuning factor (= w/w,) for the galvanometer and m(= w/w») the tuning factor for the seismometer. Therefore, eq. (9-98a) can be greatly simplified by making the two tuning factors equal, that is, making the natural frequency of the galvanometer equal to that of the seismo- graph. Then the product of the frequency factors (f,) and (fa), multiplied by w in the numerator, is n*/wo(1 + n”)’, so that the over-all magnifica- tion is , ¢ n W, = a ° + 7)? . (9-98c) The function n’/(1 + n°)’, given in eq. (9-98c), is shown in Fig. 9-109. It has its maximum at 1/n = 0.577. When galvanometer and seismograph frequencies are equal and both are critically damped, the response is peaked at a frequency 1.73 times the natural frequency. Galitzin gives an instructive example showing that one seismometer with a period of 12 seconds was peaked at a period of around 6.9 seconds, while another with a period of 25 seconds was peaked at 14.5 when connected to galvanometers of matched natural frequencies. For 0.7 critical damping the damped frequency factors are 1 1 (f,) = S/T EH and (fa) = RU snare so that for equal frequencies of seismometer and galvanometer the over-all dynamic response is given by 3 i] C n This curve is shown in Fig. 9-109. The over-all magnification is greater (less damping), the curve peak has moved closer to the tuning factor of 1. The maximum is at 1/n = 0.77, that is, for a detector and galvanometer which have equal natural frequencies and are 0.7 critically damped, the over-all peak occurs at 1.3 times their natural frequency. Conversely, a linear response may be produced by making the galvanometer frequency a multiple of the seismometer frequency. Then, for 0.7 critical damping, Cuap. 9] SEISMIC METHODS 605 (fo) = 1/ogr/1 + ni and (fe) = 1/wor/1 + ni. If the galvanometer frequency is ten times higher than the seismaometer frequency, the product of the frequency factors (f,)-(fa) = 1/w0-/ (10! + na)(1 + né), which 06 a5 ad aj a2 al Tuning Factor 42 04 06 a8 10 08 a6 ' 04 a2 0 eS Fic. 9-109. Dynamic response of seismograph and galvanometer of equal natural frequency and equal damping. is seen to indicate an approximately linear increase of dynamic response with frequency (see Fig. 9-110). In such a case it is comparatively easy to superimpose amplifier-filter characteristics upon the seismometer-galva- nometer response and to peak at any desired frequency. The over-all 606 SEISMIC METHODS [Cuap. 9 response W, of detector, amplifier, and galvanometer is (from eqs. [9-926], [9-95], and [9-98a]) = Vi(fa)- V. Henee K °Va(fa) = = W, Wa: W, -T. °@), (9-99) where V, (f,)/K = W,. The resultant dynamic magnification of the entire channel is therefore proportional to the product of all dynamic magnifications and to a trans- x Galvanometer deflection for unit oround motion n? igen >. : ‘ (shaking table) Se v)) Tuning Factor to 1] @ 0 40 o a r)] & 9 7] Fig. 9-111. Comparison of calculated and experimental response of detector, amplifier, and galvanometer for given tuning factors and damping ratios. 1. Mechanical setsmographs. Much of the first refraction work was done with the Mintrop mechanical seismograph” (see Fig. 9-112). Pen- dulum and recorder are separate as in most other mechanical seismographs. The former is a vertical-component instrument, consisting of a spherical mass attached to a leaf spring. The mass carries a long, cone-shaped extension with a thin spring at its end which rubs against a spindle carrying a mirror. The movement of the lever is damped electromagnetically. In the recorder the unexposed paper is housed below and fed through a 60 C. A. Heiland, Eng. and Min. J., 121(2), Fig. 18 (Jan. 9, 1926). 608 SEISMIC METHODS [Cuap. 9 number of rollers past a cylindrical lens and a time-marking mechanism. This consists of a pendulum which interrupts a light beam at periodic intervals and projects dashes every 1/10 second on the paper. The paper is started by pressing an idler against one of the rollers driven by the spring motor. By the above combination of mechanical and optical magnification, high over-all magnification is obtained. If V is id, nC a if Lens W' Otfset_-+ Alurninum Cone ROP SRY SETAE FAAS 1 PPPS Fia. 9-112. Mintrop mechanical seismograph and recorder. the geometric magnification of the lever, r the radius of the mirror spindle, and D the focal length of the lens in front of the seismograph mirror, the over-all magnification is 2DV/r. In this manner magnifications from 15,000 times and up are readily obtained. At a receiving station seismograph and camera are generally set up in a small tent. These are supplemented by a mirror device on a tripod next to the seismograph for the recording of the shot instant transmitted by radio. Another type of mechanical seismograph that was widely used for refrac- _ Caap. 9] SEISMIC METHODS 609 tion shooting is the Schweydar-Askania two-component seismograph. Descriptions and diagrams of it are given by Edge and Laby.” The construction of the vertical seismograph is similar in regard to suspension, mass, and lever, to the Mintrop seismograph. The mass is suspended from a horizontal spring, whereas the horizontal seismograph mass is sus- pended on a vertical spring. The combined instrument is so set up that the plane of this spring is at right angles to the firing line. In the earlier models a bow-string attachment transferred the movement of the end of the lever to a mirror spindle. The illustrations in Edge and Laby give the details of this arrangement. In later models, a string was tied to the end of the lever, wrapped around the mirror spindle, and kept taut by a spring. The natural frequency of both seismometers is about 15 cycles. Damp- ing is accomplished by a vane attached near the end of the lever and im- mersed in an oil chamber. In the models developed subsequently, the masses are cylindrical and the magnifying lever is somewhat shorter than in the first model. Provision is made for attaching a mirror device to the head of the instrument so that the shot instant may be recorded on the same strip as the two components. Several other mechanical prospecting seismographs were constructed, in the period from 1924 to 1929, by Ricker, Truman, Taylor, and others. 2. Electrical seismographs. (a) Electro- magnetic setsmographs. A modification of the Schweydar mechanical seismograph was used extensively at one time as an inductive seismograph. A coil was at- tached to the end of the magnifying lever. This was free to move in the field of an electromagnet supplied with current from a storage battery. The period of this seismograph was about 0.03 second. It was used without intermediate amplifier with a Zeiss loop galvanometer. Fig. Fie. 9-113a. Dual-coil induction 9-113a shows a dual-coil variant of the seismograph. original instrument. In the Cambridge Instrument Company’s electromagnetic refraction seismograph, the magni- fying lever makes an angle with the horizontal. A string is fastened to its end. This in turn is wound around the shaft of a galvanometer acting as a generator. The seismograph is used in connection with a Cambridge string galvanometer. 61 Op. cit., figs. 158-160 and 255-257. S fo amplitier 610 SEISMIC METHODS [CHar. 9 The Imperial Geophysical Experimental Survey used an inductive seis- mograph in which the mass consisted of an electromagnet suspended from a diaphragm. ‘The pickup coil was stationary between the poles of this electromagnet (see Fig. 259 of Edge and Laby) and was connected to a Cambridge string galvanometer. Illustrations and diagrams of a multiple- string galvanometer used for refraction shooting by the I.E.G.S. are found in Figs. 153, 154, 156, and 253 of Edge and Laby’s book. Fig. 9-1136 illustrates an inductive seismometer with single coil moving in the field of a permanent (pot-type) magnet. Fig. 9-114 represents a portable four-channel refraction seismic apparatus for shallow depth prob- lems in which inductive detectors to amplifier with electromagnetic damping are employed. Reluctance electromagnetic seis- mographs have been developed most extensively for reflection shooting. Two balanced-arma- ture types are shown in Fig. 9-115. They are very efficient, well adapted to intermediate and high natural frequencies, and may be used for both refraction and reflec- y y y y y y Y y y D y Y y y Y y y y y y éb Y f p ‘ ¢. TIZLZLZIAILZL LLL LLL LLL tion work. Fig. 9-113b. Inductive seismometer. (b) Capacitive sersmographs. The condenser (or radio) seismograph has been applied in various countries for refraction work, and it is used in this country for reflection work by one or two companies. Various ‘‘radio”’ seismographs have been described by Haeno® and Hée.” A condenser seismograph, suitable for application in reflection work, is shown diagram- matically in Fig. 9-116. The oscillatory circuit and tube are closed in the detector box, with the seismometer mass acting as the movable plate of a variable condenser. A quadruple cable supplying A and B voltage goes from the detector to a three-stage—resistance coupled amplifier, which is coupled through a*transformer to an oscillograph or string galvanometer. A detailed discussion of the condenser type detectors has been given by Irland. Various mechanical seismometers of the horizontal and vertical type were equipped with a capacitive transducer changing the phase of two coupled oscillators.” Simultaneous shaking table and instrument 82 Japan. J. Astron. and Geophys., 8(2), 39-50 (1931). 68 Union Geophys. Trav. Sci. A(9), 1933. 64 G. A. Irland, A Study of Some Seismometers, U. S. Bur. Mines Tech. Paper No. 556 (1934). 6° U. S. Bur. Mines Tech. Paper No. 518 (1982). CHapP. 9] SEISMIC METHODS 611 Hetiand Research Corp. Fic. 9-114. Portable seismic four-channel apparatus. A, Four-channel amplifier; B, blaster; C, camera with timer, dry-cell operated; D, daylight developing tank; E, detectors. ling il We (a) (b) Fig. 9-115. Reluctance detectors. records showed that a capacitive detector of proper frequency and damping adjustment records sustained ground motion and transients accurately and in proportion to the ground displacement. In the course of the experi- 612 SEISMIC METHODS [Cuap, 9 Detector Aaplitier Fig. 9-116. Condenser seismograph. RARVAARAR Baws use = WO We (LLL LLL (a) (0) (c) Fig. 9-117. Ambronn accelerometer-refraction sesimograph (partly after Sifieriz). ments a compensated-spring-type vertical seismometer was developed, which resembles in construction the La Coste” instrument. 66 J, J. B. La Coste, Physics, 5, 178 (1934); and Seis. Soc. Amer. Bull., 26(2), 176 (1935). Cuap. 9] SEISMIC METHODS 613 (c) Pressure seismographs. Modifications of the carbon microphone were employed in the days of refraction shooting and are still in use in some civil engineering applications. They have definite limitations because of high noise level and packing. Their use for reflection work has been vir- tually abandoned. The I.G.E.S. employed a Western Electric mining detector of the carbon type for shallow refraction applications” in con- nection with a string galvanometer recorder. They further used a hot wire seismograph, consisting of a geophone in which the air displaced by the movement of a diaphragm of fairly large diameter is forced through a small orifice. In this orifice a platinum wire heated by a battery is located and is cooled by the air flowing past it. The wire grid is arranged in one arm of a Wheatstone bridge, the indicating device (string galvanometer) is in the center arm of the bridge, the re- sistance of the wire being varied in pro- portion to the velocity of the motion of the air.” The Ambronn accelerometer which was used extensively in the earlier refraction + work, notably by Sifieriz in Spain (see Fig. B 9-117a), is likewise based on variations of a resistance due to ground vibrations. The mass is suspended from two springs; two contact points are arranged on the mass and on a beam balanced on a knife edge. The position of the beam and, therefore, SSS the contact pressure may be controlled from saa the recording truck by varying the current through a solenoid surrounding an armature on the beam. The contacts are arranged in a Wheatstone bridge, as shown in Fig. 9-117b. Individual string galvanometers ° eitieiaie V4T+ of high sensitivity are used at G to record the ae variations in acceleration. Thecritical pres- 8 SSW sure on the contact is adjusted on a control py, 9-118. Crataleaetee tan panel in the recording truck by the circuit with preamplifier. shown on the left side of Fig. 9-117b. A quadruple cable is required from the truck to each detector. Piezoelectric or crystal detectors have been used for both refraction and reflection applications. A crystal detector with preamplifier is illustrated in Fig. 9-118. A piezoelectric receiver and equipment suitable for refrac- tion and reflection applications was described by Ambronn.” TO AMPL. SSY SSS SS SSS SSS SSSA SSS SS 67 See p. 212 of Edge and Laby’s report. 68 See Figs. 152, 260, and 261 in Edge and Laby. 69 World Petrol. Congr. B.I., 165-168 (London, 1934). 614 SEISMIC METHODS [CHap. 9 F. PHotoGraPHic REecorDinG; TIME MaRKING In station seismographs, most recording is done mechanically by pens writing white lines on blackened paper fastened to a drum. The drum rotates and is shifted sideways by a thread cut on the drum shaft. Time marks are recorded by means of the pens being lifted or shifted by an electromagnet actuated from a contact chronometer. In light-weight station seismometers, such as the Wood-Anderson seismograph, and in galvanometric recording instruments, such as the Benioff and Wenner seismometers, records are taken photographically on sensitized paper. Time marks are provided by interrupting the light beam with a shutter actuated from an electromagnet or by deflecting the trace for a short in- terval by a mirror or prism mounted on a relay connected to the contact. chronometer. Both mechanical and photographic recording is used in vibrographs, depending on the-sensitivity of the instrument. In some types the record is made on celluloid strips by a pointed needle and is inspected under a microscope. Disk recording has not been applied in seismology. In high-speed recorders time marks are projected by me- chanically started vibrating reeds with shutters, or by electrically sus- tained indicators (galvanometers, reeds, oscillographs) driven from tuning forks or V.T. oscillators. In virtually all prospecting seismographs, records are taken photo- graphically on rapidly moving paper varying in width from 2 to 6 inches. To obtain good quality of reproduction, attention must be paid in the field to the proper concentration, temperature, and freshness of the developing and fixing solutions.” The speed at which the paper travels is about 3 to 10 centimeters per second in refraction recording and 30 to 40 centi- meters per second in reflection recording. Provision is usually made for simultaneous visual observation and photographic recording. This may be done by splitting the reflected light beam, by providing separate inci- dent and reflected beams for the visual and photographic system, or by viewing the light spots from the rear of the camera through paper. Even paper speed increases the accuracy of record evaluation ; hence, the recorder drive is usually equipped with a fairly elaborate governor. Time marking may be accomplished in various ways. In recorders used with mechanical seismographs, a small pendulum provided with a shutter arrangement is set in motion at the instant of firing. In reflection cameras, a reed of higher frequency (50 cycles) electrically sustained from a tuning fork or vacuum tube oscillator may be used. This has a shutter arrange- ment to project dashes on the paper (if the reed is mounted close to the paper), or to project time lines across its entire width (by reflecting light 70¥, A. Tompkins, Geophysics, 1(1), 107-114 (Jan., 1936). Cuap. 9] SEISMIC METHODS 615 from a mirror attached to the reed to a stationary mirror and thence to the cylindrical lens). Instead of a reed a regular galvanometer may be used to project a time wave on the record. This is the method used for calibrating time lines with a standard fork (see below). Another con- venjent -way of projecting time lines across a record of almost any width is to mount a neon tube close to the paper and to connect it to an elec- trically driven tuning fork through a high tension step-up transformer. An arrangement now in very common use is a synchronous motor driven by a tuning fork. To its shaft is attached a spoked wheel for shadow recording, or a slotted drum for black on white recording. This gives the possibility of making every fifth and tenth time line heavier, which simpli- fies evaluation of the record. Finally, a tuning fork alone may be used te project time lines across the paper by attaching shutters to its tines and projecting a light beam through them onto the cylindrical lens. In all timing devices, reeds and forks must be compensated for tempera- ture or be made of metals of low temperature coefficient of elasticity. Timing devices in field recorders should be checked once a month against a standard tuning fork which should be so arranged that it may be readily connected to one of the regular galvanometers in the recording camera. G. CALIBRATION OF SEISMOGRAPHS In station seismology, the calibration of instruments is a comparatively simple matter and involves determinations of natural period, friction, and damping. Natural frequency and friction may be obtained from free vibration records with damping disconnected; damping is determined from the ratio of consecutive amplitudes with damping mechanism connected. The static magnification V of a seismograph may be obtained by adding a known mass m, and measuring the deflection a of the pen. Then V = amwo/mg, where m is the mass and a the natural frequency of the seismograph. For electrically recording instruments, determination of galvanometer characteristics and transmission constant is necessary in addition to the calibration of the seismometer. Galitzin” has described this procedure in detail. The calibration of the mechanical prospecting seismograph proceeds in essentially the same manner as calibration of station seismometers. Natu- ral frequency, friction, damping, and magnification are determined as discussed above. Calibration of electrical prospecting seismographs is rendered more elaborate because it has to extend not merely to one, but to as many units as there are recording channels. Further, requirements 1B. Galitzin, Vorlesungen weber Seismometrie, Chaps. 6 and 7, Teubner, (Leipzig, 1914). See also F. W. Sohon, Introduction to Theoretical Seismology, Wiley (1932). 616 SEISMIC METHODS [Cuap. 9 for reflection seismographs are more rigorous than for refraction seismo- graphs because not merely the first but later impulses have to be recorded as faithfully as the particular geologic situation requires and must be balanced in regard to both amplitude and phase. The following section deals chiefly with the calibration of electrical reflection seismographs, that is, calibration of pick-ups, amplifiers, and galvanometers and determina- tion of over-all response. 1. Detectors. Both mechanical and electrical characteristics must be determined. The former include: (a) natural frequency, (b) deflection (geometric magnification), (c) friction, and (d) damping. The natural frequency of the detector may be determined in a number of ways. A mirror device” may be attached to the mass of the seismograph, and its free vibration may be recorded on a laboratory camera provided with a timing mechanism. For this test damping must be eliminated. If electromagnetic damping is applied it should be disconnected. From the record, natural frequency and friction may be determined as previously described. The natural frequency may also be obtained from the reso- nance frequency by (a) driving the seismograph with an electrical oscillator, or (b) by observing its mechanical or undamped electrical response on a shaking table. Mechanical deflection tests make it possible to determine the static sensi- tivity and thus the static magnification of detectors. A small mass is placed on the seismograph mass. Its deflection is observed as stated above, or the deflection of the magnification lever is observed by a micro- scope or mirror device. For the determination of damping, overshoot records are best suited, since the detectors are usually critically or near-critically damped. Damp- ing may be determined also from the shape of the dynamic response curve of a detector taken on a shaking table. Possibly simpler is the procedure of driving the detector from a beat oscillator with constant input at varying frequencies. This will result in a dynamic response curve of a force-driven device, from which the damping rate may be determined. Damping tests should be made for various oils and various temperatures unless an electromagnetically damped detector is used. Virtually the only important electrical characteristic of a detector is its output for a given ground amplitude and frequency. It is best defined in units of open-circuit volts per micron ground motion (see Fig. 9-105). Since it depends on the impedance of generator and load, detectors of different impedances can be compared only by using a matching trans- former whose secondary may be coupled directly to a vacuum tube volt- 72 For the details of these and other seismograph calibration methods see Heiland, op. cit., 434454 (1934). Cuap. 9] SEISMIC METHODS 617 meter grid to give open circuit voltage. With a shaking table, the var- iation of voltage output with ground frequency may be obtained; the amplitude of the table may be measured by various means described in the literature on shaking tables.” A quantity related to the voltage output is the electrical sensitivity of a detector when it is used as a motor. This is the mechanical deflection for a given current input and is thus proportional to Galitzin’s transmission constant, inasmuch as it includes the circuit characteristics and the strength of the magnetic field in the detector. However, this is a test that will give only qualitative comparisons of detectors with similar circuit characteristics. Being a static determination, it is inferior to a shaking- table test. 2. Amplifiers. In radio practice it is customary to rate amplifiers in terms of decibel gain. A test to determine gain can also be applied to seismograph amplifiers by using a fixed voltage input and determining the output on a vacuum tube voltmeter. Output should be measured in the plate circuit of the last tube, inasmuch as with most galvanometers a stepdown transformer is used. The gain so measured is useful for relative comparisons only; for seismograph amplifiers it is more convenient to measure gain together with galvanometer response as described below. 3. Galvanometers. Quantities characterizing the action of seismic galva- nometers are natural frequency and damping and static (D.C.) sensitivity. Together they determine the dynamic response. The natural frequency of the galvanometer may be determined from free oscillations by pluck- ing it or giving it an electrical impulse after removing or disconnecting the damping. This test may be made in the regular camera. Possibly simpler is a determination of the resonance frequency by using a beat frequency oscillator. Damping is obtained from overshoot records or from a dynamic response curve. The static sensitivity of a galvanometer is determined by observing the scale deflection for a given current, visually or photographically. If an even rating of galvanometers of different con- struction is desired, their natural frequency, impedance, and optical lever must also be considered. The D.C. test of a galvanometer will generally show whether the unit is performing properly and whether friction is present without requiring a separate friction test. 4. Combined amplifier and galvanometer response. This test has several advantages over separate amplifier and galvanometer tests: (a) the re- sultant response can be obtained more nearly quantitatively and in terms more closely related to the practical application (galvanometer deflection for a given voltage input of a given frequency); (b) tests for quiet operation 73 Heiland, op. cit., 454 (1934), (bibliography on shaking tables). 618 SEISMIC METHODS [CHap. 9 are readily made; (c) tests can be made in the recording truck to determine whether coupling with timing or shot instance transmission circuits, and the like, is present. , The combined amplifier and galvanometer response is measured in terms of galvanometer deflection for constant signal input. By varying the fre- quency of the signal, the combined amplifier and galvanometer dynamic response is obtained. This test should be made for all possible filter positions. 5. Over-all response. The over-all response of an entire seismic channel is measured by placing the detector on a shaking table, connecting it to its amplifier and galvanometer, and measuring the galvanometer deflection for a given ground amplitude at varying frequencies. Measurements are made for the various filter positions and for various settings of gain con- trols in amplifier and galvanometers to determine effects of automatic volume control devices, if these are incorporated. 6. Various other tests of seismic equipment include tests of the timing system by standard forks, parallax tests to determine time lag between shot instant record and galvanometric record, and phase tests. When all component parts of a recording channel have been balanced properly in respect to their mechanical and electrical characteristics, phase differences should not occur. Whether and to what extent they exist may be deter- mined by a phase shot, that is, a reflection shot taken with all receivers set together closely at the same location. Fig. 9-119 shows a phase shot made with a 12-channel apparatus. i NY ANAL ALIARY My iM AN TEMAAVAU NAAT SN BMANDKAUEENAL (|\APABA\ASUANNGNGQANT ANNAN g\UAA EO UAIAVANATANBANAVANATAUNQUUANGAUANGGERUEURUADZ yan gey yA UesUsUA LEA UOTRSEORL Ga AS ATR AA A Ve PORN EN TINEA AACR | URI MARTA HIN NAVA MRA ERAT RATA AMR AN HY NAP AAGAARREAN NL WENT NAAT VAY NH HAY YA NAA WMH MM AV UAHA AAA AAA ] VANIER Mu HE IAL UH AEA AE ATA AMAR AU 111118 Fig. 9-119. Twelve-element alignment record. | Ze) ELECTRICAL METHODS I. INTRODUCTION A. FUNDAMENTALS Execrricat PROSPECTING in the most general sense may be defined as prospecting by electricity for mineral deposits and geologic structures. Contrary to geophysical methods previously discussed, each of which makes use essentially of one field of foree—gravitational, magnetic, or elastic— there is much greater variety in the type of electrical fields and in methods of observation employed in electrical prospecting. First, an ore body may act as a battery and furnish its own electrical field; second, the ground under test may be energized by extraneous fields and the reaction of sub- surface conductors to such fields may be measured. Both direct current and alternating current are used; the latter gives not only greater sensi- tivity but additional physical quantities, which helps in the interpretation of the results. Direct current can be introduced into the ground only by galvanic contact, but alternating current can be applied by both contact and inductive coupling. The resulting fields are measured by instruments making contact with the ground by electrodes, or by employing inductive coupling with reception frames. Thus, in reference to: observation meth- ods, electrical methods may be divided into potential and electromagnetic methods. Electrical exploration uses a wide range of frequencies. Those from 5 to about 100 will be referred to herein as low frequencies, from about 200 to 1000 cycles as intermediate, from 10 to 80 kilocycles as high, and from about 100 kilocycles to several megacycles as radio frequencies. Low frequencies are applied in potential methods, intermediate frequencies in both potential and electromagnetic methods, high frequencies in electro- magnetic methods, and radio frequencies in radio methods, Since depth penetration decreases rapidly with frequency, the practical utility of high and radio frequencies is limited. With the exception of the self-potential method, electrical prospecting falls in the group of indirect geophysical procedures which involve an 619 620 ELECTRICAL METHODS SYMBOLS USED IN CHAPTER 10 Shoes ia) GS. Ses ie ss “Nescas ove i] RN MYCE ROVSENRY QTHHQ "Ss (~7) € ee ee ee eee ee eee eee — ee distance, radius, semiaxis distance, semiaxis constant distance, depth electrical charge frequency height, depth, thickness current density v-1 reflection factor distance, length electrical, magnetic moment valency adsorption potential ratio radius, distance distance, thickness time volume coordinate coordinate coordinate capacity difference electromotive force Faraday constant gravitational constant current diffusivity (of heat) inductance mutual inductance turns (solution) pressure quantity (of heat) resistance time constant vector potential potential reactance impedance angle angle ellipticity mt BwHvawp “mugdertunr gop gor a b c ™ Boa om ARARN KD qHaoynnovaer factor coefficient light velocity 2.718 conductance capacitive susceptance number number; factor ion mobility factor number factor factor ratio specific heat absolute temperature ratio velocity viscosity reading reading factor factor ion concentration displacement electrical field strength field magnetic field strength factor factor factor polarization factor radius, distance gas constant surface, area total field factor horizontal field component horizontal field component vertical field component dissociation coefficient coefficient density electrical susceptibility [Cuap. 10 Cuap. 10] ELECTRICAL METHODS 621 SYMBOLS USED IN CHAPTER 10—Concluded angle 6 temperature anisotropy dip dielectric constant wave length decrement micro- u permeability 3.141 resistivity n distance, radius conductivity | (phase) angle | angle angular frequency i i 2) excitation and consequent reaction of subsurface bodies and are not based on spontaneous effects like the magnetic and gravity methods. It is a common characteristic of these indirect methods that the depth from which reactions are obtained can be controlled by the spacing of the transmitting and receiving points. Most potential methods (resistivity and potential-drop-ratio methods in particular) have distinct depth con- trol and are in many ways comparable to seismic refraction methods. Electromagnetic, most inductive, and equipotential methods have com- paratively little depth control. The spontaneous polarization method lacks depth control completely. Physical quantities measured in electrical exploration vary greatly and depend largely on the method applied. In the self-potential, equipoten- tial, resistivity, and potential-drop-ratio methods, results are obtained in the form of electrical potentials or potential differences (sometimes referred to the primary field in regard to amplitude and phase) and in the form of ratios of adjacent potential differences. In electromagnetic methods the magnetic field produced by the currents flowing beneath the surface is determined either semiabsolutely (in reference to the phase and amplitude of the excitation current) or in the form of ratios and phase differences of the fields on successive points. Essentially, therefore, the purpose of po- tential methods is a determination of direction and intensity of the elec- trical field, whereas in electromagnetic methods direction and intensity of the electromagnetic field is measured. Measurements of electrical and elec- tromagnetic fields are made by contact probes and coils. Null methods and bridge arrangements are employed extensively for the determination of the direction of current flow, of voltages, voltage ratios, intensities, and intensity ratios. Potentials and potential gradients are expressed in volts or millivolts absolute or in volts or millivolts per unit distance. Results of resistivity 622 ELECTRICAL METHODS [CHap. 10 measurements are given in units of ohm-meters or ohm-feet. Potential ratios are plotted against horizontal distance or equivalent depth. Elec- tromagnetic fields are measured absolutely in microgauss (1.10°° gauss) or semiabsolutely in units of microgauss per ampere primary (loop) current. The fields are represented by their in-phase and quadrature components or by the value of the total vector and its phase. Ratio measurements likewise furnish the in-phase and quadrature components of the electro- magnetic field or its amplitude and phase by successive multiplication or addition respectively along a continuous traverse. In electrical prospecting, as in other geophysical methods, the distinct- ness of surface indications depends on the contrasts in the physical prop- erties of geologic bodies and their surroundings. The following properties are involved: electrochemical activity, conductivity, dielectric constant, and permeability. Comparatively little is known about electrochemical and dielectric rock properties and geologic factors controlling them; more extensive information is available on rock conductivities. While in most other geophysical methods the distinctness of surface indications in- creases in linear proportion with differences (or ratios) of the rock proper- ties involved, this is not true for all electrical prospecting methods. In potential methods, a saturation effect is encountered, so that indications from large differences in conductivity are not proportionately stronger than indications obtained from small differences. Therefore, potential methods are particularly suitable for the detection of small differences in conductivity. The same appears to hold for electromagnetic methods with galvanic power supply. Inductive methods, on the other hand, are controlled by absolute conductivities and are therefore best suited for the detection of very good conductors. Continuity of physical properties is an essential characteristic for the usability of any geophysical method. In those electrical methods that are used for the purpose of determining depths of horizontal formations (re- sistivity, potential-drop-ratio, and inductive methods), it is necessary that these physical properties remain continuous in a horizontal direction since the spacing of transmitting and receiving units is changed horizontally to obtain increased depth penetration. In the application of electrical meth- ods to ore location, these requirements are not, and need not be, fulfilled since horizontal discontinuities in conductivity are the object of detection. To obtain distinct results it is, of course, desirable that the physical prop- erties remain fairly continuous vertically and in the strike of an ore body. As in other geophysical methods the uniqueness of interpretation of elec- trical prospecting results depends on the ease with which interfering factors can be eliminated. Terrain, for instance, affects the surface potential methods much more than it does the electromagnetic methods. High Cuap. 10] ELECTRICAL METHODS 623 frequency and radio work is greatly handicapped by terrain because of the refraction of the wave front on the ground surface. There is no satis- factory way of correcting for terrain effects in potential, high frequency, and radio methods except by small-scale model experiments. Electro- magnetic and inductive methods are comparatively free from terrain effects. Field components can be measured in reference to the terrain surface, and its disposition relative to subsurface conductors can be taken care of geometrically in the interpretation of the results. Interferences of a geologic nature that may seriously affect the interpretability of electrical results include mineralized solutions in formations and on fissures, and rocks impregnated with noncommercial minerals, such as graphite and pyrite. In some electrical methods (such as the spontaneous potential, the equipotential-line, and those electromagnetic methods in which only the direction of the field is determined) interpretation is merely of a qualitative nature; that is, it is concerned only with locating areas of anomalous indi- cations. Depth determinations with these methods are generally not possible except in simple cases where the depth may be estimated or calcu- lated from the shape of the anomaly curve. However, absolute depth determinations are possible where vertical changes in conductivity are ob- tained by varying the spacing between transmitting and receiving units (resistivity and potential-drop-ratio methods). In some inductive meth- ods, depth calculations are made indirectly by comparing the field data with type curves calculated for various possible depths of subsurface con- ductors. More often, however, recourse is had in the interpretation of electrical results to small-scale model experiments. Progress and development in most geophysical methods have been largely the result of preceding developments in geophysical science. In gravitational, magnetic, and seismic methods field procedure and methods of observation are closely allied to those used in pure geophysics. Elec- trical methods lacking this background have followed their own course of development. Electrical prospecting methods have three fields of application: oil ex- ploration, mining, and engineering geology. In oil exploration, surface potential, resistivity, potential-drop-ratio, “‘Eltran,” inductive, and elec- trochemical methods have been used to delineate structure. The most widespread use of electrical methods is made in oil exploration in the process of ‘electrical logging.”’ ,This is a modified resistivity method and involves running a continuous resistivity record in uncased wells with an electrode assembly of fixed spacing. Since their early stages of development, electrical methods have been applied in mining exploration. At first this work was almost entirely 624 ELECTRICAL METHODS (Cuap. 10 confined to the location of sulfide ores. Soon this was supplemented by structural investigations. Lately the field has been extended to the loca- tion of such poor conductors as gold quartz veins and the determination of gold content in placer deposits. In the field of civil engineering, appli- cations of electrical methods have been ever increasing in number, applica- tions including determinations of depth to bedrock on dam and tunnel sites; harbor investigations; location of materials for highway, railroad, and dam construction; location of water-bearing formations and of buried metallic objects, pipes, corrosion, ammunition, and the like. B. CLASSIFICATION OF ELECTRICAL METHODS The classification adopted here distinguishes three groups of methods. In the first, ground potentials and, in the second, the electromagnetic fields of the ground currents are determined. A third group includes radio methods and treasure finders. 1. Potential methods may be divided into (a) self-potential, (b) D.C. and A.C. equipotential-line and potential-profile, (c) resistivity, (d) potential- drop-ratio, and (e) electrical-transient methods. (a) In the self-potential method the electrical field is furnished by the electrochemical polarization of ore bodies and other geologic formations. The electrical field is investigated by surveying lines of equal-potential or potential profiles. It has been found that not only sulfide ore bodies but also metals in placer deposits, faults, corroded pipe lines, and the migration of subsurface waters cause such electrochemical phenomena. Spontaneous potentials likewise occur when solutions of different character (for ex- ample, drilling fluid and formation water) come in contact with one another. Electrofiltration potentials are produced by the movement of water in porous formations and are used, together with the concentra- tion potentials just mentioned, to indicate the porosity of beds in electrical logging. (b) In this group direct or alternating current is impressed on the ground. _ The primary electrodes may be pointed or linear. The potential distribu- tion between them is studied by measuring equzpotential lines or by sur- veying potential profiles. D.C. methods require the use of depolarized electrodes and potentiometers. In A.C. methods equipotential lines, strictly speaking, do not exist but can be surveyed when out-of-phase components are not too large. A more exact method is the determination of potential differences according to magnitude and phase by a bridge compensator in which a reference voltage is carried to the instrument from the generator, is varied in phase and amplitude, and is balanced against the unknown voltage difference. Sulfide ores may be located and structural and stratigraphic conditions may be studied by these methods. Cuap. 10] ELECTRICAL METHODS 625 (c) In resistivity methods current is supplied to the ground at two points and the potential is measured between two additional points whose spacing or distance from the primary electrodes is varied. The ratio of voltage and current, multiplied by a spacing factor, gives what is known as ap- parent resistivity as a function of spacing and, hence, as a function of depth penetration. This application makes possible a determination of depth to bedrock, to sulfide ore bodies, to water level, and to beds of stratigraphic significance. If the spacing (and therefore the depth pene- tration) is kept constant and the arrangement as a whole is moved, hori- zontal variations in character or in depth of a given formation may be determined. An adaptation of this procedure is the process of electrical logging discussed in further detail in Chapter 11. (d) The potential-drop-ratto method involves a comparison of voltage differences with reference to magnitude and phase in successive ground intervals. This method is also applied to a determination of depth of horizontal and vertical formation boundaries. Although the potential- drop-ratio method has greater resolving power in determination of strati- fied formations than the resistivity method has, it is best adapted to an investigation of vertical formation boundaries, that is, to the location of ore bodies, quartz veins, and the like. (e) Eltran (transient) methods derive their name from the fact that, not quasistationary fields, but transients are studied. The so-called electro- chemical method measures the time that elapses between the application of a current impulse and the peak of the polarization current released by the primary impulse. This time interval is said to be dependent on the electrolytic properties of the formations affected. In the “‘Eltran’’ methods proper, a current impulse is impressed on the ground, and the time decay of the corresponding potential impulse is determined. The time constant is primarily dependent on the resistance characteristics of the ground circuit. 2. Electromagnetic methods may be classified according to the manner in which the currents, whose electromagnetic field is measured, are caused to flow in the ground. In electromagnetic galvanic methods, current is supplied by grounded electrodes. In electromagnetic inductive processes, currents are induced to flow in subsurface conductors by insulated loops or cables. A sharp line cannot be drawn between these methods because there are some that employ either power supply. It is difficult to classify the various electromagnetic methods except to enumerate them by name: (a) The Lundberg-Sundberg methods involve the measurement of hori- zontal and vertical field components with compensator devices giving their in-phase and quadrature constituents in reference to the primary field supply. (b) Ambronn’s method employs a similar arrangement, ex- cept that the compensator gives the phase and magnitude of three field 626 ELECTRICAL METHODS [Cuap. 10 components. (c) In the Miller method the out-of-phase components are made negligible by the use of 60-cycle power, so that the vector amplitude may be measured without reference to its phase by a vacuum tube volt- meter arrangement connected to the pickup coil. (d) The Elbof method measures merely the direction of strike and dip of the ellipse of polarization. The next three methods are closely related: (e) Bieler and Watson use two coils in fixed arrangement. One is vertical, the other horizontal; the latter picks up the vertical field component produced by the primary loop, whereas the vertical coil responds to the horizontal out-of-phase com- ponent produced by subsurface current concentrations. (f) Some of the electromagnetic-ratio methods utilize two independent coils connected in series through an amplifier detector. One coil remains fixed in direction on one station while the other, at a second location, is rotated until balance is obtained, the angle of rotation corresponding to the difference in in- tensity and phase angle. Other electromagnetic-ratio methods make use of ratio bridges by which the voltages induced in two coils (usually held horizontally to measure the vertical component) are balanced for phase and amplitude. The four remaining procedures are generally referred to as truly in- ductive: (g) In the Sundberg method a large rectangular loop is laid out, and the horizontal component is measured across one cable. Due to the “reflection” of the cable on subsurface conductors, the depth of the latter can be determined from the shape of the anomaly curve. The real and imaginary components of the horizontal field components are measured with a compensator. This method is primarily applicable to structural studies. (hk) Another procedure known as the ring induction method uses a circular primary loop of small diameter laid out concentrically with a smaller secondary horizontal coil. The effect of the primary coil on it is compensated by an auxiliary coil, and the secondary fields are measured according to phase and amplitude. By varying the radius of the ring it is possible to reach different depths and to calculate the resistivities of formations at these depths. (2) In the Mason method the primary field is produced by a vertical loop, and strike and dip of the secondary field are measured with a search coil. (j) The high-frequency Radiore method utilizes a similar arrangement, except that the primary field is produced by a circular loop of comparatively small diameter. The dip of the field resulting from a combination of the primary and secondary components is determined with a search coil. With the exception of the Sundberg-inductive, the Miiller, and the ring- induction methods, electromagnetic methods are applied principally in the location of sulfide ore bodies. The methods mentioned as exceptions have been used chiefly for structural and stratigraphic studies. Cuap. 10] ELECTRICAL METHODS 627 3. Radio methods and “‘treasure finders.’’ Radio measurements fall into two natural groups. In the first, the reaction of a transmitter to changes in surrounding media is determined. Methods in the second group measure the effect of the media, situated between transmitter and receiver, upon the latter’s reception characteristics. The quarter wave method is based on the fact that when a reflecting surface is at a distance of one quarter of the wave length from the transmitter, a maximum of the emission occurs. Hence, the depth of such reflecting surfaces as water under dry surface beds, or flat-lying ore bodies in dry formations, may be _found by varying the frequency and observing the antenna current. In- asmuch as the antenna capacity is affected by the proximity of conductors, they may be located by changes in wave length and damping. This method has no depth control and, therefore, interpretation of results is difficult except when geologic conditions are simple and interferences from noncommercial conductors are absent. Application of radio methods in the second group requires a transmitter and receiver, and measurements are made on the receiving side. By absorption measurements, ore bodies in dry country rock have been out- lined from underground workings. With the interference method depths to reflecting surfaces may be determined by observing the change of in- tensity of reception with horizontal distance. The direction of the inci- dent beam is measured in the reflection method by a search coil. Treasure finders may be divided into low and high frequency devices. The former are modifications of induction balances. In one of these, one energizing coil and two pickup coils are arranged on the same coil frame. Presence of metallic bodies changes the mutual inductance between the lower pickup coil and the primary coil. Instruments of this type have been found useful in locating fairly small buried metallic objects such as bombs. In another device two search coils a few feet apart are in a balanced bridge circuit and energized with current of intermediate fre- quency. The inductance change resulting from metallic bodies near one coil is measured. The depth range of low-frequency treasure finders does not extend far beyond five feet. High frequency treasure finders are (1) beat frequency oscillators, and (2) combinations of transmitters and receivers. In the former the fre- quency of one oscillating circuit remains fixed; that of the other varies with the proximity of conductive bodies. This changes the beat note or the plate current in a third circuit. The depth penetration of these devices does not exceed fifteen feet. In treasure finders consisting of a transmitter and receiver combination, intensity of reception is indicated by a plate current meter, and a compensating circuit is provided so that for barren ground the normal intensity gives a zero reading. The reading changes 628 ELECTRICAL METHODS [Cuap. 10 with the presence of conductive bodies. ‘Two commercial treasure finders, the ‘‘metallascope” (Fisher) and the “‘terrometer’’ (Barret), operate on this principle. The terrometer is reported to be sensitive enough to detect mineral disseminations in shallow placers to a depth of fifteen or twenty feet. II. ELECTRICAL PROPERTIES OF ROCKS It is the function of electrical prospecting methods to measure the distribution of natural and artificial potentials, of electromagnetic fields, and of the propagation of radio waves. This variety of electrical phe- nomena causes not merely one but a number of physical properties of geologic bodies to be significant. They are: (1) electrochemical properties, giving rise to (a) spontaneous and (b) polarization potentials; (2) electrical conductivity ; (3) dielectric constant; and (4) magnetic permeability. Of these, the electrical conductivity is undoubtedly the most important. Strietly speaking, none of the above properties are constants but depend on other factors, mainly frequency. A. ELECTROCHEMICAL PROPERTIES Electrochemical effects are responsible for the electrical field surrounding chemically polarized ore bodies; they give rise to interference potentials when metallic electrodes are placed in contact with moist ground; they produce electrical potentials when solutions of different concentrations come in contact with one another in wells or when a solution is forced through a porous medium; and, lastly, they give rise to counter e.m.f.’s when current is applied to the ground. The first three of these effects do not depend on extraneous electrical fields and are therefore called spon- taneous potentials, or, more specifically, (a) electrode potentials, (b) diffu- sion potentials, and (c) electrofiltration potentials. Potentials caused by the application of an electrical field are called polarization potentials. 1. Spontaneous potentials. (a) Electrode potentials. When a metallic electrode is placed in a solution it acquires a potential difference against the solution which, however, cannot be measured except by placing a second electrode in the liquid. If the metals of the two electrodes are alike and if the concentrations of the solution at the two contact points are the same, no potential difference between the two electrodes is observed. A potential difference occurs, however, if either the metals or the concen- trations are different. Practical application of this principle is made in electrical prospecting (1) in the so-called activity of ore bodies, which is due (a) to their contact with solutions of different character and concen- Cuar. 10] ELECTRICAL METHODS 629 tration near the surface and below, and (b) to differences in ore material above and below; (2) in the interference potentials which originate on metal electrodes when the latter make contact with the ground at points where the concentrations of electrolytic solutions are different; (3) in the construction of nonpolarizable electrodes. Potential differences resulting from the contact of two electrodes with solutions of different concentration may be calculated from the potential of a metal against a solution, which is dependent only on the concentration of the ions of the particular metal. The potential difference of solution minus metal is / B= Rt log. (10-1a) where R is the gas constant, or 8.309 joule per degree C.; n is the valency; F is Faraday’s constant of electrolysis, that is, the quantity of electricity liberating one gram equivalent, or 96,494 coulombs (so that the ratio R/F is 8,610 e.m.u.’s or 0.861-10~* volts); t is the absolute temperature, or 273° + 6, P’ is constant for the metal involved (its electrolytic solution pressure); and C is the ion concentration. If two electrodes of the same metal are immersed in two solutions of different concentration, C2 and C, (which may be connected by a syphon bridge to afford a return circuit with negligible diffusion potential), the potential difference between the two electrodes is AE 1.98.10. © logis © volts, (10-16) n Ci where the numerical factor contains the ratio R/F, the modulus of the natural logarithms, and the conversion of e.m.u.’s into volts. An evalua- tion of the above equation shows that for @ = 18°C. the voltage difference is AE = 1/n-0.0577 - logio C2/C; volts, so that for n = 1 and a concentra- tion ratio of 10, the voltage difference is 0.058 volts and, for a ratio of 100, 0.115 volts. The voltage gradients observed on polarized ore bodies are normally from 1 to 2 millivolts per foot, which amounts to anomalies of the order of 0.1 volt to a maximum of 1.5 volts. This is comparable to the voltage delivered from a wet cell; it is, therefore, probable that not only differences in concentration but differences in the composition of the ore near the surface (gossan!) and unoxidized portions below, where the solutions are less acid and poorer in H ions, play a part in causing such potentials. To explain the phenomenon on ore bodies showing spontaneous polarization, equation (10-1b) should be written in a form allowing for (1) electrode 630 ELECTRICAL METHODS [Cuar. 10 potentials due to differences in solution pressure P’ and (2) differences in concentration : / ria logio tuts volts. (10-1c) n C,-P% AE = 1.98.10 With this equation, voltages are calculated which are in better agree- ment with those actually observed. Under the assumption that there are no appreciable differences in concentration of solution between the upper and the lower parts of the ore body, eq. (10—1c) retains the form AK = c-logio Pi/P2 , which gives potentials sufficient to account for the anomalies measured at the surface. Pyrite in undisintegrated form is likely to have a solution pressure of around 10’ atm. and in altered form (such as limo- nite, and the like, in the gossan) probably not more than 10° atm. The equation in its last form makes it possible to allow for equivalent series connections of altered and unaltered portions of an ore body. Electrode potentials occur when metal probes are placed in contact with the ground in order to measure potential differences between them. Con- tact potentials amounting to several millivolts and even several tens of millivolts may be observed and may be avoided by the use of so-called nonpolarizable electrodes. The latter consist of electrodes (of the same metal for a pair) immersed in a saturated solution of one of its salts (copper in copper sulfate, zine in zinc sulfate, and so on). The solutions are carried in vessels made of a permeable substaice (porous clay or beef gut) so that they may filter through and make contact with the ground solu- tions. Inasmuch as identical metals and identical solutions are used for both electrodes, the electrode potentials are of equal sign and cancel when no current is flowing. Potentials arising from direct contact of metal with soil solutions of different concentrations are avoided by the interposition of a concentrated solution. To obviate diffusion potentials (see paragraph b), some investi- gators have proposed the use of two chambers, an inner one with the saturated solution and an outer chamber with a more dilute solution. Upon the passage of current, the polarization (see paragraph 2) of these electrodes is negligible; since metals in solutions containing their ions belong to the “reversible” systems, a passage of current will form no new chemical compounds. What polarization occurs is due merely to concen- tration changes in the solution near the electrodes. In the practice of electrical prospecting this concentration polarization is small because of the small current densities involved. Nonpolarizable electrodes are neces- sary in all D.C. methods of electrical exploration; in A.C. procedures ordinary metal electrodes are satisfactory. (b) Diffusion (osmotic) potentials occur in wells in connection with po- Cuap. 10] ELECTRICAL METHODS 631 rosity measurements. They are produced by the contact of fresh-water drilling mud with the saline connate water solutions in sandy or other porous layers. Theoretically, the e.m.f. generated between two solutions of the ion concentrations C; and Ce is given by R t ly rt Ic Ci AE = —.--- -log. — e.m.u. = 1.98.10°**. la — le C, ae ean C, logio — volts, la + Ic C; (10-2) where 1c and 1, are the mobilities of the cation and anion, and n is their valency. For a NaCl solution, for instance, n = 1, lc/(Ile + la) = 0.4 and 14/(lc + l4) = 0.6. Therefore, the diffusion potential at standard temperature H = 11.6 logiy Ci/C2 millivolts. If C; = 10C2, the potential difference is 11.6 millivolts. Inasmuch as the concentrations are inversely proportional to the resistivities of the drilling mud (2) and the formation water (1), p2/p1 may be substituted for C,/C., and therefore AE = 11.6 -logio p2/p1 millivolts. (c) Electrofiltration potentials are likewise important in the measurement of porosities in wells. They occur when a solution of the conductivity o and the viscosity w is forced with a difference in pressure P through a porous medium (or a number of capillaries) with the adsorption potential p (potential of double layer on wall of capillaries, depending on concentra- tion) and the dielectric constant x, so that the potential difference pPk AE = 5 4rWw-o (10-3) It is seen that the potential increases with the fluidity of the liquid and with pressure and, therefore, with the speed with which the ions can be transported. In wells the diffusion potentials are due to the penetration of drilling fluid into porous formations; and they are usually negative and of the order of 0.1 to 0.2 volts. When the drilling mud is of the same composition as the formation solution, electrofiltration potentials are the only ones giving rise to spontaneous polarization. If, however, the ion concentrations of the two liquids are different, both effects are superim- posed on each other, and it is possible that the diffusion potentials over- shadow the electrofiltration potentials in such cases. 2. Polarization potentials are produced by applying an electric field to an electrolyte. They are of importance in some “‘Eltran” methods, in the determination of rock resistivities with D.C., in some applications of the D.C. equipotential-line method, and in connection with the corrosion of pipes. If an electrical field is applied to an electrolyte or rock containing mole- cules in dissociated form, the ions move to the electrodes of opposite 632 ELECTRICAL METHODS [Cnap. 10 polarity, and the liquid becomes polarized. Since matter is transported, differences in concentration result, which in turn give rise to a potential difference. This opposes the potential difference causing the electrical field and is known as the polarization counter e.m.f., EH’. Hence, Ohm’s law, as applied to the passage of D.C. through polarized electrolytes, is often written in the form J = (EF — E’)/R. Owing to the slow speed with which the ions travel, the counter e.m.f. reaches its maximum value but gradually. After the concentration gra- dient between the electrodes has become linear, stationary conditions are reached. The time required for its establishment depends on the distance between the electrodes and the diffusion constant of the electrolyte. The counter e.m.f. cannot exceed definite values for given conditions and solu- tions, but the electrical field can be increased. Hence, in determining resistivities of rocks containing electrolytes, more reliable values can be obtained with high fields.’ The difficulty mentioned may, of course, be avoided by alternating current. B. METALLIC AND ELECTROLYTIC CURRENT CONDUCTION From the viewpoint of molecular physics the following kinds of current conduction may be distinguished: (1) electronic conduction, (2) electrolytic conduction, and (8) dielectric conduction. The first is identical with metallic conduction and is due to the movement of free electrons; the second results from the transport of ions in electrolytes. In the third no free electrons are available. Under the influence of an electrical field the effective centers of electrons and nuclei are displaced. Current propaga- tion results from changes of this polarization or changes in the electrical flux with time and is called displacement current. It will be discussed separately in section c. Metallic conductivity is associated with virtually all minerals of metallic luster, ores composed of those minerals, and impregnations of metallic minerals in crystalline and metamorphic rocks. The best conductors are | the sulfides, a few of the oxides, and graphite. The conductivity of ores and mineral deposits depends largely on the continuity of the conducting particles. Details are given below. Numerical values for the conductivi- ties of minerals and ores will be found in section «4. The fundamental difference between electronic and electrolytic conduc- tion lies in the fact that in the solids no matter is transferred whereas in the electrolytes the current propagation is invariably accompanied by a transport of matter and hence by chemical transformation. In solids 1 See B. McCollum and K. H. Logan, Bur. Stand. Tech. Paper, 25 (1914); M. W. Pullen, U.S. Bur. Mines Circ. No. 6141 (1929). Cuap. 10] ELECTRICAL METHODS 633 conduction of current is accomplished by the “free’’ electrons in the outer- most orbits of the atoms. In gases and liquids, current conduction is associated with ions, that is, molecules combined with electrons or those having a deficiency of electrons, or a positive charge. Because of this association, matter is transferred, that is, deposited at one electrode and dissolved at the other. Hence the name electrolytic (= solvent) phe- nomena. Current conduction in electrolytes depends not only on the mobility but also on the number of ions. The latter, in turn, depends on the concentration and degree of dissociation, which increases with the dielectric constant of the solvent. Hence, water with the highest dielectric constant (about 80) is of great importance in enhancing conductivity. For D.C., conduction in both metallic and electrolytic conductors is governed by Ohm’s law. By it a conductor is defined as having a unit of resistance if the potential difference 1 produces the current 1. Its re- sistivity p is defined as resistance FR referred to unit dimensions. If the length of the conductor is 1, and S its section, k= pats (10-42) Ss Although the resistance of a body of unit dimensions is numerically equal to the resistance of a centimeter cubed, resistivity should not be expressed in ohms per centimeter cubed. Since p = SR#/I, and the square of dimen- sions appears in the numerator and the first power in the denominator, the dimension of resistivity is ohm-centimeter. In the practice of electrical prospecting, the use of this unit often results in comparatively high figures, and the ohm-meter (ohm-cm- 107’) is frequently employed, in addition to ohm-inch (ohm-cm-0.3937), ohm-foot (ohm-cm-0.0328) and kilohm-cm (ohm-cm-10~°). In certain electrical problems it is necessary to convert the practical into electromagnetic or electrostatic units: 1 ohm = 10° e.m.u. = 1.111-10" e.s.u. The reciprocal of resistivity is designated as conductivity o: o=-=2.. (10-45) The unit is the reciprocal ohm-cm or mho-cm. Conductivity is the ratio of current density and electric field strength E: o= 5. . (10-5) This relation follows directly from Ohm’s law. Since V = JR and R = pl/S, dV /dl = (potential gradient or field strength) = E = (I/S)-1/c, with J/S = current density 7. 634 ELECTRICAL METHODS [CHap. 10 In alternating electrical fields the current is not in phase with the e.m_f. Current conduction is controlled by the resultant modulus of resistance and reactance, which is known as impedance. Impedances are customarily represented by conjugate numbers with the resistive component on the real axis, the reactance on the imaginary axis, and the phase shift as the argument of the complex quantity. Although most rock-forming minerals are insulators, it does not follow that most rocks are poor conductors. This is true only if they are solid throughout (such as some igneous rocks and chemical sediments). The majority of rocks and formations are porous, are filled with more or less conductive moisture, and act as electrolytes. Their conductivity depends on four factors: (1) pore volume; (2) disposition of pores (grain packing); (3) portion of pores filled with water; and (4) conductivity of the water, which is composed of (a) a primary conductivity (that is, conductivity of the water as it enters the pores), and (b) a secondary conductivity (acquired by solution of mineral matter and therefore dependent on duration of con- tact [stagnation]). These relations may be expressed by the following formula: c v Pe = —-pi OF oz = —-01; (10-6) V1 Cc where pz is the resistivity and o, the conductivity of the rock, c a constant depending on the arrangement of the pores, v; the pore volume, p; the resistivity and o; the conductivity of the water or other medium filling the pores . For specific arrangements of mineral grains of regular geometric shape, it is possible to calculate not only the pore volume and thus the resistivity as a function of the resistivity of the water filling the pores, but also the relative effect of the conductivity of the grains compared with the effect of the medium in which they are imbedded. Maxwell has derived a general relation for the conductivity oz of an aggregate consisting of a medium with the conductivity o;, im which spherical grains of the con- ductivity o2 are imbedded\in regular arrangement and in such a manner that their distance is large compared with their radius.!* If the total volume of the aggregate is v, and the total volume of the grains v2, and if the ratio of these two volumes v2/vz, = r, then the following relation obtains: Eras 201 + o2 — 2r(o1 = 9) ¢ 201 + o2 + r(oi = a2) Hence, in terms of the (pore) volume 1 (if the pores are filled completely with the medium of the conductivity a1), 0}. (10-7a) 1¢ See also J. N. Hummel, Beitr. angew. Geophys., 6(1), 32-132 (1935). Cuap. 10] ELECTRICAL METHODS 635 _ 302 + 2n (o. — g2) 301 _— 01(01 _ ES (10-76). Assuming now that v; = r (or 2x, = vz, a porosity of 50 per cent), we obtain from eq. (10-7b): ¢; = cabarad and therefore, for the ratio, 5o1 + o2 oF 4 4 PEE oh (10-7c) eee at C2 From this it follows that, for a conductivity of the pore filling medium very much greater than that of the grains, or for o1 > o2, we have oz = 201, and for o2 > 01, oz = 401. Fig. 10-1 is a graph of eq. [9 (10-7c). For a porosity 10 of 50 per cent, the conduc- tivity of the aggregate in- 8 creases almost in direct proportion to the conduc- 6 tivity of the medium fill- ing the pores (assuming 4 all pores to be filled with the medium of the con- Zz ductivity o1). For virtu- ally all porous rocks we 2 46 8 10 0 U6 6 W te th = are, therefore, justified in Ber ane eam ee é = O 1G. rat NS OcK resistivity aS a Iunction O re- disregarding the conduc- sistivity of pore-filling medium, for 50 per cent tivity of the mineral grains porosity (after Hummel). and operating only with the conductivity of the medium filling the pores. Thus, letting 2 = 0 in formula (10-7b), we get 2 = 2u1 01, AOD? peu dim cain (10-7d) on) 201 Eq. (10—7d) can be further simplified for porosities less than 25 per cent by assuming that the pore volume is equivalent to a system of cylindrical tubes of identical radius 7, not touching one another, traversing the sub- stances in the three directions. If there are n tubes per square centimeter, their area on one side of a cube (or one-third of the pore volume) is »/3 = 636 ELECTRICAL METHODS [Cuar. 10 r'.x-n. Since the resistance in the direction of the tube is inversely propor- tional to its area, Pe - , so that Pleim ag : (10-7e) pl V1 fp 40 The relation (10-7d) is y shown graphically in Fig. 10-2. Resistivities deter- mined by this diagram 0 are in good agreement with resistivities actually observed. _ Table 60 gives some values for the porosities of 20 various types of rocks, for- mations, and soils, and for the corresponding values for the resistivity ratio pz/ pi. In the derivation of pre- ceding equations, no as- sumption was made in regard to the spacing of 100% Poresity the mineral grains or pore spaces, respectively. For definite ratios of spacing to size of the grains, it is possi- ble to determine the pore volume and therefore the resistivity ratio pz/pi. Table 61 (largely from Sundberg) gives these values for various grain arrangements. This tabulation brings out the fact that the re- sistivity may in certain cases depend on the direction of current with respect to the arrangement of the particles. Materials of such nature are called anisotropic. Anisotropy of resistivity plays an important part in all stratified formations where resistivities in the bedding planes are generally quite different from those at right angles thereto. It was shown before that the resistivity of a rock can be found if the pore volume, the pore arrangement, and the resistivity of the water filling the pores is known. The latter may be determined by experiment if specimens of well or formation water have been taken. If the specimen itself is not available, but only its analysis is, the conductivity can still be calculated. For this purpose it is first necessary to recalculate the 10 Fig. 10-2. Relation between resistivity ratio pz/p1 and porosity (after Sundberg). Cuap. 10] ELECTRICAL METHODS 637 constituents in terms of gram (or better milligram) equivalents per liter. From the concentration C thus expressed, the degree of dissociation is obtained. Sundberg’ has given diagrams showing dissociation as a func- tion of concentration of a number of salts. Only the curves for NaCl are of practical importance. If the dissociation of a solution is a, the number of anions per cc is a-C gram equivalents. With a charge F per gram equivalent (= 96500 coulombs), the quantity of electricity carried by the anions is F-.a-C-v,, and F'-a-C-v¢ is that carried by the cations, if v is their velocity for a potential gradient of 1 volt per cm. Hence, the TABLE 60 Rock oR FoRMATION Porosity Ratio ra % lipneous and metamorphic rocks: Fo. 22.0356. 6.5.6) gene 3-2 100 Dense limestones and sandstones..................-.-+--- 3- 4 50 -100 Claysrand sandsiin generals: . 2.2). 2... 24. hn elds Re 8-15 20 - 40 Porous clays, sands, sandstones, cellular limestones, and GOLOMMIGESHN eet Ny ae tg Weert ee cathe Wiel ear Maa e dicta sas 15-40 3 - 20 Mark eloess clay, and sandy soil..<.6.2.20%)) 50.6.0. 00 ss 40-75 1.5- 4 Peat, diatomaceous earth.................-2 00. eee eee eee 80-90 1.0- 1.5 TABLE 61 Grain ARRANGEMENT Porosiry Ratio = % Spheres of radius 7, distance r/2....... 73.2 1.37 Spheres in cubic arrangement......... 47.6 2.64 Spheres in rhombic arrangement....... 39.5 3.38-4.40 depending on di- rection Spheres in hexagonal arrangement..... 26.2 5.81 in direction perpendic- ular to base total quantity per second, the current strength, and thus the conductivity per cm’ is ¢ = F-a-C(v4 + vc). For infinite dilution, @ is 1 and the velocities are Vie and Vco. If we designate the quantities 1, = Fv, and lc = F-Vce , a8 ion mobilities, the resistivity for any number of salts in solution is p = 1/(ZeC[l, + Ic]). For very diluted solutions in which all salts are completely dissociated (C less than 0.5 mg per liter), a = 1 and the resistivity in terms of concentration expressed in milligram equiv- alents per liter is p = 1000/(2C[l, + 1c]). Theoretically, the sum of the concentrations and ion mobilities should be taken for all salts in solution. 2K. Sundberg, A.I.M.E. Geophys. Pros., 381 (1932). 638 ELECTRICAL METHODS [Cuap. 10 A comparison of analyses of water from different sources with the results of theoretical caleulations has shown, however, that for waters of less than 1000 ohm-cm, the resistivity can be determined closely enough from their chlorine content alone. The curves in Fig. 10-3 show resistivities of NaCl solutions as a function of concentration. 23000 50 20000 40 § g 700 15000 Ss 40 & 400 = 10000 = Joo 20 $ 200 & $000 7 10 100 o ] 0 0 Q03 0066 0 03 06 @O J 6 9 ToS Per Cent Chlorine Fig. 10-3. Resistivities of salt solutions as a function of chlorine content (after Sundberg). The composition of natural waters varies widely, depending on origin and on geologic occurrence. They may be classified as follows: 1. Meteoric waters, derived from precipitation: p = 3000 — 100,000 ohm-cm. 2. Surface waters (lakes, rivers, and the like) vary from 300,000 ohm-cm for very pure water to as little as 10 ohm-cm for salt lakes. Surface waters in districts of igneous rock are estimated to range from 3000 to 50,000 ohm-cm; surface waters in areas of sedimentary rock from 1000 to 10,000 ohm-cm. 3. Soil waters (discharged into the atmosphere by evaporation) may be as low as 10 ohm-cm, but their average is around 10,000 ohm-cm. 4. Normal ground water in areas of igneous rock is of the order of 3000 to 15,000 ohm-cm and in areas of sedimentary rocks as low as 100 ohm-cm. 5. Subsurface (connate) waters (Na, K, Ca, and Mg chlorides) are generally good conductors and are between 3 and 10 ohm-cm. 6. Mine waters (usually copper, and zinc, and so on, sulfates) are like- wise of low resistivity, generally not exceeding 30 ohm-cm. Cuap. 10] ELECTRICAL METHODS 639 Contrary to metals, the conductivity of electrolytes increases with an increase in temperature, so that o = orsil + Be — 18°C.)]. (10-8) While in metals the temperature coefficient of resistivity is the reciprocal of the absolute temperature, the temperature coefficient of electrolytes (being the increase in ion mobility due to a reduction in the viscosity of the solvent) is approximately equal to the temperature coefficient of viscosity of water. For NaCl solutions the coefficient is 0.022; for an increase in temperature of 35° C. the conductivity is about doubled (see Fig. 10-4). Metals and electro- lytes also show a 4 eae difference in alternat- ing current conduc- tion. In electrolytic solutions voltage and J current are generally not in phase, particu- 3 larly when the polari- 25 zation e.m.f. is com- 2 parable with the applied e.m.f.’ The phase shift is reduced Temperature as the voltage is in- WOW 4D OW OW WC creased. If P is a fia. 10-4. Decrease of resistivity of an NaCl solution “polarization con- with temperature (after Sundberg). stant” (ratio of polar- ization e.m.f. and quantity of electrolysis products deposited per unit surface of electrode), the impedance of an electrolytic solution is p2 Z=hkh 4/3 + (10-9a) w? R?” Substituting 1/C, for P, eq. (10-9a) takes the form Z= Vit oF, (10-96) p which is seen to be identical with the formula for the impedance of a circuit consisting of a resistance with a capacity in series. The phase 3 See oscillograms in W. R. Cooper, Electrolysis as Applied to Engineering, p. 16 (New York, 1923). 640 ELECTRICAL METHODS [CHap. 10 shift in a circuit consisting of an electrolyte with the polarization P is -_1 P — — 1 — _—" gy = —tan R: (10-9c) C. DIELECTRIC CURRENT CONDUCTION In most nonmetallic, solid, and isotropic media the number of free electrons is too small to permit free passage of direct current. Alternating current, however, will be transmitted, since the electrical field produces a displacement of the nuclear and electron patterns (dielectric polarization) which is propagated when the field changes i with time. The polarization P (electric ——-—-——----5 moment of the unit of volume) is propor- ve | tional to the electrical field. P = cE, Va | where ¢ is the electric susceptibility. Treat- dt ing the electrical flux in the same manner | G that the magnetic flux was treated in Py >! z Chapter 8, the flux per unit area or the Fic. 10-5a. Relation between electric displacement D = E + 4rP. Sub- conduction current and displace- Stituting for P: eE, the displacement be- ment current. comes D = (1 + 4me)E, where 1 + 47e = x is the dielectric constant. Hence the dis- kK,@——> placement is D = x-E. An alternating electrical field produces | ‘ a current in a dielectric equal to dD/ dt ng: K'w or = x-0E/ dt, which is known as the dis- placement current. Considering the conduc- | tion current and recalling from eq. (10-5) : FI RUMA pRiapon tes Cor SAS T A Fic. 10-5b. Relation between a € < DS ETS rok, We get, conductivity and true and appar- for the total current (see Fig. 10-5a), ent dielectric constant. I, = ne + 4roE. (10-10a) For a sinusoidal e.m.f. of the angular frequency w, the differentiation gives an e.m.f. 90° out of phase with the last term of the equation, so that the peak value of the displacement current becomes kxwE. Therefore I, = 4roE + jrwE, (10-106) so that the phase shift between conduction component and resultant current y = tan nod - (10-10c) Cnape. 10) ELECTRICAL METHODS 641 In terms of the displacement current and by substituting dE/ dt = jwE, or E = = eq. (10-10a) may be written: @ rani ip ee ee Are Sn he tapas menirhiag] Me gee water so that — oe ie == KK at ) (10 10d) where x’ = x — j4mo/w is the apparent dielectric constant (see Fig. 10-5b). Moisture Content - % Fic. 10-6. Apparent dielectric constant as a function of moisture content (after Smith-Rose). Like the conductivity, the dielectric constant of an aggregate increases with water content, owing to the large dielectric constant of water. Smith- Rose gives as dielectric constants for dry soils, 2.6 to 2.8; for soils with 3.6 per cent mozsture, 2.3 to 5.6; and for soils with 16 to 30 per cent water, 18 to 30. Fig. 10-6 shows the change of dielectric constant with moisture for a frequency of 1200 kc. 642 ELECTRICAL METHODS [CHap. 10 D. Tue Errects or MaGnetic PERMEABILITY As was shown in the introduction to Chapter 8, magnetic permeability is the ratio of magnetostatic induction to field strength. It plays a part in all electric induction phenomena. In accordance with Faraday’s law, the e.m.f. induced in a conductive body depends on the time rate of change of the field: EH = — dH/ dt. If the field change occurs in a medium of the permeability u, the induced e.m.f. H = — udH/ dt. Theoretically this relation should be expected to find application in electrical prospecting methods where current is induced in subsurface conductors by insulated loops. In practice, however, it is of limited importance since with few exceptions, good conductors (sulfide ores) to which inductive methods are applied chiefly are not very magnetic, while very magnetic (iron) ores, on the other hand, are usually poor conductors, making potential methods more suitable. EK. METHODS FOR THE DETERMINATION OF Rock RESISTIVITY Methods for determining rock resistivity may be divided into two groups: (1) laboratory determinations (on rock specimens) and (2) measurements in sttu (at the ground surface, outcrops, and the like). Laboratory determination has the disadvantage that only small specimens are tested, that the effects of unhomogeneities in the specimen not.characteristic of the entire formation may be exaggerated, and that conditions in nature may not be exactly duplicated. By making measurements on location, these disadvantages are overcome, but their limitation is that unknown near-surface strata differing in conductivity may affect the results; hence an ‘‘apparent”’ instead of the true resistivity of the surface formation may be determined. In regard to technique, two major groups may be dis- tinguished: one that uses direct current and the other that uses alternating current (commutated D.C., low-frequency A.C., intermediate-frequency A.C., and high-frequency A.C.). Measurements at radio frequencies are discussed in the next section in connection with determinations of the dielectric constant. 1. Preparation of specimens; electrodes. For resistivity determination in the laboratory the sample should be cut to regular shape so that its resistivity may be readily calculated from resistance and dimensions. Rock saws with carborundum or diamond discs are suitable. The length of the specimen should be at least four times its diameter. High contact resistances may be overcome by the use of a frame shown in Fig. 10-7. Between the metal plates and the specimen various layers of tinfoil should be inserted. Contact resistance is likewise reduced with mercury elec- trodes. Two arrangements are shown in Figs. 10-8 and 10-9, the latter Cuap. 10} ELECTRICAL METHODS 643 being suitabie for testing drill cores. Drill cores may be dipped in solder of low melting point to reduce con- tact resistance. Specimens _ sus- pected of being anisotropic should be measured in more than one direc- tion. In any event, it is a good Fyg. 10-7. Clamp for rock resistivity policy to reverse the specimen and determinations (after Sundberg). to make at least two determinations. Effects of polarization are difficult to eliminate. In D.C. measurements the direction of current should be reversed in as brief periods as possible and high voltages should be used. Owing to the difficulties with direct cur- rent, A.C. methods are now in more prevalent use. 2. Continuous D.C. methods. For moderate requirements of accuracy, the direct reading ohm- meters of radio and uni- versal testing sets are quite satisfactory; they are conveniently carried in the field for rapid checks on unprepared specimens of approxi- mately regular shape. For measurements on out- crops, the Shepard earth hhh resistivity tester may be applied. This consists of Fig. 10-8. Substitution method of resistivity deter- tWO long steel electrodes mination with mercury electrodes (after Pullen). with the ohmmeter and self-contained battery mounted on one of the rods. The surface of the rod acting as the cathode is greater than that of the anode, in order to reduce polarization. As may be expected, Wheatstone bridge methods are widely applied for resis- tivity determinations by continuous’ or commutated D.C. and low-frequency A.C. Well suited for measure- ment of high resistance is the bridge shown in Fig. 10-10. Re is a comparison resistance of high order, ex from 10,000 to 1,000,000 ohms; the ratio r;/rz is adjusted Sp in steps up to 1:1000. Then R, = Rz-11/r,. Resist- Fie. 10-9. Mer- ances up to 10° ohms may be measured with this bridge. CU'Y , Clectrode z i Z Biv ve for drill cores Likewise convenient for rock resistivity measurement (after Pullen). 644 ELECTRICAL METHODS [CHap. 10 Re is the “substitution” method illustrated in Fig. 10-8. A galvanometer deflection is first observed and adjusted by means of the shunt to give a suit- able deflection with the unknown resistance in series. Then the switch is thrown over to the known resistance, which is adjusted until the same galvanometer deflection is obtained. The use of a this method with A.C. is shown in Fig. 10-12. q For a determination of the resistance of bodies Fic. 10-10. Wheat- of arbitrary shape, separate measurements of cur- stone bridge arrange- : pele ea eaiager emia voltage are made. Four connections are ity determination. then necessary for the current and voltage leads. As H. v. Helmholtz pointed out as early as 1853, the current leads may be interchanged with the potential leads without altering the resistance. This value is equal to the ratio of voltage differ- ence and current, multiplied by a factor controlled by the spacing of the electrodes; the method is particularly suitable for measurements of resistivities 7n situ. Since it employs commutated D.C., this procedure will be discussed in the next paragraph. 3. Methods using commutated D.C. have attained great practical impor- tance for the determination of resistivity in the laboratory and in the field. One reason is simplicity of technique. D.C. instruments may be used throughout, since the current through the ground may be commutated in synchronism with the current through the meters. In this category are the well-known Wenner-Gish-Rooney and the ‘“Megger” instruments. Rx — Double Commutator Potentiometer Milliammeter Electrodes making contact with earth~_ Fig. 10-11. Resistivity determination by four-terminal (Gish-Rooney) method. The Wenner-Gish-Rooney method is illustrated in Fig. 10-11. It con- sists of a set of B batteries, a double commutator, four electrodes, a milli- ammeter, and a potentiometer. Current from the batteries passes through Cuap. 10] ELECTRICAL METHODS 645 the milliammeter to the two external electrodes and through the com- mutator in such a manner that the direction of the current through the ground is reversed periodically while it is passing in the same direction through the milliammeter. The potential difference set up between the internal pair of potential electrodes is likewise of an alternating nature but is “‘rectified’’ by the double commutator, so that D.C. potentials are read on the potentiometer. The ratio of voltage and current, multiplied by a spacing factor, gives the resistivity p= nar (10-11) The derivation of this formula is given on pages 709-710. If Ris substi- tuted for V/I, the formula takes the form R = p/2za, which is seen to be the resistivity of a hemisphere with the radius a (length of current path = a, surface = 27a’) (see Fig. 10-11). On this relation is based the thumb rule that the depth penetration of the Gish-Rooney arrangement is equal to the electrode separation. The ‘‘Megger”’ differs from the Gish-Rooney arrangement in that a direct reading ohmmeter (cross-coil instrument, giving the ratio of V/J) is substituted for the ammeter and potentiometer and that power is sup- plied by a hand-cranked generator instead of by batteries (see Fig. 10-60). 4. Low-frequency A.C. methods. These methods are well suited for laboratory measurements because low-frequency A.C. is readily available, no commutation device is required, and disadvantages of continuous D.C. are avoided. For high-resistance specimens 110 volt A.C. may be used directly. For lower resistances it should be stepped down by a lamp bank, a carbon resistor, or a transformer. As an indicating instrument, a D.C. current meter of high sensitivity together with a copper oxide rectifier, a vibration galvanometer, or any other oscillographic instrument of high current sensitivity, will be satisfactory. A Wheatstone bridge circuit or the substitution method are applicable (see Fig. 10-12). Ground resistivity may be determined directly with a Wheatstone bridge, using two electrodes only. If their radius is a, if 1 is the distance between their centers, and R is the resistance measured on the bridge, the resistivity p = ee If the distance is a multiple of the Eig ates, puihere electrode radius so that a = I/n the resistivity is i 2k ny a 08 0.85, Tags Can sate 646 ELECTRICAL METHODS [CHar. 10 in which the middle term in the denominator is negligible, so that 2k | en Sb, (10-12) which for large electrode separations is equal to p = 2Ra. This shows that the resistivity between two electrodes depends largely on their radii and therefore on the material in immediate contact with them. In the double electrode setup as described, Koenigsberger used iron discs about + inch thick and 10 inches in diameter, with a contact substance of clay or soil soaked with either FeCl; and FeSO, or NaCl solution.’ He applied frequencies between 100 and 400 cycles. 5. Intermediate-frequency methods. The use of audio-frequencies from 500 to 1000 cycles facilitates the field technique of resistivity measure- ments, since phones may be employed as indicating instruments. In the QC. caste _— — —_ —_ Rectifier 60— Potentiomefer — — — Fic. 10-12. Determination of rock resistivity using 60 cycles (after Pullen). lower frequency range, effects of inductance and capacitance are generally negligible and some of the arrangements are used as D.C. bridges. Inter- mediate frequency methods are applied (1) galvanically (by contact with the specimen) or (2) inductively (by measuring the mutual inductance between two loops). The latter are best suited for resistivity measure- ments on outcrops or horizontally stratified ground, since they function better on comparatively large volumes of earth. As an example of the galvanic application of intermediate frequency methods, the soil resistivity bridge of the U. S. Department of Agriculture is illustrated in Fig. 10-13.° Current is supplied from a battery-operated induction coil or buzzer. A container for the soil sample is in one arm of the bridge, a multiplier resistance in the opposite arm; two sides of a slide- 4 J. Koenigsberger, A.I.M.E. Geophys. Pros., 221 (1929). 5R. O. E. Davis, U.S. Dept. Agr. Cire. No. 423 (July, 1927). Cuap. 10] ELECTRICAL METHODS 647 wire rheostat comprise the remaining bridge arms. A telephone is used as null indicator. This in- strument is primarily a low-resistance device and may be used not only for soils but also for electro- lytic solutions. The entire apparatus is portable and is illustrated in the article referred to. The Zuschlag in- strument for rock re- sistivity determina- tions (see Fig. 10-14) is a regular A.C. (fre- quency) bridge, and buzzer | | a provision is made to al A determine both the re- ean ‘bridge (adapted ‘Stance and the ca- from Davis). pacitance of the speci- men. Power of com- paratively low voltage is supplied from a beat- frequency oscillator or buzzer of constant fre- quency. If in this bridge pure resistances are in three arms and an inductance and capacity Wie! 10s14e Zunchiag imped: in the other, the phone will remain silent if ance bridge. Se ae artdeibuigae ea i en Ro Rs V L(G + C L) where (; is the distributed capacity, R, the resistance and L the inductance of the coil, Co the setting of the condenser, and Rp the setting of the resist- ance in the other side of the bridge when balance is obtained. If a high resistance specimen is now connected across the variable condenser, the balance is disturbed and re-established by adjustment of the condenser and resistance. Assuming that the new values to obtain balance are C2 and Re , the resistance of the specimen R, and its capacity C, are given by Fee 1 + [wCo(Re — Ro)]’ Th 2772 w Co(R2 — Ro) and (10-136) i EY ons CQ ORI E Math. Rae (OS oo: Co. If R, is too low to obtain a balance, the specimen may be connected in series with the induction coil and condenser. If C3 and R; are the capaci- 648 ELECTRICAL METHODS [Cuap. 10 ties and resistances to obtain balance, oe Ee ie =| nk Re Bae (10-13¢) so that if C. = 0, Re = Rs — Ry. Also, pi Cs C, = Cows (10-13d) (K- Z) + o's — Bol Ver C; w 3 0 A method for determining the ground resistivities by induction is ar- ranged as follows.’ A circular loop is laid out flat on the ground in such a manner that its radius may be varied. In its center a pick-up coil is set up, likewise in a horizontal position. The e.m.f. induced in it is measured, in respect to amplitude and phase, with a compensator whose pickup coil is connected to the primary loop. An amplifier and phone, or meter, indicates the balance between induced current and compensation current. The e.m.f. induced in the pickup coil (and therefore the field H) is dependent on the current J of the frequency f flowing in the primary loop with the radius R. If p is the resistivity of the medium within range, Hoe. (10-14) I p where c is a constant. The depth penetration is assumed to be equal to the diameter of the loop; hence, the resistivity measured may not be a true but an apparent resistivity. Further details will be given in the section on inductive methods (page 797). 6. High-frequency methods. The frequencies employed here range from 10 to 100 kilocycles. Several years ago when this frequency band was used extensively, the Radiore Company developed a bridge in which the impedance of the specimen in one arm of the bridge was measured by comparison with a known resistance with capacitance in parallel in the other arm. Measurements of the ground characteristics at high frequencies in situ may be made with a double wire Lecher system’ or with the single ground wire of a high-frequency generator, buried at a shallow depth parallel with the surface. The current (measured at various points with a thermo- milliammeter) decreases with distance from the source since the waves die out because of space damping. If the wire is long enough so that no re- 8 J. Koenigsberger, Beitr. angew. Geophys., 3(4), 392 (1933); 4(2), 201° (1934). See also pp. 782 and 796, this chapter. 7M. Abraham, et al., Phys. Zeit., 20(7), 145 (1919). CHAP. 10] ELECTRICAL METHODS 649 flection occurs at the end, the decrease of the current with distance is given by Dilan Chi, (10-15a) Assuming further that the displacement current is negligible, the damp- ing coefficient may be written y= 2rv/fo, (10-150) that is, damping increases with frequency f and ground conductivity o. It is seen that I, = I)/e when x = 1/y. Hence, x = aA de so 2n'V fo that 1 =>) 10-15c Y Ana? ( ) if x. denotes the distance at which the current has dropped to 7 of its value at the source. F. METHODS FOR THE DETERMINATION OF DIELECTRIC CONSTANTS Since the capacity of a condenser is proportional to the dielectric con- stant of the medium within, most laboratory methods for the determina- tion of the dielectric constant make use of the difference in the capacity of a condenser with and without the substance. (1) The change in capac- ity may be measured directly by the resonance method. (2) The more common procedure, however, is to determine the impedance of a specimen by a substitution method. (3) The ratio of the reactive and conductive components may be determined by the phase-shift method. (4) Dielectric soil properties may be studied by an analysis of the ellipse of polarization of surface radio waves. 1. Resonance method. In all laboratory methods for the determination of soil properties at radio frequencies, a soil condenser is applied, con- sisting of two concentric cylinders separated by an insulator (Fig. 10-15a). Most measurements consist of, or are equivalent to, determining the geometric capacity Cy of this condenser and comparing it with its capacity when filled with soil (C,). In the resonance method (Fig. 10-15b) a source of RF is coupled to a circuit containing the secondary of a mutual inductance in parallel with a variable condenser C’, and the soil condenser C,;. The voltmeter V in- dicates a maximum at the point of resonance. The soil condenser is first removed and the condenser C', is so adjusted that resonance is obtained. Assume that its capacity is then C’. The soil condenser is then inserted 650 ELECTRICAL METHODS (Cuap. 10 and the air condenser is re-adjusted to the value C” to give voltage reso- nance. Since C;, = C” — C’, the dielectric constant is given by x = (C” — C’)/Co, where Co is the geometric capacity of C,. This method also furnishes the conductance component or the equivalent damping factor by an analysis of the shape of the resonance curve, by varying the con- denser C’, in steps and observing the corresponding voltages on either side of and at the resonance point. If Ci and C2 are two condenser readings obtained on either side of the resonance point where the voltage is } of the maximum e.m.f., and if AC is the difference of these two readings, the phase shift of the resultant in respect to the conductive component is given by tanto. =. (10-16) According to eq. (10-10c) the phase shift is tan 9 = kw/4mro. In the equivalent circuit (Fig. 10-15c) the reactance component of the current Fia. 10-15. (a) Soil condenser. (b) Resonance method of determining dielectric constants of soils. (c) Reactive and conductive components through soil condenser. (Adapted from Ratcliffe and White.) : I, is controlled by the effective capacity of the soil condenser, or C, = xCy , whereas the conductive component is given by the resistance R = 1/4raCy. Hence, by substitution, R = 2/wAC. The method of deter- mining the conductive component from the decrement of the response curve furnishes good results only for comparatively high frequencies, of the order of 0.2 to 5 megacycles.® 2. Substitution method. In this method the impedance of the soil speci- men is determined’ by substituting for the coil condenser a simulating unit consisting of a resistance with a condenser in parallel. These are varied until the same resonant output voltage is obtained. A tuned cir- cuit loosely coupled to an oscillator and provided with a beat oscillator and low-frequency detecting unit may be used in these measurements as shown in Fig. 10-16. From the resistance and capacitance components 8 J. A. Ratcliffe and F. W. G. White, Phil. Mag., 10, 667 (1930). °C. B. Feldman, I.R.E. Proc., 21, 764-801 (June, 1933). Cuap. 10] ELECTRICAL METHODS 651 read on the simulating unit, the resistivity and dielectric constants can be calculated as in the resonance method (see paragraph 1). 3. Phase-shift method. ‘The phase shift between the resultant current and the conductance component can be determined directly.in the fol- lowing manner (Fig. 10-17): A perfect air condenser C, without appreci- able loss angle is connected in series with the soil condenser C,;. Both are placed in a high-frequency circuit and the voltages across the soil condenser and across the perfect condenser are-compared on a cathode ray oscilloscope. The current through the soil condenser J, makes the phase angle y» with the pure conductance component. If a perfect con- denser is now placed in series with the soil condenser, the e.m.f. across it will be 90° out of phase with respect to this current and, therefore, have a phase shift of 90 — y compared with the e.m.f. across the condenser. Tuning RF Det. Simulating Unit Fie. 10-16. Determination of reactive and conductive components of soils at radio frequencies (adapted from Feldman). If the condenser terminals are then connected to the four plates of a cathode-ray oscilloscope as shown in Fig. 10-17c, the light spot will trace the resultant of the two voltage components and thus give their phase shift directly.” 4. Polarization measurements. In this connection, the term ‘‘polariza- tion”’ refers to the polarization of radio waves in the course of their propa- gation over the earth. This is brought about in the following manner: The radiation from an antenna may be considered as consisting of three component parts: (a) a space wave, whose amplitude decreases inversely with the distance from the source because of a geometric spreading; (b) a surface wave, decreasing in amplitude inversely with the square root of distance; and (c) a ground wave of a depth penetration generally smaller 10 C. B. Feldman, Bell Lab. Rec., 12(12) (Aug., 1934). Ratcliffe and White, loc. cit. R. L. Smith-Rose, Roy. Soc. Proc., A130, 359 (1933). 652 ELECTRICAL METHODS [Cuap. 10 than the wave length. Because of the differences in the variations with distance, the radiation in the vicinity of the antenna consists almost en- tirely of space waves, while at greater distances it approaches more and more the character of a surface wave. In addition to geometric spreading, the amplitude decreases because of absorption. The change from space to surface wave occurs more rapidly the shorter the wave and the lower the conductivity and dielectric constant of the surface and near-surface Sh ear A ae te line (a) G E _- Lathode Ray 3 fs : Oscillograph Plates G (c) Fic. 10-17. Measurement of phase shift in soil specimen by cathode-ray method (after Ratcliffe and White). beds. Thus, the variation of the electric and magnetic fields of the radiation may be expressed by the relations: BE. = 199 78? , Zo (@mp) | 8 Cotte cmt), d r(cm) (10-17) i Oe ton aise r r where E is the electric and H the magnetic field, a is the form factor and h the height of the antenna, 7 the distance from the source, § an absorp- tion coefficient, Jo the current in the antinode of the antenna, and d the wave length. | If the earth were a perfect conductor, the electrical field would be at right angles and the magnetic field parallel with the earth’s surface, and the electrical and magnetic fields would be in phase. For finite conduc- tivity at the surface or at shallow depth, a forward inclination of the electrical wave front is produced, while the magnetic field remains sub- stantially parallel with the surface. In other words, the electrical field now consists of a vertical component Z and a small horizontal component which are out of phase with respect to each other. The ratio of the peak Cuap. 10] ELECTRICAL METHODS 653 amplitudes of the horizontal and the vertical components, as well as their relative phase shift, are functions of the effective conductivity and dielec- tric constants of the near-surface formations. According to Zenneck, 2 5 X = Jm™Mo or a — NINE teat! ° e”*, (10-182) Zz i+jm Zoey 1+ mi where the factor my = fkopo/18-10" (ko = dielectric constant, f = fre- quency, and p = resistivity in ohm-cm) refers to air, and the factor m, = fxp:/18-10" refers to the effective ground properties. The phase I J % Fig. 10-18. Elliptical polarization resulting from composition of a horizontal and a vertical component which are out-of-phase. shift between the two components is proportional to the reciprocal of the factor m;, so that 18.10" fri P1 : Curves giving the ratio X/Z and their phase shift as functions of dielec- tric constant and conductivity of the ground have been calculated by Zenneck” and Feldman.” Because of the out-of-phase condition of the horizontal with reference to the vertical component, the resultant electrical field vector describes an ellipse; this phenomenon is referred to as elliptical polarization and plays an important part in all electrical prospecting methods using inter- mediate and high frequencies. In Fig. 10-18 a large vertical component is shown as one wave train, and a horizontal component as another, with tan 29 = (10-18b) 1 Wireless Telegraphy (1915), Fig. 300, curves for 670-meter wave length. 12 7.R.E. Proc., 21, 790 (June, 1933), Fig. 22, for 16-meter wave length. 654 ELECTRICAL METHODS [CHar. 10 a phase shift of 27/10. For the sake of illustration, the horizontal com- ponent is shown at right angles to the direction of propagation (Y) while actually, in the radio surface wave, the horizontal component is in the plane of propagation (X). This, however, does not change the resulting phenomenon or the equations given later. If for each instant the position of the resultant vector is constructed and then the ends of the vectors are projected on one plane, they lie on the circumference of an ellipse. The maximum vertical and horizontal components are tangents to this ellipse, and its tilt angle depends on the ratio of the two components as well as their relative phase shift. As shown below, the ratio of major and minor axes of this ellipse may be measured conveniently in the field. If their ratio (see Fig. 10-19) b/a Position of maximum / signal of antenna Direction of Propagation Fic. 10-19. Ellipse of polarization and receptor with rotatable antenna to measure compression and obliquity of this ellipse (adapted from Feldman). is designated by r, the ratio of the horizontal and vertical components is given by XV (r — 1) sin’y +1 (*) ~ (2 — 1) cos?y + 1’ Weare, wheré y is the tilt angle of the ellipse. The following equation” for the relation between phase shift g, tilt angle y, and intensity ratio, follows from the geometry of the ellipse: ay A An apparatus for the determination of these quantities is illustrated in Fig. 10-19. It consists of a receiver with a rotatable double L antenna cos g = 3 tan 2y ( - | (10-18d) 13 Derived on p. 690. Citar. 10] ELECTRICAL METHODS 655 which is first oriented in the plane of polarization and then rotated until minimum signal is obtained. The axis of the double antenna is then in the direction of the minor axis of the ellipse. Ninety degrees from this position a maximum signal will be observed. The ratio of the maximum and minimum signals gives the ratior. The inclination of the antenna in the position of minimum signal gives the tilt angle of the ellipse and, therefore, the ratios of the horizontal and vertical components and the phase shift between them. From these, the effective ground conductivi- ties and dielectric constants may be determined by trial and error with (\ WX \X SS SEAN NA SQ NN WY A= 1000 m N SS v= AY A =2000 m SYR’ | 5 | x \N\\ Moist Surface Layer \Sround Water (p2*Zlo*chmcm, k+80) at: No Groundwater Om ick; ytOem tim | e+ 10" Qemikye2 Fig. 10-20. Ellipses of polarization for surfacc and ground waves, for various fre- quencies, and for various conductivities and dielectric constants (after F. Hack). the help of curves referred to in the last footnote. Changes in dielectric constants are of less effect than changes in conductivity. For both long and short waves it is observed that with an increase in conductivity the horizontal component vanishes and that the phase shift approaches 45°. The ground wave referred to before may be considered as a surface wave having penetrated into the ground, with concomitant modification of wave front and polarization due to the electrical properties of the surface strata. The ellipse of polarization takes different forms, depending on whether the surface beds are dry to the depth of penetration, a moist 656 ELECTRICAL METHODS [CuaP. 10 surface layer is present, or a ground water level exists. These conditions affect not only the ground wave but the surface wave as well. Both are shown schematically in Fig. 10-20." G. RESISTIVITIES AND DIELECTRIC CONSTANTS OF MINERALS, OREs, Rocks, AND FORMATIONS Resistivities of minerals, ores, rocks, and formations vary within much wider limits than their other physical properties. For instance, the density may vary between the limits of 1 and 8 for minerals and between 1.5 and 4 for rocks and formations. The range of elastic wave speeds in formations is from about 150 to 7000 meters per second; magnetic suscep- tibilities vary from 2 to 1 X 10°. Extremes in electrical resistivity are represented by silver with 1 X 10 ° ohm-cm and by sulfur with 10% ohm-cm. This range is not encountered in practice. It is probably greatest in ore prospecting and lies between 10° and 10’ ohms, which corresponds to 10 powers. For comparisons of resistivities it is therefore advantageous to apply a logarithmic scale. Minerals and rocks may be divided according to resistivity into three groups, each of which comprises a range of 8 powers: 1. Minerals of good conductivity, in the range of 10 ° to 10 ohm-cm. 2. Minerals and rocks of intermediate conductivity, covering the range from 10° to 10° ohm-cm. 3. Minerals and rocks of poor conductivity, in the range of 10° to 10” ohm-cm. In the first group are the metallic elements and graphite, the arsenides, the tellurides, the sulfides with the exception of sphalerite, cinnabar, and stibnite. The group also includes a few of the oxides, such as specularite, magnetite, pyrolusite, and ilmenite, although these are on the border line between the first and the second group. In the second and largest group of intermediate conductors are the oxide minerals except those mentioned above, most ores, virtually all rocks possessing electrolytic conductivity, and anthracite. Most minerals, particularly the rock-forming types, such as all silicate minerals, the phosphates, and the haloids, belong in the third group of poor conductors, as do also the hydrates, borates, nitrates, carbonates, sulfates, chromates, and molybdates. In Tables 62 through 70 resistivities are given in the following order: elements, arsenides, tellurides, sulfides, oxides, haloids, various rock- forming minerals, and miscellaneous commercial minerals. Then follow the ores and rocks with impregnations of conductive minerals. Next is a tabulation of resistivities of igneous and metamorphic rocks, determined (Continued on p. 664.) 14. Hack, Ann. Phys., 27, 43-63 (1908). Cuap. 10] ELECTRICAL METHODS 657 TABLE 62 RESISTIVITIES OF ELEMENTS AND MINERALS RESISTIVITY IN OHM-CM MINERAL Nv Good Conductors Intermediate 10-6 |10- |10-4 10-4 }10-2 |10-1) 1 | 10)}|102 102| 104! 105 108) 107/108) 10? Elements Graphite, C Sund- 3 berg Arsenides Nicollite, NiAs Reich 2 Tellurides " 7-|-3 Sulfides Covellite, CuS 3 Galena, PbS Sund- 5-|-5 berg Pyrrhotite, FesS, if 5 Pyrite, FeS. A 1 Chalcopyrite Edge & 1.2 Laby Bornite, CuzFeS; Time sae 3 Marcasite, FeS. Sund- 1-!-1 berg Molybdenite, MoS, * 8 Cinnabar, HgS Lowy 2 Stibnite, Sb2S; 5 Sphalerite, ZnS Sund- 1 b Oxides ire Specularite, Fe,0; Koenigs- 4-8 berger Magnetite, Fe;0, Sund- 6-|-1 berg Pyrolusite, MnO: Lowy 5-||-5 Ilmenite, FeTiO; < 5-|-5 RESISTIVITY IN OHM-CM = MINERAL TeV SeLTs & Intermediate Conductors Poor Conductors mo] 8 ie) 10} 102 | 103 |10¢| 105 |108/107 105/102), 101°| 1011 1012| 1013| 10% | 10%5| 1016 Hematite, Fe.0; Lowy 4-|—|—|-1 Limonite, a 1 2Fe.03-3H2O Wolframite, (Fe, an 1 Mn) (W0Os) 658 ELECTRICAL METHODS [Cuapr. 10 TABLE 62—Concluded RESISTIVITIES OF ELEMENTS AND MINERALS | > RESISTIVITY IN OHM-CM : a iS £ i>} 3 | MINERAL TVET; & Intermediate Conductors Poor Conductors mo] 8 (6) 10}| 102 | 103 |104| 105 | 106 107|108, 10° 1010 | 1011 | 1012 | 1013) 1014 | 1015) 1016 Halides Impure rock salt | Koenigs- 3-15 joel berger | Various Rock- | Forming Minerals | Serpentine i 2 | | | Hornblende 1, 1 lage Mica Sund- 1.5)/- || eo berg | Quartz, SiO: i 3.8|\—| 1.2 Calcite, CaCO; SRO | Misc. Commercial Hl Minerals | Sulfur Curtis & | 104 1017 Thorn- ton Bituminous coal Ewing |6-||-1 Anthracite ns 1-2 Coal Koenigs- 2-|-5 berger Coal, dry & CO, st 1 Fire clay Hawkins 1.9) | Nae | Coal seam Schlum- 4—1.0 Pee rset berger | | RESISTIVITY IN OHM-CM MINERAL ye Good Conductors Intermediate Conductors 10-8 |10-5 |10-4|10-3|10-2|10-2| 1 | 10 |/102| 103 | 104 10: 108 107 108, 10° Carbonates Siderite, Fe2(COs)3 Sund- Fae tek berg | Waters | . | Saline water, 20% Edge & heats | Laby bias | | Saline water, 10% s | 18.2 | Saline water, 3% eine | ie eco baa | River water (Mon- | Erd- | 5.5) tana) mann| | * For average values of waters in different geologic provinces, see p. 638. Cuap. 10; ELECTRICAL METHODS 659 TABLE 63 RESISTIVITIES OF ORES RESISTIVITY IN OHM-CM ORE LocaLiry INVESTIGATOR |Good Conductors Intermediate Conductors 10|10-1| 1| 10 |]102|1021104| 105 | 105 | 107 | 108 |10° Chaleopyrite Quebec Gilchrist 2.1 Pyrite Sweden Lundberg, 1 et. al. Native copper Arizona Sundberg 1 Cong. with Cu Michigan . 2 Galena Joplin, te 1 Mo. Sphalerite, dry, | Quebec Gilchrist 4.95||—|—|—|1.4 & +10% pyrite Blende ore (no | Missouri Sundberg 5 iron) Zincite Franklin Ss 3 Furnace, ING J: Chalcocite Butte, Sundberg 6 Pyrrhotite Mont. is ¢ Chromite Canada Gilchrist 1.3 Chromite New York | Lee 1.7 Hard graphite Hunkel 2-4 Magnetic ore Sweden Sundberg 1-——__|-1 Magnetite New York | Lee 7.5 Brown hematite | Sweden Sundberg 1 ore TABLE 64 RESISTIVITIES OF ROCKS WITH CONDUCTIVE MINERAL IMPREGNATIONS RESISTIVITY IN OHM-CM Rock Locauiry |INVESTIGATOR RR ase Intermediate Conductors 10-2|10-1| 1 | 10|| 102 [102] 10* [105] 108 |107 108/10" Graphite slate Sweden | Lundberg, 5-|—|-||3. Sund- berg Rock with dissemi- | Falcon- | Gilchrist 1-||——|—|—|—_|-. 85 nated pyrrhotite bridge Ont. Voleanic rock with hs 1% chalcopyrite and sphalerite—sulfides equal 20% of speci- men 660 ELECTRICAL METHODS TaBLE 64—Concluded RESISTIVITIES OF ROCKS WITH CONDUCTIVE MINERAL [CHap. 10 IMPREGNATIONS RESISTIVITY IN OHM-CM Rock Locautity |INVESTIGATOR Coe ors Intermediate Conductors 10-2|10-1| 1|10|| 102 10) 104 |105) 108 |107|103|109 Limestone with lenses | Algeria | Schlum- 1.2 of hematite berger to 4 Sericite slate with py- | Quebec | Gilchrist 3.5 rite Hornblende with Bavaria | Hunkel 8 |—| 1 graphite and pyrite Hornblende = syenite e ss 1 with magnetite | TABLE 65 RESISTIVITIES OF IGNEOUS & METAMORPHIC ROCKS | Rock Loca.ity INVESTIGATOR - Specimens Diabase Tdaho Sundberg Granite Bavaria Hunkel Devonian slate | Harz Ebert “cc “ce “cc <9 Porphyry,schis-| S. Australia| Edge & tose Laby Serpentine Eve & Keys Diorite Bavaria Hunkel Gabbro Mineville Lee & Boyer Garnet gneiss | Bavaria Hunkel Hornblende Mineville Lee gneiss | Gray -_ biotite Lee & Boyer gneiss i | Syenite | Bavaria Hunkel In Situ | Graphitic schist} Normandy | Schlum- berger Schists Missouri Poldini | Hard eale. | Belgian Geoffroy & schist Congo Charrin Mica schist |Washington, |Gish & (hard packed)| D.C. Rooney | Quartz por- | Newfound- | Kihlstedt phyry (slightly al- tered) land Drr. | | RESISTIVITY IN OHM-CM FREQ. Intermediate Conductors 2/2/2/2|8/8)2a|8 | | | 3.1 | isypes 2 6.5 | 100 3 3-|-2 1 D.C 1.0|-—/1.4 2 D.C 1-6 D.C 4 | 1 16 \|1- 1 \\2-| 6 2-|1.1 i | 16 || 13 Pe || |3.4 ha | a | Cuap. 10] ELECTRICAL METHODS 661 TaBue 65—Concluded RESISTIVITIES OF IGNEOUS & METAMORPHIC ROCKS RBSISTIVITY IN OHM-CM Rock Locaity INVESTIGATOR | Dir. | FREQ. Intermediate Conductors 2/2/2/2/8/8|28|& Keweenawan Michigan Hotchkiss, 10-15 1.2 4.4 lavas et. al. Greenstone Rooney 16 ie Porous trap- * ie 16 1.6 rock Pre-Cambrian | Sweden Sundberg 3-6 Granite Washington,| Gish & 16 5 D.C. Rooney Slightly altered | Ontario Kihlstedt 200 2.4 syenite 3.7 Massive vein af es 200 2 quartz Diabase Michigan Rooney 16 4.5 Serpentine Ontario Kihlstedt 200 Peal 5.3 TABLE 66 RESISTIVITIES OF CONSOLIDATED SEDIMENTS RESISTIVITY IN OHM-CM Rock Locanity iy eriek- Dir BER HQ! | || | mea eae NY 102} 103 | 10¢ | 105 106/107 Shales and Slates Chattanooga Cent. & south | Hub- 50 2-|—_|1.4 shale (Dev.) Tllinois bert Shale & glacial if oF 50 5 drift Nonesuch shale | Houghton Hotch- 10-15 1.8 Co., Mich. kiss, et. al. Shale W. Hancock, | Rooney 60 2 Mich. Slate Lee, 0 6.4 Joyce, Boyer Clay (wet) Jugoslavia Loehn- D.C. 21 berg & Stern ¢ Electrode spacing in four-terminal method, in feet. 16 Determined in the field. 662 ELECTRICAL METHODS TABLE 66—Continued [Cuap. 10 RESISTIVITIES OF CONSOLIDATED SEDIMENTS Rock Grinneld argil- lite Grinneld argil- lite Argillite (Mis- soula group); pre-Cambrian, thin-bedded, platy argillite; resembles Grinneld Conglomerates Great conglom- erate outcrop Calumet & Hecla conglomerates Sandstone Eastern sand- stone Eastern sand- stone Muschelkalk ss. (Triassic) Sandstone (Ter- tiary Oligo- cene); soft, friable; ex- tremely fine grained ss.; pale green to yellowish and buff; contains thin beds of lignite LocaLity Ing eee Dir. FREQ. Ni sec. 23, | Erd- dip 32° 16 T32N R20W,| mann Flathead Co., Mon- tana || to strati- fica- . tion An go) strike i a dip 32° | 16 (Water’s Edge) | to strike Sec. 27, T 32N : dip 31° | 16 R20W, Flat- head Co., Montana ee to strike Eagle Harbor, | Hotch- 10-15 Mich. kiss, et. al. Michigan Rooney 60 Michigan Hotch- 10-15 kiss, et. al. e Rooney 16 Lorraine Schlum- 16 berger Coal Creek | Erd- dip = 16 Road, Flat mann al- ‘ head Co., most Montana 0 a® 10 20 30 RESISTIVITY IN OHM-CM 102 | 103 | 104 | 108 105 |107 9.6 ee or ~I 00 NI 3-5L1.2 Cuap. 10] ELECTRICAL METHODS 663 TABLE 66—Concluded RESISTIVITIES OF CONSOLIDATED SEDIMENTS RESISTIVITY IN OHM-CM Rock Locatity Engueriah- Dir. Freq. |a® 10° | 10¢ | 105 | 108 |107|108 Armorican ss. | Normandy Schlum- 1 compact Sili- berger ceous-Ordovi- cian Ferruginous Switzerland | Koe- 4 sandstone nigs- (Jurassic) berger Limesione Muschelkalk Js.| Lorraine Schlum- 16 6 (Triassic) berger Limestone with | Algeria a 1.2- lenses of 4 hematite Muschelkalk Lorraine eS 16 1.8 oolitic ls. (Tri- assic) Limestone Mississippian | Poldini 3-4 (Missouri) Siyeh ls., hard | SWcor. sec. 5 | Erd- dip 54° |} 16 homogeneous, T29N R18SW mann 10 6.8|-1.4 dark bluish- Flathead | to 20 1.5 gray, siliceous} Co., Mon- strike 30 1.4 magnesium tana ie ato 10 3.6 Is.; pre-Camb. strike 20 5.4 7.9 30 6.6 6.9 50 6.1 8.1 TABLE 67 RESISTIVITIES OF UNCONSOLIDATED FORMATIONS (MOSTLY QUARTERNARY) RESISTIVITY IN OHM-CM ForRMATION LocauiTy INVESTIGATOR | a? FREQ 102 | 103 | 104 105,108) 107 Marls Marl & gypsum Germany Schlum- 16 3-|1.2 berger Marl & gypsum Algeria a 16 1-3 Jarnisy marls Lorraine 16 5 Marls s Geoffroy 7 ° Electrode spacing in four-terminal method, in feet. 664 RESISTIVITIES OF UNCONSOLIDATED FORMATIONS (MOSTLY ELECTRICAL METHODS TaBLE 67—Concluded FoRMATION Clay Clays with Mg salts Clay (wet) Boulder clay gravel) Marine clay Dry clay Wet clay Boulder clay (wet) Alluvium and Silt Alluvium (moist) Silt (dry) (no Glacial (dry) i “cc (T9 out-wash Fluvio (wet) glacial Glacial River gravel (wet) ce “cc “ce Yellow river (3.3% moisture) Yellow river (0.86% moisture) Stream gravel (wet) River gravel (wet) till sand sand QUARTERNARY) LocaLiry INVESTIGATOR Australia Rooney Palestine Loehnberg Montana Erdmann Ontario Hawkins New Jersey | Feldman 6c 6c 6é Montana Erdmann Montana i “ce cc Washington s (state) 6“ 6“ “cc 6c ce “ce Connecticut] Leonardon Montana Erdmann 6c “ec Sundberg (<9 Montana Erdmann Colorado “ bmc. = megacycles = 108 cycles. on specimens in the laboratory; this is followed by a tabulation of resis- tivities determined on the same group of rocks in situ. tabulations give resistivities of consolidated and unconsolidated sedimen- tary rocks, determined in the field, and of oil bearing formations, most of them measured by electrical logs. RESISTIVITY IN OHM-CM — ie) Ww P O100 Ne . o- wo TIAN OOVWRED — — . . ie.) Co eR DE & & & c 00 C100 NW WwW & The remaining Cuap. 10] ELECTRICAL METHODS 665 TABLE 68 RESISTIVITIES OF OIL FORMATIONS! RESISTIVITY IN OHM-CM FORMATION LocatitTy INVESTIGATOR 102 | 103 | 10# |105/105)107,10 109 101 |1011 Oil sand—fair Salt Dome, | Deussen & 4 Hull, Texas Leonardon | Oil sand—good $6 ‘s f WS al Lower oil forma- | Tintea Koenigsberger|| 6 | | tion (daily av. 30 | li Rega | tons) Upper oil forma- a 1.5- tion (2000 to 60 u tons) Heavy saturated | Seminole field,!] Schlumberger 9-/1.1 oil sand Oklahoma & Leon- ardon Associated beds He be s i 5.6 Very productive | Maracaibo i og 7.6 sands Dist., Vene- zuela Same ss.; no oil, 46 iY i s 5 H.O saturated Oil sands, much oil| Grozny Dist., a 2.2 Russia Sand (dry) 6c “c 3 & 2.5 Productive forma- er e Koenigsberger 5-8 tions ef Same, with shows s a3 6 Oil horizon, 320 | Dacian field, | Deussen & 4 tons per day Rumania Leonardon Oil horizon, 110 &§ us a ef 2 tons per day 16 Most of these were measured by electrical logs. TABLE 69 DIELECTRIC CONSTANTS—MINERALS AND OTHER SUBSTANCES kK = apparent dielectric constants; ko maemaces | eel) Maar | PES | De Elements or Substances Ice Pohl Petroleum Various authors Water fe a Minerals Sulfur Schmidt | 4 X 108 | 3 cryst. axes Quartz 4X 108} 1;||3 cryst. axes Gypsum o 4 X 108 | 3 cryst. axes x! true dielectric constants, e.s.u. 3.2 2.07-2.14 81 3.60; 3.9-4.7 4.3-46 5.0; 5.1; 9.9 666 ELECTRICAL METHODS TaBLE 69—Concluded DIELECTRIC CONSTANTS—MINERALS AND OTHER SUBSTANCES x’ = apparent dielectric constants; xo = true dielectric constants, e.s.u. Mymmnran | VOCE cream? || Geese Dir. Rock salt Schmidt | 4 < 108 Anthracite Ambronn Anhydrite Dolomite Schmidt | 4 X 108| ||; 1 eryst. axes Siderite 4 X 108 S Barite ri 4 X 10° | 3 cryst. axes Augite eS 4 <~108 ce Calcite “ 4X 10°) ||; 4 eryst. axes Sphalerite Rubens Muscovite Poole Limonite Lowy Cassiterite Rubens | 4 X 108 Hematite Lowy TABLE 70 DIELECTRIC CONSTANTS—ROCKS AND FORMATIONS kK apparent dielectric constants; Ko {[CHap. 10 true dielectric constants, e.s.u. MaTERIAL Marble Granite (dry) Limestone Diorite Sandstone (dry) Syenite Basalt Porphyry Gneiss Mica schist Schist Chalk (mois. 24%) Dark fibrous loam (mois. 60%) Soil (mois. 3.6%) Dry river sand Dry clay Dry clay (stone chips) Soil (mois. 11%) Sandy loam Sandy loam Dry topsoil * me. = megacycles LocaLity Germany “ce France Germany ‘cc Baldock, Eng. Rugby, Eng. Teddington, Eng. Netcong, N. J. Teddington, Eng. Holmdel, N. J. 6é &é INVESTIGATOR FREQ. Fleming Lowy Stern Léwy “ “cc cc ce “ce Stern Lowy Smith-Rose | 10 mc.¢ “f 10 me. es 10 me. Fleming by long wave Feldman 20 me. 30 mc. 40 me. Smith-Rose | 10 me. Feldman 10 me. cs 20 me. Us 10 me. Dir. ’ K Cuap. 10] ELECTRICAL METHODS 667 TaBLE 70—Concluded DIELECTRIC CONSTANTS—ROCKS AND FORMATIONS x’ = apparent dielectric constants; xo = true dielectric constants, e.s.u. MATERIAL LocaLity INVESTIGATOR FREQ. Dir. x’ Ko Dry topsoil Holmdel, N. J. | Feldman 40 me. 12 30 mc. 13 20 me. 14.5 Soil (mois. 17%) Teddington, Smith-Rose | 10 me. 17-20 Eng. Dry clay Holmdel, N. J. | Feldman 40 me. 19.5 30 me. 22 20 me. 0.5 23.5 10 me. 26.5 Loam & clay (mois. | Rugby, Eng. Smith-Rose | 10 mc. 21 15%) Chalk (mois. 26%) | Baldock, Eng. 10 me. 38 Wet topsoil Holmdel, N. J. | Feldman 20 me. 23 30 me. 23 40 me. 23 Subsoil (wet) oe fy sf 20 me. 28 30 mc. 28 40 mc. 28 Wet clay He es ie 20 me. 29 10 me. 32 Blue clay (mois. | Rugby, Eng. Smith-Rose | 10 mc. 29 23%) Blue clay (mois. & ef s 10 me. 46 25%) Daventry soil | Daventry, Eng. | Ratcliffe & 3 me. 39 (moist) White Clay and_ sand | Rugby, Eng. Smith-Rose | 10 me. 42 (mois. 21%) Cambridge _ soil | Daventry, Eng. | Ratcliffe & 2 me. 43 (moist) White Loam & clay (mois. | Rugby, Eng. Smith-Rose | 10 me. 43 33%) Clay & sand (mois. % + Si 10 me. 48 26%) III. SELF-POTENTIAL METHOD A. GENERAL The self-potential method is the only electrical method which uses a natural field, that is, one supplied by spontaneous electrochemical phenom- ena. All other electrical methods use artificial electric fields. The electrical activity of ore bodies and the potentials associated with (1) concentrations of metals in placers, (2) the corrosion of pipe lines, (3) the movement of underground waters, and (4) foundation boundaries all arise from concentration differences of electrolytic solutions in contact 668 ELECTRICAL METHODS [Cuar. 10 with metallic objects, from chemical differences of the materials coming in contact with solutions, and (in exceptional cases) from electrofiltration. These phenomena were discussed in detail in section 11. In eq. (10-la) a relation was given between the potential and the ratio of the solution pressures of two different substances in electrolytic solutions of different concentration; eq. (10-3) stated the conditions responsible for electro- filtration potentials. In the spontaneous polarization of ore bodies, the potentials arising from differences in solutions and from differences in materials appear to be related to one another as cause and effect. Differences in the solu- tions contacting different portions of an ore body (which probably con- sisted at first of the same material throughout) have brought about, largely through the medium of oxidation, a condition of unbalance which in turn is responsible for the potentials observed. Near the surface, the atmos- pheric agencies form an aerated zone rich in oxygen, while at the lower portion of the ore body the solutions are either poor in oxygen or are even of a reducing nature. The oxidation of the pyrite at the top proceeds in accordance with the relation FeS, + 70 + H,O = FeSO, + H.SO, ‘ The ferrous sulfate is readily transformed to ferric sulfate since 2FeSO, + HSO, + O = Fe2(SOx)3 + HO. Ferric sulfate in turn changes by hydrolysis to hydrous ferric oxide (limonite): Fe2(SOu)3 + 6H.O => Fe.03-3H.O + 3H.SO, 5 The sulfuric acid formed in this process is mostly neutralized by the car- bonates (calcite, limestones, and the like) in the adjacent formations. The last relation explains the formation of the gossan in the zone of oxidation. Minerals contained in it have a lower solution pressure than the unaltered ones in the lower end of the ore body. Hence, in accordance with eq. (10-1c), a potential difference is set up between the upper end and the lower end of the ore body. A current is then flowing downward in the ore body as well as around it outside; the zones of ingress of this current are above the top of the body and are indicated by a negative potential center (see Fig. 10-21). Although pyrite shows the strongest spontaneous polarization, it is not the only mineral exhibiting this property. Activity has been observed also on pyrrhotite, magnetite, cobalt ore, graphite, and anthrazite; on forma- tion boundaries; and in connection with the corrosion of iron pipes. Cuap. 10] ELECTRICAL METHODS 669 Negative Potential — ~ Aerated Moist -__ GurfaceZone — Zone (Formation of pay mt hydrogen) *MeO= Feyllhs +l 5 Gossan Neutralized by Carbonates | Ofe5+l5 0 { — | Feg(5Qyhy *614,05%,0, 5H,0*IH,50, Reduction : Zone Fia. 10-21. Chemical reaction and electrical activity on pyrite ore body. B. EQuIPMENT; ELECTRODES; SURVEYING PROCEDURE The object of a spontaneous polarization survey in mining is the locali- zation of negative centers. This may be done by surveying (a) equipo- tential lines, or (b) potential profiles. In either case nonpolarizable elec- trodes (‘‘porous pots’’) are employed. The theory of these was discussed in section 1 (page 630). Special attention is given to an identity of electrode potentials (that is, maintenance of a saturated solution). Polari- zation (and current density) is kept at a minimum by making the electrode surfaces in contact with the copper sulfate as large as possible. All elec- trode metals are usable that act reversibly, that is, metals in their salt solutions, (Cu in CuSO, , Zn in ZnSO,, and so on). In practice, Cu in CuSO, electrodes are most widely employed. The electrodes are satis- factory when the voltage between a pair does not exceed 1.10° volts. 670 ELECTRICAL METHODS [Cuap. 10 Details on construction and operation have been given by Edge and Laby” (see also Fig. 10-22). Lines of equal potential are measured by locating points between which no current flows. This is a null method and requires only a sensitive galvanometer. Tio cos 6 or, since cos 6 = h/~W/2? + h?, OB UREh 2 (x2+h232° To find the maximum potential, differentiate (10-19b) with respect to z: aV dz 20 See A. Petrowsky, Inst. Prakt. Geophys. Bull. No. 1, 87 (1925). 21 fq. (10-19b) is obtained also by applying the theory of images, that is, by assuming a reflected sphere above the earth’s surface. See E. Poldini, Univ. de Lausanne Bull. No. 61, 21 (1938). Vo (10-19b) = — 3 ER’ha(2’ +h)”. (10-19c) Crap. 10] ELECTRICAL METHODS 673 This expression is zero when z is zero, so that, from (10—19b), ER’ ‘Qh? * An approximate calculation of the depth of the doublet may be made by determining the distance of the “‘half-value” point of the curve from the point of the maximum. Equating the general expression for the potential in (10-196) to one-half the maximum value given by (10-19d), we get (x3 + h’)*? = 2h*, which gives tye =hV X/4 — 1 = 0.767h. (10-19) The expression in eq. (10-19c) signifies current density. An analysis of the curve representing the variation of this quantity with distance is Vinex. = (10-19d) Fig. 10-24. Potential curves for polarized spheres of various angles of inclination (depth h = 2). useful for depth determinations as follows: Differentiating (10-19c) again with respect to x and equating the result to zero, we find that a maximum occurs when Tmax, = a h/2. (10-19f) It follows from (10-19c) and (10-19f) that the current density above the vertically polarized sphere is zero and that on either side a maximum and minimum occur whose distance is equal to the depth to the center of the sphere (see Fig. 10-24b). It should be recalled that current density and therefore potential gradient is obtainable directly in the field from voltage readings with constant electrode separation. A dipping ore body may be considered equivalent to a polarized sphere whose axis of polarization makes an angle a with the vertical. Resolving this inclined doublet into two doublets of the respective moments m cos a 674 ELECTRICAL METHODS [CHar. 10 and m sin a, we note that m cos a acts at P as a vertically polarized sphere. Hence, the potential at P, according to eq. (10-19), is ER’ heosa 2 (x? + h?)3/2 ¥ The horizontal doublet m sin a@ is the equivalent of a horizontally polarized sphere. With z instead of h as its distance from the surface, we have for the potential of this doublet at P ER’ cxsina 2 (a? + h?)8/2_ The total potential at P is the sum of the potentials due to the components of the dipole: i Vo= ER’ (hcosa+2zsina) es ae Gt Bye : (10-20a) eae _ ER (h + 2) _ ER’ x : For a = 45°, V 2/2 (a? + ; and for a = 90°, V . @+ wie The point of maximum potential for a = 45° is given by x = h(4°/17 — 3)/4; 0.281h is a maximum and —1.781h a minimum point. At both points the current density is zero (see Fig. 10-24a). By re- peated differentiation, the points of maximum and minimum current density are found at x = 0.55h (max.), 2 = —0.425h (min.), and x = —2.1h (max.) (see Fig. 10- 24b). For a = 90°, the point of maximum potential is at x = +h/+/2; and the current density at x = O is a minimum and at x = +1.22h is a maximum. Simple relations may be derived for the self-potential of an ore body ‘ Fie. 10-24b. Current density curves considered as a polarized bar with or polarized spheres of various angles : : of polarization. a negative current source on its upper end and a positive source on ‘its lower end. Assume the ore body to be located in the zz plane, so that the vertical distance of its upper end from the surface is h; , that of its lower end is hz , its projection on the z axis is a, and the distances of its ends from a surface point are 7, andrz. The coordinates of this point are x and y and the 0-point of the system is assumed to be directly above the Cuap. 10] ELECTRICAL METHODS 675 upper end. Then the potential for the upper (negative) source or sink is V; = — pl/2mr and that for the lower source is V2 = pl /2mre , so that the total potential anit er (4 in =): (10-200) Substituting n= Vaetyt+hi and re = V(x —a) +y¥ +hi, the potential is Hi 0iks S (Gigi iy? ie — 0)? ty? n-. (10-20e) To what extent the second term is effective depends on the length of the ore body. The negative center becomes displaced from a position above the negative pole in proportion as the body becomes shorter and the dip becomes less; until, for a fiat-lying body, a positive and negative anomaly of equal strength will be observed. As before, depth rules can be calcu- lated for various angles of dip of the bar. Such calculations are simplified by moving the point P into the xz plane (y = 0). The effect of a dipping polarized sheet may be derived from the one previously treated by assuming polarized lines instead of point sources at the upper and lower ends of the body. Calculations and curves are given by Edge and Laby.””” D. CoRRECTIONS Compared with other electrical methods, few corrections and inter- ferences occur in self-potential surveying. (1) For very accurate surveys a correction for polarization of electrodes may be determined and deducted. (2) In hilly country, corrections may arise from uphill currents (due to the fact that in the earth’s electrical field, localities of higher elevation are at a different potential). The topographic effect is not so pronounced in the self-potential as in the equipotential-line method (in which the entire ground is energized and, therefore, the distribution of potential is influenced by topography). EK. RESULTS The self-potential method has been applied to the location of: (1) sulfide ore, (2) anthracite coal, (8) metals in placer deposits, (4) formation 21e Op. cit., p. 244. 676 ELECTRICAL METHODS [CHap. 10 boundaries, and (5) pipe corrosion. Since Schlumberger made his famous measurements on the Sain Bel pyrite ore body in France in 1913, nu- merous sulfide ore bodies and mine prospects have been surveyed by the self-potential method in all parts of the world. A discussion of two examples will suffice. One is the survey of the Hope Mine in British Columbia (see Fig. 10-25) (about eighty miles from Vancouver). Nickeliferous pyrrhotites with a proved tonnage exceeding 500,000 tons occur in the vicinity of a pyroxenite dike in granodiorites. In 1930 a self-potential survey showed a& prominent indication near the mine where ore was not suspected. The potential anomalies exceeded 300 mill- ivolts. A trench dug at the indication (see figure) re- vealed an ore body of pyr- rhotite about 40 feet wide. One of two inclined drill holes traversed a mineralized zone about 70 feet wide, leaving it at a depth of 176 feet. Self-potential phenomena are not necessarily limited to large and very massive ore bodies. They have also been observed on “stringer” types Scale of mineralizations. Fig. 10- 0 100 200 306 ° —~a -sr-—s«:« 26-s shows: a. self-potential Fic. 10-25. Self-potential profiles at Hope Mine, SUIVeY made in the Pallieres British Columbia (after Geoffroy). region in the Département du Gard in France. The geologic section is characterized by an extended contact zone with Paleozoic granites on the east and Triassic arkose and Rhetian shales on the west. Resting unconformably on the shales are limestones and dolomites of Hettangian age. The mineral solutions have been forced into the contact zone from below and have followed the bedding planes and shattered zones in the sandstone and shales as well as in the limestones, thus giv- ing rise to the pattern shown in the figure. The self-potential survey clearly reveals the areas of greatest mineral concentration (mostly pyrite). PiV PI Pil PM PV = ~- —— Potential Profile oe Equipotential Line Pyrrhotite Ore Body Cuap. 10] ELECTRICAL METHODS 677 Anthracite coal is a good conductor of electricity and also shows strong spontaneous polarization. A positive potential center, instead of a nega- tive one, is found on the upper part of anthracite beds.” It was found by Ostermeier” that metal concentrations in placer de- posits may show spontaneous polarization. In the rivers of the bight of @ 100 500m. Potentials between -30 & -50m. pie. 40" 00 G A, BE Fig. 10-26. Self-potential survey on mineral stringers in the Palliéres contact zone, Département du Gard, France (after Poldini). Cienaga in Colombia, conditions appear to be favorable because the river gravels contain boulders with impregnations of pyrrhotite which are prob- ably in the immediate vicinity of the mother lodes partially eroded by 22 See S. F. Kelly, Eng. and Min. J., 114(15), 1922. 43 Metall und Erz, 30(2), 21-24 (1933). 678 ELECTRICAL METHODS [CHap. 10 the river bed. A cane provided with two electrodes at its end and a simple potentiometer consisting of a rheostat, galvanometer, and dry cell was sufficient to locate the eroded veins and boulders in the river bed (see Fig. 10-27). By accurate spontaneous polarization measurements, taken at short intervals, small potential differences have been established on formation boundaries.” At five-meter intervals the potential differences are of the order of several tenths of a millivolt, whereas in undisturbed terrain their value is generally but one-tenth of this magnitude. Boundary potentials are probably caused by differences in the conductivity of solutions filling the pores, so that ‘“‘concentration elements” are formed (see 1, A, page 631). 10 Scale Divisions u) Fic. 10-27. Spontaneous polarizations obtained on ore placers and eroded veins in Colombia (after Ostermeier). In Fig. 10-28, curve b shows the potential gradients; curve b’ shows the potentials, and the section below indicates a formation boundary between granite and gneiss which was located on the basis of the potential measure- ments by four auger holes. | In areas of metamorphosed sediments it is sometimes possible not only to locate formation boundaries but also to make more detailed studies of geologic structure. Conditions shown in Fig. 10-29 made the self-poten- tial method applicable because graphite occurred in some of the kéy beds. In the copper district of Katanga the ore occurs in anticlines of the so-called mine series of the Kundelungu formation, made up largely of slates and dolomites and containing a graphitic horizon. Another similar horizon occurs in the so-called Muaslira series, immediately beneath the Great 2H. Hunkel, Zeit. Prakt. Geol., 36(7 and 9) (July and Oct., 1928). Cuap. 10] ELECTRICAL METHODS 679 Kundelungu conglomerate. It was possible to determine the boundary of the area occupied by the conglomerate and to locate the uplifted por- tions of the beds in the mine series. The extreme right of Fig. 10-29 shows plainly the rela- tion between the loca- tion of a mine and the maxima in the self- potential anomaly. The problem of pipe line corrosion is one of great commercial impor- tance. Extensive studies have been made in recent years to determine its cause and to devise reme- dies. Various electrical prospecting methods and modifications thereof have been instrumental in making possible a better understanding of the phenomena involved. When a metal is im- mersed in a conductive liquid it emits positive ions and takes on a nega- tive charge. Under nor- mal conditions an equili- brium_ is_ established, since the positive ions are held near the metal by the negative charge. Two agents will disturb this equilibrium: 1. Acid solutions (rich Folge aeons Lae fl . 1G. 10-28. Potential gradients, potential profile, a ot, sulfate, and and geologic section uncovered on the basis of the chloride ions). These survey (after Hunkel). have a tendency to elimi- nate the metallic ions as soon as they appear, and the metal will there- fore be strongly attacked. Destruction will occur at the points of lowest potential, that is, in the anodic zones or zones of positive potential. 2. Stray currents. Metallic conductors attract currents in certain zones 680 ELECTRICAL METHODS [CuHap. 10 in the vicinity of power plants, trolley lines, and the like, and discharge them again in others. Current is collected in the negative zones and leaves the conductor in the anodic or positive zones. It is again in the latter that the destruction of metal occurs. The effects described are related as cause and effect. In the former, chemical action is the cause SELF-POTENTIAL SURVEY of AREA near KATANGA Sca/e 500 100m paps SinD ins Oh Potential: 5409 600 1200 mv Fie. 10-29. Location of folds of graphitic slates in Katanga (after Poldini). Millivolts Distance, Meters 8 Pipe Collecting Current |. Current | @ orrosion Zone); | Ditterences of Potentials + D S Pipe Discharging Current Corrosion Zone) Fic. 10-30. Location of corrosion zones in pipes by self-potential measurements (after Schlumberger). of the current; in the latter, extraneous currents produce the chemical reactions. Since anodic zones are generally located in areas of low resistivity, sys- tematic studies of the resistivity of soils around pipe lines have been made. Another line of attack is to measure the acidity of soils to determine their corrosiveness. Self-potential methods are used for the determination of Cuap. 10] ELECTRICAL METHODS 681 the zones.of egress when the corrosion is of a chemical nature or is produced by stray currents not due to industrial plants. Measurements are made in the customary manner with nonpolarizable electrodes at short intervals to locate zones of positive potential. Fig. 10-80 shows measurements made in this manner along 2300 feet of pipe line in Paris, at intervals of some 65 feet, establishing two corrosion zones by their positive potential. C. and M. Schlumberger” have described these and other methods for the location ‘of corrosive zones in more detail. IV. EQUIPOTENTIAL-LINE AND POTENTIAL-PROFILE METHODS A. ConDITIONS IN STATIONARY FIELDS When electric energy is applied to two points at the ground surface, an electric current will flow between them because of their difference in po- tential. If the medium between the two electrodes is homogeneous, the current and potential distribution is regular and may be calculated. When good or poor conductors are imbedded in this homogeneous medium, a distortion of the electrical field occurs. Good conductors have a tendency to attract the current lines toward them while poor conductors force them away. Theoretically it should be possible to detect bodies of different conductivity by measuring the geometric disposition of these current lines. In practice this cannot be done with sufficient accuracy; it is necessary to determine the direction in which no current flows by locating points which have no potential difference. Using a null method has the advantage of both accuracy and ease of procedure. Quantitative measurements of po- tential difference are not required when the lines of identical potential, or “equipotential lines,” are traced. For homogeneous ground the potential variation in both a horizontal and a vertical plane is illustrated in Fig. 10-31. The potential gradient is not uniform; it is greatest in the vicinity of the electrodes. The ‘‘current lines’ are concave to the surface because of the repulsion of adjacent current fibers. Equipotential lines, at right angles to the current lines, are circles only in the immediate vicinity of the electrodes. Elsewhere in the horizontal plane and vertical section, they are curves of the fourth degree. For a stationary field the potential distribution in homogeneous ground can be calculated. By a stationary field is meant here a field which does not change with time and is produced by direct current after equilibrium has been reached. The results obtained apply also to A.C. fields if skin effect and elliptical polarization are neglected (quasi-stationary fields). A 25 A.J.M.E. Tech. Pub. No. 476. The trade journals covering oil and gas trans- portation currently carry articles dealing with pipe corrosion. 682 ELECTRICAL METHODS [Cuap. 10 V Current Flow £ | ~—N — WA — | ——&&——_ & Fig. 10-31. Potential ana current distributions in vertical and horizontal plane (partly after Schlumberger). Cuap. 10] ELECTRICAL METHODS 683 determination of the potential distribution for the horizontal or vertical plane is possible by calculating the potentials of each electrode separately from Ohm’s law for the semi-infinite space and by combining them for any given point. The resistance of a hemispherical shell with the radius r, the thickness dr, and the resistivity p is dR = pdr/2nr’, and the potential drops from the inside of the shell to the outside by the amount —dV = IdR. Therefore, from an integration of this expression and a similar one for the second electrode, the potential at any point is ve ar (2 fi a (10-214) The ‘‘equipotential surfaces’ are defined by the expression 1/r — 1/r’ = constant and are surfaces of revolution of the fourth order about the base AB. In the vicinity of either electrode 1/r’ is negligible compared with 1/r and the equipotential surfaces are nearly spherical. The poten- tial gradient or electrical field strength is proportional to the inverse square of the distance, or ea) pl At 1 ee + i). (10-216) The addition is vectorial. As applied to the surface, this becomes _ pl fl — i E = = G “- EID. (10-21c) (algebraic addition). In the center between two points of the distance (base length) b, Baieit ood (10-214) arb? arid the current density 7 at any point below the center in the vertical plane is ig = %-COs’ 9, (10-21e) where ¢ is the angle subtended by a ray from the electrode to this point with the horizontal plane. For given fractions of the current density at depth d in terms of the density at the surface center, the corresponding depths can be determined. C. H. Knaebel” and W. Weaver” have calculated the portion of the current penetrating below a depth d through a section at right angles to the electrode basis (see Fig. 10-32). 26 Mich. Coll. Min. Bull., NS, 6(2) (Jan., 1932). 27 W. Weaver, A.I.M.E. Geophys. Pros., 70 (1929). 684 ELECTRICAL METHODS [Cuap. 10 As previously stated, a determination of the direction of current lines is impracticable since there is but little change in potential away from the direction of maxi- mum current (see Fig. 10-33). In the direction x of maximum potential difference, the electrical field is -—dV/dzx. In any other direction 1, it is —dV/dr. Since r = x/COs a, aM a dr E, cos Qa, (10-22) so that the vector, for all % values of a, is repre- ; sented by a figure eight. Fig. 10-32. Fraction of current penetrating below Thi laine the stenee depth d, as a function of the ratio of depth and base Is explains the sharp length (after Knaebel). ness of the nulls observed in the location of equi- potential lines, a condition which is strictly true for direct current only. Equipotential Line Current Flow Amplitude Curve Fig. 10-33. Relation of amplitude curve, and directions of equipotential and current lines. Cnap. 10] ELECTRICAL METHODS 685 B. Conpitions ror A.C. FIeups The use of alternating current for potential investigation introduces two limitations which may prove to be severe if experimental conditions are unfavorable: (1) reduced depth penetration and (2) elliptical polarization. Contrary to direct current, the passage of alternating current is con- trolled by the capacitive and inductive reactance as well as by the resist- ance of the circuit. For a conductor of sufficient section the inductance of the current fibers in the interior is greater than that at the surface. Thus the current has a tendency to flow nearer the surface. For very high frequencies the current is confined to the outermost ‘‘skin.”’ Relations governing the depth penetration of A.C. such as used in equi- potential-line methods (300 to 1000 cycles) may be derived from the laws of electromagnetic wave propagation by introducing certain simplifications. Since for the above frequencies the displacement current may be neglected, the current density at a depth d from the surface of a conductor (where the current density is 7%) may be written 2nd, Ss i= pe ee ain (2. — = Vile), (10-23) where the depth is in centimeters, f is frequency, pu is permeability, o is conductivity (in e.s.u.), c is light velocity, and ¢ is time. The equation states that an attenuation of amplitude and a phase shift between surface and depth current occurs. The attenuation for the peak values of the current is therefore 2rd ones Te Tene ye (10-230) where the permeability has been assumed to be equal to 1. Hence, the depth at which the surface-current density has dropped to 1/e of its value, with p as resistivity, is aie p pa d= an VF (10-23c) Since the presence of good conductors at the surface or near the surface reduces the depth of penetration, provision is made in some A.C. methods to lower the frequency when greater penetration is desired. Fig. 10-34 shows the depth penetration of alternating currents of the frequencies 1, 25, 60, and 500, as a function of resistivity, in double logarithmic scale. For any other frequency the penetration may be read off on the frequency scale, which is half that of the depth scale, since the penetration is inversely proportional to the square root of frequency. 686 ELECTRICAL METHODS [CHap. 10 In a single A.C. field, the voltage oscillates between its extreme positive and negative values on a current line. The projection of its amplitude variation with time on a horizontal plane is a straight line. The voltage drop is a maximum along this line. At right angles thereto a true equi- potential line is present. Conditions are therefore the same as in the D.C. fields. If another A.C. electrical field, or fields, interferes, one of the two - following phenomena will occur. If there is no phase shift between the Frequency Scale 500 cycles Resistivity in Ohm-cm 10 6 6 4 2 0 100 000 10000 * 0000 Fig. 10-34. Depth penetration (d at Jo/e) for alternating current of various frequencies, as a function of resistivity (permeability = 1; displacement current neglected). fields, conditions remain as before. The maximum amplitude of the vector is the resultant of the maximum amplitudes of its components. The pro- jection of its time variation on a plane will still be a straight line. If, however, the other field or fields are shifted in phase with respect to the field considered, elliptical polarization of the resultant field occurs. This occurrence derives its name from the fact that the projection of the time variation of the resultant vector upon a plane is an ellipse. The out-of- phase field may differ from the original field in direction or in coordinate. Cuap. 10] ELECTRICAL METHODS 687 Elliptical polarization may be readily demonstrated if it is assumed that the additional field differs from the original field in respect to both direction and phase by 90°. If the time variation of the two fields is represented in two vertical planes at right angles to each other (Fig. 10-35) and if the main field is assumed to have the larger amplitude and the interfering field the smaller one, the length of the resultant vector I will be equal to the maximum amplitude A of the larger field at the instant 1, since the amplitude of the second field is zero. At the instant 2 the amplitude of > 3 /\ x \\) Y YK as ie. F/ \\\ \\ (==, 25 = DQ D0 fe Zi ra oF UZ Lemniscate of Potential Amplitude ING i) A Time Ellipse of x Vector Oscillation Ww Fig. 10-35. Elliptical polarization of an electric field when its components are 90° out-of-phase and differ in direction by 90°. the larger field has decreased; the amplitude of the smaller field has in- creased; and their resultant is given by the length and direction of the vector II. At the instant 3, the resultant field is given by the length of vector III. At the instant 4, the amplitude of the larger field is zero. Hence, the vector IV has the length B and is at right angles to the vector I. The same phenomenon recurs in the three remaining quadrants. A line connecting the ends of the vectors is an ellipse. The variation of the field amplitude with horizontal direction was pre- viously represented by two adjoining circles (Fig. 10-33). If this pro- 688 ELECTRICAL METHODS [Cuap. 10 cedure is applied to both fields considered here, two figures eight result, rotated 90° in respect to their larger axes. Amplitudes resulting from each are superimposed. If in any given direction the amplitude of the large field is PQ and that of the smaller field PR, the resulting amplitude is PS = PQ + 7PR. Plotting the amplitude of the PS vector for the entire horizontal plane, we get a lemniscate. If the small out-of-phase field were not.present, a single figure eight would represent the amplitude variation. An absolute zero would be obtained in the direction of the equipotential line. With an interfering field, however, the sound never vanishes. Only a minimum is observed, whose sharpness depends on the amplitude of the out-of-phase field. Out-of-phase fields in electrical prospecting may be due to a variety of causes. Currents traversing media of different conductivity, capacitance, and inductance, will be shifted in phase. Further, ground currents and electrode leads will induce out-of-phase currents in adjacent conductors. For two field components at an arbitrary angle with one another and with a phase shift of 90°, polarization conditions are the same as for two components at right angles to each other but with an arbitrary phase shift. Two adjacent currents with a phase shift of 90° produce a transverse com- ponent with a phase shift depending on the respective amplitudes of the currents. If the one component is X and the other transverse component is Y, we have, therefore, for the general case of two out-of-phase components at right angles to each other: X = Asin wi Y =B sin (@t — ¢), (10-242) where w is the angular frequency and ¢ is the phase shift. Since sin wt = X/A, and Y = B (sin wt cos ¢ — cos wt sin g), Y becomes equal to x xX. B (cos g— 4/1 — asin °) or, xX ae. © Y - Ba: cosg = 84/1 — qa sie. Squaring both sides and dividing by B’ gives YP oxy y.. eae) — —_— ———— —_> - == § — 4 RB: ap °°? + a sine (10-245) Dividing by sin’ ¢, Ve 2XY cos ¢ x’ STOTT (a aA oe FV LO LL GC ae ee 1 B?sin?g ABsin?¢ A?sin?¢ : Cuap. 10] ELECTRICAL METHODS 689 which has the form La’ + 2Mry + Ny’ = 1 (10-24) and is the expression for an inclined ellipse whose major axis is tilted in reference to the xz axis. In this equation, he LON aa COSuD I: oy Lo ~ A? sin? gy’ ~ AB sin? g’ ~ Be sin? yg If the phase shift is 90°, it is seen that the major axis of the ellipse coin- cides with the z axis, so that Yy? y’ : a aE ay ihe (10-24d) which is the standard form of the ellipse. To determine the angle of deviation y of the ellipse (given by eq. [10-24c]) from the x axis, ro- tate the system of coordinates so that x = 2, cos ¥ — y sin wy and y =x, sin y + y: cos y. By substitution in (10-24c), zi[L cos’ y + N sin’ y + 2M sin y cos y] + yi[L sin’ y + N cos’ y — 2M sin y cos y] (10-24e) + 22y:[(N — L) sin y cosy + M(cos’ y — sin’ y)] = 1. In this new system an equation of the form of (10-24d) must obtain, and therefore the coefficient of 27,y, must be zero. This leads to 2M tan 2y = Low: (10-24f) By substituting for L, M, and N their values given before, 1 _ cos¢g e Bias which is the same as eq. (10-18d) given in connection with the discussion of the elliptical polarization of radio waves (there the tilt angle was measured from the Y and not from the X axis). The axes of the ellipse may be determined from eq. (10—24e) by casting it in the form of the standard ellipse as in eq. (10-24d). Designating the coefficient of x} by U and that of yj by Q, Uri + Qyi = 1, (10-24h) 690 ELECTRICAL METHODS [Cuap. 10 where U =Lcos’ y+ N sin’ y + 2M sin y cos y (10-247) Q =Lsin’y + N cos’ y — 2M sin y cos y. Forming the difference D, we have D=U-Q=(Q1-N) cos 2y + 2M sin 2y, and substituting eq. (10—-24f) we get : 2M L—N sin 2y = + /aM? + (L — Ne and cos2y = + Vin? + (LN) The difference is D=U-Q=+V4M + (L — NY (10-25a) Since from eq. (10-242) the sum U + Q =L +N, and U — Q = D, the coefficients are U = (L+ N+ D)/2 andQ = L+N — D)/2. In the standard form of the ellipse, (X’/A’ + Y’/B’ = 1), A is the major semiaxis and B the minor semiaxis. By comparison with eq. (10-24h) the squares of the semiaxes of the ellipse in the z’y’ direction are a = 1/U and b° = 1/Q, so that 2 2 — “ "DEN — V/4Me + (L — W)? and (10-256) 2 2 TEN Var to — 3 The sign before the radical determines which is the major and which the minor axis. By substituting the values forL, M, and N from eq. (10—24e), the square of either semiaxis is 2 72 2A’B’ sin? gy B’ + A’ + +/4A?B? cos? ¢ + (B? — A’)? By substituting the ratio major axis/minor axis = a/b =r, and by further substituting the tilt angle relation given in eq. (10-24g), formula (10-18c) is obtained, allowing for the fact that the tilt angle is reckoned from the Y (vertical) component. Two fields 90° out of phase, forming an arbitrary angle with each other likewise give rise to elliptical polarization. The theory is treated in sec- tion vir (page 787), as it is of importance in electromagnetic and inductive electrical prospecting methods. Cuap. 10] ELECTRICAL METHODS 691 The amplitude variation of the electrical field in a horizontal plane, in the case of elliptical polarization, differs from that for D.C. which was previously represented by two circles (Fig. 10-33). Since elliptical polari- zation may be assumed to result from a combination of two fields at right angles to each other, their combined amplitude variation follows from a superposition of two amplitude circles at right angles to each other. Since in each circle the amplitude variation is represented by a cosine law, the resultant amplitude in a line connecting the probes OA (in Fig. 10-36) is OA = Va? cos? a + Bb? sin? a. (10-262) Numericel Values: Fic. 10-36. Relations of amplitude, direction, phase, ellipse- and lemniscate characteristics in A.C. potential fields (adapted from Ambronn). The phase 6 in the line OA with respect to the phase in the direction of the major axis may be calculated, though in practice the procedure is reversed, since the phase difference is measured and the characteristics of the ellipse are obtained from it. Assuming the ellipse to be known, a tangent drawn from the point A will give points F and B. The normal to the x axis through F intersects a circle-drawn about O with the radius a in the point C. The direction of OC with respect to the x axis is the phase angle in the line OA. These geometric relations may be expressed by the following equations: (1) ==, COs\.0; (2) y = bsin 6. 692 ELECTRICAL METHODS [CHap. 10 Since the inclination of the tangent to the ellipse is given by tan (90 — a) = b” x —-—, we have ay 2 ney (3) tan a = hice Dividing eq. (2) by eq. (1) and substituting in (3), we obtain the following relation between the azimuth of the line and phase angle tan a = 5 tan 6. (10-260) If we substitute eq. (10-26b) in eq. (10-26a), the amplitude in the line OA as a function of phase angle and ellipse axes is 0 ab? MES Ni b? cos? 6 + a? sin? 6” ate In the mapping of the A.C. ground-potential distribution, it is not customary to survey the ellipse and deduce the ratio of major and minor axes and ratio of in-phase and out-of-phase field components, as is done in the determination of propagation characteristics of radio waves. When elliptical polarization is noticeable, potentials are generally determined with a compensator which measures their amplitude and phase with ref- erence to those of the primary supply; or else the in-phase and quadrature potentials are determined, and equipotential lines are drawn separately for each. These procedures are discussed in the following section. C. FIELD PROCEDURE; EQUIPMENT Direct or alternating current may be used for surveying equipotential lines. Direct current has the advantage that the equipotential points can be located with greater precision and that the galvanometer gives a clear indication of the direction in which.to move the electrode. A disad- vantage is the necessity for porous pots and the interference from polariza- tion and other D.C. effects. Alternating current has the advantage of portability and convenience of the movable circuit, possibility of amplifica- tion of signals, and freedom from commercial current interference. Dis- advantages may arise from its use in highly conductive regions because out-of-phase components prevent a location of equipotential points. For mapping D.C. equipotential lines, a small D.C. generator (1 KVA, 200 volts) driven by a gasoline engine (of ample power margin for higher altitudes) is generally employed. Current electrodes are iron pegs, coils of copper wire, or copper screens. Equipotential lines are traced with non- polarized electrodes connected by a wire to a galvanometer. The primary Cuap. 10] ELECTRICAL METHODS 693 electrodes are laid out up to a mile or more apart so that the equipotential lines over the section of ground under consideration will be approximately straight and parallel to one another. In the planning of the survey, the general geology of the region should be considered and electrodes should be so laid out that the equipotential lines will be at right angles to the strike. Modifications may be necessary to suit special conditions. For instance, for determining the outline of partly accessible ore bodies, the primary electrode may be connected to the ore body thus making its outline an equipotential surface. Ina similar technique one electrode is connected to a formation in a well so that its strike and dip near the surface is re- vealed by its equipotential pattern. Because of an increased conductivity in the direction of the bedding planes, equipotential lines surrounding one electrode in a stratified medium are elliptical, with the major axis in the direction of strike. It is possible to number equipotential surfaces and to determine their interval by the following arrangement: Near the primary electrodes two auxiliary electrodes are placed in the ground in such a manner that their potential difference is nearly the same as that between the primary elec- trodes. These are connected to the ends of a high resistance slide wire. To find the potential of a given point or line, the point or line is connected through a galvanometer to the sliding contact, which is changed in posi- tion until the galvanometer deflection vanishes. If the resistance on one side of the tap is R; and on the other R:, Ri/Re = Vi/V2, which may also be written Ri/(Ri + Re) = Vi/(Vi + V2), since both the total re- sistance and the total potential difference between the points A’ and B’ are known. For subtracting from the measured potentials the normal potential variation due to the primary electrodes, formula (10-21a) is applied. Substituting, for the center line connecting the two electrodes, the value b for the base length and designating by z the distance of a point P from the center, the potential at that point is V = + 82r/(b” — 42’), the sign depending on whether the point is closer to the left or right electrode. A.C. equipotential-line methods may be divided into two groups: (1) methods applicable when elliptical polarization is negligible and (2) methods for the determination of potentials in respect to amplitude and phase (or by their in-phase and quadrature components). Point or line electrodes may be used; their arrangement is the same in both methods. Point electrodes should be laid out with their base line parallel to the supposed strike. Line electrodes are laid out at right angles to the strike and have the advantage that the “normal” equipotential lines are parallel with the primary electrodes; therefore, distortions are more readily inter- preted. Line electrodes are usually bare stranded copper wire and are 694 ELECTRICAL METHODS [Cuap. 10 tacked to the ground at numerous points by steel pegs. In ore prospecting their distance is 2000 feet to a half mile and their length of the same order or greater. To cover large areas, the electrodes are leapfrogged, since too great a distance between electrodes reduces the distinctiveness of response. The normal field of line electrodes is no longer given by formula (10-21a) and may be derived as follows. With reference to Fig. 10-37 the potential at the point P is given by y= a (flea mf ieee where EF is one half the potential difference between the electrodes. Hence, i ht+tvVr+ Pb + Vr + Bri V, = E log. — ——— h+Ve+B(bh+V+ Bri On a line of symmetry where 1, = J, = 1, the potential is Vi = 9 lo gle + x)(l are Ji? + (a — x)?) (10-27) (a—z)l+VJVP+ (a+) g The electrical (field and, therefore, /K— a a —— the current density) is greater with line electrodes than it is with point electrodes. In most equipotential, electro- magnetic, and inductive surveys, portable gasoline-engine driven alternators of a frequency of 500 to 1000 cycles are used, furnish- ing from 200-1000 KVA at 110 or 220 volts. The equipment for surveying equipotential lines consists of two search electrodes, an amplifier, and headphones when _ out-of-phase fields are negligible. It is supple- mented by more elaborate bridge arrangements when a complete determination of A.C. potentials in regard to phase and amplitude be- comes necessary. In many cases, Fig. 10-37. Line electrodes (adapted from 2 : Heine). even if out-of-phase fields exist, Cuap. 10] ELECTRICAL METHODS 695 the minima in the amplitude curve can be determined with sufficient accuracy for the mapping of equipotential lines. The search electrodes are usually copper-jacketed steel rods. For dry ground the Imperial Geo- physical Experimental Survey found a ‘‘self-watering” electrode helpful.” Almost any kind of a two- or three-stage amplifier may be used for equi- potential-line surveying, provided that it is light, small, and does not depend on storage batteries for filament supply. Circuit diagrams and descriptions will be found in the reports published by the I.G.E.S. In conducting equipotential-line surveys, several parties may work concur- rently. At least two parties can work in two sections of the area covered by one electrode layout and more can be kept busy with two or more simultaneous electrode arrangements, which may in many cases be sup- plied from the same power source. Two men are required to map equi- potential lines, which should be marked with stakes and be surveyed with a compass (in areas where large declination anomalies are absent) and a 100-foot tape. More quantitative surveys of the potential field require A.C. bridge arrangements. With one of these the voltage ratio and phase difference of adjacent portions of ground are measured. Details are given in sec- tion vi. Another type makes possible a determination of complex poten- tials in reference to the potential and phase of the generator; it therefore requires a ‘‘reference” lead from the bridge to the generator. The voltage difference and its phase are measured directly or the potential is split up into its in-phase and quadrature components; thus, in-phase and quadra- ture equipotential lines may be mapped. In the compensator illustrated in Fig. 10-38, the generator is coupled through a power transformer to the primary electrodes and through a phase transformer to the reference lead. The reference voltage is then supplied to the four coils of a variometer in such a manner that two of them (V; and V2) are provided with current in phase with the generator current whereas the other pair (V3 and V4), coupled to the reference lead through an air-core transformer, receive current in quadrature. The resultant field is picked up by the secondary coil of the variometer whose position determines the phase of the reference voltage that is taken off on the terminals of the potentiometer P. No sound will be heard in the headphones if the ground potential is com- pensated, in regard to amplitude (potentiometer adjustment) and phase (variometer adjustment) by the reference potential. If this compensator is used for the determination of electromagnetic fields in reference to am- plitude and phase of the generator potential, a search coil is substituted for the ground probes. Data obtained with this compensator may be 28 See Edge and Laby, op. cit., p. 265, Fig. 197. 696 ELECTRICAL METHODS [CHap. 10 represented by lines of equal potential, by equiphase lines, or by in-phase and quadrature equipotential lines. The compensator shown in Fig. 10-89 permits of determining the real and imaginary components directly. The generator side is connected, as before, to the reference lead; the reference voltage is split up into its com- Primary Electrodes Search Electrode Fic. 10-38. Arrangement for determining amplitude and phase of ground poten- tials (adapted from Ludwiger). PH, phase transformer; G, ground transformer; A, amplifier; T, air-core transformer; P, potentiometer; Vi-, variometer coils. RORY : Primary Flectrodes Search Electrodes Fig. 10-39. Bridge arrangement for determining in-phase and quadrature potentials (adapted from D. C. Gall). ponents which are applied to the in-phase potentiometer P and quadrature potentiometer Q. These are connected to the search electrodes through two switches, SS, which permit of changing the sign of the reference components. Current null is determined by a differential transformer, D, connected to an amplifier, A. Cuap. 10] ELECTRICAL METHODS 697 D. INTERPRETATION The interpretation of an equipotential-line survey is empirical and is based largely on previous experience with the method as well as on a satis- factory knowledge of the geological features of the area under consideration. Owing to its speed, this method is of value for general reconnaissance. However, it is advisable to re-examine conductive zones thus located with other electrical methods. In many cases it is relatively simple to make a general qualitative interpretation of an equipotential-line survey by mark- ing off the axes of the conductive zones indicated by the greatest line distortions. 1. Equipotential-line anomalies of simple geometric bodies. Depth esti- mates are sometimes possible by measuring the displacement of the equi- potential lines from their normal position. What may be expected in the way of displacement may be calculated by assuming, for simplicity, that a subsurface body has the shape of a sphere and is traversed (in the x direction) by a current paralleled to the earth’s surface, so that it is equiva- lent to a horizontally polarized doublet. In eq. (10-19a) the potential of a charged sphere at a surface point P was given as Vi = m cos 0/?’, in which the electrical moment is proportional to the electrical field E so that m = pE and —V2 = pE cos 6/r’. Since the undisturbed potential at the point P is —zE, the resultant total surface potential is VS — rE cos — PROSE, (10-28a) The value of the factor p may be determined from the boundary conditions at the surface of the sphere, where the current densities (p2 = resistivity of the sphere, p; = resistivity of the surrounding medium) are given by IrodVgion Tend Vig ; nig ay el eg 10- Pl dR p2 dR ( 280) Since it follows from eq. (10-28a) that at the surface of the sphere (r = R) p —Vp = Ecosé ( — a) i (10-28c) substitution of eqs. (10-28a) and (10-28c) in (10—28b) gives p2 — Pi 3 = ° R O 10-28d : 2p2 + pi ( ) Substituting this in eq. (10-28a), Ud iledas he p2 — Pi R’ a V,= —ipz (1 + Pop =), (10-28e) 698 ELECTRICAL METHODS [Cuap. 10 with z = r cos 0, andE = ip,._ If the resistivity ratio k = p;/pe, the factor ; 2p2 al Pl k +2 ae 28f) expresses the effect of good or poor conductors imbedded in another medium on the surface potential (see Fig. 10-40). A “saturation effect’? occurs since, for poor conductors. one-half of the maximum effect is reached for a (inverse) conductivity ratio of 2.5, whereas for good conductors one-half of the maximum effect occurs already at a ratio of 4. Saturation Poor Conductor Saturation Good Conductor cal 10? 10 IIS 1 19S. 10 10? Fig. 10-40. Saturation effect in potential methods, for poor and good (approximately spherical) conductors. These relations hold for spherical or nearly spherical bodies. For elon- gated bodies the effect depends essentially on the extent of the body in the direction of current flow compared with the extent at right angles thereto. For elliptical bodies of various ratios of major/minor axis (« = a/b) traversed by current in the direction of the major axis, Hummel” has calculated the ratio of current density in the body to that in undisturbed ground (Fig. 10-41). Only in a body which is very extended in the direc- tion of current is the current density ratio equal to the resistivity ratio. It is noted in eq. (10-28e) that the anomalous potential of a sphere is inversely proportional to, the cube of its distance, and that it increases in 29 J. N. Hummel, Zeit. Geophys., 4(2), 73 (1928). Cuap. 10} ELECTRICAL METHODS 699 proportion to its volume. The second derivative of the potential with respect to x indicates that the current density is a minimum directly over the sphere and that a maximum occurs at x = +1.22h, (where h is the depth to the center of the sphere). If the sphere-were not present, the equipotential lines would be parallel to one another (for line electrodes). The potential of a line at a distance x’ would be —Ez’. With the sphere, the line is shifted to a position x with the potential given by eq. (10—28e), so that go —x = Ar=c. —. (10-29) Fie. 10-41. Current densities in conductors of various relative dimensions (e = axis ratio) as functions of. resistivity ratio (adapted from Hummel). By differentiation of this expression with respect to x it'can be shown that the maximum displacement of the equipotential lines occurs at a dis- tance x = 0.707h. The effect of other bodies on the distribution of equipotential lines may be calculated if they are of simple geometric shape.” However, in most cases, it is more convenient to determine the effects of such bodies by model experiments as discussed below. 2. Equipotential-line anomalies in stratified ground. Horizontally strati- fied formations do not permit the application of equipotential-line methods. Other potential methods must be used, the most important ones being the resistivity and potential-drop-ratio methods discussed in sections v and VI. 30 See J. N. Hummel, Zeit. Geophys., 4(2) 67-75 (1928); Gerl. Beitr., 21(2/3), 204-214 (1929). 700 ELECTRICAL METHODS [CHar. 10 However, in the case of dipping formations, equipotential-line surveys can give useful information on dip and strike because of the electrical ani- sotropy of stratified media. Schlumberger has designated the ratio of the transverse and longitudinal resistivities as ‘‘anisotropy coefficient.” For vertically stratified ground, the influence of anisotropy on the shape of the equipotential lines is most noticeable. The equipotential surfaces are no longer spherical about one electrode but are ellipsoids of revolution with the major axis in the direction of stratification. In plan view the trace of the equipotential surface will likewise be an ellipse, with the major axis in the direction of strike. The ratio of the axes is proportional to the ratio of the square roots of the conductivity in the direction of strike and that at right angles to the strike. When stratified ground is covered with glacial drift or other uncon- formable layers, it is necessary that the equipotential surfaces reach deeply into the stratified portion to make the deformations detectable. Hence, large equipotential ellipses whose minor axes are at least twice as great as the assumed cover thickness should be traced. Dips may also be deter- mined directly from the displacement of the ellipses if contact can be made underground with the formation under test. There occurs a refraction of the equipotential surfaces on formation boundaries. If a given line approaches the boundary in a medium with the resistivity p by the angle a, and if it is refracted into the second medium (resistivity p’) by the angle a’, the relation obtains: p tan a = p’ tana’. (10-30) The maximum refraction is obtained if the bisecting direction makes an angle of 45° with the formation boundary. Hence, it is advantageous to lay out the electrode basis at an angle of 45° with the boundary to be located. 3. In virtually all electrical methods, model experiments play an im- portant part because of difficulties encountered in the calculation of the electrical anomalies of geologic bodies. These experiments are made on a small scale in the laboratory where it is possible to simulate a number of conditions difficult of evaluation, such as topography, irregular shape of the ore body, and soon. In duplicating actual conditions on a small scale it is necessary to pay close attention to the fundamental equations con- trolling the electrical anomalies of subsurface bodies, since it may be necessary to change the conductivity scale when the geometric scale is changed. In accordance with formula (10-28¢), the potential of a sphere depends on the relative dimensions and on the conductivity ratio in refer- ence to that of the country rock. Hence, if both are duplicated in the laboratory, the observed potential anomalies may be expected to be dupli- Cuap. 10] ELECTRICAL METHODS 701 cates of those occurring in nature. Model experiments with equipotential lines and potential profiles are usually made in tanks filled with a weakly electrolytic solution. Model ore bodies are generally made of some readily available metal. Fujita” used a vacuum tube oscillator, line electrodes of bare copper wire, a copper sulfate solution (33 mg copper per 100 cm’), and phones (no amplifier). The secondary electrodes were made of glass tubes filled with mercury in which a coiled platinum wire was immersed and made contact with the surface of the solution. The model ore body consisted of a copper sheet 5 mm thick and 100 mm square. Fujita’s results may be summarized as follows: (1) The field between the line electrodes was uniform only in the central third portion. (2) For a conductive body the maximum distortion was observed when its strike was at right angles to the electrodes. (3) For a nonconductive body the maximum distortion resulted when its strike was paraliel with the line electrodes. (4) The dip of a model ore body could be determined from the difference in the disturbed area on either side of the suboutcrop. (5) The position most favorable for indications was in the center between the electrodes. (6) The greatest area of distortion was obtained when the length of the line electrodes was five times the length of the ore body and their distance three times. (7) The depth reached increased in direct proportion to the length of the ore body, the detectable depth being about 63 per cent of the length. (8) Thickness of an ore body was effective only up to a certain point; a saturation effect was soon reached. (9) Detecta- bility increased distinctly with dip. Considerable experimental work on model ore bodies has been done by Lundberg and Sundberg.” Fig. 10-42 shows equipotential lines as traced by the ordinary method (phones), in contrast with the in-phase equipo- tential lines located with a compensator. Out-of-phase equipotential lines appear to be of equal diagnostic value, as shown by Gall” in some model experiments (where, however, the out-of-phase potentials were introduced artificially by feeding an out-of-phase current into the arrangement at right angles to the main current). 4. Distortions of equipotential lines due to power leads. Generator leads often cause induction currents which are 90° out of phase with respect to the currents produced by contact. These induction currents deflect the equipotential lines from their regular position, and elliptical polarization occurs. Since it is not possible to apply a correction for the effect of the cable (in the ordinary procedure of mapping with amplifier and phones), the leads are generally so laid out that the interference is at a minimum. 31 Proc. World Eng. Congr. (Tokio, 1929), Part 5, Paper No. 436, pp. 143-281. 32 Beitr. angew. Geophys., 1(3), 298-361 (1931). 33 J. Sci. Instr., 8(10), 311 (Oct., 1931). 702 ELECTRICAL METHODS [CHap. 10 When complete observations are made by resolving the potential into its in-phase and out-of-phase components, the effect of the leads is readily recognized and may be separated from the in-phase anomalies. As a matter of fact, the out-of-phase potentials near the cable may be of great diagnostic value (see page 801). 5. Effect of topography. Barring the existence of highly conductive layers of irregular composition or thickness near the surface, the inter- pretation of equipotential line surveys in level terrain is generally not too difficult. However, with the exception of northern glaciated countries such as Canada or Sweden, ore prospecting work is usually carried on in mountainous areas where considerable interference may result from changes in topographic conditions. Depth = 20mm LO 50 L7 LO 125 150 L75 Lio Fig. 10-42. Potential anomalies on model ore bodies (after Sundberg). Solid lines: equipotential lines, traced by phones. Dotted lines: in-phase equipotential lines, constructed from amplitude and phase measurements. Topography is, first, of geometric influence. If a line connecting the two electrodes is not parallel with the surface, the ore bodies are not located vertically below their surface indications but are on a normal to the line connecting the electrodes.“ The second effect of topography is of an electrical nature. The earth’s surface represents the boundary between a conductive and a nonconductive medium; hence, the current lines, tending to follow the surface of the conductive medium will reflect, in vertical section, the contours of the surface, and the equipotential lines will show corresponding distortions. To correct for topography by analytical methods is not practicable. The usual procedure is to plot topographic contours, together with equi- potential lines, and to eliminate from consideration equipotential lines 4% W. Heine, Elektrische Bodenforschung, p. 107, Fig. 53 (1928). Cnap. 10) ELECTRICAL METHODS 703 tending at right angles to the topographic contours (see Fig. 10-43). Where this would involve discarding an entire survey, the only procedure left is a model experiment. Notwithstanding the marked effects of topo- graphic irregularities, it is observed in most applications of the equipo- tential line method that irregularities in surface geological features are of remarkably little effect. The only exceptions appear to be areas where highly saline beds occur at or near the surface. Zs 2G 2a HOLANDA (SEVILLA) MINE Qo JO 100 250m JScaLcé Fig. 10-43. Equipotential line survey in which most distortions are caused by topography (after Heine). E. Discussion oF RESULTS Equipotential-line and potential-profile methods have been applied to (1) location of ore, (2) structural studies, and (3) military and civil engi- neering problems. 1. Ore location. Probably the most extensive work with equipotential- line and potential-profile methods has been done in the Skellefte district in northern Sweden. Close to 120 square miles have been surveyed there systematically with electrical methods and more than twenty ore fields have been found. Conditions for electrical prospecting are exceedingly favorable because of a comparatively shallow blanket of glacial moraine and frequent ore indications in the form of ore boulders and float. Al- though these had been known for centuries, it was not until 1918 that systematic electrical prospecting was started. The ores in the Skellefte district occur in a leptite formation which corresponds in age to the Keewatin. It consists largely of volcanic rocks which were intruded, in Archean times, by large bodies of granite; this led to considerable metasomatic alteration and to deposition of ore. The 704 ELECTRICAL METHODS [CuHap. 10 more important ores occur in the form of large lenses in the leptite forma- tion. Others, likewise in the form of lenses, are found in black slates. K Etctredes ond Ewuipstential Lines EZZA Sitreng Electrical Indication (0 Tremch made otter Bectrical Survey Trench made before Electrical Survey a i ; N A } N ; VY N ENG j ‘a 7), 020 \ AMY ft). \\i zzz (| | Wy axommce! @ Fig. 10-44. Equipotential-line map of the Kristineberg ore field in Sweden (after Lundberg). The ore contains pyrite, chalcopyrite, pyrrhotite, ar- senopyrite, and gold. The ore bodies are from 40 to 600 m long, from 5 to 30 m wide, and are covered by glacial moraine which has an average thickness of 7 to 8 m. The more important ore discoveries resulting from the application of equipo- tential-line methods were at Kristineberg, Bjurfors, and Bjurliden., (The Boliden gold and arsenic deposit was located largely by elec- tromagnetic methods and is discussed in that connec- tion.) The equipotential survey in the Kristineberg field is illustrated in Fig. 10-44. Intervals between the primary electrodes were of the order of 150 to 200 m. Ore boulders had __ been found early in this field, and numerous test pits and trenches had been sunk. The distribution of these boulders first gave rise to the assumption that the strike of the deposits was north-south but no ore was found by these prospecting activities. An equipoten- tial-line survey was made in 1918, and in the same year two important ore bodies were located. By 1919 the entire field had been outlined. Out of eight prospecting trenches dug to test the indications, five encountered ore. The ore Cuap. 10] ELECTRICAL METHODS 705 bodies averaged 6 to 7 m in width and contained from 70 to 80 per cent ore. The field at Bjurfors has had a similar history. At first much trenching was done because of the abundance of ore boulders in the area, but no ore was found. The equipotential-line survey, started in 1918, was at first unsuccessful. The work was taken up again in 1922 when a party consisting of both geologists and geophysicists made a detailed survey of the area and located some strong equipotential-line distortions. The indi- cations were confirmed by diamond drilling, and commercial mineraliza- tion was encountered in the eastern and central portions of the field. In the eastern part the ores were about 5 to 9 m deep while in the western portion the ores ran from 16 to 20 m in depth. Kast of Bjurfors an extended zone more than 3 km long and over 1 km wide was surveyed in order to locate more ore bodies in the direction of strike. Numerous very distinct indications were obtained, some of them accompanied by magnetic effects. The presence of wet gravels in this area made trenching difficult, and exploration by drilling proved these indications to be largely due to graphitic and pyritic slates and noncom- mercial mineral impregnations. This survey is an example of extensive and distinct indications which are not due to commercial ore. In cases of this kind only repeat measurements with other electrical and magnetic methods, accompanied by as much geological mapping as applicable, will lead to correct interpretations. In the glaciated areas of the northern United States and particularly in Canada, where conditions are very similar to those in Sweden, the equi- potential-line methods have been applied successfully. In Newfoundland an extensive equipotential survey was made covering an area about 2 miles long and 1 mile wide, following the location of lead-zinc ore at the Buchans mine in the center of the area. The ore, consisting of lead-zine copper sulfides in a baryte gangue, occurs in lenticular masses in bedded tuffs and porphyritic lava flows of Archean age. The thickness of the glacial overburden varies from a very few to 60 feet. East of the Buchans mine large indications were found at Oriental; two of these were drilled and found to be high grade lead-zinc ore. West of the Buchans mine a large area of indications was encountered and was confirmed by a number of trenches. Subsequent drilling and underground work has indicated more than 3 million tons of high-grade ore. A number of equipotential surveys for ore exploration were made by Edge and Laby”™ in the eastern part of Australia (Queensland, New South Wales, Victoria, and Tasmania). 35 Op. cit., pp. 75, 78, 83, 85, 86, 92, 122, 128, 124, 129, 132. 706 ELECTRICAL METHODS A; Az A; Fic. 10-45. Determination of strike of sieeply dipping shale beds in Normandy, France (after Schlumberger). 2. Structural studies. Kquipotential-line studies have been applied to structural problems for determining strike of for- mations under over-burden. Fig. 10- 45 shows elliptical equipotential surfaces on dipping Silurian shales, interbedded between Armorican and May sandstones, and covered by Jurassic beds 200 to 300 feet thick. This survey was made to determine strike and to trace a siderite deposit on the footwall of the Silurian shales. 3. Miliary applications. The equipo- tential-line method may be useiul for the location of iron and steel objects in civil and military engineering problems. Fig. 10-46 shows an application of this kind to the location of a buried ammuni- tion magazine whose depth was about five feet. [Cuap. 10 Foliowing his model experiments with equi- potential-line methods, Fujita conducted exten- sive studies of the poten- tial distribution on the Suwa mine, 100 miles northeast of Tokyo. This mine is operating a large vein of cupriierous pyrite in schists on six levels at 100-foot intervals to a depth of 700 feet below the surface. The experi- ments were chiefly con- cerned with various ar- rangements of the line electrodes and attempts to derive the dip of the ore body (70°) from the relative disposition of the anomalous areas. Fig. 10-46. Location of a buried ammunition magazine by equipotential methods (after Ebert). Crap. 10} ELECTRICAL METHODS 707 V. RESISTIVITY METHODS A. GENERAL The equipotential-line methods discussed in the preceding section are best suited to the location of laterally limited geologic bodies, that is, bodies with vertical or nearly vertical boundaries. If they are used on norizontally stratified ground, only the spacing, but not the direction of the lines, is affected. 'To determine differences in spacing, potential gra- dients must be measured, that is, potential differences must be determined at no less than two points. If such measurements are supplemented by observations of current in the circuit, they are referred to as resistivity methods because (as stated on page 644) current measurements at two points Fia. 10-47. Lines of current fiow in layered section. (Conductivity of lower medium is fifty times greater than that of upper.) (After W. Weaver.) and potential measurements at two others will give the resistivity of bodies of aimost any shape. The effect of vertical changes in conductivity on surface potentials is illustrated in Figs. 10-47 and 10-48. . The more conductive lower medium (Fig. 10-47) vesults in an attraction of the current lines toward it. The current density in the upper medium is less than in the lower. Since the equipotential lines are at right angles to the current lines, their spacing, and hence the potential gradient, is likewise affected by the presence of layers of different conductivity. As shown in Fig. 10-48, the effect on the gradient varies with the conductivity, but it does not vary uniformly as far as conductivity ratio is concerned. The effect of a layer a hundred times as conductive as the surface layer is only about twice as much as that of a layer five times as conductive (saturation effect). Measurements of potential differences in the vicinity of one power elec- 708 ELECTRICAL METHODS [Cuap. 10 trode, or between two power electrodes, can therefore give information in respect to the presence of subsurface formations of different conduc- tivities. When these measurements are supplemented by measurements of current, it is possible to determine the resistance of the circuit. By applying a factor depending on the spacing of the electrodes, the ground resistivity can be obtained. This is a true resistivity only if the medium is homogeneous; if layers of different conductivities are present, it is an apparent resistivity. It is customary to calculate the apparent resistivity by the same formula that applies to homogeneous ground. The depth to which the resistivity is measured can be controlled by varying the spacing between the electrodes. This gives rise to two appli- OF > Fig. 10-48. Potential variations near electrode (outside and inside spread) for layers of different conductivity, at 40 feet depth (after W. Weaver). cations of the method. In the first, the spacing is kept constant and the arrangement as a whole is moved over the ground (resistivity mapping). In the second, measurements are made at one location which is the center of the measuring arrangement. From this center the spacing of the elec- trodes is gradually increased. Thus, the depth penetration is increased and the apparent resistivity is obtained as a function of depth (vertical electrical drilling). While four equally spaced electrodes are the arrangement most gen- erally used, other arrangements can be and have been applied. A deriva- tion of the formulas for the more common arrangements is given in the next article. CuapP. 10] ELECTRICAL METHODS 709 B. ELEcTRODE ARRANGEMENTS If, at the surface of the (homogeneous and isotropic) ground of the conductivity o, an electric current J is introduced by means of two point electrodes, A and B, and if the current flows from A to B, the potential at any point P on the surface is V, = (l/r — 1/re), where 7 and 72 To are the distances of a point P from the electrodes A and B, respectively. The potential difference between two points P and R, which have the dis- tances r;, ’2, and R, and Rz, respectively, from the electrodes is Ve-Meev= i (1-114 3) (10-31a) (10-31b) This equation holds for any position of the current electrodes A and B and the search electrodes P and R, and does not change when current and potential electrodes are interchanged. Differences in the position of the search electrodes with respect to the current electrodes give rise to various resistivity methods. By selecting definite dispositions, it is possible to simplify the field procedure or to give the expression for resistivity a form that will simplify the interpretation of the results. Seven different electrode systems are discussed below. They may be classified as follows: Group I Electrode Arrangements with Finite Distance of Power Electrodes 1 2 3 4 Symmetrical Wen- | Lee partitioning | Asymmetrical Asymmetrical ner-Gish-Rooney method double probe single probe method (four ter- method method minal) Group IT Measurements Near One Power Electrode; Second Power Electrode in Infinity 5 6 7 Double equidistant probe | Double probe method with) Single probe method method unequal probe spacing 710 ELECTRICAL METHODS [Cuar. 10 1. In the Wenner-Gish-Rooney method the two potential electrodes are placed on a line with the two current electrodes, so that all four electrodes are situated at equal distances from one another. With a as the distance between the electrodes, 7, = Re = a and rz and R; = 2a. Then the expression for the resistivity, from eq. (10-310) is p = 2ra i (10-31c) 2. In the Lee partitioning method an additional potential electrode is provided halfway between P and R. Two potential measurements are made, one for the left and another for the right interval. With r; = a, Te = 2a, Ri = $a, and R2 = Za, the resistivity p = 4xra —, (10-31d) where Vpc = Vpg is the potential difference between the center stake and the adjacent potential stake. 3. The asymmetrical double probe method is an arrangement with the two potential probes placed at equal intervals from one power electrode but unsymmetrically placed in respect to the center. If 1 is the distance between the current electrodes and a the potential-electrode interval, m1 = @,7,2 = 1 — a, Ri = 2a, and Rz = | — 2a, and the resistivity V 2a(l — a)(l — 2a) p = 2x T CS ate al (10-31e) Kq. (10-31e) gives the Wenner formula when l = 3a. 4. The asymmetrical single probe method results from the last by leaving out one potential electrode and measuring the potential of the remaining electrode against that of the next power electrode. Then 7; = 0, 72 = l, R; = a, and Rz = | — a, so that with V,. as half the potential difference between the power electrodes (V.—V) a(l —a) 7 2a (10-31) p = 2 5. The double equidistant probe method is a modification of arrangement 3, with the second power electrode far removed. With m = a, m = ©, R: = 2a, and R2: = o, p = 4ra = 3 (10-319) 6. The double probe method with unequal probe spacing differs from the last by an unequal probe spacing and is generally used with a potential Cnap. 10] ELECTRICAL METHODS 711 profile at right angles to the power electrode base. If 7; = a is the dis- tance to the first potential electrode and R; = b the distance to the second one, and R2 = rz = ~, 2rab OCU - gets 10- p G2 a7 (10-31h) 7. The single probe method corresponds to arrangement 4, with one power electrode in infinity. Since 7; = 0, re = ©, Ri = a, and Rz = ~ (V. am V) (10-317) Arrangement 1 is most frequently employed, for both vertical electrical drilling and resistivity mapping. Next in order is probably 2, then fol- lows 4. Arrangements 5 and 6 are con- venient for vertical electrical drilling and are used in the potential-drop-—ratio proce- dures with one additional potential elec- trode. Arrangement 5 is also applied in electrical logging. C. PorentTIAL FUNCTIONS FOR LAYERED MEeEbDIA 1. General.” If a difference in resistivity exists on a formation boundary (see Fig. 10-49) its effect may be represented by ak : a F oslue Fig. 10-49. Conditions on placing a plate with definite transmission Hounilereibatrecmtine media and reflection characteristics in the boun- of different resistivity. dary. Assume a source at P above the plate. Considering the phenomenon for the moment as one of light transmission, an observer at A facing the plate would see the point P by looking at its image J. The light at A would be that received di- rectly from P plus the amount reflected by the plate and appearing to come from the image J. If the dimming of the apparent source at I, due to reflection, be indicated by a factor k, the light and by analogy the potential at A is equal to its amount at the source diminished by the geometric effect of distance (1/r) plus the amount reflected, so that v,= of . 4 = (10-32a) 4x \r. fe 36 For a more rigorous discussion of the theory of images than the one given here to illustrate merely its elements, see J. H. Jeans, Mathematical Theory of Elec- tricity and Magnetism, 4th ed., Cambridge U. Press, 1923, pp. 200-201. 712 ELECTRICAL METHODS [Cuap. 10 An observer facing the plate at B sees the source P at an intensity reduced by transmission through the plate. The amount transmitted is the original intensity minus the amount lost through reflection, which in turn is proportional to & times the original intensity. Therefore, the light and by analogy the potential at B is Vp eae Be (10-326) i 4aur 3 Continuity of the potential requires that in the boundary plane where vi I 1, = Te = 73, Va and Vz be equal, so that 7 (1 +k) = = sails?) Hence, ae cae ae 10-32 pe + pi ( ) so that in eq. (10-326) 2p1 2p2 1-—-k= d l+k= 7 10-32d p2 + pi MH a p2 + pi ( ) The factor k expresses the “electrification” of a plane be- tween two media of different resistivities due to a _ point source and its image. The application of this principle is illustrated by a calculation of the potential distribution re- sulting from two current elec- trodes near the ground surface, Fig. 10-50. Four points and images on corresponding to a Wenner- boundary. Gish-Rooney arrangement f with buried electrodes (Fig. 10-50). If the point A is considered as current source (I) and B as the corresponding “sink” (—J), the potential distribution at the surface is obtained by considering the effects of both sources, A and B, and their images, A’ and B’. The intensities of the images are k’I and —k’I, respectively. Applying eq. (10-32c), k’ is seen to be equal to 1, since pp = © (air). Hence, the images have the strength J and —[, respec- tively. The potential difference between P and Q due to a source I at Ais AV = = Ge — a and that due to an image 7 at A’ is ue ( xs — “aah, Similar relations apply to the potential difference at Cuap. 10] ELECTRICAL METHODS 713 the same points resulting from the source at B and its image at B’. If the electrodes are at equal intervals a in a straight line and at a depth b below the surface, the potential difference is AV pil ¢ 2 yA 1 ) 4n \a Va? +42 (Va? + 8? (10-33) _ al ( ok Fea — 4ra Vi+t4? vVit¢ j J where gq = b/a. Lp tk kUKL - hel KeLzRL KI Fig. 10-51. Image distribution in two-layer potential problem. When q is large (depth great compared with the electrode separation), AV = pil/4ra (potential for an infinite homogeneous medium). When q = 0 (electrodes on ground surface), AV = pil /2xa (potential for the semi-infinite medium). 2. Two horizontal layers. Assume two semi-infinite media with resis- tivities p: and p:, as in Fig. 10-51. The upper layer is bounded by air (resistivity p) = ©). If current is supplied at two points, O and 0’, the potential distribution at the surface can be calculated by considering a source I at O, a sink —I at O’, and the images of this source and sink 714 ELECTRICAL METHODS [CHap. 10 that are produced by reflection on the formation boundary and the earth’s surface. The source J is reflected at the formation boundary and produces the image kI. The value of k is given by eq. (10-32c) and is equal to (p2 — pi)/(p2 + px), since it applies to the formation boundary (29:). The image I; = kI is now reflected at the earth’s surface and produces the image I; = k’kI above. In this case k’ as applied to the boundary between the upper medium and air is 1, since p = «©. Hence, the image I, = kI. The potential at any surface point will therefore result from a summation of an infinite series of images. Thus, J; = kI at a depth 2h; I, = kI at a height 2h; I, = kJ ata depth 4h; I; = kT ata height 4h; so that J, = k"I at a depth 2nh, and J, = kJ at a height 2nh. Since I, = 1, , In + I, = 2k*I, and the potential at any point on the surface is =, E sey one i: (10-34) 2r |r n=l Tn The potential at a point A(x:y:) due to a source I at O and its series of images is therefore Ip, | 1 i les Sl vat ey at Val + y+ mh) and the potential due to an equal sink at O’ at the same point is Ip, 1 ~~ k? Va: = — 22 | ar LV — mn) +y3 a=t VW (1 — 2)? + y? + (2nh) (10-35b) where / is the distance between the electrodes so that the resulting po- tential is An) 1 1 — kB Vg ee |) 9 eee Vety Vila) ty2 = V2? +y?+ (2h) 20 (10-36a) —92 ; Tw (Mayans aan Similarly for another point B(2eye), tig — ete = pels RY ee ee (eee) n= ka +2 (10-36b) > V2 + y3 + (2nh)” n=0 ka 2 2 te A : 2 V (l= 22) + 3 + car} | Cnapr. 10] ELECTRICAL METHODS 715 Hence, the difference of potential between the point A and B is tal 1 1 eee © Be LV ai + yi C= a) 1 oy es amt Vx? + y? + (2nh) n=0 kp 1 2 =) a lh. = BiG adi iyi + ean) ah ee 1 4 n=0 kp SSS SSS 2 ee VU - mi) + 9: ze V 03 + ys + (nh) | mY (laa ones From this general formula the potential difference between any two points may be determined.” For the electrode arrangement in the Wenner-Gish-Rooney method, % = a, yi = 0, x2 = 2a, y2 = 0, | = 3a, so that Jie i ae a = ala Ma pte —t BT vas aa 2 1 2 dy Gaye tO eV) a5 + (2nh)? 2a ue 2 Ga re + (nh t ? Dy Va + nh)’ jana or n=0 k2 n=0 ka even gel) +4E 7 cap 4B 7a ap Onh\? Onh\? [EE oo Bh Va — Ver Ton [1 + 4F]. (10-370) 2ra The quantity p:i(1 + 4F) is an apparent resistivity. If k = 0 (homoge- neous ground) the formula becomes Vi — Vs = Ipi/2ra. Hence the 37 See J. N. Hummel, A.I.M.E. Tech. Publ. No. 418. 716 ELECTRICAL METHODS [Cuap. 10 ratio of apparent resistivity, p, , and true resistivity, p1, is ps n=0o k2 n=0 ka rt n=1 2nh \2 a= 2nh\? ie 1+ (=) y/ 4+ (*) 10-38 n=0o n n=0 ka ) | -- iS M Suh ty ER A Bake pS pe |: alo me AiO) where u = a/h, the ratio of electrode separation and depth. Fia. 10-52. Apparent resistivity ratio as a function of electrode separation in terms of depth, for various true resistivity ratios (after Hummel). Fig. 10-52 shows the ratio of apparent and top-layer resistivity as a function of the ratio of electrode separation and depth, for various re- sistivity contrasts. If the resistivities are equal, the apparent resistivity is equal to the true resistivity. If k = 1 (lower layer of infinite resistivity), the apparent resistivity increases in direct proportion to the electrode separation, the proportionality factor being about 1.386. (with a/h). The apparent resistivity ratios for the k-values between 0 and 1 approach asymptotically the true resistivity ratios for large electrode separa- tions. Cuap. 10] ELECTRICAL METHODS 717 If conductivity ratios are reversed (good conductor below), the apparent resistivity ratio lies between values of 0 and 1 and approaches 0. 3. Three horizontal layers. The theoretical treatment of this case pro- ceeds along the same lines as that for the two-layer case. The mathe- matical relations become more complex, however, because images of sources and sinks are produced by reflection on two boundary surfaces. The calculation has been carried out by Hummel™ for the general case and for a special condition where the thickness of the two top layers is the same (Ah = h;) and the bottom layer is infinite in extent and of infinite resistivity. Results obtained for the latter case indicate that (for large electrode separations) the apparent resistances follow Kirchhoff’s law for two resistances connected in parallel, so that the average resistivity of two infinite layers, of resistivity p; and pe and respective thickness hi 4 and h,, is given by Q4 08 2 16 2 Brea (10-20) Pav. Pl p2 This relation may be extended to cover the case of more than two layers of any thickness and makes possible a graphic approximation in the interpretation of resistivity curves. Fig. 10-53 illustrates the apparent resistivity curve for three Fig! 10-58: Threelayer case! (aster layers with resistivities p, p: , and Hummel). p2 and of thickness h, hi, and ~, with h = h,. The shape of the curve for distances large in com- parison with the depths of the upper layers is almost independent of the properties of these upper layers. For large spacings it is asymptotic to the line p./p = 2, since the resistivity of the lower infinite medium is twice that of the surface layer. Curves 6 and c are the “approximation”’ curves obtained by combining the upper two layers and considering the resultant layer with the bottom layer as a two-layer problem (curve b). Similarly, curve c follows by combination of the middle and bottom layer. In Fig. 10-54 the middle layer has a high and the bottom layer a low resistivity. This curve is commonly obtained in water table deter- minations. The theoretical curves prove that even for large differences in con- _ ductivity there is no abrupt change in apparent resistivity measured at the surface. If irregular curves and ‘‘breaks” are obtained in the field, they 28 Ibid., p. 409-414. 718 ELECTRICAL METHODS [Cuap. 10 are due to local conditions, usually at the contact of the electrodes with the ground, and must be eliminated before any interpretation can be attempted. 4. Effects of vertical contacts. In Fig. 10-55, let AB be the surface of the ground and DE a fault plane dividing the region into two parts, of resistivities p) and p2. If a four- 4& electrode system is moved as a 04 08 2 16 20 Za whole or if the separation is in- creased, a resistivity curve con- sisting of five portions is obtained (Fig. 10-56). These, in turn, result from five possible positions of the arrangement in reference to the fault plane: (1) all elec- trodes in the first medium; (2) only one electrode across the fault line; (3) two electrodes in each medium; (4) three elec- Fre. 10-54. Three-layer case (adapted from trodes in the second medium; Hummel). (5) all electrodes in the second medium. A sixth case arises when measurements are made in either medium parallel to the strike of the contact. (a) Case 1 (four electrodes in one medium) corresponds to the condition a < 2d/3, if ais the electrode separation and d the distance from the center R Fre. BORG: Jbe aG. G. Fic. 10-55. Four-terminal electrode arrangement on contact plane. of the electrode system to the contact. Assume a source of current J at C, and a sink —J at C.. The potential at points P; and P2 will depend on the strength of J and —I and of their images at Ci and C3 resulting from reflection on the interface DE. The potential at P, due to the source I at C, is Ip;/2ra; that at P; due to the sink —I at C2 is — Ip,/4ra. The potential resulting from the image at Cy is kIp:/2r(2d — 2a) and that Cuap. 10] ELECTRICAL METHODS 719 due to the image of —I at C, is kIp,/2r(2d — a), where k = (p2 — pi)/(p2 + pr). The total potential at P, is therefore i Ipi| (1 va 1 1 At 1 a jal (2 x) ane (a ei) Wo Nt (Opts) Similarly, the potential at P» is uae Ip, 1 i 1 1 2h 1 (Ors 1 (a 2) nail (x3 Sanam apes 33) | ) Hence we have for the potential difference: Vi-Ve2= fee fase at ieee eae , (10-40c) 27a a\ ,a? d? 4— 5-1} ] so that the apparent resistivity becomes Pe = pif 1 + 4k seat Ary faba : (10-40d) a\ ,d@? d? 45 —-4 45-1 a? (b) In case 2 (one current electrode in the second medium) the potential difference V; — V2 due to the source J at C, and its image at Ci will be the same as in case 1. However, the potential in medium (1) due to the sink —I at C: in medium (p2) must be considered as being due to a source — 2pil/(p2 + p1) (see eq. (10-32d), and the potential at P; will be the sum of the potentials due to a source J at C,, to an image kI at Ci, and toa source (k — 1) I at C.: ibetal 1 k | =o [a(t + yea) + al The potential at P: is accordingly (10-40e) dispel 1 k po(k — 2 ve= 2 lo (g + ages) + a From the difference the apparent resistivity is p= efits (1+ 7-579 — (10-40f) 41 741 (c) In case‘3 (two electrodes in each medium) the potential at P; is due to the source I at C, , kI at C;, and — 2p,0/(p2 + pi) = (k — 1)I at 720 ELECTRICAL METHODS [Cuap. 10 C,. Similar conditions apply to the potential at P,, so that nah 1 k po(k — 1) m= elaCltara)+ 2a | ; : : A (10-409) io ata . pe nd) Vs t[m(t+a%5,)+ 2a | Then the apparent resistivity becomes , bts at aay l+k—k 7 (10-40h) hea (d) In case 4 (three electrodes in second medium) we have for the ap- parent resistivity em aitgli-k(g— ap —taz-\| 0-400 fa! tice aeons (e) In case 5 (four electrodes in second medium) it is 42 ae piace Cotas fest ed ete Pn eel (10-40) 1—k d? d? a ae Fas a Figs. 10-56a and 10-56b show curves of apparent resistivity on contacts calculated for various k values. These curves are valid for the four- terminal Wenner-Gish-Rooney electrode arrangement, and they express the observed quantities as a function of spread distance from fault plane. It is seen that the apparent resistivities approach the true resistivities as the distances of the arrangement from the fault plane increase. Abrupt changes occur when d/a = 0.5 and 1.5, that is, when electrodes cross the contact plane. An application of the above theory is made in electrical logging. This method involves the location of formation boundaries in wells by means of a system of fixed spacing electrodes (see Chapter 11). When the electrode arrangement is used parallel to the strike of a fault, formula (10-33) may be applied to the contact (pe, 1), so that Ip1 [3 2k 2k | 1 gad eth ol ts lea el Lan idk aint stad DIE 7 (10-41a) 1 fin Poe a ot age apige aaa Cuap. 10] ELECTRICAL METHODS 721 which gives for the apparent resistivity Litt Wh, soveempnadeyh thentielogl [,@ /, @ 4 2 +1 4 2 +4 Tagg” has published a series of curves showing for various k values the apparent resistivity as a function of distance from the contact. These Ps = pj 1 + 2k (10-41) Fie. 10-56a. Apparent conductivities obtained with four-terminal electrode arrangements on contact (after Tagg). Fic. 10-566. Apparent resistivities obtained with four-terminal electrode arrange- ments on contact, as a function of distance of center of spread from contact plane (in terms of electrode separation) (after Tagg). indicate that if the distance of the electrode system from the fault is four times the electrode separation, its influence is practically negligible. 5. Effects of dipping beds. For dipping beds, apparent resistivities may 39G. F. Tagg, A.I.M.E. Geophys. Pros., 135-145 (1934). 122 ELECTRICAL METHODS [Cuap. 10 be calculated in the same manner as for horizontal beds and by using the theory of images. In this case the number of images is no longer infinite.” The images lie on the circumference of circles with radii equal to the dis- tances of source or sink from a hypothetical point of intersection of the interface with the surface. The number of effective images is 7/26, where @ is the dip. Fig. 10-57 shows a number of curves calculated for various dip angles for a constant resistivity ratio. The abscissa is the ratio of apparent and true surface-layer resistivity, the ordinate the ratio of electrode separation and depth (under the down-dip power electrode, 1 15 20 25 30 3.5 B ‘ k :§ R 05 10 6:75° 15 14 6=9° a A : 6:6° 6:0° Fic. 10-57. Effect of dip on apparent resistivity (k = 2/3) (after Aldredge). ? normal to the bed). For electrode separations less than one-half the depth the influence of dip is very small and is approximately proportional to the sine of the dip angle. For large ratios of a/h,the curves straighten out appreciably. Since it is difficult to calculate dip analytically from up-dip and down-dip profiles, it is better to determine dip indirectly by profiles parallel to the strike. 6. Effects of three-dimensional geologic bodies. The effects of ore bodies, lenticular conductors, and the like, can be calculated by considering them as the equivalents of electrical doublets. The calculation is simplified by assuming that the doublet is situated below the midpoint of the electrode 40R. F. Aldredge, Colo. Sch. Mines Quart., 32(1), 171-186 (Jan., 1937). Cuap. 10] ELECTRICAL METHODS 723 basis. Fig. 10-58 shows the ratio of apparent and true resistivity as a function of the ratio of electrode separation and length of spread for £ a polarized doublet. A distinct change in p,/p P occurs. This is of interest because the potential curve along the same line exhibits a smaller varia- CE) a TOY, tion. Te D. PRocEDURE; EQUIPMENT Fig. 10-58. Curve of apparent resistivity over For measurement of apparent resistivity, polarized doublet (after widely different procedures, electrode arrange- Shane. ments, and equipment are used. The latter fall into the following groups: (1) D.C. commutator method (Wenner-Gish-Rooney) with separate meas- urement of voltage and current; (2) Megger method, likewise with commutator and with direct resistance measurement by dual-coil indicators; (3) D.C. measurement with nonpolarizable electrodes; (4) A.C. method. 1. D.C. commutator (Gish-Rooney) method. A scheme of the equipment is given in Fig. 10-11. Ci and C2 are the external or current electrodes; P, and P» the potential electrodes. Current is measured with a milliam- meter between C; and C,, while the potential difference is observed be- tween P; and P2 on a potentiometer. A section of a double commutator is interposed in each circuit so that the current flows in the same direction through the measuring instruments while it is reversed periodically in the ground (about sixteen times a second). Much care must be devoted to the proper design of the commutator to insure correct and steady meter readings. Inasmuch as it takes the current a certain amount of time to build up to its equilibrium value (an effect which increases with increasing electrode separation, see formula [10-45a]), the segments on the potenti- ometer commutator are offset with respect to those on the current commutator. Because of the insulating segments, the current read on the milliam- meter is lower and hence the resistance is greater than its actual value. This difference may be corrected out by determining the value of a known resistance with commutator in motion and with commutator at rest (com- mutator factor). Unsteadiness of the galvanometer needle of the poten- tiometer can be avoided by placing a condenser of large capacity in series with one of the potential leads. Leakage between high- and low-voltage circuits in the instrument may be eliminated by the use of a grounded guard ring between the two sections of the commutator. A customary commutator design is shown in Fig. 10-59b. 2. Megger method. The “Megger’ (abbreviation for “megohmer’’) in- strument was developed primarily for the use of power and communication 724, ELECTRICAL METHODS [Cuap. 10 companies to test the grounds of power stations and transmission towers, and the like. The Megger differs from the Gish-Rooney arrangement in two respects: (1) power is supplied from a generator mounted with the commutator on the same shaft;(2) measurements of voltage and current are made with cross-coil instruments so that automatically the ratio of een e Ses AES A WL AU ARS ANAS NC ie SB EAINEG RS ARETE DANE AET AR Ae BS AEA N AAG RAEI Colorado School of Mines Fia. 10-596. Close-up of double commutator. voltage and current and therefore the resistance is determined. In the scheme of Fig. 10-60 the cross formed by the current and potential coil is not shown. The current coil is in series with the current or external leads, while the potential coil is across the internal or potential pair of electrodes. Although the potential coil is in series with a high resistance, this is gen- erally not sufficient to give the same accuracy as the potentiometer method. Therefore, resistivities determined with the Megger are generally lower Grae. 10) ELECTRICAL METHODS 795 than the resistivities determined with either the Gish-Rooney commutator or porous-pot resistivity equipment. 3. D.C. resistivity measurements with porous pots. By the use of porous pots, polarization on the potential electrodes and -hence the commutator can be eliminated, although it is still necessary to provide for a reversing switch to eliminate effects of stray currents and leaks from the current into Potential Coi/ James G. Biddle Co. Fig. 10-60. Schematic Megger circuit. Fig. 10-61. Measurement of apparent resistivity with four-terminal A.C. method (adapted from Wenner). the potential circuit. The Shepard earth resistivity meter and the Lee “geoscope” are representative of instruments using porous-pot electrodes. In the latter the galvanometer of the potentiometer is used with resistances in such a manner that the current is kept adjusted to a predetermined value. This value is made numerically equal to 27a, (= 191, if a is in feet) so that the potentiometer readings give directly the value of the apparent resistivity. 726 ELECTRICAL METHODS [Cuap. 10 4. A.C. resistivity method. An arrangement for measuring resistivity with A.C. by compensation is illustrated in Fig. 10-61, in which A is an ammeter in the current circuit, J a variable inductance, 7 a transformer K negative Zadicex) Fic. 10-62a. Tagg interpretation diagram (k negative). used to supply a reference voltage to the potentiometer, V a voltmeter, S a slide wire, and PH a phone for detecting balance. Another A.C. indicator must be substituted for the phone if currents of lower frequency and hence greater depth penetration are applied. Cuap. 10] ELECTRICAL METHODS 127 E. INTERPRETATION Interpretation of data, obtained with resistivity mapping or resistivity sounding, may be made (1) qualitatively (using the appearance of the curves); (2) quantitatively, by analytical interpretation methods; (3) Fic. 10-62b. Tagg interpretation diagram (k positive). quantitatively, using “type” curves calculated for given conditions; (4) with the help of model experiments. 1. Qualitative methods. Qualitative interpretation has a definite place in resistivity mapping. High apparent resistivities indicate the presence of bodies or formations of high resistivity within the depth range and 728 ELECTRICAL METHODS [CHar. 10 vice versa. Examples are given below in section F. In some instances it is possible (especially with the help of borings) to represent the lateral variations of apparent resistivity on such a scale that they may be trans- lated directly into changes of depth of formations of different resistivity (bedrock profiles, and the like). Qualitative methods are also frequently used in a preliminary interpretation of resistivity depth curves although, as stated below, complete reliance on such methods may lead to serious misinterpretation, since the apparent resistivity continues to change with electrode separation long after the true resistivities have ceased to change with depth. 2. Quantitative interpretation (analytical). Analytical, direct methods of depth interpretation are primarily applicable to simple two- and three- layer conditions. One most frequently used is known as T'agg’s method. This method establishes a number of simultaneous equations, giving depth h as a function of resistivity factor k. Hence, a family of curves giving p:/p1 aS a function of h/a must be prepared (see Fig. 10-62). Since the apparent resistivity, for a given electrode separation, is only a function of the depth and the k value of a contact, theoretically two resistivity values for two electrode separations are sufficient to obtain both h and k. In practice, several equations are set up for various electrode separations, and depths are calculated numerically or graphically. It is convenient to use two diagrams: one for resistivity ratios (when the resistivity of the under- layer is less than that of the upper layer) and the other for conductivity ratios (when the resistivity of the underlayer is greater). Each diagram contains ten curves for k from —0.1 to —1 and from 0.1 tol. Since a is known, fA values as functions of k may be tabulated or plotted for each electrode separation. The correct depth is indicated by the intersection of the curves or by h values, which do not vary with k (see example). From the k value thus determined, the resistivity of the lower layer is ob- tained from pe = pi(k + 1)/(1 — k). If necessary, field curves are smoothed out for small electrode separations in order to obtain a reasonable average value for the surface resistivity. The results in Table 71° were obtained from Fig. 10-63a to determine depth to limestone, overlain by loam, sand, and clay. For separations of less than 70 feet, the resistivities were averaged, obtaining a surface: resistivity of p; = 6703 ohm-in. Since p;/p: > 1, the ‘‘conductivity” curves will be used for interpreta- tion. In Table 72 the vertical columns contain ten values of h/a for 10 values of k. This is repeated for all electrode separations and correspond- ing o,/e, values. 41 Tagg, op. ctt. Cnap. 10] ELECTRICAL METHODS It is noted that, for the value k = 0.7, the ‘depth h remains practically constant; h = 142 may be taken as the depth to the surface of separa- tion between limestone and clay or sand. If the A values are plotted as a function of k (Fig. 10-63b), the curves in- tersect at about 140 feet. The most probable value of k is 0.702. The true depth in this case ranged from 145 to 150 feet. Tagg’s method of interpre- tation may be extended to the three-layer case, provided the infinite third layer does not influence the first part of the curve too much. This requirement is satisfied when the thickness of the second layer is two to three times the thickness of the top layer. The procedure followed is equivalent to a reduction of the three-layer to a two-layer problem, that is, it is equiva- lent to the construction and App. kesistivity Ohm-inth k- values 0.2 100' 130° 200° 2H Fic. 10-63. Resistivity curve (a) and ‘graphical depth interpretation (b) (after Tagg). evaluation of the approximation curves shown in Figs. 10-53 and 10-54.” The order to be followed is as follows: (1) Average the surface resistivities for ELECTRODE SEPARATION TABLE 71 RESISTIVITY (ohm-in.) ae 8,960 ak 10,740 bai 12,320 AOA 13,860 fl 15,220 ee 16, 480 ps/p, 1.338 1.601 1.840 2.068 2.270 2.460 as/o, 0.748 0.625 0.544 0.483 0.441 0.407 42 See also Sundberg, A.I.M.E. Geophys. Pros., 146 (1934); and S. J. Pirson, A.I.M.E. Geophys. Pros., 148-158 (1934). 730 ELECTRICAL METHODS [CHap. 10 spacings from 5 to 20 feet, thus obtaining the resistivity (p1). (2) Plot p: to scale on the resistivity’ axis and draw a line from p; to meet tangentially the first part of the curve. (3) Read resistivities at six or eight points on the curve just drawn and apply Fagg’s method to that part of the curve. TABLE 72 ELEc- TRODE 150 Feet 200 Fret 250 Freer 300 Fert 350 Fert 400 Feet SPACING os/c, 0.748 0.625 0.544 0.483 0.441 0.407 k h/a h h/a h h/a h h/a h h/a h h/a h 1 1.19 179 | 0.915} 183 | 0.770) 193 | 0.675) 202 | 0.61 | 214 | 0.560) 224 0.9 1.12 168 | 0.850} 170 | 0.705) 176 | 0.610} 183 | 0.545) 191 | 0.500) 200 0.8 1.045} 157 | 0.775) 155 | 0.640) 160 | 0.545) 163 | 0.485) 170 | 0.485) 174 0.7 | 0.96 | 144 | 0.700] 140 | 0.565] 141 | 0.478] 143 | 0.41 | 144 | 0.36 | 144 0.6 | 0.87 | 180.5) 0.620} 124 | 0.485) 121 | 0.390) 117 | 0.325) 114 | 0.28 | 112 0.5 | 0.785} 118 | 0.525) 105 | 0.39 | 97.5) 0.295) 74 | 0.226) 78 | 0.17 | 68 0.4 | 0.66 99 | 0.42 84 | 0.27 67.5| 0.16 40 | 0.06 21 nee ut 0.3 | 0.525) 79 | 0.26 | 52 | 0.08 al oe ne 1 Foal Geele OF2> |. 0.315)" .405| - 2S. sie ace de 0.1 ae sbaly oF sauldapnog aS 737 738 ELECTRICAL METHODS [CHap. 10 In many instances faults have been located by the resistivity contrast of the formations on either side, or by the effect of the fault itself resulting from highly mineralized waters in the fault plane.” Structural investiga- tions with resistivity methods are often facilitated by tracing certain key beds of high or low resistivity. An example is the survey of the Bibi- I mile Gypsum Wl Redbeds; shale ES Limest. ()Salt Harailanand Fic. 10-68. Results of electrical vertical drilling with single-probe method, and corresponding geologic section in an area in New Mexico. Eibat® anticline near Baku and is of in- terest because measurements were made at the bottom of the sea. A tri-conduc- tor cable with three electrodes was dragged along the sea bottom, the fourth electrode being a fixed ground on land. The key bed in this area (Apsheron limestone) could be clearly noted in the resistivity curve. The possibility of electrical salt dome location was demonstrated at an early date by Schlumberger and his associates.” Fig. 10-69. Equiresistivity con- Jn 1926 and 1927 the salt domes of Aes AOR age wae Re aot Meyenheim and Hettenschlag in Alsace- sia (after Schlumberger). Lorraine were found by resistivity map- ping. They appeared as resistivity lows, contrary to what would be expected. The lows result from the occur- rence of highly conductive marls above the salt which in turn are cov- 48 Hubbert, op. cit., 40-47. 49 A.I.M.E. Geophys. Pros., 127 (1934). 50 G. Carrette and S. F. Kelly, A.I.M.E. Geophys. Pros., 211-220 (1929). Cuap. 10] ELECTRICAL METHODS 739 ered by alluvial beds of high resistivity. The latter thin out where the marls have been forced up by the salt intrusion. Conversely, the salt uplift shown in Fig. 10-69 shows as a resistivity high. It is located at Tschernaja Rieschka and is one of the numerous domes found by geo- physical methods in the Emba district in Russia. 2. Applications in mining and mining geology. (General structure in mining districts can be outlined by means of resistivity mapping, provided that key beds with greatly differing resistivities exist in the section. Faults may be located if the beds on either side differ in resistivity or if mineralized solutions circulate along the fault plane. In this manner, nonconductive minerals accumulated on the fault planes may be found in- directly (fluorspar veins in Illinois, see footnote 43, page 735). Resistivity methods have been used exten- sively in the location of sulfide ore bodies, both at the surface and under- ground. Fig. 10-70 il- lustrates electrical re- sults at the Abana mine. The resistivity curves were obtained by survey- ing with constant elec- trode spacing. The ore body is indicated by a apes We pas i ee rere Deere oi . ei IG. -4U. esistivity Curves an seli-potentia resistivity low. Fig. 10 profiles across Abana ore body (after Schlumberger 71 shows resistivity- [Eve & Keys]). depth curves for a dip- ping vein taken along three profiles, laid out 15° off strike, at increasing distances from the outcrop. The lows in the curves move out to greater distances (or depths) as the distances of the traverse from the outcrop are increased. In this instance these distances were found to correspond to depth to the dipping vein, although they would be expected to be reckoned perpendicular to the bed. | Several attempts have been made to apply resistivity methods in lig- nite prospecting. If the lignite beds are soaked with mineralized waters and overburden formations are poor conductors, fairly definite results may be obtained (see Fig. 10-72). However, if conditions are less favorable 740 ELECTRICAL METHODS [Cuap. 10 (clayey overburden, small conductivity contrast, varying water content), the data may become very unreliable, as indicated by Stern’s measurements in the Niederlausitz and Hawkins’ observations in Ontario. Extensive resistivity measurements have been made by Ewing and-Crary on anthra- cite coal beds. Further references to geophysical results on coal measures are given in an article by the author.” In the prospecting for salt, potash, Resistivity-Depth Curves Section No. 10 Profile along Section No. 10 700 17 pg 75 600 Wo. \_ /55¢ | 1 We Z ‘ ea a 200 No. 16 \ | er fj S | x | Be s £00 ‘ ae: 1 | s Conducfer Indications ol sat ! | x Conductors = | i | | | RS ! ! ! ! 3 I ! | it & \ ! \ aes 00a 10 Bt He | | 200 Stake Interval | 300") | 7 Fig. 10-71. Apparent resistivity curves on three traverses (15° off strike) above Peach Bottom Vein, Alleghany County, North Carolina (after Griswold). 2.4 1678 5K AN ca Die ay Saar SOE rf 2 rc) od =| Grave/ 4 cad 6 6 oO 8 8 & 0 lignite = ® 12 z 100 41 Deol 6 meters Fig. 10-72. Apparent resistivity curves on lignite beds, Ville, Germany (after Stern). or sulfur for mining purposes, the geologic problems are the same as in the location of salt domes in oil exploration. Determination of overburden thickness, a problem frequently encoun- tered in mining operations in connection with sinking shafts, driving tun- nels, and excavations from surface, has been accomplished successfully by 51 R. H. Hawkins, A.I.M.E. Geophys. Pros., 76-120 (1934). 52 ‘‘Geophysics in the Non-Metallic Field,’? A.I.M.E. Geophys. Pros., 546-577 (1934). Crap. 10] ELECTRICAL METHODS 741 both resistivity mapping and sounding. Fig. 10-73 shows the application of resistivity mapping in a section consisting of glacial drift at the surface and limestone with ore bodies below. The limestone is underlain by con- glomerates. The three curves represent: (solid curve) actual subdrift topography; (dotted curve) apparent conductivity obtained with 40-foot electrode separation; (dashed curve) apparent conductivity with 120-foot electrode separation. The conductivity curve obtained with the 40-foot separation does not give a true picture of the subdrift topography because the average thickness of the glacial drift is greater than this separation, and the results also reflect irregularities in the composition of the drift. The closest relation between subdrift topography and apparent conductiv- ity was obtained with 120-foot electrode separation, which is the greatest thickness of the drift encountered in the area investigated. dilddigatuds Surtace of rock ones = Conductivity at aa interval Co" Horizontal Scale ° 60 220 Fe. a Vertical Scale lets A Pa I alt Conductivity Scale Fic. 10-73. Apparent resistivity curves, with different electrode separations to determine subdrift topography (after Lancaster-Jones). Location and depth determination of placer deposits is closely related to the problem of determining depth to bedrock in foundation problems, discussed in the next paragraph. 3. Applications in civil engineering (foundation and highway problems). Application of resistivity methods in this field is threefold: (a) determina- tion of depth to bedrock; (6) determination of physical rock characteristics for dams, structures, tunnels, and the like; and (c) location of construction materials. Bedrock depth determinations by resistivity methods have been made on numerous occasions. Many of these have been carried out by Schlum- berger and his associates.” An example was illustrated in Fig. 10-64. In this particular survey, predictions could be verified within 1 to 2 meters 53 Leonardon and Crosby, A.I.M.E. Geophys. Pros., 199-210 (1929). 742 ELECTRICAL METHODS [CHap. 10 (10 per cent of depth); only two wells showed discrepancies. Where bed- rock consists of unaltered crystallines and the overburden is glacial drift, the conductivity contrast is great enough to assume an infinite bedrock resistivity in the interpretation. On the other hand, when altered crystal- lines or sediments are overlain by river graveis traversed by water, the opposite type of resistivity indication (good conductor below) may be observed. : Fig. 10-74 shows the resuits of a resistivity survey made fcr a determina- tion of physical rock characteristics at the site of a proposed aqueduct. It revealed a fault zone 350 feet wide in which the crystalline rocks were Survey No. 4 Resistivity Traverse 1000 Profiles Section No. 2F Granite Mountain Fault l \ zone of Crashed rane Resistivity ohm-ft F 57 2 7 6 4 Geophysical Stations - Fic. 10-74. Location of fault zone by resistivity mapping (after Henderson). crushed and waterlogged. (reduced resistivities), making it necessary to reject the site for the proposed structure. In highway construction, resistivity surveys can be of considerable help by locating construction materials. There are still many projects where sand and gravel are hauled for considerable distances, while sources of near-by supply might be located by resistivity measurements without much trouble. The curves reproduced in Fig. 10-75 show how effectively a gravel and sand lens in a clay bed can be mapped. Many more examples of this type are given by Kurtenacker in an article dealing especially with the applications of geophysics to highway problems.” 54K. S. Kurtenacker, A.I.M.E. Geophys. Pros., 49-59 (1934). Cuap. 10] ELECTRICAL METHODS 743 4. Location of water. Resistivity and related surface-potential measure- ments are probably the most promising geophysical methods for the location of water. “The problem is not simple and requires a careful study of the stratigraphic situation since the occurrence of groundwater is quite variable and the conductivity of water itself may vary. The manifold conditions applying in electrical water prospecting have been discussed in detail by Heiland” and Tattam.” Experience has shown that in many cases the water itself, though pot- able, is conductive and occurs at the bottom of a dry layer, which in turn is covered by a surface medium of intermediate conductivity (see Fig. s 8s j=) oO 8 6 8 Apparent Resistivity, foot- ohms Apparent Resistivity, foot -ohms Cay A Water-. ” dp a er Pepa Catia ~ 20 Fic. 10-75. Location of gravel lenses by resistivity mapping (after Wilcox). 10-76, diagram [a]). Conversely, the bottom layer may have a high resis- tivity (crystalline bedrock, and the like) and the water may occur as an in- termediate layer of good conductivity above it (6). The typical three-layer curves so obtained may degenerate into the extreme curve ([a], e) when the top layer is of very good conductivity, and into (c), e when the top layer has poor conductivity. Water subject to rapid circulation in beds of large pore volume and permeability often acts as a nonconductor compared with other beds (curve[c]). Curve (d) is less frequently observed and occurs when 6 Amer. Geophys. Union Trans. (Hydrology), 574-588 (1937). 56 C, M. Tattam, Colo. Sch. Mines Quart., 32(1), 118-138 (Jan., 1937). 744 ELECTRICAL METHODS [Cuap. 10 moist layers of different capillarity occur above one another. It is seen that three-layer curves encountered in water prospecting require a careful analysis of near-surface stratigraphic conditions and that the same resis- tivity curve may indicate totally different conditions. pS * RES . Sie e Ve . me uN J Bry Sand "> Water ind i N x } S és er, . ae Fi (oh Zam = = 3s g S y Als 3 Ss % --L~ ye) -— -—— —~—- —~— — Clays —_— /<_—_—_- — Water of Poor Conductivity Fie. 10-76. Various resistivity indications on conductive and nonconductive ground waters. G. ELEctrRicAL LOGGING Electrical logging is the application of resistivity mapping with fixed electrode separation to the location of formation boundaries in uncased wells. Methods and equipment, theory and results are discussed in Chapter 11. VI. POTENTIAL-DROP-RATIO METHODS A. GENERAL Compared with resistivity methods, the advantages of potential-drop- ratio procedures are that sharper indications are obtained on vertical formation boundaries, and that in favorable cases of horizontally stratified ground the indications are more directly related to depth. The P.D.R. Cuap. 10] ELECTRICAL METHODS 745 method is also superior in resolving power because potential differences are not measured absolutely but in the form of a ratio of successive dif- ferences. However, this increase in precision frequently results in in- creased near-surface interference, and special precautions are necessary to reduce it. P.D.R. arrangements consist essentially of Wheatstone bridge circuits with adjacent stake intervals in two arms, known resist- ances in the other two arms, and an indicating instrument in the center arm, connected to the center stake (see Fig. 10-82). Hence, for a D.C. circuit, the ratio of the two voltage differences is equal to the ratio of the two resistances when adjusted for balance. B. THEORY 1. Horizontal layers. In all applications of P.D.R. method for the ex- ploration of stratified ground, measurements are made outside the elec- 6 3 8 Fig. 10-77a. Electrode arrangement for constant spacing. trode basis and usually at right angles to it. By this means the effect of the second electrode is virtually eliminated (Fig. 10-77a). For two layers of arbitrary conductivity ratio, with a lower layer of infinite depth extent, the P.D.R. may be calculated from the potentials at three surface points, using the equations previously derived. According to eq. (10-35a), in the vicinity of one ae electrode n=0o vs - 21; ri 22 LiNAte a em: Applying this to three ee points with the interval b, and with a center distance r from the power electrode (see ha 10-77a), we get Ip: _ Kg el pt? d Vee Sane Jerre + Ip, n=00 ka i eg 2| a3 t 22 eae = eam | Coane) x Ip, 1 n=0 k2 | Lites tae jee V/r? + (2nh)? |" 746 ELECTRICAL METHODS [Cuap. 10 By introducing the ratios x = r/h and c = b/h, we obtain the following equations: re Ip. 1 n=0 kn aor leas Gem ac | Tp = Verora Vasgy 2Qrh ES +c) ae 22, (V(e+ c)? + 4n? (10-420) ile +? var c= +22) SS Saas Therefore, the potential differences are: es i) Ip, f Cc mein Qrh \a2(a —c) ame 1 1 +2 20k l exo - vec} (10-42c) ny | fg ols ulh eke tas Uo Ve 2rh i +c) — on 1 1 +2208 l Ee Ty int Jers}: If we let V(c — 0)? + 40? = VA Va? + 4n? = V (a +c)? + 4n? = VC, the potential ratio is given by ae — . (10-42d) Cos B See a When k = 0 (homogeneous ground), the series in both numerator and denominator vanish and the P.D.R. becomes Va fe +e Ve 2—c (10-42e) The P.D.R.’s measured in the field must be referred to a “normal” ratio, that is, the ratio for homogeneous ground. To this end, they are CuapP. 10] ELECTRICAL METHODS 747 multiplied by the reciprocal of the ratio in eq. (10-42e). Hence, the correc- tion factor is (r — b)/(r + b), and it is always less than and gradually approaches 1 (for ratios figured in terms of V4/Vz) as the separation be- comes smaller in comparison with distance. Ratios expressed in terms of Vz/V. are reduced with the reciprocal of the above correction factor. In stratified ground either a constant-spacing or an expanding-electrode | system is applied. As shown in Fig. 10-77), the spacing b may be in- creased in proportion to the center stake distance. A convenient electrode separation is one-third of the center stake distance. Then, if EA:EC:EB = 2:3:4, c equals 2/3, so that eq. (10-42d) becomes pay 1 1 1 Difco a | ed ag + 2 4/ (2) +2 / (8) + Va View: 3 2 Vce— Vs al Re _ iL (10-42f) a ie b3r- ‘A’ “B.S Fig. 10-776. Expanding electrode system. With the expanding system, the normal P.D.R. for homogeneous ground (k = 0) is Va/Vzp = 2. Hence, the correction factor is then constant and equals 4. In comparison with the constant electrode system, the ex- panding system has the advantage that the P.D.R.’s are larger and less influenced by near-surface variations. For positive values of k, the series in eq. (10-42f) converge rapidly. When a good conductor is underlain by a very poor conductor (k = 1), the extreme ratio is about 1.3 for a constant electrode spacing of one half the depth. This ratio occurs at a center stake distance of 1} times the depth (see Fig. 10-77c). The same relation prevails for lesser resistivity contrasts, although the curves become flatter and the peaks shift toward values slightly greater than 14. The simple relation between depth and peak distance makes it possible to interpret measured P.D.R. values more readily than resistivity values, provided that (1) a poor conductor occurs beneath a good conductor, (2) only two layers are effective, (3) surface interference is carefully eliminated, and (4) the observed ratios are reduced for normal ratio. Curves like those illustrated in Fig. 10-77c may also be calculated for an 748 ELECTRICAL METHODS [CHap. 10 expanding electrode system. - If the electrode interval is one- ood cond. in ° ae half the distance to the first (A) stake (which is the same as one-third of the center Pages: stake distance), the curves Deth * weak at a depth closely equal to the A stake distance (for positive k values). [3 cond When a good conductor 600d cond. occurs below a poor conduc- tor, k is negative and the Electrode series terms in eq. (10-42f) spacing: : ane A become alternatingly positive 2 . : and negative. The series con- verge less rapidly and the peaks are located at center stake distances nearly twice the depth (for constant elec- bites kel 07 Reduced Potential-Orop Ratio ef a6 trode spacing equal to one-half Dae the depth). For extreme con- Fic. 10-77c. Potential-drop ratios for two ductivity contrasts, the con- layers as functions of distance, for constant BT : ; vergence of the series is ver electrode separation (adapted from Baird). 8 y slow and the ratio drops rapidly. Preliminary calculations” indicate a ratio peak at about 33 times the depth. 2. Dipping layers. The effect of dip on P.D.R. may be calculated from the corresponding apparent resistivity relations. Only one set of images is required for one source, since the other electrode may be assumed to be at infinity. The potentials must be figured for three instead of two points and their difference and the difference ratio must be formed.” P.D.R.’s so calculated are shown in Fig. 10-78 for various angles of dip of a single layer. It was assumed in all cases that the near-power electrode was so located as to make the depth, normal to thé dipping bed, 18.5, regardless of dip. Calculations were carried out for one resistivity ratio only (k = 1). The results are valid for an electrode system moved downward in the direction of maximum dip. Results in Fig. 10—78a are for a constant elec- trode separation and in Fig. 10-78b for an expanding system. 3. Vertical contacts. A determination of the effects of vertical bound- aries is of practical importance for the location of contact zones, faults, 57 John Baird, Doctor’s Thesis, Colorado School of Mines, May, 1940. 58 M. Jameson, Master’s Thesis, Colorado School of Mines, 1937. Cuap. 10] ELECTRICAL METHODS 749 and veins. The P.D.R.’s for simple contacts with resistivities of p: on one side and p2 on the other may be calculated from eqs. (10—-40a) to (10- 407), which can be simplified, since only one source has to be considered. Details of the calculations depend on whether the source is moved or kept stationary with respect to the fault plane. The theory of this case has ME cre? ali 5 oF | | le ner a fq pita iesieaae tect oa Distance from =a a Ist Stake (a) (b) Fig. 10-78. Potential-drop-ratio curves for dipping bed: (a) constant spacing, (b) expanding system. Depth is reckoned perpendicularly to bed. (After Jameson.) been discussed by Hedstrom.” Curves have been published by Hedstrom and T. Zuschlag.” Some of these are reproduced in Fig. 10-79. When the power electrode is stationary, the greatest P.D.R. is obtained when the center stake crosses the boundary. When the good conductor is the me- 59 H. Hedstrom, Min. Mag., April, 1932. 60 A.I.M.E. Geophys. Pros., 48 (1932). 750 ELECTRICAL METHODS [Cuar. 10 dium on the left, the P.D.R. (in terms of V;/V4), is greater than 1; if the poor conductor is on the left, the ratio is less than 1. For vertical veins the calculation of theoretical P.D.R.’s can be made in three ways. In the first, the assumption is made that the vein is very wide and that for the left side of the vein the effect shown in Fig. 10-79a can be compounded with that shown in Fig. 10-79b. This procedure is Sis (6) QQ Z NG BY, SN 9 » NEN ‘. 20 Wis 15 (d) \ SO Y Y f WY Poor Fic. 10-79. Potential-drop-ratio curves for contacts and vertical dikes (after Zuschlag). N permissible only when the vein is so wide that the effect of the electrifica- tion of one side on the other side can be neglected. The more rigorous procedure is to figure with a reflection of the source not only on the bound- ary close to the power electrode but also on that away from the electrode. In this manner the curves shown in Fig. 10-79c and d were obtained. They show the effect of a poorly conductive vein in a medium of good con- ductivity as well as the effect of a vein of good conductivity imbedded in a Cuap. 10] ELECTRICAL METHODS 751 medium of poor conductivity. Another procedure is to consider a vein as a sheet of negligible thickness, that is, equivalent to a plane of ideal reflecting characteristics. If the plane is a good conductor, its effect is equivalent to producing an image of opposite sign, while an insulating sheet, assumed to be so thin that charges do not collect on it, produces an image of a source of like sign. In this manner both resistivity and P.D.R. distributions can be calculated.” 4. Ore bodies. The method by which anomalies of ore bodies are calculated depends entirely on their shape -and geometric disposition. For ores in horizontal or nearly horizontal stratification (certain types of lead-zine and lead-silver ores) the treatment is the same as for horizontal beds. For vein-type deposits in vertical positions the P.D.R.’s may be calculated by assuming two adjacent contacts or a thin conductive or in- sulating sheet. This procedure is applicable when the depth of overburden is small; if such is not the case, the problem can be treated as a two-layer case with a vertical vein in the lower medium that reaches up to the interface. Dipping ore bodies may be considered as two contacts of equal dip or as thin sheets, as the case may be. Lenticular bodies of limited dimensions may be assumed to be equivalent to polarized doublets. The more complicated cases are best treated by model experiments. 5. Surface geologic features. Owing to the great sensitivity of the P.D.R. method to horizontal resistivity variations, considerable anomalies will be produced by slight changes in the composition and structure of surface and near-surface formations. In regard to vertical contacts, the theory holds only if beds are infinite in vertical direction; for horizontal formation boundaries, the theory assumes that they remain the same in a horizontal direction. ‘The field technique described below is intended to eliminate surface geologic features which are characterized by a limited extent in either horizontal or vertical direction, or both. In Fig. 10-80, A’, C’, and B’ are the three potential stakes and E the next power electrode. The arrangement is moved over a conductive body of limited depth extent, with an electrode separation equal to the width of the body. Assume as unit of length one-half of the electrode separation and let the depth extent of the conductive body vary from one to eight units. The corresponding ratio curves become more unsymmetrical with increasing depth extent. Therefore, to detect bodies of great depth extent and to eliminate near-surface interference, it is but necessary to take a reverse profile. Upon averaging the two curves, one obtains curves with amplitudes proportional to depth extent, and anomaly peaks over the center of the body.”” 61 Howell, op. cit., 34-37 (1932). 61a F, Kihlstedt, A.I.M.E. Geophys. Pros., 62-74 (1934). 752 ELECTRICAL METHODS [Cuap. 10 C. EquirpMENT; PROCEDURE Various types of equipment have been developed for P.D.R. surveying. DC. bridges have been used for recording corrosion effects on pipes (Schlumberger). Alternating current bridges are operated with audio frequencies of from 250 to 900 cycles, which has the advantage that phones can be used as indicating instruments. In the Imperial Geophysical Experimental Survey series-capacity ratiometer, each arm consists of a condenser and a resistance in series. Fig. 10-80. Elimination of surface geologic anomalies by ratio curves taken in opposite directions (after Kihlstedt). The ratio of the potential drops V; and V2 between the equidistant pairs of contacts AB and BC, and their phase differences are determined by adjusting the capacities and resistances in each arm to balance. Thus Vo = (Z2/Z1) Vi, where Z, = VR? + X2and Z, = VR? + Xi, Zand Zz are the total impedances in the arms of the bridge, Ri and Re resistances, and X, and X» are capacitive reactances, with X; = 1/27fC, and X2 = 1/2rfC,. Hence, =D. G Ve R, cos tan R Vi _1 Xe R, cos tan R (10-43a) and the phase difference Cuapr. 10] ELECTRICAL METHODS 753 In a modification of the original ratiometer, the I.G.E.S. used con- densers in parallel with the resistances. Then the admittance 1/Z in each arm is + = 5 + j2nfC. 42nfC If 1/R = g, the conductance and 2z2fC = h, the capacitative susceptance of the circuit, then the admittance is g + jh, and the ratio is Ve gi + ghi Vi ge+ jhe Soa In the parallel ratio-arm instrument (see Fig. 10-81) the variable capaci- ties and resistances are so graduated that the conductances gi and ge and the susceptances h; and hp are in the same units, the unit being the conductance of a 300,000 ohm resistance. When the frequency is 535 cycles per second, this is approximately equal to the suscept- ance of a condenser of a 0.001 microfarad capacity, and the various portions of the variable capacity come out as whole numbers. In the Swedish-American Racom (ratio com- pensator) bridge, inductive reactances take the place of the capacitive reactances; phase differ- ences are not read but merely compensated by the use of a variable mutual inductance. A schematic circuit diagram is given in Fig. 10-82. The P.D.R., as computed from the resistance Fig. 10-81. Parallel ca- : t é pacity ratiometer (after ratio, represents the ratio of the in-phase com- Edge and Laby). ponents of the potential drops. With R, and Rz as contact resistances of the stakes A and B, and R,, and R,, as resistances of coils LZ, and Lg , the ratio is (approximately) Vizeramlog =e in attr = é 10-44 Vee Re+ Rip + Bs ( ? The contact resistances may be determined and eliminated by a second setting of the resistances Rj and R;. Then Vac _ Rat Ri, + Ri (10-440) Vee Ro+Ri, + Bs Hence, by combination, Vac a - Ri Vac R, ee Ri (10-44c) 754 ELECTRICAL METHODS [Cuap. 10 Field procedure in P.D.R. surveys depends entirely on their purpose. In prospecting for ore bodies, veins, contacts, and faults, field practice differs somewhat from that used in stratigraphic investigations. A third procedure is applied in corrosion surveys. In mining exploration, the P.D.R. traverse is usually run along a line between the two power elec- trodes and, if possible, in the vicinity of one of them. The electrode separation is kept constant, and observed P.D.R.’s are corrected for normal ratio. If ratio stations have been taken with 50 per cent overlap, the potential gradient per unit distance may be obtained by assuming an arbitrary potential gradient (usually 1) in the first A—B interval and by calculating the gradients for all other intervals by successive multiplica- tion. Potential gradient (electric field intensity) values are then plotted against the center of the respective intervals. A continuous phase curve may be plotted by starting in the first interval with an arbitrary phase angle and by calculating subsequent phase angles Fic. 10-82. Schematic of Swedish-American Racom. by successive addition. As seen in Fig. 10-84, ore bodies are indicated by zones of low potential gradient and maximum phase anomaly. For the elimination of surface anomalies, ratio curves are surveyed in opposite directions from two power electrodes which may be switched on alter- natingly so that two ratio readings are taken at each setup. In determining depths to horizontal formations, measurements are usually made in the vicinity of one electrode; the other is kept at a distance from five to ten times the depth to be reached. Profiles are run out from the close electrode at right angles to the base. Then the power electrode is moved to another position and a second profile is run again normal to the base. The potential ratios thus obtained must be corrected for normal ratio. From a survey made with constant electrode interval and overlap, potential gradients and apparent resistivities may be calculated. In cer- tain problems, expanding electrode systems are preferred. Profiles radi- ating out from the power electrode in different directions are useful for determination of dip. An electrode arrangement in which the power elec- Cuap. 10] ELECTRICAL METHODS 755 trodes are close together and the spacing of the secondary electrodes is a function of the base length, has been proposed by Koenigsberger.” In corrosion surveys, the potential ratiometer has been used to deter- mine zones of positive potential (where the greatest destruction is likely to occur), and to record fluctuations in corrosion potential. In the latter, the bridge is set at a fixed ratio, and galvanometer fluctuations with time are recorded.” D. RESULTS P.D.R. methods have been applied in mining, in oil exploration, and in civil engineering. Applications in mining fall into two groups: (1) struc- tural and stratigraphic investigations and (2) prospecting for ore bodies. The former include location of faults, shear zones, and quartz veins. Mineralization may accompany such zones or may be related to it in some way. F. Kihlstedt™ has pub- lished a number of examples ly, where the P.D.R. method was GZ 2 supplemented by magnetic tests. Extensive use has been 1 made of the potential-ratio method in search for (gold 05 0 100 20 300 bearing) quartz veins. Fig. 10-83 is reproduced from an article by Hedstrom” and shows the P.D.R. curve above an andesite dike, flanked by volcanic conglomerates on one side and slate on the other, ob- tained near the Lebong Donok mine in Sumatra. Since the Fig. 10-83. Potential-ratio curve on andesite andesite is a poor conductor dike in Sumatra (after Hedstrom). with respect to the conglom- erates and the slate, the observed ratio curve (in terms of B/A) is in accord with the theoretical curve shown in Fig. 10-79c. Edge and Laby have published a number of ratiometer curves, largely for known deposits. In comparison with curves by other investigators it should be noted that measurements were made between two electrodes and that no ; i Volcanic enh Conglomerate 6 Beitr. angew. Geophys., 1(1) 57 (1930). 63 C. and M. Schlumberger, A.I.M.E. Tech. Publ. No. 476 (1932). 64 Loc. cit. 65 H. Hedstrom, loc. cit. 756 ELECTRICAL METHODS [Cuapr. 10 correction for normal ratio was applied. Observed ratios were generally converted to a potential ‘‘variation” curve, the latter being identical with the potential gradient referred to above. Fig. 10-84 shows a profile taken in the Uley graph- al ite area near Port Lincoln, s P 40° South Australia. The graphites 3 are believed to have originated BS y +30" § from a metamorphism of Pre- 2 $ cambrian rocks, probably con- 33 ea = sisting originally of magnesium s § limestones. The potential gra- = 2 10 § dient curve shows a minimum in « the middle of the profile, indicat- 20 1200 900 Aa Graphite lode, 50’ wide, dip 45° located after electrical survey Fic. 10-84. Potential gradient and phase curve on graphite deposit at Port Lincoln, South Australia (after Edge and Laby). ing a good conductor; the small peaks on either side signify a crowding of the equipotential lines. The phase curve has a maximum, corre- sponding to out-of-phase cur- rents induced in the conductor. On the basis of the electrical survey, a graphite body about fifty feet in width was located, dipping about 45-50° to the NW. Application of P.D.R. surveys in oil exploration has been made to deter- mine depth to key beds and to locate structure. Those known to date do not involve depths exceeding several hundred feet. In some P.D.R. surveys in Alberta,” depth interpretation was first based on peaks in the reduced ratio logs and was later supplemented by an evaluation of apparent resistivity curves calculated from the P.D.R. readings.” To what extent the simple two-layer relations between the distance of the peak in the P.D.R. curve and depth hold for more than one interface has not been determined, although it is probable that peaks in opposite directions appear near the upper and lower boundaries. P.D.R. methods offer a rapid means of measuring depth to bedrock in foundation problems, of locating faults and shear zones, of determining the general characteristics of formations, and of locating water. The survey shown in Fig. 10-85 was made near the Oriental ore body at Buchans in Newfoundland, where glacial drift occurs above arkose bed- rock. The potential-ratio (B/A) curves are plotted in such a manner that 66 Lundberg and Zuschlag, A.I.M.E. Geophys. Pros., 61 (1932). 87 Kihlstedt, op. cit., 199. Cuap. 10] ELECTRICAL METHODS 757 ratios greater than 1 are to the right, and those less than 1 to the left. A peak to the right signifies a transition from a good to a poor conductor, and a peak to the left a transition from a poor to a good conductor. The Solero 0 10 20 0 00 20 0 00.20 Fig. 10-85. Potential-drop-ratio curves indicating water level in glacial moraine and bedrock, Newfoundland (after Lundberg and Zuschlag). electrical indications were interpreted as showing the effects of both water and bedrock, the dry upper portion of the moraine being the poor, and its water-bearing portion above bedrock being the good conductor. VII. ELECTRICAL TRANSIENT (“ELTRAN”) METHODS Electrical methods previously discussed involve the measurement of stationary potentials or potential differences. In electrical transient meth- ods, on the other hand, their variation with time is observed. The recorded time constants of the ground are primarily related to the resistance of the ground circuit; it is likely that capacitive and electrolytic-polarization effects introduce a reactive component. When a ground circuit is closed or opened, the equilibrium values of voltage and current are not reached immediately. Because of the change of the current with time, induction currents are generated. ‘The greater inductance of the lower paths causes the current to flow at first near the surface (skin effect). The variation of the e.m.f. with time may be ex- pressed by a relation of the form cd E, cay Ey = CH ese are Eve cure (10-452) where Emax. is the maximum initial potential difference between the ground electrodes when the circuit is closed, Ey is the steady state value, ¢ is time, p is resistivity in ohm-cm, yu is permeability, b is the distance between the electrodes, and c is a constant™ equal to 2.32-10°. Withy = 1, the time required for the difference Emax, — Eo to drop to 1/e of its value (time constant 7’) is given by 2 Lis a (10-45b) 68 T. M. Pearson, A.I.M.E. Geophys. Pros., 34 (1934); C. and M. Schlumberger, tbid., 1389 (1932). 758 ELECTRICAL METHODS [Cuap. 10 Since the time constant depends on electrode separation and resistivity, methods have been proposed to measure the time variation in the ground circuit, either with only two electrodes” or between two potential electrodes in the Wenner-Gish-Rooney or similar arrangements.” In most Eltran arrangements used at present, the transients are meas- ured in a separate potential circuit. It has also been found that the Wenner-Gish-Rooney setup is not so suitable for Eltran work because of the large voltages that may be induced by the current circuit into the potential circuit. Therefore, most arrangements now provide for observa- tions outside the current basis in a potential circuit of about 1000 feet electrode separation. The interval between adjacent electrodes of the current and potential circuits varies between one thousand and several thousand feet. Various techniques have been used to record electrical transients. They are: (1) direct oscillographic recording, (2) neutralization of transients by two opposing generating circuits, (3) compensation of the transient by a reference signal furnished by the power generator or by a locally syn- chronized generator, and (4) controlled alteration of the received transient to give a predetermined (saw-tooth) wave form. Direct oscillographic recording was probably first used by Karcher and McDermott.” These investigators employed in the primary circuit two electrodes about a half mile apart, supplied through a switch from a storage battery of several hundred volts with currents of 10-20 amperes. Measurements were made half to three-quarters of a mile away in the extension of the primary electrode basis with two nonpolarizable electrodes about 0.1 to 0.2 mile apart, connected to a calibrated D.C. amplifier and oscillograph. The time constant was represented in the form of an ‘inductance function” which, according to the foregoing, is the apparent inductance due to the skin effect and therefore chiefly dependent on elec- trode base length and resistivity. Hence, the similarity in Karcher’s “inductance” and “‘resistivity-slope-function” curves at the same locality. In a method described by White,” power is supplied by a 60-cycle generator through a rectifier capable of delivering several thousand volts on open circuit. The rectifier charges a bank of condensers totaling 10 to 15 microfarads in capacity. The condensors are discharged by a fast mechanical switch which is released by a radio signal received from a transmitter synchronized with the sweep of the cathode-ray oscillograph on the receiving end. In this method the records are evaluated by taking 69. W. Blau and L. Statham, U. 8. Patent No. 2,079,103. 70. W. Blau, U.S. Patent No. 1,911,137. 1 J.C. Karcher and E. McDermott, A.A.P.G. Bull., 19(1), 64-77 (Jan., 1935). 7G. White, A.I.M.E. Tech. Publ. No. 1216, 4 (Feb., 1940). Cuap. 10] ELECTRICAL METHODS 759 the time gradient of the surge or by measuring the maximum height of the transient and dividing it by the total charge of the current surge. These transient voltage maxima, when contoured across a structure, give a picture very similar to a resistivity contour map. The difficulties encountered in the evaluation of oscillographic records lead to the adoption of neutralization and compensation methods to deter- mine magnitude and shape of the transients. Statham” tv Ov developed a method based Hl on a comparison of tran- sients in adjacent ground intervals. In Fig. 10-86a, I and III are the two pri- mary circuits of opposing polarity energized simulta- neously through two screen- grid thyratrons by closing MA the switch Sin their parallel grid circuits. II is the potential circuit connected aba a a | | ee cul Seas through a two-stage direct- Le pp ae els flaw coupled amplifier to the Fig. 10-86a. Circuit for comparison of electrical vertical plates of a cathode- transients (after Statham). ray oscillograph on which a 4-inch deflection corresponds to a (ground) potential difference of 4 millivolts, while the horizontal plates are actuated by a tuning-fork—con- trolled linear sweep circuit. With currents flowing in circuits I and III, resistors | and 2 are first adjusted so that no steady potential occurs in circuit II. If the switch S is then closed and the transients due to circuits I and III are equal, no transient will be recorded in circuit II. When transients appear, they are compensated by moving the potential electrodes. The direction and distance required for cancellation are in- dicative of direction and rate of increase in effective conductivity. Statham has published a map showing the effect of a deep-seated Gulf coast oil field on the conductivity vectors thus determined. Another group of Eltran methods involves a determination of the shape of the transient by compensation with a simulating network. This net- work may be synchronized by using a reference lead to the generator. For large electrode separations, a local oscillator feeding the simulating . 73 Louis Statham, Geophysics, 1(2), 271-277 (June, 1936), and U. S. Patent No. 2,113,749. 760 ELECTRICAL METHODS [CHap. 10 network is synchronized by the received transient itself. Fig. 10-86) shows an arrangement developed by West,” in which the primary impulses of 50-cycle frequency and rectangular wave form are supplied by a thy- ratron relaxation oscillator controlled by a tuning fork. In the figure the synchronization of a reference signal by this oscillator is indicated; the reference lead may be dispensed with by synchronizing a local oscillator with the transient of the potential circuit. In still another Eltran method, the technique is based on the assumption that the ground circuit has capacitive reactance in addition to resistance. The transient potential feeds two parallel circuits. One portion is ampli- fied to actuate the sweep while the other is mixed in a double triode with the reference signal, after it has passed through an adjustable network. 50 un Thyratron Relaxation Oscillator Fig. 10-86b. Arrangement for comparison of transients with simulating network (after West). From the mixer the signal goes through an amplifier and thence to the vertical plates of a cathode-ray oscillograph. Time constants of transients are then expressed in terms of the value of the variable element in the compensating network required for balance (probably RC) and maps are contoured in units of reciprocal time constants. Fig. 10-87 shows such contours for the Sandy Point oil field in Brazoria County, Texas. The productive area coincides with contours of high reciprocal time constants. Recent developments in mixing, synchronizing and simulating circuits have been discussed by Klipsch.” In the mixing of the reference signal with the received impulse, a bridge circuit has been found advantageous. The potential transient and the reference signal produced by an oscillator 74S. S. West, Geophysics, III(4), 306-314 (Oct., 1938). 75 P. W. Klipsch, Geophysics, IV(4), 283-291 (Oct., 1939). Cuap. 10] ELECTRICAL METHODS 761 and distortion network are in opposite arms of the bridge, the former syn- chronizing the latter. An amplifier and oscilloscope are connected to the detector arm. ‘Two potentiometers in series are connected across the input to the distortion network. The tapped portion of one potentiometer carries a resistance and a capacitance in parallel, while the tapped portion of the other potentiometer has a capacitance in series and a resistance in parallel. Transients can be simulated with sufficient accuracy by the four variable resistances in this network. A technique referred to under (4) above, that uses a controlled distor- tion of the received impulse to produce a linear saw-tooth transient (Saw- tran), has likewise been described by Klipsch. In this case the distortion network consists sim- ply ‘of a tapped resistance with capacitance in series, both across the input line. By adjusting the sliding contact on the resistor until the resultant wave consists of a straight-line saw tooth, the time constant (RC) of the tran- sient can be determined. Opinions in the literature differ concerning the superiority of the transient over standard resis- sh ty BREN Te : Sots " manne Fig. 10-87. Eltran contours, Sandy Point claim that transient indications oil field, Brazoria County, Texas (after cannot be duplicated by resis- Rosaire). tivity measurements, that data on hitherto unobservable rock properties may be obtained, and that depth penetration is much greater. Others contend that the depth penetration is no greater than for other electrical methods under similar field conditions and that the observed anomalies are essentially due to shallow stratigraphic variations.” It is possible that the Eltran method and related electrical methods designed to measure ground circuit react- ance, will reveal formation properties of diagnostic value not obtainable with the straight resistivity method. As was stated on page 639, the capacitive reactance of the ground is probably related to its electrolytic polarization properties. An attempt has been made to measure this polarization directly by a so-called “electrochemical” method,” likewise based on the observation 1 mile 76}. E. Rosaire, Geophysics, III(2), 96-115 (March, 1938). 77M. Miller, Beitr. angew. Geophys., 4(3), 302-315 (1932). 762 ELECTRICAL METHODS [Cuap. 10 of transients. When current is sent into the ground, there result changes in the concentration of electrolytic solutions which in turn give rise to a counter (or polarization) e.m.f. It was noted before that this phenomenon is responsible for corrosion potentials and that it is utilized in stimulating the “activity” of ore bodies by passing current into the ground before a self-potential survey. An arrangement for measuring these counter e.m.f.’s is shown in Fig. 10-88.” The upper portion represents a beat oscillator furnishing fre- ies of th Beat frequency oscillator quencies of the order of fifi nol 1-5 cycles. The output is coupled to the ground J0eps 3cpst —_ circuitthrough the trans- | former T and is recti- fied on the secondary Coup Coil side, so that impulses in only one direction pass through the ground. wh) | The potential difference between the electrodes E, and Ez, as well as their time variation, is recorded on the string galvanometer or oscillo- graph G,. In parallel with this circuit is an- other one, consisting of a second rectifier with condenser in parallel, going into the grid of an amplifier with record- ing galvanometer in Fie. 10-88. Circuit in electrochemical polarization the plate circuit. With method (adapted from Miiller). proper selection of the capacity C in parallel with the second rectifier, the galvanometer G2 will record only the return impulses because of the unilateral impedance of the rectifier tube. The fluctuations of both the input e.m.f. and the polarization e.m.f. are recorded on the same film with time marks every hundredth of a second. The ratio of charging time to discharge time is always greater than 1 and is a function of the electrolytic polarization properties of sub-surface forma- 78 Ibid. Cuap. 10] ELECTRICAL METHODS 763 tions reached by the action of the electrodes. It is claimed that the depth penetration is the same as the electrode separation. Since the ability of formations to furnish polarization e.m.f.’s is,closely related to their elec- trolytic content and hence to their resistivity, there is some question as to whether an altogether different physical property is recorded in these measurements. Although the power supply to the ground is small (1-2 watts) the question arises further how much polarization e.m.f. is produced in the nonpolarizable electrodes. VIII. ELECTROMAGNETIC METHODS Electromagnetic methods constitute one of the largest and most diversi- fied groups of electrical prospecting. They differ from the potential methods in that the electromagnetic field and not the surface potential of the ground currents is measured. Electromagnetic methods are divided into two groups. In the first, energy is supplied to the ground by contact; in the second group, energy is supplied inductively, that is, by insulated loops. The first group is sometimes called electromagnetic, and the second inductive. A frequency of 500 cycles is most commonly used in electromagnetic methods. When a simpler technique is desired, when phase shifts are to be kept to negligible values, where a substantial depth has to be reached (as in Schlumberger’s method of electromagnetic dip determination or in | Koenigsberger’s ring induction method), low frequencies of the order of 25-60 cycles are preferred. More than one operating frequency may be required when highly conductive layers near the surface are to be pene- trated. Electromagnetic methods using frequencies of the order of tens of kilocycles are referred to as “high frequency” methods. Such fre- quencies are likely to energize noncommercial conductors and to produce excessive terrain effects. A band between 300 and 900 cycles is a prac- tical compromise. Lower frequencies would make energy transmission too inefficient and would eliminate the telephone as a practical null de- tector. Higher frequencies lack depth penetration and, produce too much interference. Transmission units are: long cables, connected to a generator and grounded at both ends; rectangular or square loops; or circular coils. They are fed by generators driven by gasoline engines, storage battery operated buzzers, commercial lighting plants, or vacuum-tube oscillators. Receiving devices are of widely diversified construction, depending on quantities measured. Their two fundamental constituents are a reception frame with several hundred turns of wire and an amplifier. Use is made of null methods wherever possible, with telephones as null indicators. 764 ELECTRICAL METHODS [Cuar. 10 The more complex arrangements measure the field components by ampli- tude and phase, or as in-phase (real) and out-of-phase (imaginary) com- ponents. Fields at successive points may also be measured relatively in regard to amplitude ratio and phase difference. Following is a summary of observed electromagnetic field parameters: Strike and dip of the, ellipse of polarization. Absolute values of intensity and intensity components. Semi-absolute determination cf intensity components in reference to amplitude and phase of the primary current. Out-of-phase field components in terms of corresponding in-phase com- ponents. Field ratios and phase differences in successive intervals. Ratios of in-phase components at successive points. Potential methods of electrical prospecting are preferred whenever pri- mary power may be readily applied by contact and when the objects sought are not very good conductors. Electromagnetic-galvanic methods are suitable where bodies of good conductivity are to be located, where surface beds of good conductivity would produce too much screening effect on potential methods,” where requirements of depth penetration are not too great, and where contact of the primary electrodes with ground is readily possible. When this is difficult (as in deserts, on the ice of lakes, and the like) inductive methods must be applied. A. ELECTROMAGNETIC METHODS WITH GALVANIC POWER SUPPLY 1. Electrode arrangements are like those used in equipotential-line or potential-profile methods. Line electrodes are laid out at right angles to the strike so that maximum distortion of the current lines occurs; profiles are run at right angles to the strike. Where large amounts of ground are to be covered and where the uniformity of the primary field does not play an important part (as in field-ratiometer measurements), point electrodes are preferred. A long cable is laid out each way from the generator and grounded at the ends with.a number of pins or wire screens. The line must be in the direction of strike so that profiles can be measured at right angles thereto. The field produced by the line connecting the electrodes to the generator may be reduced by carrying the leads around the area in a square or rec- tangle or by taking the measurements on the outside of a short current basis. For the simpler layouts, the field due to the leads may be calcu- 79 See J. N. Hummel, Zeit. Geophys., 7(5/6), 258 (1931). Cuap. 10] ELECTRICAL METHODS 765 lated and corrected for. Corrections need not be applied when com- pensators are used with inductive field excitation, since the loop field appears in the in-phase component, whereas the field induced in an ore body will generally affect most strongly the out-of-phase component. 2. Recewing equipment used in electromagnetic methods is virtually identical with that in inductive methods and is discussed in that connection. A piece of equipment not described there is the Darley pipe locator, since it is a direct application of the electromagnetic method with galvanic current supply. One pole of a small A.C. generator (buzzer) is connected to an accessible point of a system of pipes; the other pole is grounded. The receiving device is a small rectangular coil (carried in horizontal position over the ground), connected to an amplifier with phones. As such a coil will respond to the vertical component, which is zero directly over a conductor (see Fig. 10-92a), the point of minimum or zero signal will indicate the position of the pipe. In other types of pipe locators where the coil is carried in a vertical position, the horizontal component is re- ceived and therefore the pipe is indicated by a maximum. A method not strictly classifiable under the groups tabulated on page 764 has been proposed by Haalck.” It is based on a comparison of the hori- zontal field of the ground currents with the field produced by the electrode leads. The latter are predominantly vertical; the former predominantly horizontal, at least on the electrode base. The receiving arrangement is set up in the center of the electrode base and the cable is carried around this location in a half rectangle. If the current flows in the cable from front to back, the cable field Z) is upward and that of the ground return current is to the left. The two fields are approximately in-phase. If the reception frame is set up with its horizontal axis of rotation parallel with the electrode base, a2 minimum of sound will be observed in the head- phones when its plane is in the resultant direction of the two fields, that is, if tan g = Zo/ H. The sensitivity may be increased by using two frames, one stationary and the other rotatable (Fig. 10-96). In investigating stratified ground with this method, the electrode separation is increased in steps and the change in tilt angle is observed. If the ground is homogeneous, the hori- zontal field will decrease with an increased electrode separation due to greater depth penetration of the current. Hence, the tilt of the frame will increase. If bodies or strata of different conductivity are present, the depths of the effective current concentration will change; therefore, changes in the regular trend of tilt variation will occur. There is a definite relation between electrode separation and depth, the factor being 23 to 3, depending on conductivity contrasts involved. 80 H. Haalck, and A. Ebert, Zeit. Geophys., 8(8), 409-419 (1932). 766 | ELECTRICAL METHODS [Guana 3. Interpretation procedures applied in electromagnetic-galvanic pros- pecting vary with the completeness and nature of observed field parame- ters. If only the direction of the field is measured (Elbof method), inter- pretation has to be largely qualitative. The direction of the field obtained with a vertical pickup coil, or the strike and dip of the ellipse of polariza- tion determined with a coil rotatable about both a horizontal and a vertical axis, is a function of (a) the normal ground field due to the regular current distribution between two point or line electrodes, (b) the field produced by subsurface current concentrations, and (c) the field of the generator leads. The normal “4 field can be calculated from relations previously Fre. 10-89. Magnetic field piven for the potential field. It is expressed due to currents between two - electrodes. by” H = VX ap Y’ = Ia/n — 1/r2)-10° (Gauss), where the total current J is in amperes and r is in meters (see Fig. 10-89). The field direction is given by tan a = Y/X in the horizontal plane and by tan yg = Z/H in the vertical plane, where the components due to subsurface conductors follow from eq. (10—- 46a). A similar relation applies if the field of the cable is used for com- parison as in the Haalck method (see page 765). When the field intensities are measured at low frequency, phase shifts are small and the observed anomalies may be compared to advantage with fields calculated for simple geometric bodies as shown below. This pro- cedure is likewise applicable when the components have been measured separately with a compensator and normal fields and cable effects have been deducted. The electromagnetic anomalies of subsurface bodies may be determined with sufficient approximation by assuming equivalent current concentra- tions in such bodies. Hence, if the width of an ore body is small compared with its depth, the total field is T = 2I’/r (see Fig. 10-92a), where r is the distance to any point at the surface and I’ is the current in the con- ductor. In the following equations, let d be the depth of a current con- centration and X, Y, and Z be the components of the electromagnetic field (where X is the horizontal strike component, Y the horizontal component at right angles to the strike, and Z the vertical component). Further, let y be in the direction at right angles to the strike, x in the direction parallel with the strike, and ¢ be the angle between y and r. Then the 81 J. Koenigsberger, Phys. Zeit., 28, 342 (1937). A. Graf, Zeit. Geophys., 5(8), 331 (1929); and Beitr. angew. Geophys., 1(3), 286 (1931). Cuap. 10] ELECTRICAL METHODS 767 X component is zero and the other components are given by Y = T sin ¢ andZ = Tcosy. Since cos ¢ = y/r and sin g = d/r, we have y = 2d _ td a y? + a and (10-46a) z= 2I'y a w2hy r2 ye + a" j Since dY/dy = 0 if y = 0; 0Z/dy = 0 for y = +d,Z = 0 if y = 0 and aZ/day’ = O for y = 0. The horizontal component has a maximum directly over the current con- centration (y = 0) and the maximum intensity is Ymax. = 2/'/d. .The maximum gradient in vertical intensity is directly over the ore body where the vertical intensity itself is zero. A maximum in vertical intensity occurs on either side at a distance from the zero point equal to the depth. The distance between the maximum and minimum vertical intensity anomalies is therefore equal to 2d. For an ore body of definite width and infinite depth extent which can no longer be considered equivalent to a current concentration (see Fig. 10-92c), Z = 2I’-log. 2 rn (10-46b) Y = 21’ (a + )). Curves for bodies of various dimensions, dip, and depths have been published by Mueller.” Heine has calculated the electromagnetic field for rectangular sections of various dimensions, at right angles to the direction of current flow.” He assumed that the current density throughout the section was uniform which is permissible within the conductor itself. It is necessary, however, to allow also for the decrease of current density with depth, which was previously discussed (see Fig. 10-32 and eq. [10-21e]). Belluigi has compiled a set of curves, showing the variation of current in the median plane between two electrodes as a function of base length.” When the current density for a given depth has been found, the electro- magnetic field components may be determined” for a conductive body of 82 Gerl. Beitr., 21(23), 249-261 (1929). 83 W. Heine, Elektrische Bodenforschung, 137, Borntrager (Berlin, 1928). 84 A. Belluigi, Beitr. angew. Geophys., 1(4), 370 (1931). 85 Tbid. 768 ELECTRICAL METHODS [Cuap. 10 arbitrary section by the use of gratings similar to those applied in gravi- metric interpretation (see page 154). Since the magnetic field is propor- tional to the section of an element in which the current density is uniform, the field components are, for an element dydz traversed by a current in the x direction: Y WED PX he a gppue ’ y Substituting y = R cos 6, z2 = R sin 0, and dydz = R-d@dR, we have for the same components (10-47a) Z 6 aap | sin 6d@ dR —2I’ If cos 6dé dR. N I | (10-47) Fig. 10-90. Subsurface element traversed by current between two electrodes. Hence, for a plane element, as in Fig. 10-90, the intensities are given by %i4n . Ryyy Yu = — Ti sin 6 d@ dR 95 k and (10-47c) isn Rui Y Ae [ cos 6 dé [ dR. | 95 Ry The fields of all elements in the section are therefore Y = >) 21’ (cos 641 — cos 6) (Rati — Rx) (10-47d) Ze » —2I’ (sin 6:41 — sin 6;)(Re+1 — Rx). Cuap. 10] ELECTRICAL METHODS 769 For a current’ density of 1 amp./100 m’, a unit effect (H;; = 1.10 * Gauss) is produced when cos 6:4, — cos 0; = 0.1 and Ry; = 10 m. This applies to both horizontal and vertical com- ponents; for the latter, the dia- gram is rotated 90° (see Fig. 10-91). Grounded electrodes cause cur- rents to flow not only by galvanic action, but by inductive action as well. Since the ore body, with the cable or loop, acts as a trans- former with a short-circuited turn, Fic. 10-91. Interpretation grating eddy currents are produced along for electromagnetic-galvanic methods the edges of the ore body, and flow (after Belluigi). Each compartment, An mutheidiaras welliasvaround. its when it is traversed by current at right , angles to its section, produces the same upper edge. The latter cause the effect on the horizontal component of greatest portion of the field observed the electromagnetic field. For calcula- at the surface. The field may. be tions of the vertical component, the dia- i y gram is rotated 90°. calculated from formula (10—46a) by adding the effects of the two current concentrations. With 2a as the width of the ore body, we have for the components z San, (Se 1 T2 Y = 2I/d A hd DE NGL Bray’ where J; is the induced current. Use of grounded cables results in a superposition of currents produced by galvanic and inductive action. Considerable phase shifts may occur between the currents, so that in the absence of definite phase data only approximate curves can be given for the resulting fields (see Fig. 10—92c). Since one side of an ore body is usually much closer to the primary cable than the other is, the maximum on that side is greater than the minimum on the far side. The latter can be brought out by reversing the position of the primary cable or loop. The curves shown in Fig. 10-92d represent the variation of the X and Y vectors compounded from fields with greatly differing phase angles produced by both galvanic and inductive action. Separate measurement or calculation of in-phase and quadrature compo- nents has the advantage of segregating the induced from the galvanic and (10-48) 770 ELECTRICAL METHODS [Cuap. 10 ¥&Z, galvanic only | VEZ, inductive only | VEZ, galv. ples induct. x x Fia. 10-92. Horizontal and vertical field components due to galvanic and inductive action of vertical ore bodies. 8 g 8 8 8 1 ar alll. B+ 8 S| 3 Si- 8 8 1800 BS < 3H ||- iN MS 1200 1250 1300 Fia. 10-98a. Normal field components for profile, at right angles to electrode basis of 200 m length, taken with 30 cycles (after Miller). g iS Cnar. 10] ELECTRICAL METHODS 771 normal fields. A further advantage is gained by using insulated loops whenever possible, because the galvanic effects are then eliminated. Since conditions in the field are not so simple as those assumed in the theory, interpretation is simplified by such applications of primary energy and observation methods as will produce the clearest type of indication. In electromagnetic-galvanic methods, corrections are required for: (a) cable leads, (b) topography, and (c) normal field. The field of the cable depends on the position of the point of observation with reference to the cable. It can be calculated for all three intensity components (see page 777). The topographic effect may be of an electrical or geometric nature. The former is due to a distortion of current lines on the ground surface (see page 702) and may be determined by small-scale experiments. The geometric in- fluence is due to a change in rela- tive position of ore body and plane of observation. A correction for the normal field is necessary in order to obtain the best picture of anomalies due to subsurface bodies. The normal field distri- bution may be calculated from the formula previously given (see page 766). A better procedure is to measure actually all field com- . Fig. 10-936. Horizontal and vertical f } intensity anomalies on parallel ore bodies ponents in a location known to be (after Lundberg and Sundberg). free from outstanding anomalies (see Fig. 10-93a). In the interpretation of electromagnetic survey data, considerable help may be expected from model experiments.” 4. Results. Electromagnetic-galvanic methods have been used for the location of ore bodies and structural investigation. Fig. 10-93b shows two sets of curves on parallel bodies of steep dip, observed in Sweden. The horizontal and vertical components are those of a thin sheet as illustrated schematically in Fig. 10-92a. Fig. 10-94 shows the variation in the dip of a reception frame for minimum sound (Elbof method) for a profile near the Horne mine in Rouyn, Quebec. The range in the angles is 50°, undoubtedly because the ore bodies are very near the surface. Various electromagnetic methods have been used for structural studies. 86 K. Sundberg, Beitr. angew. Geophys., 1(8), 335 (1931). Heine, op. cit., 141-145. Vd2 ELECTRICAL METHODS [CHap. 10 Fig. 10-95 shows a syncline of slates of upper Devonian age near Meggen (Sauerland, Germany). Results obtained there demonstrate the impor- tance of corrections for cable and topography. If a third correction had Fic. 10-94. Curve showing dip of polarization ellipse on Horne ore bodies, Rouyn, Quebec (after Mueser). & Ss ue S Ss 4, Ss Scale for Z & & © Scale for X and V % Fic. 10-95. Upper curves: electromagnetic field components (in Gauss) as meas- ured. Lower curves: same, corrected for cable and topographic influence, showing influence of Devonian syncline (after Dieckmann). Cuap. 10] ELECTRICAL METHODS 773 been applied for the normal field, the curves might have been improved further. The maximum in the Y component and the trend of the Z curve indicates that the syncline acts as a current concentration, probably because the shales in the center of the syncline are of good conductivity. The Haalck electromagnetic method (see page 765) was used for depth determination of lignite beds in the Ville area by observing changes in the tilt angle of the detection coil with changes in spacing of the primary elec- trodes (Fig. 10-96). For the same area, resistivity-depth curves were illustrated in Fig. 10-72. Fic. 10-96. Effect of electrode separation on tilt angle of electromagnetic field in determining thickness of lignite beds at Ville, Germany (adapted from Haalck). Left seale, electrode spacing; right scale, depth. B. ELECTROMAGNETIC MrEtTHops witH INDUCTIVE POWER SUPPLY The application of primary energy by insulated loops gives the electro- magnetic-inductive methods a number of advantages over the electromag- netic-galvanic methods. First, power can be transferred to the ground without great loss, particularly in areas of poorly conductive surface beds. While galvanic methods appear to be better adapted to massive geologic bodies, inductive methods are more suited for sheet-like deposits. Good conductors may be reached when covered by poor conductors; depth pene- tration can be regulated by using different frequencies. 774 ELECTRICAL METHODS [CHap. 10 Electromagnetic-inductive methods may be divided into horizontal- and vertical-loop methods. The choice between them should theoretically be controlled by the closeness of coupling (loop and geologic body in parallel planes). For instance, in exploration of stratified ground, the loops should be horizontal; in prospecting for vertical or steeply dipping ore bodies, the loops should be vertical. However, a limitation is placed on this pro- cedure, since large vertical loops are difficult to handle and since, with practical sizes, their range is comparatively small. Hence, horizontal loops are used more extensively. The following frequency ranges are applied in inductive methods: (1) low frequencies (30 to 100 cycles), (2) audio fre- quencies (250 to 1000 cycles), and (3) high frequencies (several tens of kilocycles). 1. Horizontal-loop methods. (a) Power supply. A large variety of transmission and generating equipment is available for use with insulated loops. A simple procedure is to feed the loop from the industrial power network through a suitable rheostat and transformer. This method has been applied where ore veins, fault conditions, and the like, were investi- gated in or near electrically operated mines. As a rule it is preferable to employ frequencies that are removed from the commercial frequencies to avoid interference. Gasoline-engine driven generators provide ample power (3 to $ kw.) for this purpose. It is desirable to provide them with a frequency meter or frequency bridge.” For absolute intensity measure- ments with a vacuum tube voltmeter, great constancy of output™ and frequency are required. Although of low power (15 to 20 watts), storage battery operated buzzers are satisfactory for moderate depths. Two types are illustrated in Fig. 10-97. Motor generators have been applied with storage battery driven (6 or 12 volt) D.C. motors and A.C. generators of low or audio frequency. Vacuum tube oscillators are used where both constancy of a given fre- quency and adjustability of frequency are desirable. Their output can be increased to about 80 watts when they are used with a power amplifier. The oscillator shown in Fig. 10-98 may be adjusted in frequency between 5 and several hundred cycles and has an output of several watts. In the power amplifier shown in the same figure, the plate supply is furnished from an A.C. generator, rectified, filtered, and connected to the center tap of the output transformer and the cathodes of six screen-grid tubes. (b) Transmission units. Transmission units in inductive prospecting have the form of extended lines, rectangles, or circles. Single cables and rectangles are arranged parallel to the strike and profiles are surveyed at right angles to the strike. 87 Canad. Geol. Survey Mem., 165, 150. 88 Miiller, Gerl. Beitr., 21(2/3), 241 (1929). Cuap. 10] ELECTRICAL METHODS 775 6v Tap Switch Fig. 10-97. Buzzers for electromagnetic prospecting. (EN (EN IT CEN (EN ape acer: | 7); © ray 3S Fig. 10-98. Vacuum tube oscillator and power amplifier for electromagnetic methods (adapted from Miller). 776 ELECTRICAL METHODS [Cuap. 10 _ The electromagnetic fields of cables or loops are readily calculated. For a long cable the field some distance away is practically vertical if the observation points are located at the same elevation. Since the magnetic intensity of a current element ds at a point P having the polar coordinates R and ais equal to Ids sin a/R’, the normal field is Z= lea (sin a2 + sin ay), (10-49a) 10r where r is the distance normal to the line, and the current I is in amperes (see Fig. 10-99a). The minus sign applies if P is below E£,. If P, fi, fe A b ny r<4 an qo (c) Fig. 10-99. Horizontal cables and loops. and EH are all at the same elevation, the horizontal components are zero. If P is halfway between EF; and E2, a, = a2 and 10 ot eee | where 21 is the distance between FE; and Fp . If the point P is not at the same elevation with the cable and if a line connecting the center of the search coil and the line E,-E, makes an angle ¢1 With the vertical (Fig. 10-99b), a horizontal component is produced in (10-49) Cuap. 10] ELECTRICAL METHODS Me addition to the vertical, and Tie ' , —— (sin a2 + sin a) sin ¢1 Ay 0a Yo = ne (sin a2 + sin a1) COS gy (10-49¢) 10r X, = 0, J where Yp is the horizontal component at right angles to the line E,-E2 , and Xp is the component parallel with it. If the line E,-E2 is inclined at an angle g: from the horizontal, all components are effective and Ly ae (sin a2 +E Sin ay) SiN ¢g1 COS ge 10r ] Oe ‘ Y = 0% (sin a2 + sin a) COS ¢1 (10-49) Te ve i 5 ; X) = -— (sin ag + sin q;) sing SIN ~. i0r } The field of a horizontal loop (see Fig. 10-99c) may be calculated by adding the fields of its straight portions, so that 24) Ls) Se ema Es ea if (10-49¢) 5171 sin 2a; ro sin 2as 73 Sin 2a3 74 Sin 2a4 At the center of a square loop with sides a, 7. = r2 = 73 = | = 7 = a/v/2. Then the sum in the bracket is 4+/2/a, and the intensity z, = v2 (10-49/) i waa ioe In the central portion the field is very nearly uniform. Hence, formula (10-49f) may be applied in a fairly large area. In hilly country these formulas remain the same, provided the loop is laid out in a plane on a slope and the vertical component is measured at right angles to the ground surface. The field in the center of a rectangle with the sides a and b is, by application of eq. (10-49e), il 2 Zo = : Veit (2 -- ‘ (10-499) G50 778 ELECTRICAL METHODS [CHap. 10 Miller” has measured the field outside a rectangle 200 meters in length and 150 meters in width and found a decrease approximately proportional to the third power of distance. This is also true for the space outside a circular loop (see below) and is in accordance with the well-known fact that a closed loop is equivalent to a magnetic doublet with the moment IS (S = area). For a circular loop of the radius R, the (axial) component Z and the (radial) component Y, are given by Z= rla+3 (2) 32 | talk) Peta + | ‘: 10-50a) 52/7 \" . 925 2. 105 + 64 (5) "Te RT ge (=) + where J isin abamperes. The radial component becomes zero ‘ie in the axis (r = 0) and in the plane of the loop (2 = 0). In the center (r = 0, =°0), the vertical component Zo = ae (J in abamps.) or a (Tinamps.). (10-50b) The variation of Z inside and outside a circular loop is shown in Fig. 10-100. For outside points, the vertical component is ZL = IRs 1 += 45) +B (A) -b |. (10-50c) For large distances the series terms approach zero and the vertical com- ponent is Z) = [R’x/r’ = m/r’, that is, the vertical component is propor- tional to the magnetic moment m of the loop and inversely proportional to the cube of distance. (c) Reception equipment. Reception equipment in electromagnetic pros- pecting varies from the simplest to the most complex, depending on what information about the field is sought. If only the strike and dip of the ellipse of polarization is desired, a simple coil with amplifier and phones is sufficient. For intensity measurements without reference to phase, a vacuum-tube voltmeter is used in the output stage of the amplifier. In- 89 Miiller, op. cit., 30(1/2), 185 (1931). Cuap. 10] ELECTRICAL METHODS 779 tensities and phases are determined in reference to the loop current by compensator arrangements. The out-of-phase component (generally due to subsurface conductors) may be obtained in reference to the in-phase field (usually due to the loop) by the Bieler-Watson method. Fields in successive intervals may be determined relatively by measuring the ratio of the field vectors and their phase difference. Finally, the in-phase com- ponents on successive stations may be compared (field ratiometer). With a reception coil of round or square shape the orientation of the plane of polarization of the ellipse and its projections can be determined. When elliptical polarization is small, this is equivalent to a measurement of the direction of the resultant horizontal field and the inclination of the field. The reception coil must be capable of rotation about a vertical and a horizontal axis. Transit bases are frequently used for this purpose. Zs peep a2 06 67 & (edhe SbF. Je (a) (b) Fig. 10-100. Fields of circular loops: (a) inside of loop, (b) outside of loop (adapted from Miller). The standards are changed to a semicircular support in which the reception frame can be rotated about a horizontal axis. A small vertical circle is usually provided so that the tilt angle of the frame in the minimum position may be determined. The horizontal azimuth on the horizontal circle is read in respect to markers on the base line or in respect to magnetic north. The Swedish investigators have used a long staff with a horizontal cross- bar, about which a square frame may be rotated. The crossbar is pro- vided with peepsights and a clinometer so that both horizontal azimuth and tilt angle of the frame can be determined. Coils are generally wound on wooden or aluminum frames. They have a diameter of 40 to 50 centi- meters, from 500 to 1000 turns of wire, a D.C. resistance from 75 to 150 ohms, and an inductance of from } to 3 henry. The amplifiers are usually transformer coupled; they have two to three stages; and carry headphones 780 ELECTRICAL METHODS [CHap. 10 in the output circuit. Reception coils and amplifiers are common to all receiving arrangements discussed below. When the frequency is too low for audio detection, the telephone is replaced by a galvanometer in the plate circuit of the output stage (see Fig. 10-101). The sensitivity of the galvanometer is 10° to 10’ amperes Fic. 10-101la. Resistance-coupled amplifier for electromagnetic prospecting, with output meter (adapted from Miller). Bucking Grcuit Fig. 10-101b. Transformer-coupled amplifier for electromagnetic prospecting, with output meter (adapted from Muller). per scale division; that of the reception arrangement, of the order of Lon gauss. The amplifiers should remain in good calibration and should have constant gain. The latter may be expressed as galvanometer deflection for a given input voltage. The corresponding field is then Ev/2 8 = E —51 H SSN 10° gauss, (10-51) Cnap. 10] ELECTRICAL METHODS ’ 781 where E is the e.m.f. induced in the coil of the area S and turn number N, and w is the angular frequency. Absolute measurements of field intensity have the disadvantage of de- pending on generator voltage and frequency. Hence, it has become more general practice to measure A.C. fields semiabsolutely, that is, in reference ' ' ' ' ' ' 1 ' ' ' ' ! ' ' ' ' ' ' ' ' ' i ' 1 ' (a) Fia. 10-102. Larsen compensator with (a) resistance coupled reference, and (b) inductively coupled reference. Fig. 10-103. Compensators giving (a) intensity and phase of field and (6) in-phase and quadrature field. to generator voltage and phase. With a voltage divider or a transformer (see Fig. 10-102) a portion of the generator voltage is carried to the field- measuring network by a separate cable. Two compensators for the meas- urement of potentials with reference to generator amplitude and phase are described on page 696. Adaptations of these to electromagnetic measure- ments are shown in Fig. 10-102 and 10-103. The Larsen compensator 782 ‘ ELECTRICAL METHODS [CHap. 10 gives the in-phase and quadrature components of the field, the former being obtained by adjustment of the slide wire, the latter on the secondary of a variometer. When the bridge is balanced, the in-phase voltage drop rt on the resistor R, plus the quadrature e.m.f. induced in the secondary of the mutual inductance M, is equal to the voltage V, induced in the pickup coil: Mo agen (10-52) Heiland Research Corp. Fig. 10-104. Compensator with amplifier and receiving coil. with 2 = V/(R + jLlw). A complete compensator arrangement with coil on tripod and instrument case containing network and amplifier is shown in Fig. 10-104. In the ring-induction method” compensation is accomplished by creating in-phase and out-of-phase fields outside the detector coil. When alter- nating current is passed through the primary loop in Fig. 10-105, a quadra- » J. Koenigsberger, Phys. Zeit., 31, 487-498 (1930), 35(1), 6-8 (1934); Beitr. angew. Geophys., 3(4), 392-407 (1933), 4(2), 201-216 (1934), 7(2), 112-161 (1937). W. Nunier, Beitr. angew. Geophys., 3(4), 370-391 (1933); Phys. Zeit., 36(1), 8-10 (1934). A. Graf, Beitr. angew. Geophys., 4(1), 1-75 (1934). S. Stefanescu, Beitr. angew. Geophys., 5(2), 182-192 (1935), 6(2), 168-201 (1936). Cuap. 10] ELECTRICAL METHODS 783 ture field is caused by currents induced in subsurface conductors. The field depends on frequency, radius of the primary coil, current strength, and the apparent conductivity of the subsurface section. It is measured by a compensator coil which is connected to the primary coil through a “reference” transformer and mounted in the same level (h) with the de- tector coil, while the effect of the in-phase (primary) field is compensated by a neutralizing coil laid out on the ground. The detector coil is con- nected to an amplifier with a vacuum-tube voltmeter circuit. A receiving arrangement involving the determination of (horizontal) out-of-phase components in terms of (vertical) in-phase fields is known as the Bieler-Watson method.” It makes use of a dual coil receiver, con- sisting of a large rectangular frame rigidly connected to another smaller Primary Coil; h=0 Fie, 10-105. Compensator and primary loop arrangement in Koenigsberger ring induction method. one at right angles to it. The purpose of the small frame is to pick up the field corresponding to the major axis of the ellipse of polarization (almost vertical, due to the in-phase loop field), while the large frame will pick up the field in the direction of the minor axis of the ellipse (Fig. 10-106a). This field is usually horizontal, and is in quadrature with the loop field. The e.m.f.’s induced in the coils are pulled back into phase by a condenser across the vertical coil and connected in opposition to a de- tector. The number of turns in the horizontal coil is changed until balance is obtained. The detector is a three-stage, transformer coupled, 9 Edge and Laby, op. cit., pp. 64-67, 283-286. H.G.I. Watson, Canad. Geol. Sur- vey Mem. 165, 144-151. J. McG. Bruckshaw, Phys. Soc. Proc., 46, 350 (1934). 784 ELECTRICAL METHODS [Cuar. 10 plane-tuned amplifier with phones. At each station the observer records the number of turns in the horizontal coil required to obtain a balance, holding the axis of the double coil vertical with the plane of the large coil first in a north and south, and then in an east and west direction. Com- pounding of the two readings yields the ratio of the quadrature horizontal to the vertical in-phase field and gives, therefore, approximately the ratio of the axes of the ellipse of polarization. This resultant may be plotted as an arrow whose direction points toward the conductor and whose length is greatest near its edges. Points of equal vector amplitude may be joined by lines of equal intensity of the out-of-phase component. Fie. 10-106. (a) Double-coil arrangement in reference to polarization ellipse (after Edge and Laby). (b) Bruckshaw’s modification of Bieler-Watson system. With the simple Bieler-Watson system sharp nulls are often unobtain- able. If the ellipse is not vertical, an in-phase e.m.f. appears in the vertical coil and a quadrature e.m.f. appears in the horizontal coil. Fur- thermore, the phase shift between the vertical and horizontal components is not always 90°. An instrument designed to measure any phase shift between the vertical and horizontal components has been constructed by Bruckshaw”™ (Fig. 10-106b). The circuit is comparable with that of a compensator if one considers the horizontal frame as ‘‘reference” coil. An inductance with resistance, as well «s a capacitance with resistance, are connected in two parallel branches to this coil and its (reference) e.m.f. 9 Loc. cit. Cuap. 10] ELECTRICAL METHODS ' 785 is split up into its in-phase and quadrature components. The currents in these two branches differ by 90° if L = CR’. To measure the in-phase and quadrature components of the e.m.f. induced in the vertical coil, the latter is connected across two slide-wire resistances as shown in Fig. 10-103. Equal sensitivity for in-phase and quadrature components may be ob- tained by making the currents in both branches equal to each other and +45° different in phase from the main current. This is true when Lw = 1/oC = R. If, further, Lw = R + Re, and if r is the setting of the potentiometer in the upper branch (in-phase with Vj) and s is the setting of the potentiometer in the lower branch (in quadrature with Vi), the condition for balance is given by Var eisai, 1 Van 2(R + Re) Relative determination of electromagnetic fields may. be made by meas- uring field ratios and phase differences in successive ground intervals. In other words, the field at one loca- tion serves as a reference for that at an adjacent location. In the application of this procedure to the vertical component, two coils are laid flat on the ground in horizon- tal position or are carried by two surveyors with straps around their waists (see Fig. 10-1076). For horizontal-intensity determinations, two coils are held in a vertical posi- tion; their direction is kept parallel with the direction of strike if the primary cable has been laid out parallel with the strike. Instru- ments for the relative measurement of intensity ratios and phase differ- ences have been constructed as Fic. 10-107a. Dual-coil instrument for adaptations of potential ratiometers measuring intensity ratios and phase dif- : ferences. Adaptation of capacity ratio- and compensator bridges. The jeter. type shown in Fig. 10-107a is an adaptation of the parallel capacity ratiometer of Fig. 10-81. Other compensator bridges are likewise adaptable to dual-coil ratiometer con- struction. Comparison of in-phase components at successive stations may likewise be made with two coils, but this process does not require a compensator. (s + jr). (10-53a) 786 ELECTRICAL METHODS [Cuap. 10 The coils are connected in series opposition to a detector. One coil is laid flat on the ground at one location; the second is placed at another location. With the second coil, the plane of the ellipse of polarization is determined first on the second location. The axis of rotation of the coil is then so oriented as to be in the plane of the ellipse. After this, the coils are connected and the coil on the second location is rotated about a J. E. Hawkins Fig. 10-1076. Colorado School of Mines dual-coil field ratiometer. horizontal axis until a null is obtained. If the phase difference between successive locations is small, this method will give the ratio of the in-phase components at the two locations with sufficient accuracy. For a complete determination of intensity ratios and phase differences between two points, a three-frame arrangement must be used.” (d) Elliptical polarization. In the discussion of potential methods % Sundberg, A.I.M.E. Geophys. Pros., 134 (1929). Cuar-10), ELECTRICAL METHODS 787 (page 687) it was shown that elliptical polarization results from a combina- tion of two vectors which differ in coordinate and phase. The combina- tion of two vectors that differ in direction and are in quadrature, likewise results in elliptical polarization. This combination applies in electromag- netic methods. As illustrated in Fig. 10-108, a horizontal loop laid on the ground surface induces a current to flow in opposite direction along the upper edge of an ore body whose magnetic field at the distance r from the current concentration is given by the vector T. This vector combines with the vertical loop field Zp) and is in approximate quadrature with it. The components of T are: Y = T cos 0, and Z = Tsin 6. The difference Fie. 10-108. Composition of loop field and eddy current fietd. in the vertical components is Z; = Z) — Z. If all vectors oscillate with the same frequency and T = B cos wf is in quadrature with Z) = A sin ot, then Z, = Asinwt — B cos wt sin 0 and (10-530) Y =B cos wt cos 6. ~/ B? cos? 6 — Y? B cos 0 the first equation becomes, by substitution, Z:B cos 6 + BY sin @ = Since, in the second equation, sin wt = 7/1 — cos? wt = 788 ELECTRICAL METHODS [Cuap. 10 A \/B? cos? 9 — Y®. Squaring and dividing by A’B’ and cos’ @ give aif tl tan 6 »(B’ sin’ 6 + mi) Ag zi(i) a 224 ( A? ) ane ( A°?B? cos? 9 / eee This equation has the standard form of an inclined ellipse (see eq. [10—24c]), so that LL = 1/A’; M = tan 0/A’; N = (A’ + B’ sin’ 0)/A’B cos’ 6. The tilt angle y from vertical is then 2M 2 tan 9 B’ sin 26 mn Nok. Ae Bent | A= Breos 26° ae B? cos? 6 tc Fig. 10-109. Elliptical polarization resulting from a quadrature field (produced by a conductor at C), which is equal to the in-phase (loop) field above C (after Edge and Laby). The squares of the major and minor semiaxes of the ellipse are, in accord- ance with eq. (10-25b), 2 2 L+N+ /4M? + (L — N)? 22 2 een ZALB COST ON hn MR 6 (52) A’ + B + +/[A? — B? cos 26]? + [B? sin 26}? For two fields of equal maximum amplitude, A = B and tan 2y = sin 26/(1 — cos 26) = tan (1/2 — 6), sothaty = 7/4 — 0/2. Eq. (10-53e) is then a, b = B cos 6/+/1 F gin @- Fig. 10-109 shows the variation of compression and tilt angle of the polarization ellipse with distance for a conductor carrying a quadrature current at depth d. If the out-of-phase field is directly above the con- ductor, it is equal to the in-phase field (A = B), and if T declines from there in proportion to d/r (since Tmax. = 22'/d and T = 2I/’/r), it is seen 9 a,b Cuap. 10] ELECTRICAL METHODS 789 that B declines in the same proportion, so that B = Bmax. d/r. Since Bmax. = A,B = A cos @, so that by substitution of the above and of tan @ = y/d in eq. (10-53d), sin 26 cos 26 — tan?@ — 1 (10-54a) tan 2y = The axes of the ellipse follow by substituting B = A cos 6 in eq. (10—-53e) and by dividing the result by B’: 2 a,b = aE . (10-546) see hy 2+ tan’ 6 st age + tan eta N/ 2 cos? 6 — 3 cos‘ 6 Further relations for elliptical polarization may be developed by con- sidering different surface variations of the quadrature fields and different ratios of their maximum amplitude to the loop field. (e) Theory of interpretation. Although, for complete definition, the electromagnetic field theoretically requires six quantities (three compo- nents and their phases), it is seldom necessary to determine all of them. If the primary loop has been laid out parallel with the strike, the X com- ponent is generally negligible, and measurements are concerned with the in-phase and quadrature constituents of the Y and Z components only. Of these, the vertical and horizontal quadrature components are of greatest diagnostic value. From the theoretical relations given below for the out-of-phase fields produced by various geologic bodies, the requisite formulas for any other electromagnetic method not directly measuring these components may be deduced. For instance, the horizontal and vertical direction of the field determined with a simple induction coil follows from the character- istics of the ellipse of polarization, that is, by compounding the in-phase loop field with the quadrature field of subsurface bodies. Intensity ratios and phase differences (as determined by ratiometers) may be calculated by compounding the loop field with the subsurface fields and their correct phases for successive points.” Interpretation of results obtained by inductive-electromagnetic methods in mining differs greatly from procedures applied in the investigation of stratified ground. Absolute values for the magnetic fields of subsurface currents may be calculated if the strength of the induced current is known. It is difficult to determine these currents theoretically. However, since most inductive procedures measure the magnetic field relatively, it is suffi- % If long grounded cables are used, the observed fields result from a combination of in-phase components (due to conduction) with quadrature fields (due to induc- tion), and the phase shifts are calculated accordingly. 790 ELECTRICAL METHODS [CHap. 10 cient to consider the induced current as a constant parameter as far as applications in mining are concerned. For stratified ground, expressions for the relation of induced and primary current will be given later. The type of indication produced by current concentrations in subsurface ore bodies depends primarily on their geometric disposition. The mag- netic fields follow from relations previously given (eq. [10-46]). As shown in Fig. 10-110, relations are identical for electromagnetic and inductive methods for a single current concentration (thin vertical ore body). In this case the eddy currents flow in a vertical plane around the sheet. The effect of the return circuit at the bottom and at the sides can be dis- regarded, and formulas (10—-46a) then apply. In a wide ore body the induced current flows in opposite directions on opposite sides. Disregarding the effect of current concentrations on the hebydiK 7 KT (a) Thin, vertical Wide, vertical Horizontal Thin, dipping Fie. 10-110. Calculation of electromagnetic fields produced by currents induced in various types of ore bodies (current concentrations indicated by dots). bottom of the body, the horizontal component due to the upper concen- trations is *) 33 81; yad r ae (y? + a? + d?)? — 4a2y?” The vertical components are additive, so that i 1 aie Y= ana ( (10-55a) 2 ft aty,a-y\_ 4i,a(a’ +d’ — y’) . if the zero point of the coordinate system is above the center of the ore body. In a thin horizontal bed the current distribution is the same as in the upper surface of a wide vertical ore body. Therefore, the horizontal and vertical components are given by the preceding formulas. In a dipping thin ore body the eddy current will be concentrated along the upper and Cuap. 10] ELECTRICAL METHODS 791 lower edges. When the sheet is short, the lower current concentration is effective. If we place the zero point of the system of coordinates above the upper edge of the ore body, we have, with the notations of. Fig. 10-110, a We ogee d sor (G Hs 5) GT (" 2 Sea ‘ (10-55c) 1 < | 2 2 dy Um) and i’ Us Cae an ed 2a cost — y Z = 21; (4 *) = 2/; @ + rp ). (10-55d) In structural and stratigraphic investigations, both fixed loops and ex- panding loops are applied. The former procedure is known as the Sund- berg inductive, and the latter as the central ring induction (Koenigsberger) method. Interpretation theory in the first is based on an evaluation of the fields of thin layers of good conductivity in a section con- sidered a poor conductor. In the second, the effect of a section of progressively increasing thickness is evaluated as the radius of the primary loop is expanded. The theory of the first method has been developed by Levi-Civita, Sundberg, Rostagni, Hummel, Hedstrom, Focken, and others. \/ Coble imoge_ A list of pertinent literature is Fig. 10-111. Electromagnetic field in P found in Focken’s article.” resulting from cable and cable image. Assume that a long cable is laid out on the ground surface in the x direction (Fig. 10-111). A formation, whose thickness s is small compared with its depth d, is parallel to the surface and extends to infinity in the x and y directions. The electro- magnetic field is measured at a point P, whose horizontal distance from the cable is y and whose vertical distance from the sheet is z. If the point P is sensibly in the surface and if no sheet is present, a horizontal compon- ent does not exist and the vertical component is due only to the primary cable. The action of a sheet of very good conductivity is to reflect the cable and to produce, at twice the depth of the sheet, an image current concen- tration with a phase shift of 180°. In that case, the total vector at P can be readily calculated (see below). Its vertical component is sub- tracted from the component due to the primary cable; its horizontal com- % Colo. Sch. Mines Quart., 32(1), 225-252 (Jan., 1937). 792 ELECTRICAL METHODS [CHap. 10 ponent is likewise readily obtainable; and a phase shift beyond 180° does not occur (disregarding absorption through the overburden) As a rule, however, conditions are complicated by the finite conductivity of the sheet. The fundamental equations for the potentials of the electrical and electromagnetic fields of a cable in the presence of a conductive sheet have been derived by Levi-Civita. The electrical forces are- virtually inter- cepted by the sheet and need not be considered. The potential U of the electromagnetic field is given by = ape? (log | — toe 5) #5 geen) 0 U = —2he log ~ — log - wae OBe ; (10-56) in which J) sin wt is the current in the primary cable, 7, and 72 are distances (as in Fig. 10-111), and q is an induction factor. The first part of this expression indicates the direct effect of the cable at the point P if the sheet is not present; the second is the effect of a perfectly conductive sheet, equivalent to a field 180° out of phase caused by the cable image; the third is a quadrature term indicating the phase shift resulting from finite conductivity. The induction factor q is defined by 4nr'f nfs — — 4 —9 _—— ir or ae 1On: (10-57) Pohm—cm where f is the frequency in cycles per second and # is the resistance of 1 cm’ of the sheet. With s as the thickness of the sheet and p as the resistivity, R = p/s. The horizontal and vertical field components are then obtained by differentiation of the potential given in eq. (10-56). There is no strike component; X = 0, Y = — 0U/dz, and Z = dU/dy. Hence, 1g, ae eee (ioe | "| je ( ‘)] ¥ = Qe log — log a + q a2 log Ps eis ‘ (10-58a) i, ese eh = — —] log =e Z 2hhe [s be og ) =f AEOIE og Fs Since r? = y + (zg — dy andr = y + (2 + d) forz > 0, d —d d)2 — y? Yi — i 27ysin (4 ne 2 ) — 2Iy cos a i) Ty q7re ; (10-58b) Zi = 2] isin’ ot @ aah 4) + 2] cos wt eet: 2 v1 qre Crap. 10] ELECTRICAL METHODS 793 For the field at the earth’s surface, where z is always closely enough equal to d in level terrain, 2 2 yee _Alod (sin wt + Mee u cos ot) 2+ y dq 4d? + y and © (10-58c) bee Slee . Sa) aecanie y ) Z= e+ yp es aie tee a From eq. (10-58c) the phase shift in the horizontal component is Pipl Ad yt tan YY = 2dq 4d? ai y (10-58d) and that in the vertical component is 2 oe lg 2 tan gz = dq We pt (10-58e) Their difference is tan ¢y — tan ¢z = (10-58/) 1 aaah Depth and induction factor of a conductive sheet are calculated by dia- grams as shown in Figs. 10-112a and 10-112b. A large loop (about 6000 by 2500 feet) is laid out (longitudinal direction parallel with assumed strike) and a number of parallel profiles are run at right angles to the cable. Along each profile the in-phase and quadrature components of both the vertical and the horizontal fields are measured at a number of distances. Theoretically, one distance on each profile is sufficient to calculate both depth and induction factor. Assume this distance to be y = 100 m, for which the diagrams of Fig. 10-112 have been calculated. These diagrams contain, for both vertical and horizontal component, lines of equal depth (solid) and lines of equal reciprocal induction factor (1/q, dotted). If at 100 m distance from the cable one has observed an in-phase vertical com- ponent of 174 microgauss per ampere primary current, and a quadrature component of 14 microgauss, the depth as read from the diagram is 100 m and the induction factor is 100 (meters, since the reciprocal induction factor has the dimension of length). For the horizontal field the in-phase com- ponent would be 7 microgauss per ampere and the out-of-phase component —2 microgauss per ampere. For horizontal beds the in-phase horizontal component has a maximum directly above the cable. For a dipping bed the image point moves to 794 ELECTRICAL METHODS (Cuar. 10 one side and the corresponding maximum is displaced by Ay = 2h sin 1, where h is the depth perpendicular to the bed and: the dip. Relations readily understood in their geometric significance may be obtained from Fig. 10-113 by considering a perfectly conductive layer, for which p = 0, q = o (see eq. [10—-57]). Since the quadrature components cancel, 2 Aig ape ls easing “e+e ery (G08) Fic. 10-112a. Sundberg interpretation diagram for inductive methods, vertical component, 100 meters from cable. Solid lines represent depth; broken lines, 1/q (reciprocal induction factor). These relations follow likewise by combining the primary field (Fig. 10-118, dotted circle) with the image field (solid circle). At P the horizontal com- ponent of the primary field is zero and that of the secondary field T is Y = 2I;d'/r’. With perfect reflection, J; = Ib; d’ = 2d; r = re = V 4d? + 7; and, therefore, ¥ = 41od/ (4d° + y’). The vertical component of T due to the image is (eq. [10-46a]) Z = 2J;y/r° or, with the present notation, Z = 2Iyy/(4d’ + y’). The field of the cable at the same point is Z) = — 2I)/y, since r = y. Hence, the resultant vertical component equals y 4 + y?J y(4d? + y?) *(10}08} UOTJONpUl [BooIdi0e1) b/T ‘seul, UexoIg ‘yydep yuoseidei seul] pljog *e[qvo WO} S199 KOT ‘JUeUOdUIOD [By UOZIIOY ‘ SPOY}OU SATJONPUI JOJ WIBIZBIP UOTye}oId1E}UI Z1aqpung “QS1T-OT “OTH 795 796 ELECTRICAL METHODS [Cuap. 10 If more than one conductive sheet is present, the interpretation pro- cedure makes use of the fact (proved by experiment) that the electro- magnetic field beneath one conductive sheet is independent of its position. Hence, when two sheets occur, their effect is equivalent to one sheet, produced by dropping the upper sheet on the lower. The field of the combined sheet is therefore given by the depth of the lower sheet and the sum of the induction factors. The procedure of depth determination has been described in detail by Sundberg and Hedstrom.” In the central-ring induction method the fundamental theory is the same as that discussed above, except that the 180° component practically vanishes and the quadrature component predominates. The magnetic field inside the loop is proportional to the conductivity of a portion of ih a ots Image of Cable Fig. 10-113. Combination of primary and secondary fields for perfect conductor. ground whose depth is roughly equal to the radius R of the loop. The arrangement used by Koenigsberger and his associates is illustrated in Fig. 10-105, and references to the pertinent literature are given on page 782. Only the vertical component is measured. The magnetic field in the loop is affected by the ground conductivity and differs from the field of a loop suspended in air. As shown in eq. (10-58), the field near a straight cable is composed of (1) the direct vector, (2) the vector due to the image of the cable, and (3) a vector arising from finite conductivity of the bed. Since the first two are in opposition and in quadrature with the third vector, the vertical component for any medium below may be written Z = Zp + jZo , where 96 Sundberg and Hedstrom, World Petrol. Congr. Proc., B(I), 107 (1934). Cuapr. 10] KLECTRICAL METHODS 197 Zp is the combined in-phase component and Ze the quadrature component. According to Stefanescu,” the 180° component is negligible for low fre- quencies, and Zp = 27J)/R (field in air, see eq. [10-50b]). The quadrature component isZg = 3aIok’R, where I is the loop current, R its radius, and k’ an induction factor similar in significance to the factor q previously defined by eq. (10-57). Since k” = 4row (w = frequency, ¢ = conduc- tivity), the quadrature component is 3 —=9 Ze ete ore eee) TE 10 Gt 608) p p where Jp is in amp., R in cm, f in ¢.p.s., and p in ohm-cm. As a rule, the ground is not homogeneous, so that when the loop radius is increased, beds of different conductivities affect the magnetic field. As in the resistivity method, formula (10-60a) is still applicable, provided that p is understood to represent now an apparent resistivity, p., which in accordance with (10-60a) follows from the observed parameter, Zo/I (quadrature field in gauss/amp. primary current): 1 Zo/T In resistivity methods the effect of layers of different conductivity is calculated by reflecting the source on the formation boundaries. The same procedure is applicable here, with the significant difference that, for each interface, only one image is required.” The analysis is simplified considerably by considering low frequencies only, in which case the 180° field is always zero and the quadrature field is given by Zo = —lim. oo OZo/ of. If a circular loop energized by low-frequency current is suspended at an elevation d above an interface (for example, the surface of the ground), the magnetic field at any point P(z) in its axis is equal to the gravity potential of a disk at a depth 2d (see Fig. 10-114) of thickness 1 and density 2m°Iyo1 , if o; is the conductivity of the medium above which the loop is suspended. The gravity potential above a disk at a distance h from its center is given by U = 2rGo dh(r — h), where G is gravitational constant and 4 is density. If dh = 1, Gb = 0’, h = 2d — 2, andr’ = R’ + (2d — 2z)’, the magnetic field at the point P is pe = 124-10 fR:- (10-60b) Zo = 2r'i[/R? + (2d — z)? — (2d — 2)], (10-61a) so that when P is moved up to the center of the loop (z = 0), Zo = 2rd:[+/R?2 + 402 — 2d]. (10-61b) 97 Beitr. angew. Geophys., 5(2), 188 (1985). 98 Ibid. 798 ELECTRICAL METHODS [Cuap. 10 When the loop is laid out on the surface of the ground (d = 0),Z9 = 2x%:R. Substituting the electrical density 22°Ioc1 , Zo = 40° IoR. (10-61c) Fi Pry on fag) Etats Prine | \ Gre Gs SS pg umn 7 7 a : if ap ne d Pec Ca GL mm Second Disk dp = 2n*1,(6-6) Fic. 10-114. Representation of magnetic fields of loops by potentials of disks and disk images of equivalent densities. This is obviously the same as eq. (10-60a), differentiated with respect to f. When the ground is not homogeneous, the same relation can again be used for an apparent conductivity, so that, analogously to eq. (10-605), Zo 4 1)R’ 06m) Ca = Cuap. 10] ELECTRICAL METHODS 799 By analogy with the gravitational potential, the magnetic field for two layers with conductivities ; and oz is readily obtained (see Fig. 10-114). As the loop is on the ground surface, the magnetic field due to the effect of the upper layer is equal to the potential of a disk with the density = 2a Ic; in its own plane. The effect of the interface below is given by the potential of a disk at twice the depth of the interface d, with the density 8: = 2mrJ)(c2 — o1). The magnetic field due to the latter is therefore, according to eq. (10-61b), Zo = 2nbe[/R? + 4d? — 2d)], to which must be added the field of the disk inside the loop, so that Zi = 4m Io{orR + (o2 — o)[VR? + 4d? — 2d]}, (10-62) from which the apparent conductivity is as = ou = ZT NR a — 27] (10-62b) For small values of R, or small depth penetration, the second term in eq. (10-62b) approaches zero, and therefore the apparent conductivity ap- proaches the conductivity in the upper layer. On the other hand, if d, < R (large loop radius), the apparent conductivity approaches az. If two interfaces exist (see Fig. 10-114), the magnetic field is composed of three potentials: (1) due to the surface disk with density 3, , (2) due to the disk image of density 5: , and (3) due to the disk image with density = 2n'Iy(c3 — o2). Hence, the magnetic field Zo = 4x Io{oiR + (a2 — o)[WR® + 4d? — 2di] (10-63a) + (a3 — o2)[V R’ + 4d: — 2d,]}. The apparent conductivity in this case is pop ee) Reeds: 2h (10-636) ++ 2 IVR + 4de — 2a]. It follows from eq. (10-63b) that the effect of the n** interface on the apparent conductivity is given by Can = [VR + 4a — 2p]. Substituting the ratior, = tie a ty ee (10-64) 800 ELECTRICAL METHODS [CHap. 10 Fig. 10-115 shows in double logarithmic scale a diagram for the calculation of the function of eq. (10-64). (f) Model experiments. In the interpretation of field data obtained by horizontal loops, experiments with small-scale models play an important part. They are applicable to both mining (ore bodies) and oil exploration problems (stratified ground). To obtain perfect similitude, it is necessary to change the physical properties of the materials as well as the frequency.” If the fields are expressed in terms of primary current and the model scale is reduced n times, it is necessary to increase both frequency and conduc- tivity n times. If the conductivity cannot be increased n times, it is necessary to increase the frequency n’ times. ae h*2q, Fic. 10-115. Diagram for the calculation of apparent conductivity as a function of conductivity contrast on the n th layer, and of the ratio of loop radius (= R) and layer depth (= d,) (after Stefanescu). (Note: for tn, read rn.) Extensive experiments with model ore bodies have been made by Lund- berg, Sundberg, Hedstrom, and their associates. Some of the results are reproduced in Figs. 10-116 to 10-118. Fig. 10-116a@ represents the dis- tribution of the vertical primary field inside the loop as well as the vertical and horizontal components of the (combined primary and secondary) fields without regard to phase, for a vertical ore body. The anomalies are sym- metrical, the vertical intensity having a maximum over the center of the body, the horizontal intensity two maxima over the edges. When the ore body is dipping (Fig. 10-116b), the maximum in vertical intensity over the up-dip edge of the ore body is greater than the anomaly over the down-dip edge. A clearer picture of conditions is obtained when the field vectors are split up into their in-phase (P) and quadrature (Q) components 99 Sundberg, Beitr. angew. Geophys., 1(3), 334 (1931). L. B. Slichter, A.I.M.E. Geophys. Pros., 446 (1934). Cuap. 10] ELECTRICAL METHODS 801 (Fig. 10-117). It should be noted that these experiments represent a combination of electromagnetic and inductive methods, excitation being produced by a long grounded cable. Hence, the effects of current con- centration due to conduction are superimposed upon those due to induction. Loop Plane 32cm Ve, Mode! Normal Field Vertical Component Z \ 77---Hortzontal Component Y \ ‘ v6 \ Amplitude of Magnetic Field Components ~S WIR, WN OTR IS | ON TE NEN SSN ONSITE WSS if / / ! \ Weaker? 0 yen \ \ ‘ aay RRQ RY OY RW SO lia. 10-133. Single energizer (7') and pickup coil (R) combination; reaction to sub- surface metal object (after Joyce). by detecting the beat frequency. tion of the induction balance, since the inductance in one circuit remains fixed while the other is being varied. The same idea has been used in treasure finders, one coil being carried over the ground, the other being housed in a shielded box with the fixed oscillator. kind was constructed by Joyce.” 425 U. S. Bur. Mines Cire. Inf. No. 6854, Oct., 1935. This may be considered as a modifica- An instrument of this Cnap. 10] ELECTRICAL METHODS 823 Probably the majority of present-time treasure finders employ fixed combinations of high-frequency transmitters and receivers. Arrange- ment and operating principle are the same as in the low-frequency trans- mitter and receiver combinations, except that an R.F. carrier is used for Upper Pick-up Goll Amplifi suse Detector Generator | _) (headphones) Switch Leorgiting to Resonating Condenser Lower Pick Fic. 10-1346. Modification of metal detector of Fig. 10-134a (after Joyce). the 1000 cycles. In the Fisher Metallascope and the Barret Terrometer the transmitter and receiver are arranged as on the lower right of Fig. 10-135a. A circuit diagram of the Metallascope is given in Fig. 10-135a. Fig. 10-135b shows a more elaborate type of the Fisher Metallascope for operation as separate transmitter and receiver. In the Barret Terrometer the trans- 824 ELECTRICAL METHODS [Cuar. 10 mitter is behind the operator and emits an approximately vertical field. The receiver, equipped with a sensitive galvanometer, is forward and so adjusted that either a maximum- or medium-size scale deflection is ob- Fig. 10-135a. Circuit of Fisher Metallascope, with combined transmitter and receiver (after Chapel). (R2, 5 ohms, 1 W.; Rs, 2 ohms, 1 W.; 1, milliammeter (0-1); 2, R.F. choke, 1500 turns No. 34ECC; 3, 1 megohm; 3A, 3 megohms; 4, 0.1 megohm; 5, 0.0005 mfd., fixed; 6, 0.006 mfd., fixed; 7, 0.001 mfd., fixed; 8, 0 to 0.0005 mfd., trimmer adjuster; 8A, 0.00025 mfd., fixed; 9, push-pull switches; 10, phonetip jacks.) ' A 1 , ‘ -vihe—— — 4 ' f ---- o7J— -- 5 tt - - ---- -- -- Fig. 10-135b. Circuit of Fisher Metallascope, separate transmitter, and receiver (after Chapel). R2, 5 ohms, 1 W.; Re, 2 ohms, 1 W.; 1, milliammeter; 2, R.F. choke, 1500 turns, No. 34ECC; 3, 1 meg. resistor; 3A, 3 meg. resistor; 4, 0.1 meg. resistor; 5, 0.0005 mfd., 1 W., fixed; 6, 0.006 mfd., 1 W., fixed; 7, 0.001 mfd., 1 W., fixed; 8, 0 to 0.0005 mfd. trimmer adjuster; 8A, 0.00025 mfd., 1 W., fixed; 9, push-pull switches; 10, tip jacks for phones.) tained on barren ground. A decrease in scale deflection then indicates the presence of a metallic body. The depth penetration of the high-frequency treasure finders, for a medium-size metal chest, is probably not in excess of 6 to 7 feet. II GEOPHYSICAL WELL TESTING' ‘Tue essence of geophysical well testing is a determination of physical rock properties in situ. Its purpose is (1) to correlate wells by using physical formation characteristics which either are more significant or can be obtained more readily than their petrographic and geologic character- istics; (2) to detect commercial minerals (oil, gas, coal) or other media which are of significance in the process of drilling (water, cement, and the like); (3) to determine data required in the interpretation of geophysical surface measurements (seismic wave velocities and the like). Somewhat removed from our field is a fourth application, the determination of crookedness of holes (by seismic measurements). In regard to procedure, geophysical well-testing methods may be divided into (1) electrical logging, (II) temperature measurements, (III) seismic measurements, and (IV) miscellaneous measurements (magnetic, radio- active, and so on). I. ELECTRICAL LOGGING Electrical logging in the most general sense is the examination of the electrical properties, electrical reaction, and geometric disposition of sub- surface formations by electrical measurements in wells. It involves a determination of the following quantities, in order of present commercial importance: (A) resistance or impedance of formations, (B) spontaneous potentials (porosities), (C) resistance of drilling mud, (D) dip and strike, and (E) casing depth. A. DETERMINATION OF RESISTANCE OR IMPEDANCE OF FORMATIONS In respect to the determination of impedance or resistance in (uncased) wells, electrical logging is equivalent to resistivity mapping with fixed elec- trode separation (see page 708). Hence, a variety of electrode arrange- ments is possible. In fact, most of those described at pages 710-711 have 1 The symbols in this chapter are the same as in Chapter 10, except where other- wise noted. 825 (4) “‘BUIBSO| [BOIIJOII9 UI SJINIILO OIVBULOYOS puv S}UDWIIZUBLIG BPOIPIT| “[-[ “DIT SZ, S N \ N aN (4) (P) (7) 2h) (2) 826 Cuap. 11] GEOPHYSICAL WELL TESTING 827 been used or proposed. While in resistivity surface mapping a simple circuit with but two electrodes would not be suitable because of the pre- ponderance of the contact resistance at the terminals, such an arrangement is permissible in electrical coring, since the distance between electrode and wall is small enough for the formation resistivity to affect: the contact resistance of an electrode suspended in drilling mud of generally uniform resistivity. Fig. 11-1 illustrates various electrode arrangements in increasing order of electrode number. The measuring devices indicated are not necessarily limited to the electrode arrangement with which they are shown and may be interchanged. Scheme ais used by the Halliburton Oil-Well Cementing Company (Blau patent) and in the Karcher system. In the latter, the electrode is the (insulated) bit at the end of the drill pipe. Scheme (b) is a Wheatstone bridge arrangement; it is used by Lane-Wells in a modified form, the upper electrode being represented by the cable sheath. The two-electrode scheme of Fig. 11—1c is well suited for separate self-poten- tial and resistivity measurements. The three-electrode arrangement shown in Fig. 11-1d (Schlumberger) is now in most extensive use. The D.C. source indicated in the current circuit may be replaced by an A.C. generator, or a commutator may be provided, together with an A.C. meter in the potential circuit to record resistivity. One of the potential elec- trodes is then switched by a second commutator to a D.C. meter and a — grounded electrode as in scheme (c) to give the self-potential record. Fig. 11-le (Hummel) shows a modification with potential electrodes down; Fig. 11—1f is the conventional four-terminal arrangement with commutator, adapted to well surveying. The spacing of the electrodes in schemes b and c is usually ten to twenty times the diameter of the hole; in schemes d and e, the distance CP; is ordinarily about 60 feet and P,P: is about 15 feet. These distances may be decreased and increased to obtain two curves of different side penetra- tion. Because of the uniform constitution of the drilling fluid, it is gen- erally satisfactory to use ordinary metal electrodes in the hole; however, some companies use porous-pot electrodes. Two- or three-electrode arrangements usually have the form of a weighted insulated bar, the weight at the bottom representing the energizing electrode and the rings at the other end representing the potential electrodes. The electrode assemblies are lowered on cables that contain as many heavily insulated conductors as there are electrodes, and that protected by stranded flexible steel wire and surrounded by a steel sheath on the outside. Current is straight D.C., commutated D.C., or, most often, low- frequency A.C. (20 to 100 cycles) as indicated above. The current can be held sufficiently constant so that a recording potentiometer, whose drum 828 GEOPHYSICAL WELL TESTING [CuHap. 11 or camera drive is coupled to the cable winch, gives a direct graph of apparent resistivity against depth. Resistivities and self-potentials are usually recorded simultaneously as indicated schematically in Fig. 2-15. In homogeneous ground, the relation between resistivity and potential readings given at pages 710-711, apply. Since the electrodes are buried in an infinite and not a semi-infinite medium, the spacing factors given in these formulas change from 27a to 47a, so that, for the Schlumberger arrangement, with the notation of Fig. 11—ld, 4arr’ AV eT lee) p= which follows directly from eq. (10-31h). Since r, r’, and I are kept con- stant, it is seen that the resistivities are directly proportional to the poten- tial difference recorded. Formula (11-1) holds for homogeneous ground only. In the presence of layers of different resistivity, an apparent instead of a true resistivity is recorded. The relation of apparent and true resis- tivities for given formation thicknesses and resistivities can be calculated in the same manner as on page 719 since by rotating the geologic section 90° the bedding planes are equivalent to the vertical formation contacts treated in resistivity mapping, assuming for the moment that the effect of the drilling fluid is negligible. When a formation contact is passed with the four-electrode system (Fig. 11-1f), an apparent resistivity variation as in Fig. 10-56 is obtained with four breaks near the formation boundary instead of one. As the number of electrodes is reduced, the number of peaks decreases, as illus- trated in Fig. 11-2 for the Schlumberger electrode arrangement. The two upper diagrams are for one formation boundary and the two lower diagrams for two boundaries. The distance of the breaks is uneven and corresponds to CP; in one and P,P» in the second case. The resistivity of the second medium is approached in steps and not all at once. For formations whose thickness is large compared with the electrode separa- tion, the corresponding apparent resistivity curves may be derived by joining curves such as those given in Fig. 11-2 (upper part).” For thin formations, the images of the current electrode, due to reflections on both formation boundaries, must be considered, which means that resistivities must be calculated as in a three-layer case. Results of such calculations are illustrated in Fig. 11-2. It is seen that a formation whose thickness is less than the distance of one potential electrode from the next current electrode will not allow the apparent resistivity to come up to the value of the true resistivity. This is possible only when the electrode separation is smaller than the formation thickness. 2 J. N. Hummel, Beitr. angew. Geophys., 6(1), 89-99 (1936). Cuap. 11] GEOPHYSICAL WELL TESTING 829 The influence of the drilling fluid on the ap- ?] 4/ parent resistivity can be 4 B calculated’ by assuming C b the mud-filled hole to represent the ‘‘cover’’ of c resistivity pi on a layer of a uniform resistivity p (two- pre layer case, page 714). As may be expected from the similarity of electrical log- ging and resistivity map- ping, the drilling fluid 2 decreases in effectiveness 7 with an increase in elec- ¢ trode separation. If the resistivity of the forma- tion is ten times greater than that of the drilling fluid, and if the electrode interval CPi HS) WE Una Fig. 11-2. Variation of apparent resistivity with the hole diameter, the true resistivity and electrode separation in elec- apparent resistivity is 75 trical logging (after Hummel). per cent of the true re- sistivity. If the drilling fluid is of high resistivity compared with the formation, the electrode spacing need be but two to three times the hole diameter, to produce an apparent resistivity virtually equal to the forma- tion resistivity (Fig. 11-3). Conversely, for measuring mud resistivity, it is necessary to reduce the electrode separation and make the electrode interval less than the diameter of the hole. In that case the electrode intervals are made equal. To suppress any possible wall influence, the electrodes may be enclosed in a nonconductive cylinder, open at both ends. For a still closer approach to true conditions, a third layer representing a zone flooded by drilling mud, may be interposed between the formation and the drill hole in the above calculations. As a matter of fact, the replacement of formation water by well water near the hole may be so pronounced as to obliterate formation resistivities and to require the so-called “third” curve, which is a resistivity curve taken with larger electrode spacing and, therefore, greater depth penetration. Pel. NBN fa 3 J. N. Hummel and O. Rilke, Beitr. angew. Geophys., 6(3), 265-270 (1937). ‘olge ey) a (Ch) Liectrode Interval 5 70 Hole Diameter Fic. 11-3. Variation of apparent resistivity with ratio of electrode spacing and formation (p1) F H Des 20n drilling mud (p) seine : electrode interval CP; is as shown in Fig. 11-1d. hole diameter for two resistivity ratios ie = 107 10? Ss SSS rf ESE) igs eemieses 0 10 20 W 40 50 60 70 60 90 100 % Ol 100 90 50 70 60 50 40 30 20 10 O 2 Salt Water Fic. 11-4. Variation of formation resistivity with oil and water content (after Martin, Murray, and Gillingham). (I, porosity 45 per cent; II, porosity 20 per cent; resistivity in ohm-meter.) 830 Cuap. 11] GEOPHYSICAL WELL TESTING 831 Of considerable practical interest is the problem of how the true forma- tion resistivity changes with the proportion of salt water and oil. Such experiments have been conducted by Martin, Murray, and Gillingham‘ (see Fig. 11-4). Oil contents up to 60 per cent increase the formation resistivity about ten times. As was stated before, (see page 665), this ratio between the resistivities of productive and barren formations is frequently encountered in the practice of electrical logging. It is further seen in Fig. 11-4 that oil contents exceeding 70 per cent bring about a sharp in- crease in formation resistivity, of the order of one hundred to several thousand times. B. DETERMINATION OF SPONTANEOUS POTENTIALS (POROSITIES) When porous formations are penetrated by the drill, they give rise to spontaneous potentials in two ways: (1) by movement of liquids through the formation into or from the hole (electrofiltration potential), and (2) by differences in concentration between formation water and drilling fluid (diffusion potential). The former, discussed on page 631, is practically the only source of spontaneous potentials in the absence of concentration differences between formation water and drilling fluid. These potentials are positive when water is discharged into the hole but negative when water flows from the hole into the formation. Hence, the magnitude of the potential anomaly depends on the pressure or height of the mud column in the hole. The extreme potential anomaly in the well illustrated in Fig. 11-5 was +20 millivolts. No diffusion potential was present, since the mud contained about 2 g NaCl per liter and the formation water about 3 g NaCl per liter. Usually the electrofiltration potentials are negative in sign, since the drilling fluid penetrates the porous formation under excess pressure. Diffusion potentials are produced by porous formations because the (fresh water) drilling fluid is generally lower in ion concentration than is the (connate) formation water. As shown in Fig. 11-6, currents flow from the drill hole into the layer and cause negative potential peaks which may amount to 100 to 200 millivolts. This phenomenon was discussed on page 631. The theoretical potential difference, according to eq. (10-2), is E = 11.6 logo p2/p: millivolts, so that, for a formation water of 0.5 ohm-m and a drilling fluid of 5 ohm-m resistivity, the potential difference would be 11.6 millivolts. However, because of an additional potential difference set up along the return circuits at the points CB and C’B’, respectively, the potential difference is actually greater than for only one boundary, so 4 Geophysics, III(3), 258-272 (1938). 832 GEOPHYSICAL WELL TESTING [CHap. 11 that the factor in eq. (10-2) is about 17 instead of 11.6 for the contact of clay and siliceous sand. Hence, in an experiment where p2 was 24 ohm-m and p; varied from 17 to 0.04 ohm-m, the potentials varied from 2.5 to 46 RESISTIVITY POROSITY POROSITY ° 10 20 #20 +10 O 40 20 +20 +10 O 10 .20 mv. Deptus, METERS Mud seve/ Mud /eve/ -80 m Om Fig. 11-5. Variation of self-potential effects in drill holes (electrofiltration phe- nomenon) with pressure of mud column, in Grozny field (after Schlumberger). millivolts.” Fig. 11-7 shows results of some trials made with drilling muds of three different resistivities. 5 C. and M. Schlumberger and E. G. Leonardon, A.I.M.E. Geophys. Pros., 278 (1934). Cuap. 11] GEOPHYSICAL WELL TESTING 833 Frequently, the electrofiltration and diffusion potentials reinforce each other. Hence, self-potential records (taken with the electrode arrangement illustrated schematically in Fig. 11-lc) give a good indication of the porosity of a forma- ‘tion and furnish valuable information supplementary to resistivity data. Since a low-resistivity indication may be inter- preted as a salt-water sand or clay bed, the porosity indication would decide which interpretation is correct. The same is true for high-resistivity indications which could mean a limestone bed or an oil sand, un- less a porosity record is available. POROSITY POROSITY -3 ° -40 .10° volfs ° 10 1 2 nua = 267 ohin-m = 044 ohm-m Pilayer-water) ~ OF ohin-in — O—<———— = eS Resistance **- = Sets). Formation ay Soe AVOREE te High Resistance Drilling Flurd Fia. 11-6. Origin of diffusion po- tentials in drill holes (adapted from Schiumberger). POROSITY fe} -10 3 e =0.76 ohm-m Fig. 11-7. Variation of diffusion potential with resistivity of drilling mud (after Schlumberger). 834 GEOPHYSICAL WELL TESTING [Cuap. 11 C. DETERMINATION OF RESISTIVITY OF DRILLING Mup The resistivity of the drilling fluid is determined with closely spaced electrodes. Its practical importance lies in the location of water flows. To this end, the hole is first conditioned by washing with fresh-water mud, and the first run indicated in Fig. 11-8 is taken immediately afterward. The level of the mud is then lowered, allowing formation water to pene- trate the hole. Another run (second curve in Fig. 11-8) is taken, which indicates the portion of the hole filled with (low-resistivity) formation water. Ohm -m ° 0.5 1 5 WATER FLOW canals Fig. 11-8. Location of water Fig. 11-9. Electrode arrangement for flow by measuring resistivities of measuring dip and strike in wells (after drilling mud (after Schlum- (Schlumberger). berger). D. MEASUREMENT OF DIP AND STRIKE Since in stratified formations the conductivity in the bedding planes is greater than at right angles thereto, the equipotential surfaces about a source are not spheres but ellipsoids of revolution. These ellipsoids are tilted when the strata dip. If an electrode configuration, as illustrated in Fig. 11-9, is lowered into the hole with a rigid rotatable connection between Crap. 11) GEOPHYSICAL WELL TESTING 835 N and M, a maximum potential difference, proportional to dip, will occur between the electrodes when they are in the position shown. When the configuration is then rotated to a position at right angles to the plane of the paper, the potential difference vanishes, whereby the direction of strike is established. In practice, the two directions are determined with ref- erence to magnetic north, which may be established with an earth inductor well compass.° E. DETERMINATION OF CaAsING DEPTH Since the casing is a much better conductor than the mud or the adjacent rocks, its depth can be established from the abrupt change in apparent resistivity when the electrodes pass through the casing shoe. Inside the casing, the resistivity is zero. For these measurements, intermediate and small electrode separations are used. F, Discussion oF RESULTS How closely electrical logging data may coincide with results of core analysis is illustrated in Fig. 11-10. The section represents the oil zone Per poabillty Wafer 5 fn an Fic. 11-10. Comparison of core analyses with results of electrical logging (after Schilthuis). of the Woodbine sand in the east Texas field. Porosities were determined by the Washburn-Bunting method,’ permeabilities in accordance with A.P.I. Code No. 27, and connate water and oil by vaporization and com- bustion.”’ Porosities indicated by the self-potential curve are closely paral- 6 Schlumberger and Leonardon, loc. cit. 7 Amer. Ceramic Soc. J., 4, 983-989 (1921). 8 Barnes, A.P.I. Drilling and Production Practice, 191-203 (1935). 9R. J. Schilthuis, A.I.M.E. Tech. Publ. No. 869, 1937. 836 GEOPHYSICAL WELL TESTING [CHap. 11 leled by the permeabilities and porosities measured on cores. Likewise, the resistivity and water-analysis curves are quite similar. The main value of electrical logs lies in the possibility of well correlation by the ‘“‘character” of the indication. A structural correlation can be made, regardless of whether the geologic significance of an indication is known or ra not. Small changes in moisture and __lithologic character are detected much ISS i ti ~ Ss more readily and with more Witte Sand $= continuity in an electrical 0 WE log than is possible by any mechanical coring process. Even if formations do not NN ahah NN appear to be differentiated XY Ne in respect to lithologic and 4000 paleontologic characteris- tics, the electrical log can usually be depended on to segregate them. Fig. 11-11 shows corre- _. SNS Sacto UE lation on the basis of resis- tivity logs between two wells three-quarters of a NN Shale RN mile apart in the Oklahoma XN ) RX City field. The water sands there are quite readily dis- tinguished by their low Resistivities in obm-m (O35 2 Ba 35.0 50 5000 resistivities. The jagged Salt Water Sand —~kK peaks indicate limestones NN NYY wy (Tonkawa lime at II) or sandy shales; the smooth portions (I and III) repre- Fig. 11-11. Electrical log correlation between sent fairly homogeneous eet in Oklahoma City field (after Schlum- shales and clays. In some oil fields, such as in Ru- mania, correlations have been possible over considerable distances. Fig. 11-12 shows well logs taken in the Gorgoteni field. The wavy appearance of both porosity and resistivity logs in the Dacian formation (composed of alternating sands and marls) is in striking contrast to their smooth character in the Pontian, which consists of argillaceous marls. The sandy Distance: 2 mile Cuap. 11] GEOPHYSICAL WELL TESTING 837 section of the Maeotic below is again indicated by the irregular saw- toothed appearance of porosity and resistivity curves. In this section, correlations have been made over distances of the order of 50 miles. In some areas in this country, long-distance correlations are likewise possible. Very good correlations are the rule in the mid-continent fields.* Fig. 11-13 is an outstanding example of how electrical logging may be applied to indicate productive horizons. In this section of the Maracaibo field, the three important oil horizons are very well indicated, as are the depths to correct water shutoff and the low-resistivity clay formations. In some fields a direct proportionality has been established between re- sistivity and productivity of oil horizons. At Grozny, for instance (Fig. 11-14), a high resistivity of the H horizon corresponds to gusher produc- Dacian Pentien FR Meeohic =F 00 Fic. 11-12. Resistivity and porosity correlation of eight wells in the Gorgoteni field, Rumania (after Schlumberger). tion and an intermediate resistivity (well 2), to oil shows with water. In well 3, where the amplitude is about the same as that of other beds, the horizon is dry. Electrical logging has become daily routine in many oil-producing fields and wildcat wells. Results are accumulated at a much more extensive rate than the few examples given above indicate. Il. TEMPERATURE MEASUREMENTS It is an age-old belief that the interior of the earth is hot, and it is a matter of long-standing experience that ground temperature increases with 10 A.A.P.G. Bull. No. 23 (11), 1622-1626 (Nov., 1939). 10a Personal communication from H. Guyod. oS ‘OSM S EES ay mSSord S93 PASS USS ) Lf RRS 4 y i y 4 059 Y ose Yes? we ° ow oe o Ww oe ° ad P anon? " r:) anver osm $ ye § a20091g y ose: ow ook ° oot 000% Cuap. 11] GEOPHYSICAL WELL TESTING 839 depth. One of the earliest accounts of rock temperatures in mine workings was given by Athanasius Kircher in 1665, but about 150 years elapsed before systematic underground observations were conducted in England, Germany, and France. Reliable temperature measurements in wells were ° - °o o DEDTHS iN FEET 2 8 8 J ° ° 2 e © e @ 7 — a “ Lad GUSHER DRY GUSHER ORY OIL SHOWS WITH WATER ‘Macaca as eae DRY or” PROOUCTIVE on 1609 1600 Fig. 11-14. Correlation between productivity of oil horizons and electrical resis- tivities in the Grozny field, Russia (after Schlumberger). made possible by the development of overflow thermometers in 1830. In the eighties, this was followed by a systematic inquiry into the influence of rock conductivities and of other factors. With progress in well drilling (see Fig. 11-15), much material was accumulated after the turn of the ' century and was made the object of exhaustive studies by Van Orstrand, 840 GEOPHYSICAL WELL TESTING [Cuap. 11 Koenigsberger, Heald, and others. The development of the electrical logging process in the past five years has made it possible to obtain de- tailed and continuous records of well temperatures and to study their relation to geologic conditions and production technique. A. APPARATUS; PROCEDURE Apparatus used in geothermal well testing depends entirely on the pur- pose for which the test is undertaken. In present practice measurements are made (1) in shallow holes for the location of near-surface formations, 1909 (Wh 0019851095 71058 a a 16000 Fig. 11-15. Trend of drilling depths in the United States in the past eighty years (from Union Oil Bulletin). near-surface structure, spring waters, and the like; (2) in deep wells for correlating the mean gradient between wells with geologic structure; and (3) in deep wells individually, for locating gas, oil, and water flows, and for determining cementation depth. For shallow well testing, ordinary thermometers are suitable, if they are provided with some sort of a cover (paraffine, rubber, or the like) to slow down rapid temperature fluctuations. If they are so protected and are hauled up rapidly, they will give the true bottom-hole temperature. Re- sistance thermometers and thermocouples have the advantage that two of them may be so connected as to give the difference in temperature of adjacent holes. Thereby, the daily or any other temperature variation is Cuap. 11] GEOPHYSICAL WELL TESTING 841 eliminated, since it affects adjoining holes alike. Thermocouples may be used with the hot junction in the hole and with the cold junction in a liquid kept at constant temperature. Van den Bouwhuijsen™ used a Moll galva- nometer of 2.7 X 10°’ volt sensitivity with a thermocouple supplying 4.10 ° volt e.m.f. for a temperature difference of 1° C. In underground workings, ordinary mercury thermometers are suitable if they are properly protected. A thermometer constructed by L. R. Ingersoll” maintained its temperature for about one minute by being inclosed in a bakelite tube; the bulb was insulated with vulcanite and paper. In seven-foot holes sunk from rock faces but a few days old, measurements were made with sets of two or three thermometers in tan- dem. These were read about every two hours for one day and the readings were repeated after two or three days. This made it possible to determine the cooling of the walls in drifts, tunnels, or shafts, and to calculate the virgin rock temperatures. The mean temperature gradients in deep holes are generally determined by maximum thermometers. Their use is predicated on the fact that the temperature in deep holes is greater than the mean annual temperature. (Maximum thermometers may also be used at shallow depths provided they are chilled with ice before and after the run.) An overflow type of maximum thermometer is illustrated by R. Ambronn.” In it, the maxi- mum temperature has to be determined by a separate testing operation and by measuring the temperature at which the mercury overflows. In another type of maximum thermometer, the upper 2-3 mm of mercury are separated from the main stem by an air bubble. The most extensive application has been made of the constriction type of maximum ther- mometer which requires resetting in some sort of centrifugal device after each use. The thermometer used by the U.S. Geological Survey has a length of about 20 cm, a stem diameter of 6-7 mm, and an accuracy of 0.1°-0.2° F.; and it is divided in Fahrenheit degree intervals between 32° and 212° over a length of 17-18 cm. Usually two or three thermometers are employed for each run to increase the accuracy and to reduce errors due to jarring of the assembly in hoisting and lowering. Fig. 11-16 shows a number of thermometer carriers” with their con- tainers adapted to various types of wells. Fig. 11—-16A’ is a holder for three thermometers which fits the container B’ for use at the end of a rope in shallow wells; C’ is a container suitable for clamping to a piano-wire line; D’ is a steel container for use, at the end of a wire line, in oil or water wells. 1 Eng. and Min. J., 135(8), 342-344 (Aug., 1934). 12 Physics, 2(3), 154-159 (March, 1932). 13 Klements of Geophysics, p. 275. 144C, E. Van Orstrand, Econ. Geol., 19(3), 229-248 (1924). 842 GEOPHYSICAL WELL TESTING [Cuap. 11 Several containers may be arranged in tandem with the T joint. The open containers are applied in dry, open holes. In wells filled with water, drilling fluid, or oil, the use of the closed containers (A-C) prevents the pressure of the liquid from reaching the thermometers and altering the reading. ‘Thermometers in European equipment are enclosed in cotton- packed and capped steel cylinders, which are arranged in tandem in a tube of larger diameter. Leather diaphragms are provided around the ends of the large tube to reduce circulation. The thermometers may be lowered into the well on the end of the sand line, inside or outside the bailer, or on a separate line, using an apparatus developed especially for this purpose, illustrated in Fig. 11-17. This ma- D' Fie. 11-16. Holders and containers for maximum-thermometers (after Van Orstrand). chine holds 9000 feet of No. 19 or No. 20 piano wire and is equipped with a speoling and depth indicating mechanism. The use of nfaximum thermometers requires that the well be in tempera- ture equilibrium and that jars and other sources of error be carefully avoided. Since this technique is intended for structural correlations, dis- turbances arising from an influx of oil, water, and gas into the well are considered sources of error and are carefully avoided if possible. Drilling with a standard rig should be discontinued for at least twenty-four hours before a test is begun. For a rotary outfit the time required for tempera- ture equilibrium is much greater and may be several days. When meas- urements between 100-1000 feet are taken with maximum thermometers, outside temperatures may be higher than the well temperatures, and the Cuap. 11} , GEOPHYSICAL WELL TESTING 843 thermometers must therefore be chilled before and after the run. Other- wise they may be left in the well over night and be hauled up in the early morning hours: The time required for the thermometers to acquire forma- tion temperature is about 1} hours in air and 3 hour in water. Since the reading at 100 feet is from 1° to 4° F. higher than annual mean tempera- ture, the latter provides a convenient check on the upper portion of the depth-temperature curve and may be obtained from the volume on Climato- logical Data for the U. S. by Sections, published by the U. S.. Weather Bureau. With maximum thermometers, readings are taken at intervals of 250-500 feet. Such thermometer assemblies are lowered at the rate of 200 feet per minute maximum and removed at the rate of 100 feet per minute maximum. Readings are taken with a telescope and corrections for constant and stem deviation are applied. Fic. 11-17. Device for well-temperature measurements (after Van Orstrand). For detailed temperature investigations required in connection with pro- duction tests, continuously recording thermometers are more suitable than maximum thermometers, since they do not require hoisting after every reading. The following thermometers are suitable: (1) bimetallic ther- mometers, (2) thermocouples, and (3) resistance thermometers. The former require a recording mechanism inside a water-tight case and do not require wires for remote surface indication. Thermocouples and resistance thermometers are widely used, since cables are usually available in con- nection with electrical logging. Fig. 11-18 shows three arrangements of resistance thermometers. Fig. 11-18a represents a Wheatstone bridge circuit with Siemens lead-resistance compensation. Fig. 11-18b shows a customary method of measuring resistance variations by galvanometer -deflection. For recording, the switch S is in position 2; for calibration (by adjusting R to a predetermined 844 GEOPHYSICAL WELL TESTING [Cuap. 11 galvanometer deflection), it is in position 1. In the arrangement of Fig. 11-18c, the resistance of the thermoelement is determined by measuring the potential drop across it, with the switch to the left, and determining the current in the circuit from the potential drop across the known resistor r, with the switch to the right. During a run the current measurement can be dispensed with, and an automatic self-balancing potentiometer can be used to record the temperature. In the Schlumberger apparatus, measurements are taken with an accuracy of 0.25° F., and the thermometers are lowered at the rate of about 1000 feet per hour. Fic. 11-18. Resistance thermometer arrangements for well-temperature recording. (a) Wheatstone bridge with Siemens lead-resistance compensation (adapted from Johnston and Adams); (b) deflection bridge; (c) potentiometer method. For general structure correlation of deep wells, temperatures are meas- ured and plotted beginning with a depth of about 100 feet. From this curve a mean temperature gradient can be calculated by assumption of a straight-line function 6; = % + bd, where 6, is the temperature at depth d, % is the mean annual temperature, and b the mean slope of the curve, or the temperature-depth gradient. The gradient can be measured di- rectly by recording the difference in temperature between two thermome- ters mounted a definite distance apart. In some cases, gradient records have advantages over the direct temperature records. The reczprocal gradient 1/b is the number of feet or meters one has to advance in vertical Cuap. 11] GEOPHYSICAL WELL TESTING 845 direction to obtain an increase in temperature of 1°C. or F. For a detailed analysis of individual wells, the slope or gradient is taken over limited portions of the temperature-depth curve. Areal temperature dis- tribution is represented by lines of equal reciprocal gradient for a given depth, or by contour lines of equal temperature. In profile view equi- temperature lines or “isogeothermal surfaces” are useful for correlation with regional and local dip. ‘Temperature measurements, made in con- nection with electrical logging for purposes of production engineering, are represented in the form of a temperature curve, deviations from the (normal or regional) gradient being shaded to indicate the anomalies. Results of shallow-well investigations are plotted by showing lines of equal temperature for a given depth of investigation. When temperature differ- ences have been measured with two thermometers between adjacent wells, temperature gradients are plotted in profile or plan view. B. THe UNIVERSAL GEOTHERMAL GRADIENT Wherever great depths have been reached, an increase of temperature has been observed. In the Simplon tunnel (maximum cover under moun- tain crest, 7000 feet) the highest rock temperature was 132°F. In the Robinson Deep mine in the Rand of South Africa, the temperature was (only) 103° F.““* at a depth of about 8500 feet. The Wasco well in the San Joaquin Valley, California (15,004 feet deep), revealed a bottom temperature of 268° F.,”° which is higher than the boiling point of water. Yet, the greatest depth reached to date is but a 14 thousandth part of the earth’s radius. This makes any deductions in regard to the tempera- ture in the earth’s interior and the age of the earth highly speculative, to say the least. Of the many approaches to the problem of temperatures in the earth’s interior, the so-called Kelvin theorem is probably the best known. It gives the temperature at any depth as a function of an initial temperature, time of cooling and an absorption coefficient, for an infinite slab heated at one face while the other is kept at 0° temperature. The solution appears in the form of a probability integral’® which, when differentiated with respect to depth, gives the geothermal gradient SOE a i BB =e e 4k (11-2) M4a Other mining districts have shown reciprocal gradients of the order of 175-375 feet per degree F. 15 Probably mud temperature. Actual formation temperature was probably around 300°. (Personal communication from H. Guyod.) 16H. Cecil Spicer, Geol. Soc. Am. Bull., 48, 75-92 (1937). 846 GEOPHYSICAL WELL TESTING [CHap. 11 in which © is temperature, d is depth, ® is initial temperature, ¢ is time since beginning of cooling, and k is thermal diffusivity. Therefore, for the earth’s surface, 00/dd = /+/rkt. Substituting a value of 1° F. per 50 feet for the temperature gradient and a value of 64-10°* C.GS. fork, and assuming further a temperature of 7000° F. for the initial condition, it follows that the time elapsed since the beginning of the cooling is about 175 million years. This is generally considered too low for the age of the earth, yet it is nearly of the right order of magnitude. An earth with the temperature distribution postulated by the Kelvin theorem has been claimed to be unstable against tidal and similar forces. Therefore, the assumption has been made that the cooling process is partly compensated Shale, limestone, sandstone Granite Depth — Feet Fie. 11-19. Trends of temperature depth curves (1) near basement rocks, and (2) in sedimentary areas (after Van Orstrand). by the heat generated at moderate depth by a layer of constant or expo- nentially decreasing radioactivity. Whatever the cause of the earth’s heat, the amount of heat transmitted to the surface is exceedingly small and barely sufficient to melt a layer of ice 3s of an inch thick in one year. The heat quantity Q transmitted in the time ¢ between the faces of surface S and distance I of a slab of the conductivity c is given by Q= St. (11-3) If for 1/A® the normal reciprocal gradient, or 50 feet for 1° F., is substi- tuted, it follows that the amount transmitted is only 200 B.t.u.’s per square foot in one year. Cuapr. 11] GEOPHYSICAL WELL TESTING 847 As was stated above, the normal reciprocal gradient varies from about 27.5 meters per degree C. (or 50 feet per degree F.) to about 35 meters per degree C. (or 64 feet per degree F.) in normal areas. Regionally, the observed reciprocal gradients may be quite different from these values, depending on geologic structure.’ In wells where the drill has penetrated uplifts of basement rocks, the temperature-depth curve is concave toward the depth axis; that is, the reciprocal gradient increases with depth. This is because of the better heat conductivity of the basement rocks (see Fig. 11-19). Conversely, in areas of sedimentary beds of great thickness the reciprocal gradient decreases with depth (Fig. 11-19). This may be caused by the decrease of porosity’ (hence, water content” and thermal conductivity) with depth, or by the compression of the isogeothermal surfaces as the basement rocks are approached. However, when the base- ment is entered, these types of curves turn again toward the depth axis. According to Van Orstrand,” only 5 per cent of 400 wells investigated up to 1932, had a linear depth-temperature curve; 26 per cent were concave, and 59 per cent were convex to the depth axis. C. THERMAL PROPERTIES OF ROCKS The thermal behavior of rocks and formations is characterized by three properties. They are: (1) the thermal conductiity, or the heat current traversing the unit section for the unit of heat gradient, expressed in cal. em. sec. centigrade’; (2) the specific heat, which is the quantity of heat required to raise the unit of mass by the unit of temperature, in cal. gram” centigrade’, or B.t.u. per pound per degree F.; and (3) the diffusivity K, a property derived from the first two, and given by c K = 38” (11-4) where c is thermal conductivity, s is specific heat, and 6 is density. A fourth property, the heat given off in certain chemical reactions, is like- wise of importance. However, it is difficult to define and is discussed in the next section. Since diffusivity is a derived property, this discussion will be confined to specific heat and thermal conductivity. The specific heat of most minerals 17 Van Orstrand, A.A.P.G. Bull., 19(1), 78-115 (Jan., 1935). 18 For correlations of depth-temperature with depth-porosity curves see Van Orstrand, zbid., 18(1), 19 (Jan., 1934). 3 Depths to boiling point of water are 7000 feet or less in one-third of the loca- tions investigated by Spicer (A.A.P.G. Bull., 20(3), 279 [March, 1936]). In the remaining two-thirds, they are 10,000 feet or less. 20 Physics, 2(3), 1389 (March, 1932). 848 GEOPHYSICAL WELL TESTING [Cuap. 11 and rocks is in the neighborhood of 0.2 for dry rocks, but it may increase to 0.5 to 0.7 for moist. formations. Wet peat, with 0.9, approaches the specific heat of water. Table 76 gives a few representative values, in cal. gram centigrade ~. TABLE 76 SPECIFIC HEATS MINERALS Peldspariy.. (ise, eee Le O21 Caleite i...22.402010. 2 he See 0.20 Dolomites. 5306s taithase sae O22 2 Quiante red. bd cieacialer seat ae ee 0.21 GYPSUM, hea: Sth poi aiie epee 0.26 SEDIMENTARY ROCKS Sandstones.ce. 2 ee g2 a ee ee 0822. Loam (wet). s.6..6 wks rhe oe ee 0.51 SISter he eee ones tanec ce ee Uses andy loam (dry): ic 0. cee 0.49 Clay: 2008 ROSE, SEO 22 sa Sandy: loam (wet) 2500s 427 eee 0.75 Quartz sand. 2.26. bi eso 025 sore haere oO 9 ums soil e232 .,.:,262 . Lenore eee 0.44 CB ve U Fea eae os ae Re een eer mr as He 0.21) 4 River sand. (moist)'......,... aqme 0.32 COR erie Rak Mere nM Ae re ate O73l2Peate(dry) yo... sch nencty a aoe 0.15 Loam (dry) (2 SU, 2h Me ee O231eReat (wet) icky 2 Ro A 0.9 IGNEOUS ROCKS Granpter yes eee ease O.19) Andesite i420 ot.) 0 eee 0.20 (GNGCIBS stat has nk air os eens RT eae es 0:20" i Basalttz.. 07, «aches qe. 215 eee 0.21 Porphyry oe ae eee ees 0.20 “ Syenite:. eis c2gs «hl ae eee 0.20 Specific heat of rocks is determined by any one of the calorimetric methods used for other solids. For instance, the specimen may be heated to a given temperature, and then be dropped in a calorimeter. The quantity of heat given off until both specimen and bath have reached the same temperature is dependent on the specific heat of the specimen. Compared with the metals whose conductivity, when expressed in units of cal. cm.” sec.’ centigrade ', may be as much as 1 unit (silver), most rocks have only a conductivity of third decimal value. Most sedimentary and some metamorphic rocks are distinctly anisotropic with respect to heat conduction. The anisotropy ratio is about 14:1 (gneiss) to 3:1 (schists). Table 77 gives heat conductivities for a few minerals and rocks in 10° C.GS. units. TABLE 77 HEAT CONDUCTIVITIES MINERALS Coalisnet ee hile pu aches tee omen 0.3-0:8° (Caleite:\ i. .0c% 1.3. 3c eho eee 10 Petroleum)..55.40 000 eee cee 033°. ;Graphite,. sy45h" ¥.. See eee 12 DR Gaia. siaps-saraeds preys ator su seyost de yerth (set 0:9 Rock $galtecuh,. Sey-ssnqar ibaa eee 17¢ Wistte Tce x mare uy ven mtn igeas V4 Quabah ls. Nee Bek a ia a 17 Teeek 38..3y nee tnonis aces aoe Beye 226), » BIMOTItE Soy. efi sess bcd ee GOR 25 Gypsum)! vents. 2 Boa td ee ee Bat Migonetitels si tote gd. doce eee 30 Meldspar®. 22.5) c2": Siilet:s, Se ee 5 an Quartzalltc.. i aa plek obese eee 32 ? This value is for crystals and is probably too high for salt formation. Leonardon (Geophysics, 1[1], 115, [Jan., 1936]) gives 6.6, which value is also quoted by Alexanian. Cuap. 11] GEOPHYSICAL WELL TESTING 849 SEDIMENTARY ROCKS# WerynGry SANG. joe f igen Vaal Wee 0.8 Molasse sandstone, 6 = 2.57....... 8.1 Sand with 11.3% moisture.:........ 2H AIDING LIMES: .5h eee eel Ly 4.9 Cmaciavnand, (ANY)! ) ics )u.e Gcisinaie a TOW amMestone:! 520 eq aeRO NEY elena o 5.2 @partzisand: (moist) 0020007008. .0).. 8:2!) Clayey lime, 6 =)2.59) 00.0 se... 6.7 Red sandstone (dry)................ DE OC lAVeY: LIME, (Oi eal enue as 8.1 Red sandstone (moist).............. GROM TE RING 43... sae estate ra Me ae OR ee 8.8 (OR SEO SE (06151 Jn Rte Oe OR, fe 2s OWiiueNagelfiue;’) B= 2-035. sea se. 5.9 BOTA NOISE) 200. cos se cools is chs tears 30. Nagelflue,’”’ 6:= 2:73) 0 0.0000 9.0 Molasse sandstone, 5 = 2.06........ 3.0 IGNEOUS AND METAMORPHIC ROCKS Granite, 3, =)2:66) 6 ote oe MEO OLAtC ae ie iid ose ce eRe Cenete ee 5.7 Gramite io). =) 2:6) ea heed ae: OeSrs PHY Mites 6% ls. oie choca leosnatacetows aes 7.0 Granite, 6 = 2:66......00085...5... Sa Lava; 0 25620 a we ee ee 4.0 Basalt, 8 = 2.97.................... 6.7 Traprock, Calumet & Hecla....... 3.4 INATESOPAMI LES Oe. cota a aki ace AAO Ti SOLDOVEY sete cat anteil cose ein hoe etc 8.4 15504 dire? §\ 0,0) 910) Oh he sale URE ee ee Deo pyreAndesite: ii. gee one te ee ayer 6.9 BIERINETLLANGly eee cc an eo tne ee 8.4 Trachyte, 8 = 2.55................ 4.6 HEISE Os es Ne onc a ts 53 Trachyte, & = 2:43.0)0%. 2 ak. 3.0 JNFTY0 Vets} WGI soe eae cr RE eC eee RO ool Garnet. schist: nq) oa ee 6.5 CSE: V6 IiEV a), Oe aE IST Maa reapt aden A eT 1.9 Calcareous phyllite................ 4.7 IV Mea rsly] @ apart daccuscestel-nonawieoreoicctcins oie, chatens 2 | Wa viay BS 2 Ba ee enantio a tok fat 4.6 The values for sedimentary, igneous, and metamorphic rocks indicate that the thermal conductivity is greatly dependent on porosity” and moisture. From molecular theory, the following relation has been de- duced,” in which c is thermal conductivity, v is longitudinal wave velocity, and 6 is density: e-10.. ="vi-5 108. Since approximately v; = V E/S, the conductivity c =E.3-10 “, (11-5) where E is Young’s modulus. This relation has probably not been tested experimentally on rocks. However, calculations made for various ho- mogeneous rocks and for representative values of E and 34, give reasonable figures for the heat conductivity. The high heat conductivities of igneous and metamorphic rocks are in good agreement with high elastic moduli and densities. Thermal rock conductivities may be measured in the laboratory by ab- solute or relative procedures. An absolute method, illustrated in Fig. 11—20a, provides a heater and a plate of constant temperature on both sides of a specimen. Holes of smal] diameter are drilled into it and are 21 Largely after H. Reich, Handb. Exper. Phys., 25(8). 22 See also Van Orstrand, A.A.P.G. Bull., 18(1), 19 (Jan., 1934). 23 N. M. Thornton, Phil. Mag., 6, 38, 705, 707 (1919). 850 GEOPHYSICAL WELL TESTING [Cuar. 11 fitted with thermocouples or resistance thermometers. If § is the surface of the plate and (@ — 6)/z is the temperature gradient, the thermal conductivity zQ S 02 — 6,’ where Q (cal. sec. ’) is the heat current which may be calculated from the current and the resistance of the heater circuit. Another absolute method™ c= (11-6) xs Cb) () re Sec INNA PRR. al Mle bi Hil 00 08 Tel Fic. 11-20. Arrangements for measuring thermal conductivities of rocks: (a) absolute method, (b) and (c) relative methods. uses a thermocouple in the center of a slab whose two faces are exposed to constant temperature for twenty-four hours and then abruptly chilled to and kept at 0° C. The conductivity is calculated from the time required for the center temperature to fall to its half-value. A simple relative method for comparison with a material of known con- ductivity is shown in Fig. 11-20b. Two plates of triangular shape are joined with their hypotenuses and covered with a wax film. If heat is 24 Ingersoll, Phys. Rev. 24, 92 (1924). Cuap. 11] GEOPHYSICAL WELL TESTING 851 applied on one side, the wax will melt along a broken line which makes the angles g; and g: respectively, with the diagonal. Then c¢ = C, tan g;/tan ¢g2, where the subscripts 2 refer to the standard material. Another convenient relative method,” shown in Fig. 11-20c, places the specimen, of the conductivity c: and thickness d; , in series with a standard of the conductivity c2 and thickness dz , with a copper plate between them. If a thermal gradient is now produced by heating one side and cooling the other, the conductivity of the specimen follows from that of the standard and from the respective thermal gradients: d, % — 9 a (17) C1 = C Anisotropy of heat conduc- tion may be determined by Sia ea sat covering the surface of a specimen with wax, apply- ing heat at one point, and measuring the axes of the melting ellipse. Variations in thermal conductivity of rocks and formations are of profound influence upon the thermal gradient. Since the heat current, that is, the quan- tity of heat transferred in the unit of time through a plate of section S and thick- ness d, is given by Depth Fig. 11-21. Depth-temperature curve, showing a c(® — 6)S (11-82) effect of change in thermal conductivity (15 miles ma eee 2 southeast of Thompsons, Grand County, Utah). (After Van Orstrand.) and since d/(@2. — 4) is the reciprocal temperature gradient, or 1/b (see page 844), it is seen that eae) b = One (11-8) Hence, the reciprocal gradient is directly proportional to the heat con- ductivity of a formation. This is well illustrated in Fig. 11-19 and par- ticularly in Fig. 11-21, where a reduced slope (large reciprocal gradient) corresponds to the increased conductivity of the salt. With the value of 25 C, Christiansen, Ann. Physik., 14, 23-33 (1881). 852 GEOPHYSICAL WELL TESTING [Cuap. 11 6.6 given on page 848, the conductivity should be about 2.8 units for the overlying sediments, which agrees with the values for sands and clays given on page 849. An increase in the reciprocal gradient in salt is also evident in Fig. 11-22 from the arrangement of the isogeothermal surfaces. Usually the contrast on the contact of two media is not so sharp as that indicated in Fig. 11-21 but is more gradual because of the crowding of the lines near a medium of better heat conductivity.” Where formations are definitely anisotropic in respect to heat conduc- tivity,” the reciprocal gradient changes with dip. If b is the (normal) 500 750 Salt Dome Fic. 11-22. Isothermal lines through Grand Saline salt dome, showing increased interval in the salt and a decrease in interval above it (after Hawtof). vertical gradient, c; the conductivity in the bedding planes, cz the con- ductivity normal thereto, and 7 the thermal anisotropy that is equal to ¢:/ce, then the normal gradient is reduced in the ratio if ) ae eam 11-9 n sin’ ¢ + cos’ gy’ ( ) 26 Mathematically, the problem is similar to the calculation of electrical potential distribution about a conductive body. See, for instance, J. Koenigsberger, Gerl. Beitr., 18(1/2), 115-126 (1927). 27 Van Orstrand, Amer. J. Sci., 15, 507 (June, 1928). Cuap. 11) GEOPHYSICAL WELL TESTING 853 where gis dip. The normal reciprocal gradient of 1° F. in 50 feet changes, therefore, with dip to the extent shown in Table 78, if the anisotropy is 1.765 (slate). TABLE 78 1/b 1/b ORE Tron a re Te 50.0 feet 7.) AR AVR SOR Y 54.5 feet et i, A 50.3 DASA RO SAM Cea ae 56.8 LO evar ike ter aan se Dlie2 BO Este eee 59.6 Sea: US PAOTAR S aR 52.5 The influence of dip can be so pronounced as tomake the isogeo- _ thermal surfaces almost parallel with the structural contours. Two well-known examples are the Salt Creek field (Fig. 11-23) and the section from Oklahoma City to Sapulpa (Fig. 11-24). The A.P.I. report on geothermal investigations” contains many more instances of this character. Faults may be indicated in geo- thermal maps: (1) by a slight deflection of the isogeothermal surfaces if the fault has thrown blocks of different conductivity against one another;” and (2) by a peak in the temperature curve, as shown in Fig. 11-25, if waters of different temperature circulate in the fault plane. D. Heat GENERATING PROc- ESSES; CAUSES OF TRAN- SIENT TEMPERATURES As shown in the preceding sec- tion, static distribution of temper- Ye fre fe os Fig. 11-23. Lines of equal reciprocal temperature gradient and contours on sec- ond Wall Creek sand in Salt Creek dome, Wyoming (after Van Orstrand). atures is a function of the variations in the heat conductivities of rocks and formations. With the exception of factors of geologic periodicity (such as volcanism, glaciation, and radioactivity) most of the heat-generating proc- 28 Am. Petrol. Inst. Prod. Bull. No. 205 (Oct., 1930). 29 T. O. Haas and C. R. Hoffmann, A.A.P.G. Bull., 13(10), 1257-1273 (Oct., 1929). 854 GEOPHYSICAL WELL TESTING [Cuap. 11 esses discussed below produce transient temperature conditions of widely varying duration. When such processes are to be detected by geophysical well investigation, it is, of course, not necessary to wait until temperature equilibrium has been established, as was the case in the structural applica- tions described in the preceding section. 1. Radioactivity. Much has been written about the part played by radioactivity in the retardation of the cooling of our planet. It is im- possible to deal with this problem extensively here from the theoret- ical viewpoint. Reference is made to the review and bibliography by Van Orstrand.” It is noteworthy that virtually no verification of the Oklahoma City Davenport Key West Bristow Kellyville Sapulpa Depth in Feet Fig. 11-24. Isogeothermal surfaces and depth to granite between Oklahoma City and Tulsa (after McCutchin). theory has been obtainable, the outstanding observation being that” the pitchblende deposit in Joachimstal, which is in one of the richest radium localities, does not exhibit abnormally high temperatures. 2. Volcanism. In volcanic areas large anomalies in geothermal gradients may arise (a) from rapid changes in conductivities of formations (inter- calation of highly porous lavas, and the like), or (6) from circulating hot waters. In Oregon, Van Orstrand” observed reciprocal gradients as small 30 A.A.P.G. Bull., 18(1), 13-38 (1934). 31 J. Koenigsberger, Inst. Min. Eng. Trans., 39, 1-28 (1910). 32 Van Orstrand, Am. J. Sci., 35, 22-46 (1938). Cuar. 11] GEOPHYSICAL WELL TESTING 855 as 3.3 feet per degree F. and as large as 20-21 feet per degree F. In such cases, the depth-temperature curves may consist of both extremely flat and abnormally steep portions. High rock temperatures should naturally be expected in areas of volcanic activity even without the presence of circulating waters. There is frequent evidence of this condition in mines located in volcanic areas. Underground workings in ores deposited by thermal waters will show high temperatures if deposition is still going on. era Gravity Gradient \ Tesh tae Die Sfations 0? 40 20 — inn > == VLU be 1474, H+ +++ : s es Ce e277) ee GA Ea) Tert Cret Permian Triassit = Coal Fig. 11-25. Torsion-balance and geothermal indication of fault near Winterswijk, Holland (after Van den Bowhuijsen). 3. Glaciation. As shown below (section £), any change of temperature at the earth’s surface is propagated downward in the form of a wave. Short-periodic changes, such as the diurnal temperature variation, are damped out within a few feet. Long-periodic variations, such as those occurring during glacial and interglacial periods, may be expected to have affected the thermal gradient down to several thousand feet of depth.” With sufficient data on geologic section and heat conductivities, the effect of temperature changes of given periodicity on the depth-temperature 33 A. C. Lane, Geol. Soc. Amer. Bull. No. 34, 711 (1923). 856 GEOPHYSICAL WELL TESTING [Cuar. 11 curve may be calculated. In this manner, Ingersoll, e¢ al., estimated that 30,000 years have elapsed since the last glacial period. 4, Oil. Opinions were expressed in the earlier literature that chemical processes associated with the formation of oil deposits (polymerization, and the like) should have given rise to geothermal anomalies. However, no definite evidence of such anomalies has yet been found. Of particular significance have been (a) the measurements in the Burbank pool* where no rock deformation is in evidence and where no temperature anomaly is found, in spite of extensive oil accumulation, and (b) observations on salt domes, whose geothermal reaction appears to be the same regardless of the presence or absence of oil. Even in oil deposits which occur so near the surface that they are mined by shafts, as in Pechelbronn,” there is no evidence of a direct heat influence of the oil. On the other hand, it is possible to determine the influx of oil into a well by a slight drop in the temperature curve,” which is probably caused by the expansion of the gas dissolved in the oil. In drilling wells, the well is conditioned with a light mud, and the survey is made several hours after circulation. In producing wells, it is preferable to swab the well down and to take the temperature run while it is filling up. 5. Gases in subsurface formations are generally confined under con- siderable pressure. When they are tapped and liberated by a well, the reduction in pressure produces a decrease in temperature in accordance with the relation (11-10) ° 2 re e-ap (28 =n 273 + 6 where c is a constant depending on the gas, AP is the difference in pressure, and 6 is the temperature at which the gas escaped. As Fig. 11-26 shows, the effect is quite noticeable and may readily amount to several degrees (F.) drop in temperature. The location of the base of a gas formation is of considerable practical importance for determining the depth at which to set casing. If it is set too low, part or all of the oil formation may be cased off; if too high, a weil with a high gas-oil ratio, or even a practically dry gas well, will result. In some areas, such as West Texas, temperature well surveys for gas are an indispensable adjunct to electrical logging. 6. The location of water in wells is likewise of importance in connection with shutoff and cementation depth control. The interaction of formation 34 A.I.M.E. Tech. Publ. No. 481, Feb., 1932. : 35K. C. Heald, A.P.I. Proc. Bull. No. 205, 1930. 36 Haas and Hoffmann, loc. cit. 37 W. J. Gillingham and W. B. Steward, Petroleum Engineer, 9(7), 52-55 (April, 1938), and 9(8), 84-92 (May, 1938). Cnap. 11] GEOPHYSICAL WELL TESTING 857 water and drilling fluid will produce quite different geothermal effects, depending on relative temperatures, hydrostatic head, and agitation. As shown in Fig. 11-27, the trend of temperatures in static condition may be as in curve a. Drilling will result in cooling the lower portion of the well by the drilling fluid, and in heating the upper portion in comparison. Resist Pores. Temp. aynm oO 200 6 -f0m« 00°F 720° Fic. 11-26. Anomaly in depth-temperature curve due to escaping gas (after Leonardon). When the well is left idle, the lower portion will again tend to take the temperature of the sur- rounding formations and cool the upper portions further. A gradual approach to static con- ditions takes place. In practice, the order of events is reversed when several runs are taken for locating water flows. If the well has been idle for a time and a first run is taken, curve c is ob- tained. If, then, the mud is circulated for a few hours, a second run will give curve 6.3” Following this, the hydrostatic head of the mud is generally re- i? es ae duced by bailing to allow (warm) Fie. 11-27. Depth-temperature curves inidle, water to flow into the hole. drilling, and flowing wells (after French). This will give rise to a definite peak in the curve. Fig. 11-28 shows a series of water sands with their corresponding temperature peaks recorded through the casing. Note the 372 R, W. French, Oil and Gas J., April 27, 1939. \ 858 GEOPHYSICAL WELL TESTING [Cuap. 11 similarity of the temperature and the self-potential curves taken before the casing was run. Close supervision of temperature conditions in a well is valuable in con- nection with water encroachment problems. ,It is frequently observed that the temperature of oil flowing into a well remains fairly uniform until the well turns to water; then a rapid increase in temperature of the flow is noted. This may be explained on the basis of the difference in heat conductivity of oil and water. The temperature of the latter is likely to be higher than that of the tm 6 9 _ Homa former but not felt until the oil envelope separating it from the well becomes too thin. In shallow wells water does not always produce an increase in temperature; de- scending surface waters may produce negative deflections of the temperature-depth curve. In areas of volcanic activity circulation of ther- mal waters may produce unpredictable anomalies in the records (see paragraph 1). Since water-bearing beds are better heat conduc- tors than dry formations, depth-temperature curves 7600 5000 8200 Temperature 6400 a a 7 sil : WL flatten at times near the sur- Fiac. 11-28. Temperature Anomalies of water f (i ¢ : 1 sands (after Guyod). (Note similarity of tem- Beer increase mM reciproca perature and self-potential curves.) gradient) as the ground- water level is approached.” In some instances, temperature curves indicate that water leaves a well at one level and enters it at another. In such cases, virtually uniform temperatures may be maintained for appreciable depth intervals. 7. Cementation problems are successfully handled by well-temperature surveys. To seal off water-bearing formations effectively, it is important to know at what point behind the casing the cement ring begins (Fig. 11-29). There is an appreciable rise in temperature during the setting period of the cement. For most Portland cements the temperature rise, 38 Van Orstrand, Problems of Petroleum Geology, p. 999 (1934). Cuap. 11] GEOPHYSICAL WELL TESTING 859 eam Fic. 11-29. Location of top of cement collar by temperature measurements (after Schlumberger). ~ & 8 8 8 - Degrees Re Ss) S YS Bureau of keclamation Denver Concrete Laboratories Temperature ki: Ss Temperature Rise of Mass Concrere Modified Portland Cements as OZ i'd ja Ole WOa ON SA ATO Ihe 20 i Zeiasa ZO LO Elapsed Time - Days Fie. 11-30. Temperature rise during setting time of various cements (after Savage). 860 GEOPHYSICAL WELL TESTING [CHap. 11 approached asymtotically within about one month (Fig. 11-30), is between 40° and 65°F. The corresponding temperature variation through well casing is of the order of 10°-20° F. and therefore quite readily detected. 8. Other chemical transformations affect well and underground tempera- tures when the reactions are of an exothermic nature. Well known in mining are such sources of heat as: active fires of broken sulfurous ores, or of coal, carbonaceous shales, and timber; the decay and oxidation of timber, aided by bacteriological action; and oxidation of sulfurous ores, ~ coal, and shales (not sufficient to raise the temperature to the point of ignition). An example of this kind is the pyrite deposit of Sain Bel in France. Evidence of its oxidation is a zone of strong self-potentials above it (see page 676). In workings 100-150 meters deep, the temperature is as high as in other mines at depths of around 1000 feet. Although some increase of temperature occurs in the transformation of anhydrite to gyp- sum, the main reason for the high temperatures of salt domes is probably the high thermal conductivity of the salt. E. Errect oF SurFACE RELIEF AND SURFACE TEMPERATURE Since the earth’s surface may be considered, in very close approxima- tion, an isothermal surface, and since all irregularities due to near-surface distributions of conductivity and topography must be expected to be equalized at a certain depth (geothermal ‘‘isostasy’’), it follows that the isothermal surfaces must be compressed under the depressions and ex- panded under topographic highs.” The deflections of the isothermal sur- faces due to topographic irregularities may be calculated for a medium of constant diffusivity if the topographic profile and the gradients under the apex of a hill and the adjacent plane are known. This calculation is readily made for ridges of two-dimensional configuration.” Fig. 11-3la shows such theoretical isothermal surfaces for the topography at the Long Beach field, and Fig. 11-316 represents actual rock temperatures in the Moffat Tunnel near Denver. Temperature variations at the surface of the earth penetrate into the ground to a depth which can be calculated from their periodicity. The diurnal variation is relatively unimportant for well measurements; its penetration is of the order of 3 to 4 feet. The annual variation, however, penetrates to a depth of about 80 feet in high and 50 to 65 feet in inter- mediate latitudes. For deep well measurements this variation is not im- portant if observations are started below 100 feet. The variation must be 39 This phenomenon is analogous (and mathematically almost identical) to the - effect of topography on the equipotential surfaces in an electrical field (see p. 702). 40 Van Orstrand, Physics, 2(3), 144 (1932). Cuap. 11] GEOPHYSICAL WELL TESTING 861 considered in shallow holes unless temperature differences betw en ad- jacent holes are measured. The temperature ®,, at a given depth d and ———> Actyal Surface Theoretical Surface /solherms Fig. 11-3la. Topographic effect (calculated) of Long Beach dome on isothermal surfaces (after Van Orstrand). James Feak 12000° 11000' 10000 iisba x Temperature Sia a p 60° 9000 Tunnel 40° Fig. 11-31b. Observed temperatures in Moffat Tunnel near Denver (after Van Orstrand). time t (in days, from a reference instant) may be calculated for ground of known diffusivity K from 2,2 = 9% + =o ie (cos 7 os Zt, 1 ey (11-11) where 6,, is the mean annual temperature, A®, is the annual range, and T is the period (365 days) of the variation. The exponential indicates the penetration, and the bracket term indicates the phase shift; K follows from eq. (11-4) and is expressed in m’ per day, if depth is in meters and 862 GEOPHYSICAL WELL TESTING [Cuap. 11 time in days. It follows from this equation that the depth penetration of the daily variation is 1/+/365, or 1/19, of that of the annual variation. Ill. SEISMIC MEASUREMENTS Seismic measurements in wells are made (1) to determine the vertical velocity distribution, (2) to extend the range of refraction exploration vertically and laterally, and (3) to determine crookedness of holes. Seismic (deep) well shooting is applied widely to secure data on velocities along refraction and reflection paths. To this end, shots are fired a certain distance away from the top of a well, detectors are lowered to successive depths, and travel times are recorded. This method was mentioned on page 465 in connection with total and differential vertical velocity deter- minations. On page 568 its relation to average reflection velocities was discussed. Seismic well shooting detectors are usually reluctance seismo- graphs of small diameter.“ Several units may be arranged in tandem to increase the sensitivity. Precautions are required to protect their interior from the pressure of the drilling fluid. Shot instant and travel times are recorded as usual; over-all or differential velocities can then be readily calculated if the depth to the detector or detectors is known. For dis- tances from the top of the well comparable to the detector depths (oblique incidence) more elaborate calculations are necessary” in order to obtain the vertical velocity distribution from travel-time records (see Fig. 11-32). In shallow holes the procedure is reversed and shots are fired at the bottom of the hole while the detectors are set up at the surface. This is the present practice in connection with weathered-layer procedure and for securing average vertical travel times and velocities at the shot point (see page 576). In the vicinity of salt domes, faults, and other vertical contacts which are difficult to delineate by surface refraction measurements, deep wells can be used to advantage to extend the vertical range of refraction observa- tions.” Detectors lowered into wells on the outside of a dome will help to obtain more data on the flank formations. Wells used with shot points on the opposite side of the dome are useful for determining overhang. The velocities in the salt and surrounding formations at various depths are usually well enough known to determine proportionate paths in the salt and in the sediments. The crookedness of drill holes may be measured by seismic procedures 41C. A. Heiland, Explosives Engineer, Dec., 1935, Fig. 14. 42 C. H. Dix, Geophysics, 4(1), 24-32 (1939). 43. B. McCollum and W. W. LaRue, Oil Weekly, June, 1931. Cuap. 11] GEOPHYSICAL WELL TESTING 863 in areas of simple stratigraphic and structural conditions. If a detector is lowered to the bottom of a well, and if shots are fired at three or four equidistant points (with reference to the top of the well), the travel times are equal, provided the bottcm of the well is located exactly below the top. If the travel times differ, the corresponding hole deviation may be calculated from the geometric relations involved.“ The accuracy of this method is not comparable to that of standard well surveying procedures. In addition, its application is limited to areas in which the velocity distri- bution around a well.is absolutely uniform. 506 m A a3 Od s8e. Time S ig ” me Sl 2000 2500 = m-sec’ Velacity Fig. 11-32. Travel times (heavy curve) to various well depths from a point 500 meters off well top, with calculated velocity distribution (light curve) (after Dix). IV. MISCELLANEOUS MEASUREMENTS IN WELLS A. DETERMINATION OF RADIOACTIVITY Measurements of radioactivity of rock samples taken from wells, mine workings, and tunnels have been made (since about 1905) by various investigators; the literature has been compiled by Ambronn.” In most instances the a radiation was examined, and radioactivity and type of formation could be correlated. Continuous measurements in deep wells by the wire-activation method were suggested by B. Ostermeier.*® Interest in radioactive well examination was recently revived, inasmuch as the penetrating y radiation is about the only rock property permitting 44D). C. Barton, A.I.M.E. Geophys. Pros., 587 (1929). 45 Hlements of Geophysics, pp. 125-126. 46 Zeit. Tech. Phys., 7, 196-198 (1926). 864 GEOPHYSICAL WELL TESTING [Cuap. 11 of well logging through casing.” A radioactive well logging arrangement is shown in Fig. 11-33. Two Geiger counters® (to eliminate chance varia- tions) are connected separately through two low-impedance secondary transformers to two A.C. amplifiers feeding into thyratron-controlled fre- quency meters. The latter are provided with @ tank circuit (12 micro- farads across 1 megohm) to FREQUENCY smooth out the current varia- auc | Pana | au tions, so that the galvanometer FREQUENCY indication is proportional to reed eran ey an average pulse frequency. The measuring cylinder may ALLE L be lowered and records may be taken at a rate of about 44 1500 feet per hour. As Fig. 11-34 indicates, the y-ray in- dication is markedly parallel to the potential and to the impedance record of the elec- tricallog. High porosity sands are indicated by radioactivity lows, shales by radioactivity 7 Geiger Counter highs.” The sand indications do not appear to be affected by variations in oil content. While a-ray determinations made on oil sand cores show an increase of radioactivity, y-ray logging does not seem to be sensitive to the presence of oil. However, it has been Geiger Counter found that gamma rays will pick up readily the presence of unconformities, which is Fig. 11-33. Geiger-Mueller tube arrangement probably due to the concen-— f -ra ll loggi fter Howell and d ‘ ‘ : Tees Hey Ber eee aren a tration of radioactive materials on such surfaces. Comparison of the two lower curves in Fig. 11-34 gives an idea of the absorption of gamma, radiation in the well casing. 47 L. G. Howell and A. Frosch, Geophysics, 4(2), 106-114 (1939). 48 See pp. 881-883. 49 The high radioactivity of shales is due largely to the ability of colloids to absorb radioactive substances and possibly to the presence of potassium compounds (see p. 875). Cuap. 11] GEOPHYSICAL WELL TESTING 865 Measurements of radioactivity in shallow holes are made in connection with the mapping of faults, contacts, dikes, radioactive ores, and the like. In this case the emanation method is applied. This involves the with- drawal of soil air from the hole into an emanation chamber, as described on pages 880-881. B. MaGnetic MEASUREMENTS Most magnetic well investigations involve laboratory tests of cores after removal from the well. Procedures for determining magnetic suscepti- bilities, remanent magnetization, and hysteresis curves of cores were de- scribed on pages 300-309. In the magnetic core orientation method devised by Lynton™ (Sperry-Sun), the direction of dip is determined by locating the direction of magnetization in a well sample. With the exception of 1600' £000 2200 Qpen Hole Electrical Log Qpen Hole Gamma Ray Log Cased Hole Gamma Ray Log Fig. 11-34. Comparison of electrical (impedance and potential) logs with gamma-ray logs in open and cased hole (after Howell and Frosch). limestones, anhydrites, and dolomites, cores with distinct bedding planes generally retain a sufficient amount of magnetism after removal and ship- ment. As shown in Fig. 11-35, the core, with axis horizontal, is placed close to the lower needle of an astatic magnetic system which, with the core, is shielded by a steel cylinder. The core is revolved slowly through 360°, and the deflection of the system is recorded photographically. The record will show a sine wave whose extreme amplitudes are proportional to twice the remanent magnetization. The effect of induced magnetiza- tion which shows no reversal with rotation” may be eliminated by taking a second run in reverse direction and forming the difference of the two curves. To obtain absolute dip, a correction for the crookedness of hole must be made. Magnetic measurements have also been used in wells to determine their 50 A.A.P.G. Bull., 21(6), 580-615 (1937); Geophysics, 3(2), 122-129 (1938). 51 See Chapter 8, section 11 B, p. 300. 866 GEOPHYSICAL WELL TESTING [CHap. 11 deviation from vertical and the azimuth of deviation. For this purpose, an earth inductor with vertical axis of rotation has been applied. As in the earth inductor compass,” the e.m.f. induced in the coil depends on the orientation of the brushes, and, therefore, on the orientation of the appa- ratus with respect to the magnetic meridian. By suspending a pendulum (which can be magnetized at will from the surface) in a universal joint vertically above the coil, an e.m.f. is produced when the apparatus (and the hole) is not vertical. An accuracy of 0.5° is claimed.” This apparatus can naturally be used only in an open hole. Wcrometer It appears possible that earth- inductor measurements can be used to determine the magnetization of subsurface formations in open hole. Astatic Soft tran System Shield C. Acoustic MEASUREMENTS Water flows in deep wells and gases escaping from formations, or from behind the casing, may be detected by acoustic measurements. Geo- phones of high frequency (about 1000 cycles) are lowered into the well in the same manner as are seismic detectors. In shallow holes (maximum of several feet) acoustic measurements are applied in the location of leaks in water pipes under pavement, side- walks, and thelike. A rod provided with a directional vibration pickup Fia. 11-35. Magnetic core orientation : apparatus (after Roberts and Webb). may be lowered into the hole so that (since the approximate course of a buried pipe is generally known) the longitudinal component in the direction of the pipe, as well as the transverse component of vibration produced by a leak, may be measured.” Since the transverse component is much more 52 See Chapter 8, section 111 c, p. 363. 53 C. and M. Schlumberger and E. G. Leonardon, A.I.M.E. Geophys. Pros., 269, (1934). 64 Known as vibration differentiation method, Western Instrument Company (see also p. 962). Cuap. 11] GEOPHYSICAL WELL TESTING 867 rapidly damped out than the longitudinal component which follows the pipe, the ratio of the two components at different frequencies (tuned amplifier) as a function of distance gives a clue to the location of the leak. D. Fiurip-LEvVEL MEASUREMENTS BY SOUND REFLECTION The depth to the fluid level in a deep well may be measured by recording the reflection travel time of an acoustic wave. The wave may be initiated by the release of compressed gas from a tank or by the firing of a cartridge. In the latter case the higher frequencies are filtered out mechanically by a tube which may be combined with a flame arrester.” The reflections from the fluid level and other obstructions in the weil (such as tubing collars, tubing catcher, and the like) are picked up by a microphone, stepped up by a selective amplifier provided with automatic volume con- trol, and are recorded photographically, or by a pen and ink recorder. - The sound velocity is not constant under all conditions and depends on the composition of the gas mixture in the hole. An incremental velocity arises from the expansion of the gas used for initiating the impulse. The record may be readily calibrated, however, (1) by an auxiliary (coiled) tube of known length, (2) by the reflections from tubing collars of known depth, or (3) by the reflection from the tubing catcher or other refiector purposely placed at a known depth. EK. Hicgu-FREQqUENCY MEASUREMENTS IN OPEN HOLES In the earlier days of geophysical exploration, much thought was devoted to the possibilities of high-frequency methods for determining the charac- teristics of formations in an open hole. These ideas probably received their impetus from the demand for some method of ascertaining wall thick- ness in connection with the freezing method of shaft sinking. Small leaks in the freezing pipes, spreading of the freezing pipes at the bottom, and other causes leading to a break in the ice wall were known to produce disastrous results. It was thought that the measurement of the damping of an antenna lowered into the shaft would give good leak indications, owing to the considerable difference in the conductivity of brine, and ice or frozen ground. The method was then extended to measure antenna capacity in open holes, with the object of determining the dielectric con- stant of the surrounding formations. These procedures were covered by a number of patents, since expired. Beyond a few brief references in the literature” nothing further has been published about them. 55 J. J. Jakosky, Petrol. Tech., 2(2) (May, 1939). 56 G. Leimbach, Phys. Zeit., 14, 447-457 (1913). H. Lowy, Phys. Zeit., 12, 1001- 1004 (1911); 20, 416-420 (1919). 868 GEOPHYSICAL WELL TESTING [Cuap. 11 F. Gas DETECTION In shallow holes, gas detection methods have been used to locate gas leaks in buried mains and pipes. A bar of small diameter is driven through the topsoil or pavement at closely spaced points, the sampling pipe shown in Fig. 11-36 is inserted, and the soil air is passed through a combustible gas detector, either by an aspirator or by open flow.”” The detector con- sists of a sampling system and a hot wire detecting circuit. The sampling system is essentially a gas chamber with two platinum filaments; one of these is exposed to the gas sample, and the other is sealed in air. The filaments form two branches of a Wheatstone bridge that becomes un- balanced when the temperature (and, therefore, the resistance of the gas Heiland Kesearch Corp. Fic. 11-36. Combustible gas detector with sampling tube and aspirator. filament) increases as the result of gas combustion. A_ triple-screen explosion check surrounds the filaments inside the gas chamber. By systematic reconnaissance and detail surveys it has been found possible to locate leaks correctly in 90 per cent of the surveys made. Gas surveys for the location of subsurface oil and gas accumulations are likewise made in shallow holes. These methods require detectors of much greater sensitivity, as described on pages 892-898. The double filament detector previously mentioned may be used in a deep well provided the hole is uncased and dry. During drilling, the gas content of drilling fluid 57 P. C. Dixon, Gas-Age Record, 76(24), 517 (Dec. 14, 1935). Crap. 11] GEOPHYSICAL WELL TESTING 869 can be logged continuously by connecting a gas detector to the discharge system in a suitable manner. G. PHOTOELECTRIC MEASUREMENTS When formation water is discharged into a well, the transparency of the drilling fluid increases. This change may be measured by a photoelectric detector. This unit contains a light source which projects a beam through a portion of the drilling mud to a photoelectric cell connected to a pre- amplifier. The resulting current fluctuations are further amplified and are recorded at the surface. In operation, the well is first conditioned with a light mud and then bailed out sufficiently to allow formation water to enter the hole.” H. Srpre-WaLut SAMPLER BULLETS These bullets are short cylindrical shells fastened to two retaming wires and are shot electrically into the sides of an open hole. The cores thus recovered are analyzed in the laboratory for porosity, permeability, salinity, and content in colloids and organic matter. This procedure is useful for correlation with electrical resistivity and porosity (self-potential) logs; but, strictly speaking, it is not a geophysical method. Details are given in the paper by E. G. Leonardon and D. C. McCann.” 58 Gillingham and Steward, loc. cit. 59 Petrol. Tech., 2(2) (May, 1939). 12 MISCELLANEOUS GEOPHYSICAL METHODS’ I. RADIOACTIVITY MEASUREMENTS A. GENERAL A ppLicaTIons OF radioactivity measurements in geophysical exploration are concerned with the location of concentrations of radioactive material and radioactive rocks. Other applications of radioactivity in geology, such as its possible contribution to the earth’s temperature and its use in the measurement of ages of rocks, are not discussed in this chapter. As a whole, radioactive substances are fairly uniformly distributed all over the earth and are present in the atmosphere, the water, and the solid earth. Local enrichments occur by association with certain rocks (mostly acidic igneous rocks), absorption in certain liquids (radon in water and oil), and confinement to predetermined transportation channels (faults, crevices, dikes, and the like). As is well known, radioactivity is a group of phenomena characteristic of substances with high atomic weight (except potassium and rubidium), of which the best-known examples are uranium, radium, and thorium. Probably tremendous energies were required to build up and hold these atoms together in the very early stages of the earth’s history. Since these conditions no longer prevail, they are now in a process of spontaneous decomposition. This process affects almost entirely the nucleus of the atom and is therefore unaffected by ordinary physical and chemical proc- esses such as heat, electrical and magnetic fields, and mechanical pressure. It can be changed.and produced, however, by bombardment of the nucleus with particles comparable with, or identical in velocity and nature to, those released by radioactive atoms. If it were possible to produce such nuclear changes by thermal energy, temperatures of the order of 10° degrees C. would be necessary (Nernst). While in chemical transforma- 1 The symbols in this chapter are the same as in Chapter 9, except where other- wise noted. 870 Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 871 tions and combinations the nuclear properties, such as mass and charge, remain unchanged, the radioactive decomposition of the nucleus alters its mass and charge and, therefore, alters the number of electrons in the outer orbit and usually its chemical properties.” Nuclear transformations in radioactive substances are accompanied by a release of energy in the form of corpuscular emission, heat, and other elec- tromagnetic radiation. The corpuscular emission may be positive elec- trically, analogous to “canal” rays. It is then referred to as alpha radia- tion. If it is negative (analogous to ‘“‘cathode” rays), it is called beta radiation. The electromagnetic radiation may be at the low-frequency end of the spectrum. Then it is noted as heat and will not be further discussed here. It may also be at the very high-frequency end of the spectrum. If so, it is more penetrating than X rays and is spoken of as gamma radiation. As the decomposition of radioactive products proceeds and new elements are formed, the character of these radiations changes. Some of them emit only alpha, others only beta and gamma, and still others all three radiations. Asa rule, their velocities (and for the gamma rays, their absorption) are characteristic for the element present. In other words, it is possible to identify radioactive elements by their radiation. Moreover, the radiation zntensity is found to be proportional to the quan- tity jof radioactive matter present. As a matter of fact, radioactivity measurements are virtually the only means of quantitative study of radio- active elements, since approach by chemical analysis is not only difficult but frequently impossible. Very schematically, the origin and relation of the various radiations is as follows: Within the nucleus there is probably a central nucleus (Ruther- ford) which carries virtually all the mass of the atom. Its number of positive charges is equal to the atomic order number (92 for U, 88 for Ra, 82 for lead, and so on). This central nucleus may be assumed to be sur- rounded by neutral helium satellites (possibly on internuclear quantum orbits) consisting of alpha particles with two electrons. When these elec- trons are lost, a doubly positive alpha particle is expelled with tremen- dous energy by repulsion from the central nucleus. The alpha particles have the greatest individual energy of any particle known to science. _ They are identical in mass for all types of radioactive elements emitting them and have velocities approaching 10,000 miles per second. Each radioactive substance produces alpha particles of characteristic speed. The shorter the period of transformation of a radioactive element, the greater is the velocity of the alpha particle. One gram of radium emits 2 This chemical change is most striking in the case of radium, which is a solid resembling barium, then changes into a chemically inert gas (radon) which in turn changes to a solid (Ra A). 872 MISCELLANEOUS GEOPHYSICAL METHODS [Cuap. 12 alpha particles at the rate of 3.6 x 10° per second. These particles are assumed to consist of two neutrons and two protrons (= H nucleus, mass = 1 unit,’ charge 1 unit positive). Therefore, when an alpha particle is released, the atom number decreases two units and the atomic weight four units. Despite their great velocities, alpha particles are readily stopped, the fastest (of thorium C’, v = 2 x 10° cm-sec.’) being absorbed by air of 8.62 cm thickness. An aluminum foil of 0.05 mm thickness is sufficient to keep the apha radiation out of an ionization chamber. In different elements the range of the apha particles is proportional to the square root of their atomic weights. Nevertheless, it is probably the most important radiation for the measurement of radioactivity, particularly in connection with emanation measurements. In a chamber of 10 cm side length, the ionizing effects of alpha, beta, and gamma radiations are as 10,000:100:1. When an alpha particle is released, two electrons become available and may be captured by the central nucleus or shot off as beta particles. Only one of the radioactive elements (radium C) emits beta particles simulta- neously with alpha particles. The others alternate, by themselves or in groups, between emitting alpha and beta particles. The release of a beta particle (charge — e) raises the atomic number by one unit, but it is not believed to affect the atomic weight (since m = 1/2000 unit). The ve- locity of beta rays may be as much as 99.8 per cent of light velocity. The harder components are very penetrating. An aluminum sheet of 0.5 mm thickness absorbs about one-half of the uranium beta rays. This radia- tion possesses much less energy than does the alpha radiation. More than half of the beta radiation incident on a metal plate is reflected and dis- persed; when it passes through matter, X rays are generated. Similar in nature is the emission of gamma (“‘penetrating’’) rays from the nucleus of the radioactive atom. Since gamma rays never occur by themselves but always in conjunction with alpha or beta radiations, it is probable that they are produced by internuclear orbit rearrangements following the emission of beta particles Some of the softer radiation possibly originates outside the nucleus by changes in the inner electron orbits. The wave length of gamma rays is of the order of 10° to 10” em. Their penetrating power is so great that 55 mm of aluminum or 12 mm of lead is required to reduce the gamma radiation of radium by one-half. Gamma rays produce a secondary beta radiation (whose pene- trating power is almost as great as that of the primary radiation) not only when they pass through other materials but also in their own atoms by releasing electrons from the inner extranuclear orbits. The absorption of 3 The unit of mass is 1/10 of the weight of the oxygen atom or approximately equal to the atomic weight of hydrogen. Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 873 gamma rays depends on the density of the substance traversed and is, therefore, usually expressed in terms of a ‘‘mass-absorption-coefficient.” It is seen that all radioactive radiations are analogous to tube discharges in high electrical fields. For instance, the energy of an alpha particle of Ra C’ is 8 million electron-volts. To produce electrons having the same velocity as the beta rays from Ra C’, 3 million volts would be required. To excite X rays of the frequency of gamma rays (10” to 10” cycles), a tube with 2-3 million volts would be necessary. Incidentally, the volt- ages employed in atom-smashing machines are of this magnitude. It was mentioned before that radium breaks up into one atom of (ionized) helium and another of radon (radium emanation). ‘This gas is of special importance in the technique of radioactivity measurements, since its alpha radiation and the quantity of radium in radioactive equilibrium with it can be readily determined. At normal pressure and temperature, 0.6 mm°* of radon weighing 6-10 ° grams is in equilibrium with 1 gram of Ra and is called a curie. For radioactivity tests of liquids, the Mache unit (1 M.U. = 4-10” curie units) is often used. This represents the amount of radon in one liter producing a “saturation” current* of 1-10° e.s.u., that is, 1 curie produces a saturation current of 2.5-10° e.s.u.’s. Com- pared with radon, the corresponding gases in the thorium and actinium series are unimportant because of their rapid decay. The half-value period of thoron is 54 seconds, that of actinon 3.9 seconds, and that of radon 3.82 days. B. Raproactiviry oF Rocks The radioactive elements and decay products, respectively, of uranium, thorium, actinium, rubidium, and potassium are, geologically, of very unequal distribution and importance. Rubidium and actinium are so rare that they may be disregarded completely. Although potassium occurs abundantly and often rather uniformly throughout geologic formations, its radiation is of low intensity and noticeable only where rocks contain potassium compounds in chemically recoverable quantities.” Of the two remaining radioactive elements, uranium is geologically more important. Its decomposition series contains a greater number of products of long life and strong radiation than does the thorium series. In the uranium series, radium and associated products are most readily detected in quan- tities much beyond the reach of the analytical chemist. It is customary to express the radioactivity of rocks in units of 10°” grams per gram (or 4See p. 880. 5G. Kirsch, Handb. Exper. Phys., 26(2), 32 (19381). 874 MISCELLANEOUS GEOPHYSICAL METHODS [CHap. 12. em’) of substance. The radioactivity of gases is generally characterized by the amount of Ra-emanation present. Table 79 gives a few representative figures for the radioactivities of soil, water, and air. Table 80 gives a number of average values for the radium and thorium contents of igneous and metamorphic rocks. The radioactivity of igneous rocks increases with an increase in SiOQe content. Basic rocks are generally less radioactive than are acidic rocks, although there are considerable regional and local variations. The average TABLE 79 REPRESENTATIVE FIGURES FOR THE RADIOACTIVITIES OF SOIL, WATER, AND AIR U R Th PE sa) TB (g/cm) (g/em’) (g/cm!) eee a Gone eat) aac Sout. ts wsder 7-10; 2.3-10°2 1.4-10-5 3-5 I (up to 20 I on ra- dium deposits) Water........ Ons ton O21 AOm torlOn)|\ ey Al ae eee Soiltains se. 2 10e13) |) \icua- eee Atmos. air... 10-6 | about 4 I on land 10-48 0-2 I at sea 2] = ions. TaBLE 80 AVERAGE RADIOACTIVITIES OF IGNEOUS ROCKS§® Ra Th R Th Roce (10-2 g/e-1)| (10° g/g) foes (10-1 g/e)| (10-*g/e~) Granites PRET | 20 Gabbro, norite 123 5.0 Quartz-porphyry 3.9 22 Diabase, dolerite 1.0 202 Syenite 2.4 17 Basalt 1.4 5.6 Diorite 16 9.9 Basalt, high values 5 15 Trachyte 3.0 17.9 Basalt, low values 0.5 + Porphyrite 2.8 15.4 Recent lavas 2-20 Gneiss 2.1 8.7 6 After Kirsch, loc. cit; A. Born, Lehrb. Geophys, p. 26. for acidic igneous rocks is about 3-10” g Ra g-; for basic rocks the average is about 1-10 ” and may reach 0.5- 10 ” for extremely basic con- stituents. Effusive rocks are more radioactive than are plutonic rocks; the radioactivity of metamorphic rocks is largely dependent on whether they are derived from igneous or sedimentary rocks. The average radioactivity of sediments is comparable to that of the basic igneous rocks, as shown in Table 81. This tabulation does not in- clude the (recent) deep-sea sediments which range from about 10 to 40-10” g Ra. Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 875 Radioactive mineral concentrations, not only in sedimentary but also in igneous rocks, may exceed their surroundings in radioactivity by 1000 to 100,000 times. Radioactive ores low in uranium oxide (from 0.3 to 0.5 per cent) have a radium content of the order of 10° g Rag ’, while those of high concentration (80 per cent uranium oxide) reach LOM keeRaigi. Of interest is the observation of Béhounek that the range of a radium deposit is fairly limited.* The pitchblende deposit in Joachimstal could not be detected at distances exceeding 1000 feet. It is further significant that the anomalies caused by local concentrations of radioactive products (faults, and the like, see below) may exceed those due to radioactive ores. Hence, radioactivity prospecting is more useful for detailing local concentrations than for finding radioactive ores by reconnaissance. Likewise, the delineation of rocks of different radioactivities, the separa- tion of sedimentary from igneous rocks, and similar applications based on the data given in Tables 80 and 81 will be possible only in exceptional cases because of interferences from such local concentrations. On the : TABLE 81 RADIOACTIVITIES OF SEDIMENTARY ROCKS’ Roce (10-8 g/e) Roce (10-1 g/e) Slates 3-8 Limestones 2-3 Quartzite 5 Gypsum ul Sandstones 2-4 Dolomites 8 7 Largely after Born, loc. cit. other hand, radioactivity methods can be quite useful for locating faults, fissures, and other openings along which radioactive products have been deposited or radioactive waters are circulating. Radon is readily absorbed by water much in the same manner as is carbon dioxide; it also has a tendency to accumulate in porous and shattered rocks, that is, in and near fractured and faulted zones. Experiments indicate that, to be radio- active, it is not necessary for such concentration channels to remain open; mineral dikes deposited in fault zones exhibit as much and sometimes more radioactivity than do open fracture zones. Organic matter appears to have a considerable affinity for radon. For instance, oil absorbs from 40-50 times as much radon as does water (at temperatures from 20°-60°C.). Certain spring sediments containing vegetable matter are more radioactive than are the rocks on which they are deposited. Deep-sea ooze rich in animal remains is more radioactive than are ordinary sediments. Radio- active ores are frequently found in beds rich in carbonaceous matter and 8 Fr. Béhounek, Phys. Zeit., 28, 333-342 (1927). 876 MISCELLANEOUS GEOPHYSICAL METHODS [CHap. 12 plant remains. In some localities carnotite is associated with fossil wood. An increased radioactivity of oil sands has been observed when the drill cores were tested by the alpha-ray method. However, gamma-ray logging has failed to indicate an increase in this radiation.” Radioactivities of minerals and rocks may be determined in the labora- tory in three ways: (1) by measuring the total radiation of a given weight of substance in an ionization chamber, (2) by preparing a solution and measuring the radiation of the radon contained in it, (3) by measuring the 48 Fig. 12-1. Measurement of rock radioactivity by emanation method (Mache and Bamberger, after Kirsch). (a) Motor, (b) shaking table, (c) drying tube, (d) ion trap, (e) dry-cell battery, (f) ionization chamber, (g) electroscope, (h) manometer, (¢) guard ring, (k) battery. penetrating (gamma) radiation of a given weight of substance with a Geiger counter or gamma-ray electroscope. Measurements under (1) are made as follows: The specimen is ground, dried, and weighed; and a definite amount (say 2 g) is placed in the tray of the ionization chamber of an electroscope whose scale value (volts per scale division) and normal dispersion rate are known. Assume the former to be 51 volts per scale division and the latter 3.5 millivolts per second. Then, if a 2-g specimen produces a total decay of 10 scale divisions in 8 minutes, 50 seconds, the reduced decay is 96.2 — 3.5 = 92.7 millivolts per second, and the decay per unit weight is proportional to 46.4-10° 9See p. 864. Crap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 877 volts:sec. The equivalent Ra content is obtained by comparison with a standard powder of identical thickness. If the standard weighs 3 g and produces a decay of 10 scale divisions in | minute, 8 seconds, the reduced decay is (750 — 3.5)/3 = 238.8-10 ° volts-sec ' per gram of substance. Assuming the standard to contain 2.5-10 °g Rag ’, the equivalent radium content of the specimen is (46.3/238.8) -2.5-10 > = 4.86.10 °g Rag’. In this method, therefore, the entire radiation (inclusive of that of thorium) is expressed by the equivalent Ra content. Measurement of the activity of the emanation under (2) gives the Ra content alone.” The specimen is ground up and about 3 g is fused with Per Cent 1002+ Xadon 60% 40% 102, 58 Time in hours 5 10 20 a 200 400 600 Fig. 12-2. Percentage of radon (developed in confined space) as a function of time sodium carbonate. The alkaline and basic solutions are kept separately in two sealed flasks for about twenty-five days. Within this time a maxi- mum amount of radon has developed and is in radioactive ‘‘equilibrium”’ with the Ra in the solution, since, from then on, as much radon is formed as in turn decomposes. For strongly radioactive solutions it is not necessary to wait twenty-five days, since the amount of radon present at any time may be calculated in relation to the maximum amount developed (see Fig. 12-2). One of the flasks is then placed on a shaking platform as shown in Fig. 12-1, and air is forced through the solution by a pump or aspirator whose intake connects to the ionization chamber outlet so that 10 Within the time required for this experiment, the short-lived thoron (54 sec. half-value time) has decayed completely. 878 MISCELLANEOUS GEOPHYSICAL METHODS [Cuap. 12 air is continuously circulated through the apparatus. The air-radon mix- ture then passes through a drying tube and ion trap, and then into the ionization chamber. The calculation of the equivalent radium content is done as follows, after a standard Ra solution has been treated in the same manner as the acid and alkaline solutions of the sample. If } g of rock was treated and the acid solution was left alone for 26 hours, 17.9 per cent of the maximum radon was formed. When the air-gas mixture was forced through the ionization chamber, the dispersion was 10 scale divisions in 2 minutes, 22 seconds. With a scale value of 51 volts and a normal dispersion of 3.5 millivolt-sec”’, this is 359 — 3.5 = 355.5-10°° volts-sec’ and, reduced to maximum emanation emission, 1985-10 ° volts-sec. The alkaline solution was kept more than thirty days and produced, in 8 minutes, 10 seconds, a decay of 10 scale divisions. This yields, with the above scale value and normal dispersion, 104 — 3.5 = 101.5-10 ° volts-sec. If this is added to the decay of the acid solution and reduced to 1 g of substance, the emanation yield of the specimen is proportional 4173-10 ° volts-sec ~. To obtain the equivalent Ra content, the specimen is now compared with a standard solution of, say, 1.19-10 ° g Ra, which, when treated in the same manner as the two sample solutions, produces a dispersion of 200- 10° volts-sec’. Hence, the specimen contained (1.19-10°°-4173)/200 or | 2.29.10 *g Rag. In method (3) the radium content of a specimen is determined from its penetrating radiation. The specimen is set up at a fixed distance from the electroscope, which may be protected from the alpha and beta rays by. a lead screen about + inch thick. The equivalent Ra content may be determined by comparison with a standard. The electroscope method is suitable only for strongly radioactive minerals and rocks; more universally applicable are Geiger counters (see section c). The specimen is placed at a fixed distance from the counter and its radiation is compared with that of a standard preparation. It is advantageous to surround the lower half of the counter (axis horizontal) with a heavy lead shield and to expose only the upper half of the counter tube” to the radiation so that the effective counter area is the section of the tube. The ionization of the gamma radiation from a milligram of Ra at a distance of 1 m amounts to about 120 impulses” per em’ per minute of the effective counter area, and it decreases with the square of the distance. C. INSTRUMENTS AND PROCEDURE IN RADIOACTIVITY EXPLORATION Radioactivity exploration may be carried out in two ways: (1) by taking soil samples and testing them in the laboratory for their radioactive prop- 11 A. K. Das and K. Wolcken, Phys. Zeit., 31, 186-139 (1930). 12 Thid. Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 879 erties, or (2) by determining the activity of formations in situ with portable ionization chambers. ' The first exploration procedure is identical with the methods described in the preceding section; the second group of procedures includes: (a) measurement of the entire radiation with open-bottom ioniza- tion chambers, (b) measurement of the soil-air emanation (mostly radon), and (c) measurement of the penetrating (gamma) radiation. (a) An open-boitom ionization chamber is illustrated in Fig. 12-3. It consists of a metal box with insulated dispersion rod and double-leaf electroscope. The latter is detachable (as in most other chamber-electro- scope combinations). The dispersion rod may be charged by a rubber rod or small dry-cell battery. The charge is so dimensioned that approxi- mately the same leaf deflection is ob- ; tained for every measurement. The instrument is first tested in a room where no radioactive substances are present, and the normal dispersion rate is determined. When the chamber is placed on the ground (after the surface vegetation and top soil have been cleared off), the radioactivity of the surface formations and soil air will ionize the air in the chamber (mostly by alpha radiation) and pro- duce a corresponding decay of the a : charge. In a calibrated” electroscope Fig. 12-3. Open-bottom ionization the potential difference corresponding chamber (schematic, after Hummel). toascale division is known, and there- % iCase 7 (2) electrometer) (a) ileal, ; ‘ insulator, (5) dispersion rod, (6) fore the decay or dispersion dH /dt may charging rod. be expressed in volts (or millivolts) per second. The latter is proportional to the conductivity of, and there- fore to the (saturation) current, J, in the chamber: dE I = C.—e.u.’s. - C 7 ests (12-1) Cis the capacity of the chamber (in centimeters) and dE/dt is the dis- persion (in statvolts = (volts/300) sec *). Current in amperes is obtained by multiplication by 1/9 X 10°” instead of by 1 /300. The current is proportional to the number (n) of ions formed, so that C dE mM 300-6. a’ coy 13 By a dry battery and precision high-resistance voltmeter. 880 MISCELLANEOUS GEOPHYSICAL METHODS [Cuap. 12 where e is the elementary quantum of electricity or 4.77-10°” e.s.u.’s, V the volume of the chamber in cm’, and dE/dt is in volts-sec’. In the calibration of the equipment, it is first necessary to be certain that saturation current is measured at all times. For this purpose the voltage loss dH/dt is determined for a given ionization and for various voltages. This gives the voltage range for which the current is constant. According to Kohlhoerster,* a 4-liter chamber has its saturation current for potentials exceeding 100 volts and a 2-liter chamber for potentials greater than 80 volts. If these measurements are to be made accurately, the air in the chamber must be completely dry. The same is required of the field observations. The volume V is determined by filling the chamber with water and weighing it. The capacity C may be obtained by cali- brating the chamber with a standard U;Os; preparation of known disper- sion, usually rated for 1 cm capacity and 1 cm’ radiating surface. To avoid infesting the chamber with radioactive decay products, a duplicate chamber may be tested instead. Another method of measuring the ca- pacity uses a U;Os preparation and an additional condenser of known capacity.” It has also been suggested that bore holes be used as ionization chambers and that a dispersion rod with electroscope be introduced after stationary conditions have been established.” (b) The activity of the soil-air emanation (mostly radon) may be meas- ured with the instrument shown in Fig. 12-4.” A hole several feet deep and about 1-14 inches in diameter is pounded down in the surface soil with a steel bar. A pipe having a bulge midway of its length to prevent the influx of atmospheric air is inserted in the hole. This pipe is con- nected to the intake of a suction pump whose outlet in turn connects by a rubber hose to the dryer and filter tube of the instrument. The soil air is thus forced under pressure through the chamber. After several strokes of the pump, the chamber is shut off by two cocks, and the measurement is made in the usual manner by observing the dispersion rate. An alcohol lamp is provided to obviate insulation difficulties resulting from moisture. It is necessary to sample the soil air always at the same depth; if possible, soils of nearly identical consistency should be used and observations should be taken within the same time interval after the air has been pumped into the chamber. 14 W. Kohlhoerster, Phys. Zeit., 27, 62 (1926); 31, 280-288 (1930). 15 Kohlhoerster, loc. cit.; V. F. Hess and A. Reitz, Phys. Zeit., 31, 284 (1930); R. A. Millikan and G. H. Cameron, Phys. Rev., 31, 921 (1928); and A. Lomakin, Inst. Pract. Geophys. Bull. 4, 151-156 (1928). 16 J. Koenigsberger, Zeit. Prakt. Geol., 34, 187-190 (1926). 17R, Ambronn, Phys. Zeit., 28(12), 444-446 (1927). A similar apparatus is de- scribed by A. Lomakin, op. ctt., 3, 124-136 (1927). Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 881 The type of emanometer described here may be applied also in meas- uring the activity of spring and soil waters (‘‘fontactometer”’). The water is placed in a bottle similar in construction to that shown on the shaking table of Fig. 12-1 and connected to a rubber bulb aspirator in such a manner that the air circulates continuously through the water and the ionization chamber. After the bottle has been shaken for about 1 or 2 minutes and the air been circulated for about the same time, the cocks of the chamber are closed and the electroscope is read in the usual manner. The dispersion is referred to a water volume of 1 liter, and the current is calculated from formula (12-1) (in e.s.u.’s); multiplication by 1000 gives the activity in Mache units.” (c) The penetrating radiation is measured with an ionization chamber which is shielded above and on its sides against the “softer” radiations.” Theoretically, a minimum thickness of 2.93 inches of (inactive) lead is required. Bogoiavlensky used a chamber with brass walls 3 mm thick and lead shields 10 mm thick. The bottom is closed off by filters of varying thicknesses, which make it possible to determine the absorption coefficient and therefore the wave length of the radiation. It is probable that the radiation inereases in hardness with the depth of the source. In Bogoiav- lensky’s apparatus the filters were each 2.5 mm thick, the volume was 1650 cm’, the capacity 0.725 cm, and the sensitivity 0.65 volts per divi- onE : Fig. 12-4. Ambronn on emanometer. (1) Ioniza- Another convenient method of measuring tion chamber, (2) elec- gamma radiation is the use of a Geiger counter. trometer, (3) microscope, In its most widely used form it consists of a ae (6). ee wire surrounded by a cylindrical metal tube, burner, (7) tripod. sealed in a glass tube in an atmosphere of argon under about 8 mm pressure. The cylinder is usually at a nega- tive potential with respect to the wire. Alpha and beta radiation is almost completely rejected by this type of counter. The gamma radiation, however, passes readily through the glass and liberates electrons 18 Since one M.U. produces a saturation current of 1/1000 e.s.u.’s, see p. 873. 19L. N. Bogoiavlensky and A. Lomakin, Zeit. Geophys., 3, 87-92 (1927); U. S. Bur. Mines, Circ. Inf. No. 6072, 1928; Inst. Pract. Geophys. Bull. 1, 57, 69, 184 (1925), 2, 184-195 (1926), 3, 87-112 (1927), 4, 165-178 (1928). 882 MISCELLANEOUS GEOPHYSICAL METHODS [Cuap. 12 from the metal. These electrons, in rushing toward the wire, form positive ions and new electrons, building up the current exponentially until the potential difference drops to a point where ionization by collison can no longer occur. Thence, the potential recovers at a rate depending on the time constant of the circuit (current ‘‘pulse’”’). The current is practically independent of the number of ions formed by the original electron;” the same is true for open counters sensitive to alpha particles and beta rays. The pulses may be counted by an arrangement shown in Fig. 12-5 in Counter Fic. 12-5. Geiger-Mueller tube, with amplifier and counter (after Neher). Ry = 5 meg.; R2 = 1 meg.; R; = Ry = Re = 5 meg.; Rs = } meg.; A; = 10,000 ohms; Rs = current-limiting resistor; Ry = 80,000 ohms; Ci = 50 uu f; C2 = 0.2 uf; Cs = 0.1 uf; Vi = 100 volts; V2 = 250 volts. The tube following the counter is a 57 and the output tube an 885. which the cathode, grid, and screen of the 57 tube and the wire of the counter are all at a high positive potential. When a rush of electrons passes the counter, the grid goes negative, blocking the current through the tube. Cathode, grid, and so forth, drop rapidly to ground potential. When the counter potential drops below the threshold value, the current ceases. The negative charges leak off the grid; and the tube, counter, and associated circuit are recovered for another count. The positive pulse thus produced gives rise to a gas discharge in the 885 tube, actuating the re- corder K and charging the condenser C, which, by its effect on the bias, stops the discharge in the tube. In a portable instrument, the high voltage batteries required for a counter are annoying and may be elimi- 20H. V. Neher, in J. Strong, Procedures in Experimental Physics, p. 259, Pren- tice-Hall, 1938). Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 883 nated by employing a V.T. oscillator, as shown in Fig. 12-6. Another feature of this apparatus 1s an output stage in which the pulses are rectified and passed into a tank circuit containing two 40-uf condensers and a counting-rate meter. The Geiger counter and first amplifier tube are carried in an extension handle connected to the remainder of the instru- ment, so that the ground radiation at any point may be readily in- vestigated. G =a a 10°-10°. 10" Fig. 12-6. Portable Geiger counter detector, with oscillator replacing high- voltage batteries (after Kaiser). C, = 500uy f; C. = 0.01 pf; Cs = 0.02 pf; Cy = 0.01 uf; Cs = 5 uf; Ce = 0.5 wf; Cr = 80 uf (midget electrolytic); N = G.E.-CD-1010-Cl neon lamp, 40 milliwatt; 71, T2 = telephone jacks; TR = output transformer, 1:6; GT = Geiger-Mueller tube; = 0-200 or 0-100 microammeters; Zi, Lo, Ls = oscil- lator air-core transformers. D. RESULTS AND INTERPRETATION OF RADIOACTIVITY MEASUREMENTS Measurements of radioactivity have been made (1) in wells, to indicate oil sands or formation boundaries; (2) underground, to locate concentra- tions of radioactive ores; (3) at the surface, to locate radioactive ores; (4) to locate radioactive springs; (5) to locate oil; (6) to map faults and contacts; and (7) to locate mineral veins. These measurements have been 884 MISCELLANEOUS GEOPHYSICAL METHODS [Cuap, 12 made by taking and testing samples, by open-bottom chambers, by ema- nometers, and by Geiger-Mueller counters. Results of radioactivity tests of ozl well samples have been published and discussed by Ambronn.” In one of these, an increase of activity (alpha radiation) immediately below an oil sand was noted. Because of the high absorbing power of oil for radon, a peak of alpha-ray activity should be expected to coincide with the sand. As stated in Chapter 11,” there is no noticeable increase in gamma radiation in oil sands. Underground observations of radioactivity for locating pitchblende seams have been re- ported by von dem Borne” and Béhounek.” At a distance of 6 meters from a pitchblende seam, the latter observed an activity of 200 M.U. (per liter air, taken from drill holes) while at 17 meters distance the activity had dropped to about 3 M.U., and at 29 meters to about 2 M.U. It is likely that measurements have been made at the surface for the same purpose in the more recently discovered radium districts of the Belgian Congo and in Canada, although definite reports have not been published. In balneological work, the activity of spring waters is tested in routine fashion. The rather extensive literature on the subject has been reviewed by Ambronn.” Location of oil by surface measurement of the penetrating radiation appears possible only on shallow deposits, according to Bogoiav- lensky and Lomakin, who published the results of some experimental pro- files across the Maikop field in Russia.” Above these shallow deposits, the radiation increased only 1 or 2 ions, the error being of the order of 0.2 ions. Radioactivity measurements seem best adapted to the location of faults, fissures, contacts, and some types of mineral veins. An increased activity (alpha radiation) was first observed by Ambronn on some faults near Blankenburg and above an iron ore vein near Ilfeld in the Harz Moun- tains.” Similar observations on fracture zones in the Black Forest (near Wildbad) were reported by Link and Schober.” Mueller” verified these results on mineralized veins and contact zones in the Siegerland. Some of his results are reproduced in Fig. 12-7. Patriciu surveyed a number of profiles across the Leine graben near Goettingen and located some hitherto unknown fault zones through an alluvial cover of 20 or 30 feet.” 21 Elements of Geophysics, p. 125, McGraw-Hill (1928). 22 P, 864 23 Habilitationsschrift (Breslau, 1905). 24 Loc. cit. 25 Elements of Geophysics, p. 131. 26 Op. cit., see p. 881. 27 Jahrb. Hall. Verb, 3(2), 21 (1921). 28 Gas und Wasserfach, 69, 225-28 (1926). 29 F, Mueller, Zeit. Geophys., 3(7), 330-36 (1927). 30 Preuss. Geol. L-A. N. F., 116 (1930); curves reproduced by J. N. Hummel, Handb. Exper. Phys., 25 (8), 537 (1930). Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 885 All the measurements discussed above were made by testing the activity of soil air. According to Lane, a fracture zone could be located in Michi- gan by an analysis of the radioactivity of well waters.” Measurements of the penetrating radiation are reported to show fault zones much less distinctly than do observations of the alpha radiation.” If a fault is covered by a layer of alluvium, the thickness of cover may be calculated” by assuming a linear source of concentration, Cy , located it 60 60 40 40 20 20 0 20 &@ 6 % 10 19 meters 0 20 40 CO 8 [00 20 meters = “y \< WG Fig. 12-7. Effect of mineralized dike and contact zone on radon content of soil air (after Mueller). in the boundary between impervious rock and cover. The gas ascends through the latter by diffusion. A maximum concentration, C,, , is located directly above the source and is given Cx Se (12-3) ah ‘ where d is the sampling depth and h the thickness of the cover. At a dis- tance x = 0.76 h from the maximum, the concentration (activity) has dropped to one-half its maximum value. Il. HYDROCARBON (SOIL AND GAS) ANALYSIS Methods for the detection of hydrocarbons in the surface soil are desig- nated in the literature either as geochemical or geophysical. Their classifi- 31 Science, 79, No. 2040, 34 (Feb., 1934). 32 Ambronn, op. cit., p. 131. 33 Koenigsberger, Zeit. Geophys., 4(2), 76-83 (1928). 886 MISCELLAN EOUS GEOPHYSICAL METHODS [Cuap. 12 cation as a chemical method results from the fact that certain characteristic chemical compounds are the object of separation and quantitative detec- tion, whereas their inclusion among geophysical methods is justified on the grounds that they constitute a definite prospecting method and that procedures of detection and analysis are physico-chemical if not entirely physical. A. Macroscopic AND Microscopic METHODS Soil analysis, in principle, is a refinement of the observation methods used for some time by the geologist in his quest for indications of sub- surface oil accumulations. Although these indications have always been present and some of them were well known to the ancients,” their signifi- cance was then not appreciated® and thus the vast subterranean reservoirs of oil and gas remained untapped up to the middle of the past century. Surface indications of oil deposits may be of a direct nature, for example, emanations of hydrocarbons in the form of oil seeps, gas exhalations, oil impregnations, asphalt deposits, earth wax (ozokerite), iridescent oil films, or gas bubbles in water. Indirect indications are: shows of characteristic inorganic compounds, such as hydrogen sulfide (“sour’ dirt, ‘“sour” waters), sulfur bacteria, brines, and bromine and iodine waters; character- istic vegetation; or signs of mechanical displacements associated with gas emanations, such as mud ‘‘voleanoes,’”’ gas mounds, sandstone dikes, brec- ciated clay dikes, and mud flows. Careful observations of these phe- nomena have led to considerable success in recent years. In the Gulf coast salt dome province alone, 75 out of 219 domes discovered prior to February, 1936, were located by the application of such ‘‘macroscopic” detection methods.” These methods have the disadvantage, however, that the indications are not always-unique. For instance, methane may be formed by decaying vegetation in swampy areas (and in coal and lignite seams), and salt 34 Examples: the oil seeps near Cuba in southwest New York, used by the Seneca Indians for medicinal purposes; the St. Quirinus spring on Tegern Lake in Bavaria, known to the monks since the fifteenth century; the asphalt deposits near the Dead Sea (Genesis 14: 10) and between Babylon and Nineveh; those at Apsheron, at Sakhalin, and in Trinidad (Sir Walter Raleigh, 1595); and, further, the ‘‘eternal fires’? of the Chimaira in Lycia, as described by Herodotus about 450 B.c., and the fires of Burma, Mesopotamia, and Baku, the latter well known from the fire-worship- ping Zoroastrians or Parsis. 35 Plutarch relates that the Macedonian warriors of Alexander the Great found, in 328 B.c., oil oozing out of the rock on the banks of the Oxus (Amu-Darya) River (near Bukhara, U.S.S.R.) and were much surprised since in the vicinity ‘‘no olive trees’’ were in evidence. % G. Sawtelle, A.A.P.G. Bull. 20 (6), 728 (June, 1936). Another table in the same article gives 35 out of 141 domes. Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 887 waters may originate from the leaching of salt deposits. Further, active seepages indicate a depletion of a subsurface reservoir and there is always doubt as to whether it is in its initial or final stages. Conversely, many of the best sealed (mid-continent, Paleozoic) fields have no seepage indica- tions at all. ven when they are accompanied by structural and strati- graphic observations, the use of surface indications has the obvious limita- tion that it is impossible to determine the length and direction of the supply channel from the visible surface concentrations. The surface evi- dence may be far removed from a commercial subsurface accumulation. In this respect, microscopic methods of observation and analysis are more TABLE 82 DETECTION OF HYDROCARBONS AND ASSOCIATED INORGANIC COMPOUNDS I. Macroscopic Methods A. Direct Indications 1. Oil seepages 2. Gas emanations 3. Asphalt deposits 4, Oil impregnations 5. Wax (ozokerite) B. Indirect Indications 1. Salt, sulfur 2. Bromine and iodine waters 3. Gas mounds 4. Mud volcanoes 5. Sandstone and clay-breccia dikes II. Microscopic Methods A. Gas Detection (volatile constituents in interstitial soil air) B. Soil Analysis for Occluded Constituents 1. Volatilizable fraction Hydrogen, methane, ethane, propane, butane 2. Extractable fraction Organic liquids, waxes, inorganic solids successful, since they locate not only concentrations on outcropping fissures, faults, and the like, but also accumulations resulting from the continuous flow by diffusion from the reservoir through the overlying strata. The pattern of indications furnished by the microscopic methods is therefore more uniform and has been found to show certain character- istic patterns in the fields thus far investigated. The micro methods fall into two groups: gas detection and soil analysis. In the former the concentration of gases in the interstitial soil air is deter- mined by withdrawing it from shallow holes and passing it through a portable detector, usually of the “hot wire” type. Soil-analysis methods, on the other hand, require an analysis of soil samples for their content of hydrocarbons and other significant constituents. There are two main pro- 888 MISCELLANEOUS GEOPHYSICAL METHODS [CHap. 12 cedures of soil analysis, one depending on a determination of the volatiliz- able components—usually methane, ethane (propane, butane), and hydro- gen—and the other involving the extraction of organic liquids and waxes and inorganic constituents. The quantities investigated are exceedingly small and, therefore, the accuracy requirements are high. The gaseous paraffin hydrocarbons occur in quantities ranging from 10 to 1000 parts per billion by weight. The solids (waxes) vary between several tens to several thousand parts per million by weight, and the liquid organics from 1000 to 10,000 parts per million by weight. Table 82 shows the relation of the more important gas and soil analysis methods, compared with the older macroscopic procedures. B. SIGNIFICANT HyDROCARBONS; OCCURRENCE The question arises as to which of the hydrocarbons present in and detachable from a subsurface oil concentration are the most significant, the most unique, and lend themselves most readily to observation and analysis. Crude oil is an exceedingly complex mixture of hydrocarbons; the composition varies greatly with locality and therefore with the original constitution of the organic source materials. It is assumed that they were converted by anaerobic fermentation of cellulose and proteins to methane and unsaturated fatty acids, probably in the presence of bacteria and salt water; these presumably changed by polymerization, aided by pressure and moderate temperatures, to the compounds of the naphthene series. D. C. Barton has assumed that the originally naphthenic petroleums were transformed to the more paraffinic types with time and depth.” According to Brooks,” “‘no petroleum has ever been found which contains unsaturated hydrocarbons of the olefine type, at least in the lighter fractions which can be separated by distillations without decomposition.” Table 83 illustrates schematically the relation and variety of the various groups of the natural hydrocarbons. In crude oil the aliphatic group is the most important; in coal and its derived products the aromatic com- pounds predominate, alhough they are also found in certain types of crudes. The saturated open-chain aliphatics (paraffins) are the chief con- stituents of the paraffin-base oils; the saturated closed-chain aliphatics (naphthenes) occur chiefly in the asphalt-base crudes. The monolefin and diolefin groups, both open- and closed-chain, are represented chiefly in cracked oils and artificial products. Table 84 gives the composition of some of the crude oils, (a) in the low-temperature range from 60°-95° C., 37 Problems of Petroleum Geology, p. 109 (1934). 38 Dunstan, A. E., et al. (eds.), Science of Petroleum, I, 48, Oxford (New York, 1938). (eueyued 04 euBynq) sult -0883 [81N}BvU :(euUBdepop 04 eusyzued) eur] -0863 ‘(auBy}e o1eqyuds ‘oueqyoul) Ay}sour ‘auez ses = [B1n4eu S[lO spnio ut S[IO0 BsBq | -UAq IB} [BOD S]IO | fs]Io oseq QUIOS /89z8]][I}SIP IB [BOD | silo Zuyeouqny | oneyyuds AjUO -ysqdsy | ‘[lo poyoeig pole PeyxoB1d_ -uyeleg mt) aug] 7k) ye) 040 079 eueynqgoja{D eusaiyqyAIgq | -Aqyaov[Ay}q | oueTAyng-u eusyng euefAX yt) euajAdoid-oJoAQ | auedoidopaA9 aueT[V eusfAT[y | eue[Adoig eusdolg 039 euen[oy, eua[A}a080 [DAD eua[Aqyao0]9£Q eueyya0[9AD wes eus[Ayooy | euelAqyq eueyy a oualeyyden auezueg eee coe oles Siete Paci) otterre aueyyeyl oI-te H"O0 9—-UZ H" b-U H" c-U H"0 Aird H"O t—-UZ HO bathed © h@) wy s+uz HO (sauayzydv jy) (sauarpey[Bo[d4p) | (seuey[eo[oAD) | (souvypeo[dAD) | (souerpeyTy) | (seuAHTY) (seusy[V) (sousyly) sauajpyjydvyy | sauazuag suyajorpoj9fi) surfajoo79fiD suyfoivdoj0hi) suyfaj01q sauaphiaop suyaio - sufoing | pe}einyesuy) pezeinyeg pe781nyesuy—) pe}8inyeg EES SESE SEES apg (ureyo paso]d) d1[04Q (ureyo uedo) o1[aA0v OLLVNOUY OILVHdITY SdNOUD NOPUVOOUGAH 'TVUOALVN AHL JO NOLLVTAY 8 HAV, 890 MISCELLANEOUS GEOPHYSICAL METHODS [Cuar. 12 which incidentally corresponds approximately to the temperature range at the depths where most of these oils are found, and (6) for the 250°-300° fraction. In natural gases, methane predominates, then follow ethane, propane, butane, and pentane. Contents generally decrease with molecular weight (Table 85). Other gases present may include oxygen, hydrogen, helium, nitrogen, and carbon dioxide. According to this table, therefore, the most significant hydrocarbons of the crudes and natural gases are the paraffins, TABLE 84 COMPOSITION OF SOME CRUDE OILS? 60°-90°C. 250°-300°C. TYPE ala ae nan || mnaaa. — - Paraf- | Naph- Aro- Paraf- | Naph- Aro- fins thenes | matics fins thenes | matics Grozny, high paraffin............... 72% | 25%|- 3% 61% | 22%) 17% Grozny, paraffin free................| 69 26 5 35 37 28 Texas; (Mexia)iic. i oo sacs eh eee 54 17 29 59 29 12 Oklahoma (Davenport)............. eae 21 5 |p 451 32 17 California (Huntington Beach)..... 65 31 7 |e 33 40 29 39 From G. Egloff, Reactions of Pure Hydrocarbons (Reinhold, 1937). TABLE 85 SOME U. S. GAS ANALYSES? PRES- MertnH-| Eru- | Pro- Bu- PrEN- FIetp 4 (ib. ber ANE ANE | PANE | TANE | TANE Sourcr Bi ince le ep zoe lie Sa te ol: |e Oklahoma City ..... D:| 265.) 8723.| 7.9.) 3.074) 1.8. .. | Separator gas Oklahoma City ..... D 16 | 60.4 | 16.9 | 13.8 | 6.3 | 2.6 | Oil gas Kettleman Hills....| F | 1672 | 85.6 | 8.2} 3.6] 1.6 | 1.0 | Free gas Kettleman Hills....| F | 52 | 51.2 | 18.5 | 15.1 | 9.7 | 5.5 | Gas in solution 40 A. R. Bowen, Science of Petroleum, op. cit., Vol. II, p. 1504. naphthenes, and aromatics. Of these, the aromatics take last place, are not present in all crudes, and would probably not be a unique indicator at the surface. Of the naphthenes and paraffins, the latter are unquestion- ably the more important for gas detection and soil analysis, since at least the first members of the series are more readily isolated and determined quantitatively. It must be remembered that the determination of the constituents in a hydrocarbon mixture is a very difficult and sometimes impossible pro- cedure. Bowen” refers to an analysis of one oil by eight Bureau of Standards investigators who isolated in one fraction twenty-three par- affinic, eighteen naphthenic, and six benzenoid hydrocarbons. This work 4 [bid. Cyap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 89] took several years. Even a qualitative approach of this sort would not be possible in soil analysis where hundreds of samples must be analyzed in the course of one survey. This narrows most of the analytical work down to the paraffin series whose first members, at least, can be isolated satisfactorily. From butane upward, however, isolation by fractional dis- tillation is difficult because the number of isomers of different boiling and melting points increases considerably toward the end of the series. In one phase of soil analysis (for liquid and solid ‘‘pseudo’’-hydrocarbons) isola- tion is not attempted, and these constituents are determined collectively o° 100° +200° C Temperature Gaseous ™ Molecular Wx NS Molecuter Weight #0 60 90 120 180 Fig. 12-8. Melting points, boiling points, and molecular weights of some of the paraffin hydrocarbons. by extraction with certain solvents. In the “gas method,” using the hot-wire type of detector, no differentiation in the type of combustible hydrocarbon molecule is made. Fig. 12-8 shows the variation of the melting points, boiling points, and molecular weights for the first members of the paraffin series up to decane and inclusive of hydrogen. The variation of the molecular weight is linear; that of the boiling point, being a function of the molecular weight, is regular but not linear; and that of the melting point is irregular, particu- larly at the beginning of the series. At ordinary temperature and pressure, methane, ethane, propane, and butane are gaseous. The differences in 892 MISCELLANEOUS GEOPHYSICAL METHODS [Cuap. 12 melting and boiling points of the earlier members in the paraffin series are utilized for their isolation by low-temperature fractionation, as shown below. C. Gas-DEtTEcTION METHODS Gas-detection methods are aimed at the measurement of the content of combustible gases of the interstitial soil air near the surface. For this purpose, portable detectors of the hot-filament type may be employed. Samples of the soil are not taken. In these detectors no differentiation 10 20 Ohms 4.5 Ohms 6 50 bab ; 4 5 Ohms p | Calv. ts Pr Wire NH ¥ 3 American Askania Corp. Fig. 12-9. Original Laubmeyer gas apparatus. between ethane and methane is made; the effective amount of ethane depends somewhat on the technique of evacuation of the drill hole (because of the different densities and diffusion rates of ethane and methane). The air is sampled from shallow holes. These are drilled to a depth of about five feet, and are then sealed off with a lid provided with two concentric cylinders of large radius and a piece of tubing ending in a stop cock.” The hole is left alone for twelve to twenty-four hours before the air is pumped into the combustion chamber, shown in Fig. 12-9. Because of their natural agitation, the gas molecules in this chamber come into contact with 42 Tllustration in G. Laubmeyer, Petroleum, 29(18), May 3, 1933. Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 893 the heated platinum filament and are burned with the oxygen of the air, thereby raising the temperature of the platinum filament which in turn increases its resistance. To attain sufficient sensitivity, the measurements must be made with the gas mixture at rest, and the current must be turned on after the gas has been introduced into the chamber Hence, a ballistic galvanometer is best suited for the purpose. The instrument is calibrated by a mixture of air and methane and is said to be sensitive to one part in 10 million. However, at the smaller dilutions the sensitivity drops rapidly. For instance, in one of the original Laubmeyer instruments, the deflection was 2.8 scale divisions for a dilution of 1:10°, and 2.0 scale divisions for a American Askania Corp. Fig. 12-10. Graf-Askania double-chamber combustible gas detector. dilution of 1:10’. The measurements are made by comparing the reaction of the galvanometer in an empty combustion chamber with that in one filled with the gas-air mixture. Difficulties arise from the fact that the voltage of the battery supplying the filament current cannot be kept suffi- ciently constant. This is avoided in the double-chamber instrument shown in Fig. 12-10 in which the two combustion chambers are arranged in opposite arms of a bridge circuit, much in the same manner as in the regular double-filament combustible gas detector (see Fig. 11-35). The zero instrument is a Zeiss loop galvanometer which may be used also for photographic recording. The bridge is first balanced for air in both chambers, and the bridge 43 A. Graf, Oel und Kohle, 11(36), 644-648 (Sept. 22, 1935). 894 MISCELLANEOUS GEOPHYSICAL METHODS [CHap. 12 current is fixed for the desired ignition temperature of the wire. Then the sample is introduced into one chamber and the (ballistic) galvanometer deflection is observed. A mixture of gases may be analyzed by raising or lowering, in steps, the temperature of the wire, that is, by changing the bridge current. This has been demonstrated successfully for mixtures of methane, carbon monoxide, and hydrogen; but it would be difficult to accomplish it for a mixture of methane and ethane. Nevertheless, the same apparatus is usable for a separate quantitative analysis of air- methane and air-ethane mixtures if the ethane and methane have been separated from each other by some other means (such as low temperature fractionation, see page 900). Fig. 12-11a. Gas indications (methane-ethane) measured with Laubmeyer apparatus on Pierce Junction Salt Dome. (N. Gella). In its application as described, the bridge apparatus proposed by Graf measures the content of combustible gases in the same manner as the Laub- meyer instrument, without differentiation between methane and ethane. Fig. 12-11a shows the results obtained with a combustible gas detector on the Pierce Junction salt dome near Houston, Texas, in units of galvanom- eter scale deflections. The anomalies are most pronounced on the flanks, are unsymmetrical, and are almost zero above the top of the dome. Another type of gas detector“ measures the amount of carbon dioxide liberated upon the combustion of the gaseous hydrocarbons pumped from a well into the apparatus. Again, no differentiation is made between methane, ethane, and heavier hydrocarbons. The hydrocarbons are 44V. A. Sokolov, Neftianoe Hoziaistvo, 27(5), 28-34 (May, 1935). Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 895 burned, in the presence of (purified) air (or oxygen), to water and carbon dioxide. The volume of the latter and, therefore, the reduction of the original volume bears a definite relation to each other if the number of hydrocarbons present and their molecular formulas are known. This pro- cedure (combustion and volumetric carbon dioxide determination) is also widely used in those soil-analysis methods in which gaseous members of the paraffin series are measured. SS | Leaeg I Pia. 12-11b. Apparatus for measuring volume contraetion in the combustion of hydrocarbons (partly after Sokolov). TEN S. ‘es 45 ‘. The combustion of hydrocarbon gases” of the molecular formula CyHonpox (where n is the number of carbon atoms and k may vary from —3 to +1) is governed by the relation 3n + k CrhHonjox + ey — n-CO, + (n + k)H.O, (12-4) so that ope od, CON an aban dea a alae) 1 (O85) with V as the original volume, AV as volume reduction due to combustion, and O2 and CO, representing the volumes of these gases. For the mem- bers of the paraffin series, k = | and n takes values from 0 to 4, since soil 45 And of CO, CO», Oo, and He, according to L. M. Dennis, Gas Analysis, Chapter xi. 896 MISCELLANEOUS GEOPHYSICAL METHODS [CHap. 12 analysis is concerned only with the members from hydrogen to butane. With k = 1, eqs. (12-4) and (12-5) take the form Cura = 10; = n00; 4a 4 RO and (12-6) Gp ey CO, = nV, Ay See so that, for methane, CH, + 20. = CO2 + 2H,0, and, for ethane, CoH, + $O2 = 2COe + 3H20, and similarly for the other paraffin hydro- carbons (see Table 86). TABLE 86 COMBUSTION OF PARAFFIN HYDROCARBONS CoMBUSTION EQUATION CONTRACTION IN HC Vo.LuME UNITS HYDROCARBON with CO: absorp- |without CO: absorption HC +Oxygen= COz + Water tion = HC vol. = HC vol. + Oc: vol. + O2 vol. — COs: vol. Methane CH, 2 1 2 3 2 Ethane CoH.6 3.5 2, 3 4.5 285 Propane C3Hs 5 3 4 6 3 Butane C,H |)""625 4 5 leo 3.5 ] II III IV (I + II) (I + II — III) The volume contraction may be measured by an apparatus of the type illustrated in Fig. 12—-11b, fashioned after the Burrell methane indicator and consisting of a combustion bulb, B, connected through an equalizing vessel, A, with a capillary and compensator, C. The latter is provided to obviate changes in reading due to changes in volume resulting from variation of temperature. The gas is introduced through the bubbling tubes and burned by heating the platinum filament. The corresponding volume contraction follows from readings of the capillary before and after combustion. The sensitivity of the apparatus can be increased by using, in place of water, potassium hydroxide, which has the property of ab- sorbing the carbon dioxide and which, therefore, raises the contraction, as shown in Table 86. If methane alone is present, its quantity follows directly from the amount of carbon dioxide developed and, therefore, from the contraction. However, admixtures of heavier hydrocarbons will con- tribute proportionately greater amounts of contraction, since the volumes of carbon dioxide are equal to the numbers of carbon atoms. This type of apparatus, like the second Sokolov field instrument to be described next, Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 897 does not differentiate between the hydrocarbons contained in the soil air and gives greater indications for the heavier constituents. Difficulties experienced with instability of the capillary induced Sokolov to design another combustion instrument, illustrated in Fig. 12-12. Its action is based on a determination of the amount of air which must be burned to liberate a minimum detectable volume of carbon dioxide. De- tection is made by the turbidity produced by the passage of the gas mixture through a barium hydroxide solution after combustion. A carbon dioxide content of about 0.03 per cent is required to cause turbidity. The corresponding volume of air may be read on a burette and is called the apparatus constant C. If air containing hydrocarbons is then burned and carbon dioxide is liberated, and if V is the volume of air required to Fic. 12-12. Portable (combustion-absorption) gas detector (after Sokolov). (a) Caustic potash tubes for removal of carbon-dioxide; (b) burette; (c) combustion tube; (d) absorption capillary; (/) leveling flask. start turbidity, then the content of carbon dioxide in percentage is 0.03 <* C/V. The smaller the hydrocarbon content, the greater there- fore is the volume required to cause turbidity. Hence, it is a virtue of this apparatus that the readings increase as the hydrocarbon content decreases. It is obvious that the air must be well cleaned of carbon dioxide before being injected into the apparatus. For this purpose the two bubble tubes a filled with caustic potash are provided. In applica- tion, the soil air is first passed through these tubes, and through the com- bustion chamber c (cold filament), the turbidity capillary d (constructed like the Hankus type of Orsat pipette), and the burette b. Then the capillary pipette d is filled from a jar with (N/10) Ba(OH)- solution, the filament turned on, the stopcocks closed, and the burette read. As soon as turbidity appears, the burette is read again, the filament turned off, and the capillary tube washed. The apparatus is calibrated by known volumes of CO, or CH, and is reported to be accurate to 1- 10° to 1-10. 898 MISCELLANEOUS GEOPHYSICAL METHODS [Crrap. 12 Sokolov also developed an apparatus for the separate determination of methane and heavier hydrocarbons by low-temperature fractionation, com- bustion with air, and volumetric determination of the carbon dioxide thus formed. This procedure is very similar to that applied in soil analysis and will be discussed in section D. An adaptation of the mass spectrograph to gas and soil analysis was recently proposed by H. Hoover, Jr., und H. Washburn.” The mass spectrograph is an electron gun for determining the mass of positive ions (canal rays) by deflection in a combined electrical and magnetic field. It consists of an ionization chamber in which gas molecules are bombarded by electrons. The positive ions thus formed pass through a small slit, are accelerated to a high velocity by a potential of several hundred to a thou- sand volts, and then pass through another slit into a semicircular evacuated tube placed in a magnetic field. At the end of the tube is a slit through which only ions of a predetermined radius of path curvature can pass. Behind the slit is a collector for measuring the number of arriving ions. The ion current is stepped up by an amplifier and recorded as a propor- tionate plate current by an oscillograph galvanometer. If the magnetic field H is held constant, the only quantity determining the radius of curvature r of the ion path is the accelerating voltage E, since for a given ion m/e = 7 H’/2E. A mixture of gases can therefore be analyzed by slowly varying the accelerating voltage so that ions with various masses are admitted successively by the exit slit, where their number is recorded. It is claimed that an accuracy of 0.2 parts per billion by weight is readily obtainable and that an analysis for the first members of the paraffin series in a gas mixture takes only a few minutes. Other methods of gas analysis which have been proposed include: (1) infrared absorption spectroscopy, (2) Ramann effect spectrography, and (3) low-voltage excitation and observation of resonance radiation. Although some of these methods may also be applicable to laboratory pro- cedure, none of them has found, as yet, practicable application in gas and soil analysis work. D. Som ANALYSIS As the name indicates, soil analysis differs from gas detection in that soil samples and not gas samples are analyzed. By breaking down the mineral grains mechanically and, if necessary, chemically, it is possible to obtain access to the entrained and occluded hydrocarbon constituents in- stead of depending solely on the interstitial air. Otherwise, in some phases 46 Loc. cit. 47 A.I.M.E. Tech. Publ. No. 1205, May, 1940. Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 899 of the work, the analytical procedures are similar if not actually alike. For instance, for an analytical determination of methane and ethane, it makes no difference whether the sample introduced into the apparatus is pumped out of the ground or is obtained by boiling a soil sample with water and solvents. While such analytical procedures in which the volatilizable frac- tion is determined are therefore equivalent to gas-analytical methods (see Table 82), there are other soil-analysis methods relying on the fractions which are extractable by solvents (so-called liquid pseudo-hydrocarbons and soil waxes). For an analysis of the volatilizable components—hydrogen, methane, ethane (plus propane and butane if present)—soil samples are taken usually by hand augers or light machine drills at depths varying from 5 to 15 feet. Where practicable, they should be secured below the ground-water level or below the surface-weathered layer. Contact with any oil- or greasc- contaminated soil, vicinity of pipe lines or roads, and the like, must, of course, be avoided. Duplicate samples are usually taken at each location and are shipped to the laboratory in mason jars. They are then freed of moisture, and definite quantities are weighed out and transferred to a degassing apparatus. Some companies liberate the occluded gases from pulverized specimens at fairly high temperatures. Others prefer to boil them off from an aqueous solution to which, if necessary, certain solvents may be added to accelerate the degassing process. After the gas has been driven out of the soil sample, it is passed to an analytical apparatus consisting essentially of low-temperature condensa- tion, combustion, and pressure-measuring components Descriptions and illustrations of such apparatus or procedures, respectively, have been given by V. A. Sokolov,” L. Horvitz,” E. E. Rosaire,” and D. H. Stormont.” - The diagram of Fig. 12-13 is a simplified scheme incorporating the more important features of these descriptions. The pressure in the component parts may be indicated by a compression manometer of the Arago-McLeod type, as shown, or by some other low-pressure gauge. The vacuum is generally produced by rotary Gaede or Cenco pumps working in conjunc- tion with a mercury diffusion pump. More than the two condensers shown in the scheme may be employed to increase the number of fractionation components. To produce low temperatures, liquid oxygen (— 183° C.) or liquid nitrogen (—196° C.) is used. The number of purification stages is subject to varia- 48.V. A. Sokolov, loc. cit. 49. Horvitz, Geophysics, 4(3), 212 (1939). 50K. E. Rosaire, Handbook of Geochemical Prospecting, fig. 4, p. 20, Subterrex (Houston, 1939). 51 1). H. Stormont, Oil and Gas J., 53 (Sept. 14, 1939). 900 MISCELLANEOUS GEOPHYSICAL METHODS [CHap. 12 tion. Additional purifiers of solid caustic potash and absorption tubes with sulfuric acid may be added to take out unsaturates and aromatics. In operation, the entire apparatus is evacuated, the Dewar flask containing the liquid air or nitrogen is moved up to the condenser C,, and the gas sample is admitted at a. As the sample passes through C,, ethane and the heaviest hydrocarbons are retained and the remaining noncondensable fraction (methane and hydrogen) are allowed to pass through C2 into the combustion tube 7’. Upon isolation from the rest of the apparatus, hydrogen and methane are burned with the oxygen of the air to carbon dioxide and water, which are frozen out in condenser C,. The remainder of the air is then pumped out, the Dewar flask is withdrawn from C2 , and readings are taken on the compression manometer, M, at various temperatures. This allows calcu- Fic. 12-13. Scheme of laboratory apparatus for gas and soil analysis (partly after Sokolov). (a) Inlet from degassing apparatus; (V) vacuum; (C) condensers; (M) manomettr; (D) Dewar flask; (T) combustion bulb. lation of the partial pressures and, therefore, of the relative amounts of water vapor and carbon dioxide. Assuming that the volume of the CO: formed upon combustion equals that of the methane, the content of the latter in terms of volume or weight of the sample can be calculated. The hydrogen content follows” (in approximation) from the excess of water over that to be expected in accordance with eq. (12-6). After condenser C, , manometer M, and combustion tube T have been evacuated, they may be used in the described manner for the determination of the heavy fraction retained in C;, which may be passed over into 7’ upon warming of C, ; its combustion products may be condensed as before in C2. In practice, it may be necessary to deviate from this simple procedure to increase the efficiency of combustion in this fraction and to narrow down the number of hydrocarbons in one fraction by additional condensers and smaller steps in the distillation temperatures. With increasing molecular weight of the 52 Horvitz, op. cit., p. 212. Cnap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 901 constituents, the difficulties of isolation increase because of isomerism. Even for a mixture of normal homologues of one series, the calculation of the constituents from the carbon dioxide and water formed in the com- bustion is difficult if their number is greater than two.” The second group of soil-analysis methods (see Table 82) is concerned with the determination of extractable liquids and organic and inorganic solids. Since these occur in proportionately larger quantities than the gaseous hydrocarbons, this determination is much easier and requires less complicated apparatus. The so-called “liquid hydrocarbons” and ‘“‘soil waxes’”’ are not members of the paraffin series, as has been stated in some articles, but are probably more or less complex fatty acids. They may be extracted by a variety of solvents, such as carbon tetrachloride, chloro- form, ether, benzene, and so forth. Since these liquid organics and soil waxes are found in their greatest concentration at the immediate surface, the samples are taken (at undisturbed locations) with the grass roots and are air dried. Definite quantities are weighed out and placed in an ex- traction apparatus. The Soxhlet type or a modified form of the Bailey- Walker apparatus, or some other form of extractor, preferably permitting continuous operation, is suitable. The liquid containing the waxes, and the like, is then placed in a dis- tillation apparatus; the solvent is distilled off through a condenser; and the residue, in liquid or semisolid form, is determined by weighing. The range encountered in soil analysis (from 0.01 to 1 per cent by weight) is quite within the reach of ordinary accurate analytical procedure and there- fore requires no special apparatus. An extraction method used in con- junction with semiquantitative colorimetric analysis is briefly mentioned by Rosaire.* While the soil wax samples are taken at the immediate surface (depth 3 inch), the specimens for colorimetric analysis are collected at the depth of supposedly greatest bacterial action (about 6 inches). Naturally, any topsoil samples must be taken.at locations undisturbed by wind or water erosion, agriculture, and so on. Inorganic constituents, likewise determined by extraction, include halides, sulfates, and carbonates; more rarely there are bromides, iodides, bicarbonates, and the like. Inasmuch as some of these constituents may also be determined by their physical (for example, electrical resistivity) expression, it is seen that a close relation must exist between results ob- tainable by certain soil analysis and geophysical (resistivity, Eltran, and similar) methods. 83 7,, M. Dennis, Gas Analysis, Chapter XII (Macmillan, 1929). On. cit., p- 10: 902 MISCELLANEOUS GEOPHYSICAL METHODS [CHar. 12 EE. INTERPRETATION AND RESULTS OF GAS AND SoIL ANALYSIS Gas and soil analysis in its present form is of comparatively recent development. There is still some dispute over its merits. Divergent opinions have been expressed regarding the type of organic compounds to be considered significant and the relation of their surface distribution to subsurface accumulations of oil and gas. More information is needed, particularly about the variation of organic and inorganic constituents with depth in wells, and on known fields. In any event, whatever interpreta- tion procedure is developed will not be the equivalent in physical and mathematical rigorousness to procedures currently employed in other geo- physical methods. The fundamental problem is, in principle, no different from that which faced the surface geologist a number of years ago, namely, that of locating subsurface oil and gas accumulations from the surface distribution of seeps. Factors which have made possible an advance in his interpretation methods are: (1) the,\greater areal completeness of sampling points and greater independence of random indications; (2) a segregation of the surface materials by physico-chemical analysis, in regard to geologic significance; (3) information on their variation with depth, by the analysis of well samples; and (4) data on geologic structure, by simulta- neous application of other geophysical methods to a given problem. Any attempt to deduce from the surface or near-surface accumulations of organic products the existence, location, or depth of a subsurface oil deposit must, of necessity, involve some definite assumption regarding the mechanism of their migration. Various ideas have been advanced on the basis of observed horizontal and vertical distribution and_ theoretical possibilities. What little data have been released on the variation in organic and inor- ganic constituents at the surface and in wells suggests a picture indicated schematically in Fig. 12-14. Above an oil deposit, the heavier gaseous hydrocarbons of the paraffin series show the most significant indications; they appear to be the most reliable indicator of subsurface oil deposits, since they are not known to be associated with near-surface decomposition of organic materials. The heavy hydrocarbon content (ethane, propane, and the like) of rocks overlying an oil deposit decreases toward the sur- face, although that decrease is far less regular than the scheme suggests and varies with the permeability and related characteristics of the indi- vidual formations. Methane appears to be more irregular in its vertical distribution, since decomposition processes within formations tend to be superimposed on the regular decrease away from the deposit. This is particularly true near the surface where anaerobic decomposition resulting from fermentation of vegetable matter (as in marshes, peat, lignite) may Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 903 produce large quantities of methane without relation to the underlying oil deposit (last curve in Fig. 12-14). The role played by hydrogen is still somewhat obscure. It appears to reach its maximum somewhere above and at the sides of an oil deposit ;” in some areas its surface distribution is conformable with that of methane and the heavier gaseous paraffin hydrocarbons.” In wells it may go some- what parallel with methane. The greatest concentrations of the heavy gaseous hydrocarbons and of methane may or may not coincide at the Sub- Surface Origin | Near-Surface Origin Paraffin Hydrocarbons “Pseudo”- Hydrocarbons Frhane, Chlorides, Calalysis,| Bacterial) Actinic Propane, Methane ttydragen Sulphares, ied aches Beto Butane ere, Yguid"W6\ “wer” wor oY z ay 4 a D7. SANWNGZ LOS 7 A A, VIS ti Ug ESTAS Usually in halos Fic. 12-14. Scheme showing variation of several organic and inorganic constituents in the subsurface section and near the surface above an oil deposit. surface and may occur directly above an oil deposit. More often, however, the heavier hydrocarbons and sometimes the methane have a maximum in the form of a halo surrounding the deposit. Possibilities of origin of such halos will be discussed below. The same appears to be true for some of the significant inorganic min- erals, such as chlorides and sulfates, and for the four secondary products of near-surface agents indicated on the right side of Fig. 12-14, namely, the so-called liquid and solid pseudohydrocarbons and oxidized and poly- 55 Personal communication from E. E. Rosaire. 5¢ Horvitz, loc. cit. 904 MISCELLANEOUS GEOPHYSICAL METHODS [Cuap. 12 merized paraffin hydrocarbons Most of these are assumed to be reaction products of organic materials and inorganic agents. In the case of the liquid and visco-solid pseudohydrocarbons, the organic materials are prob- ably furnished by surface vegetation. The solutions carrying the sub- stances (chlorides?) with which they enter into (catalytic?) reactions are assumed to come from below. Since the significant inorganics have their greatest concentration. usually in halo fashion, the pseudohydrocarbon reaction products are likewise arranged in the form of halos.” The depth at which the maximum amounts of these reaction products occur varies greatly. The maximum of the “liquid” hydrocarbons may be found several inches to several feet deep. One kind of “‘wax,” assumed to be caused largely by bacterial action, occurs in greatest concentration about six inches from the surface,” whereas another, resulting from oxida- tion and actinic effects, has its maximum at the immediate surface. The chemical nature of these pseudohydrocarbons has not been definitely deter- mined; they are assumed to be fatty acids. In the second case conditions are reversed. The organic materials are assumed to come from below and are changed near the surface not so much by catalytic reactions as by oxidation and polymerization. The product so formed is a heavy paraffin hydrocarbon” and occurs in much smaller quantities than do the pseudo- hydrocarbons. This very generalized scheme of the distribution of hydrocarbons and pseudohydrocarbons is subject to revision as more field data are accumu- lated and the chemical nature of the substances mapped becomes better known. It is but partially in accord with what should be expected theoretically from the laws controlling the migration of gases and liquids through homogeneous media. According to Pirson,” there are three ways in which gases emanating from a subsurface source may reach the surface: (1) by permeation, (2) by effusion, and (3) by diffusion. Permeation takes place by virtue of the porosity, or better, the per- meability of rocks; it is governed by d’Arcy’s law which states that the velocity of gas flow is proportional to the pressure gradient, multiplied by the ratio of permeability times density, divided by the viscosity of the gas. Limes, slates, and moist strata have litte permeability; therefore, migration by permeation is hardly to be expected across the bedding planes of stratified formations (except sands and sandstones) and is con- fined to loose overburden, faults, and fissures. Assuming, therefore, that a fracture zone of high permeability crosses a series of impermeable forma- 57 Rosaire, op. cit. p. 8. 58 bid. 59 ““Pseydohexane,’’ Horvitz, loc. cit. 60 Oil Weekly, Oct. 10, 1938. Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 905 tions covered by overburden of uniform permeability, the depth of the suboutcrop of the fault can be determined from the variation of the gas concentration along the surface. Formulas for the effect of a linear source of infinite strike extent have been derived by Antonov, Sokolov, and Pirson.” ‘Those of the first author were derived under the assumption of diffusion through the overburden, are equally valid for migration by per- meation, and are identical in form with those given by Koenigsberger for the effect of a source of radium emanation (eq. [12-3]). Very simple in application is a modification of Sokolov’s formulas for the gas concentra- tion C at a station with the distance x from a point directly above the center of a linear source of finite width and depth, h: Cc C= ee (12-7) where c is a constant involving permeability, pressure at the source, and viscosity of the gas, and ¢ the angle under which the edges of the source appear from the station. Effusion of gas takes place through very small capillaries whose diameter is less than the mean free path of the molecules; the rate of flow is propor- tional to the pressure differential and inversely proportional to the square root of the molecular weight of the gas involved. This phenomenon would account for the greater ease with which the lighter paraffin hydrocarbons (hydrogen and methane) are carried to the surface. However, the greater portion of the available gases may be expected to travel across the bedding planes of seemingly impervious rocks. by diffusion, that is, by penetration of gas molecules through the intermolec- ular space of solid substances. Diffusion of light gases (for example, helium) through metals is well known in vacuum technique; hence, a phenomenon observable over a short period of time must be expected to assume correspondingly larger proportions in the course of millions of years that elapsed since the oil deposits were laid down. The diffusion laws are similar in form to those controlling permeation, and they indicate that the velocity of flow is dependent on the diffused medium, the size of the diffusing molecules, and the pressure gradient. Gases diffuse readily through liquids; therefore, diffusion of gases through moist formations should take place with comparative ease. Since the lighter gases diffuse more readily, it is understandable why hydrogen (expected to be associated with gaseous hydrocarbons) occurs in comparatively small quantities, probably having made its escape much ahead of methane. In addition to migration of gases by permeation, effusion, and diffusion, 61 References in idem. 906 MISCELLANEOUS GEOPHYSICAL METHODS [Cuar. 12 it is likely that some of them have been carried in solution by circulat- ing waters along fissures, and the like, or up the dip in formations. Modifications may occur along the path because of adsorption on colloidal matter; they do occur near the surface in the aerated zone because of oxida- tion, polymerization, and actinic action. Besides, changes must be ex- pected from one formation to another when there is a difference in diffusion constants. If the process of diffusion of gases through formations without lateral variations were alone responsible for the distribution of hydrocarbons and related organics at the surface, their maximum concentration should in all cases occur directly above the source, since the migration may be as- sumed to take place from it in essentially a vertical direction. As a matter of fact, this has been found to be true in many cases, particularly above faults and fracture zones. It has also been claimed, particularly by the Russian investigators, that maximum concentrations of methane should be formed above gas fields, and those of the heavy hydrocarbons above oil fields. Further, it has been stated that in a given field where both oil and gas are found, the maximum methane concentration should occur over the highest point of a dome or monoclinal trap where the gas occurs, and the heavy hydrocarbons should occur above the oil accumulations at the flanks. The Russians’ own data do not bear out this conclusion in all cases. To begin with, natural gas is not pure methane but is frequently asso- ciated with ethane and other heavy hydrocarbons (Table 85). Con- versely, methane is often absorbed in and liberated by oil deposits. Hence, a clean-cut separation of oil and gas occurring in the same structural or stratigraphic trap appears hardly possible by surface measurements. Furthermore, the process of diffusion is not so simple as theoretically indicated, and the surface expression of subsurface hydrocarbon distribu- tion is modified considerably by lateral variations in the permeability and diffusion characteristics of the overlying formations. For this reason, the simple explanation given by Pirson,” that heavy hydrocarbon halos are due to the marginal arrangement of oil below the gas on the flanks of an anticlinal or domal trap does not appear tenable, besides being in dis- cord with the observation that in many cases production is found under the bare spot in the center of a halo and not under the halo itself. It is evident, therefore, that other causes besides uniform diffusion must be responsible for the halo formation or must at least interfere with the process of normal diffusion. The solution of the problem is rendered difficult because the published data frequently lack information about 62 Thid. Crap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 907 geologic structure and nature of hydrocarbons mapped; besides, there is confusion in some of the recent articles in regard to geologic significance of the earlier data on the subject. The claim is certainly unjustified that in regard to halos, different results are obtained by the free-gas analysis (using the Sokolov or Laubmeyer techniques) and the soil analysis (map- ping adsorbed and entrained constituents). Laubmeyer definitely states in his publication that a sharp drop above production was observed in the Oberg field and attempts to explain the phenomenon by the withdrawal of gas from the productive formations by the wells in the center of the field. A survey of the Nienhagen field® re- vealed a maximum gas concentration above the western part of the field, while the eastern portion shows nearly normal concentration. On the north side of the Wietze dome” the gas maximum is forced northward or away from the preductive zone, and the same trend is indicated by the gas measurements on the Pierce Junction dome (see Fig. 12-l1a). It may be argued that in the vicinity of salt domes, the indications are related to fracture zones; however, this still leaves it unexplained why the indications should be forced consistently outward and away from them. On the other hand, this argument shows the necessity for considering closely the geologic structure associated with a halo. It is evident that a halo around a salt dome is not directly comparable with a halo around production above a stratigraphic trap because in the former we deal with steeply dipping beds around an impervious core (unless production occurs above the dome) while in the latter any evidence of folding or faulting is absent. Mac- roscopic halos have been reported for several Gulf coast fields,” such as Goose Creek, Humble, and Sour Lake. The true halos, then, may be assumed to occur in regions of gentle folding and above stratigraphic traps. They have been variously ex- plained, the prevalent assumption being that some sort of clogging occurs near the center of the productive structure. McDermott” believes that because of the tendency of oil and gas to migrate to the highest point of a fold, monocline, or lenticular deposit, these become clogged first, the seal- ing action working its way down the dip. This clogging is not noticeable at the surface if subsequent folding has developed cracks in the caprock and thus provided an avenue of escape for the gases near the top. The surface effect is thus similar to that of a buried fault (lmear source). Rosaire,”’ on the other hand, assumes that such clogging occurs fairly near 63 G. Laubmeyer, unpublished reports. 64 Rosaire, Geophysics, III(2), 107 (March, 1938). 66 Geophysics, IV(3), 1-15 (July, 1939). 66 Handbook of Geochemical Prospecting, op. cit., p. 22. 908 MISCELLANEOUS GEOPHYSICAL METHODS [CHap. 12 the surface because of the action of ascending mineralized” solutions along minute fissures and cracks developed in the overlying formation by dif- ferential settling over a fold or lenticular deposit. He points out that surface formations above oil deposits are frequently indurated, due to WELLS ORY IN MAIN Pay SANO BUT PRO- OUCING FROM DEEPER “ HORIZON . WELLS DRY IN MAIN bet PAY SAND BUT PRO- OUCING FROM DEEPER HORIZON 2 EUREKA OIL FIELD HARRIS COUNTY, TEXAS SUBTERREX SOILANE FOR ETHANE + PROPANE dsewells COMPLETED BEFORE SOWAKE GURVEY @OOWELLS COMPLETED AFTER SOILANE SURVEY Sonreue INTERVAL = 2K CAI TOP-SOIL 260 90 FAULT FROM —SUB-SURFACE DATA a“ SUBTERREX SOILANE | FOR WAX 10 $00 vt LLS COMPLETED aries Somane SURVEY CONTOUR INTERVAL = 2x SCALE © 1000" 2000’ 3000° 4000’ 3000° MAY 1938 Fic. 12-15. Ethane and surface-wax halos in Eureka field (after Rosaire) silification and calcification, and that this has been verified by low drilling rates (“dome digging”), high seismic refraction speeds, erroneous dips in reflection shooting, and high resistivities mapped in Eltran surveys.” 87 McDermott (A.A.P.G. Bull., 24[5], 859-881 [May, 1940]) assumes that the mineral waters are carried upward by the gases escaping from oil deposits below. 63°F 817: Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 909 Since this induration works progressively outward from a point above the field, the mineralized solutions are diverted toward the edge of the field. This is in harmony with the halo arrangement of both characteristic min- erals (see Fig. 12-15) and pseudohydrocarbons, presumably formed by the reaction between these solutions (chlorides?) and organic materials, and with processes occurring near the surface. Methane, hydrogen, ethane, and the heavier paraffin hydrocarbons are diverted in the same manner by the near-surface “‘plug”’ into halo arrangement. The observations and interpretation of soil and gas analysis surveys may, therefore, be summarized thus: The maximum concentrations of (significant) hydrocarbons occur above the suboutcrop of fissures or high points of subsurface oil and gas traps except where clogging of the reservoir or near-surface forma- tions has diverted them. ‘This diversion is generally outward from the high- point, that is, in down-dip direction. Virtually all results published to date can be explained in this manner. Laubmeyer was first to measure gas concentrations (mostly methane) on the proved German fields of Oberg, Nienhagen, and Wietze, whose maxima, as pointed out before, were shifted outward, away from the centers of known production. Laub- meyer also found maxima (in both hydrocarbon and radioactivity curves) above the suboutcrop of faults. Graf likewise obtained a maximum near the suboutcrop of a fault in the Oberg field with a down-dip shift, and maxima with outward shift surrounding the Pierce Junction dome in Texas. Pirson observed maxima in ethane above fault outcrops in the Woodhull gas field in New York. Sokolov observed that the maxima in methane and heavy hydrocarbons were, in some cases, shifted away from the axis of the anticline of the Malgobek field in Russia. Although Antonov’s results appear to indicate a definite tendency to halo arrange- ment, the latter considers the maxima as being directly related to the suboutcrops of the gas formations and faults in this area. He claims to have obtained fairly good agreement between drilling data and calcula- tion, but details on the actual geologic situation are too meager in his article to decide his evidence for or against the halo theory. In the Ishimbaev field, however, the area of greatest concentration defi- nitely surrounds the productive area in halo fashion, as pointed out by Sokolov.” The same is true for the Turkiana and the Kala fields.” McDermott reports that in the Big Lake field (Reagan County, Texas) not only the significant heavy hydrocarbons, but also the pseudohydro- carbons and significant minerals show a maximum directly above the field, which is explained by the existence of a fissure zone in the axis of e20c: ct. 70 Located on the Apsheron Peninsula (east of Baku), the scene of extensive electrical and gravity work. 910 MISCELLANEOUS GEOPHYSICAL METHODS [Cuar. 12 the fold developed by 2x10 P% subsequent folding. In all other cases reported by McDermott (La Rosa field, Refugio County, Texas; Cedar Lake field, © Gaines County, Texas; Monu- Yj ment field near Hobbs, New Mexico; Riverside | 4/77 Hydrocarbons area, Nueces County, Texas; Atlanta area, Columbia County, Ar- kansas; Coles-Levee, Ca- nal, and Ten Section fields in Kern County, California; and the East Texas field, Fig. 12-16), the halo (in significant gases, pseudohydrocar- bons, and minerals) is associated with a pro- ducing area. Only halos are described by Rosaire for the Ramsey (Payne County, Oklahoma), Griffin (Gibson County, Indiana), Hastings (Bra- zoria County, Texas), Fig. 12-16. Variation of ethane, surface wax, liquid Lopez (south Texas) and pseudohydrocarbons, and mineralization near edge Eureka (Harris County of East Texas field (after McDermott). D] Texas) fields (see Fig. 12-15). Ill. VIBRATION RECORDING, DYNAMIC TESTING, AND STRAIN GAUGING The following section is concerned with various geophysical methods which find application in structural, transportation, and mining engineer- ing. Collectively, they constitute the major portion of the field of engi- neering seismology which has as its main objective the reduction (if not elimination) of the damage done to structures by earthquakes and indus- trial vibrations. Most fruitful in this field has been the recognition that Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 911 damage should be considered not in the light of static, but of dynamic, phenomena. Specifically, the damage depends on the frequency response of a structure and therefore on its interaction with the ground, whose re- sponse to carthquakes and industrial vibrations, in turn, is likewise a fune- tion of its frequency characteristics. Damage is therefore primarily a local phenomenon, depending individually on the design of the structure and the surface geologic conditions. It is the function of vibration- recording and dynamic-testing methods to determine the frequency re- sponse of both structure and ground and to devise means by which reso- nance between the two can be avoided. In both eases, the significant characteristics of ground and structure are natural frequency and damping. They may be determined by observa- tions of (1) free vibrations, and (2) foreed vibrations. In the first case, the ground or building is subjected to a static deflection and is released. From the free vibration that follows, natural frequency and damping may be calculated. Deflections leading to free vibrations may be due to natural causes, such as wind, or they may be produced at will by blasts, mechanical shocks, and so on. To obtain the vibration characteristics of buildings before construction, it is convenient to use models. Methods of measuring free vibrations are briefly referred to here as vibration recording. In dynamic investigations, the building or ground under test is set into forced oscillation by vibrators (also called oscillators or agitators) whose frequency is varied during the experiment. Thus the frequency (or dynamic) response of the structure is obtained, from which natural fre- quency and damping may be calculated. For proposed structures, similar tests are made on models before construction. Dynamic ground tests furnish the frequency response of the foundation and thus, indirectly, its bearing capacity and vibration absorption characteristics. Since the speeds of the sustained waves produced by a vibrator may be determined from measurements in various distances, it is possible to arrive at depths of formation members and their elastic moduli. For complex geologic sections whose geometric dimensions and elastic characteristics have been determined previously by other geophysical methods, it may be con- venient to supplement the 7n s¢tu work by model experiments, particularly if the natural setup is likely to be disturbed by later excavations. Strain gauging, discussed at the end of this section, is concerned with the measurement of displacements in structures and rocks under the in- fluence of natural or artificial loads, static or transient. Structural tests are made on bridges, road beds, dams, and the like, after completion, or on models. Strains in rocks are measured in connection with under- ground operations in transportation, hydraulic, and mining engineering. Closely related to this application is the observation of rock bursts and fault activity. 912 MISCELLANEOUS GEOPHYSICAL METHODS [CHap. 12 A. VIBRATION RECORDING (FREE VIBRATIONS) 1. Vibrations of buildings and other structures. Free vibrations occur in buildings and other structures (bridges, water tanks, dams) as a result of wind gusts, earthquakes, traffic vibrations, blasting, and other industrial activity. Observations of free vibrations usually have to depend on the random occurrence of such agencies; only when the structures are small (water tanks, bridge models) may the initial deflections be produced by pullbacks with predetermined load. Vibrations are recorded with vibro- graphs or seismographs of moderate magnification, equipped with mechani- cal or optical recorders. It is advantageous to make measurements on various portions of a structure in both horizontal and vertical directions, so that various vibration modes in the planes of symmetry and the varia- tion of amplitude with height may be obtained. When a multiplicity of records has to be secured simultaneously, electrical seismographs with central recording are preferred to mechanical instruments. In this work, moderate magnifications ranging from 200 to 1500 are sufficient; natural instrument periods vary from 1 to 3 seconds; damping should be nearly critical. Observations are arranged to yield natural frequencies and damping (in at least two directions) and variation of vibration amplitude with height. For buildings whose ratio of height to width is great, flexural vibrations are most important. In the opposite case, where the width is much greater than the height, flexure is unimportant and shear predominates. When the ratio of height to width is between 3 and 4, both kinds of vibrations will be encountered. Torsional vibrations may also occur. In addition to the fundamental, several harmonics are generally observed. If shear predominates,” the ratios of the translational and torsional fundamental periods to higher mode periods should be near 3, 5, and 7 (for a building on rigid foundation). When flexure predominates, the translational period ratios should be near 6.2, 17.5, 34.6, and so on. Observations on com- pleted buildings are of value in establishing a reference file for future use, particularly when such measurements have been made on buildings that have been through an earthquake. In this manner, the damage done may be correlated with the frequency response of both building and ground. Before construction is commenced, the natural frequency of a building may be calculated if it has a simple geometric form. It is more satisfac- tory, however, to determine the natural frequency on a model by a pull- back test (free vibration) or from the response on a shaking table (forced vibration). 2. Free ground vibrations. Free ground vibrations are produced by 1 U.S. Coast & Geod. Surv., Spec. Pub. No. 201, 51 (1936). Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 913 blasts, traffic, various industrial activities, earthquakes, wind, surf, and the like. They are largely responsible for the phenomenon known as seismic unrest. Since there are, at almost every locality, well-defined geologic formations that are capable of oscillation and impress their fre- quency characteristics on microseismic and earthquake records,” the action of the ground and its constituent parts may be considered like that of a seismograph and may be characterized by a single or by several natural frequencies and damping ratios. Harmonics of such frequencies, where recorded, are in the ratio of 1:3:5." The frequency characteristics of the ground determine its response to external impulses, this reaction being defined in seismology by the so-called “‘station factor.’’ The pres- ence of formation members capable of free oscillation accounts for the observation of identical predominant frequencies in the microseismic unrest in earthquake and in explosion records, and these usually agree with the resonance frequencies excited by vibrators. Statistical analyses of earthquake records have been made by various investigators to determine predominant ground frequencies. Examples are the investigations carried out recently by B. Gutenberg” as part of a U. S. Coast and Geodetic Survey earthquake research program in California. As stated before, the damage done by earthquakes and artificial vibra- tions depends (1) on the dynamic response of a given building or structure to the ground vibrations, and (2), although to a lesser extent, on the reaction of the ground to incoming earthquake waves. The frequencies of distant quakes are usually so low as to be completely out of resonance with the natural ground frequencies. Therefore, such quakes rarely do any damage;” besides, their amplitudes would probably be too small even if resonance did occur. Greater damage may be expected from near- quakes and industrial vibrations, since they have greater amplitudes and their frequency is likely closer to the predominant ground frequencies. In some instances it has been possible to correlate prevalent frequency with formation thickness, which is approximately equal to one-quarter of the transverse wave length. Hence, d % v/4fo where v is the velocity of the transverse waves and fy is the natural frequency of free-layer oscilla- tion. How earthquake damages to structures may be evaluated approxi- mately when natural frequencies and damping of ground and structure are known, will be discussed below. Related to the problem of recording free ground vibration is that of 72 R. Koehler, Nachr. Ges. Wiss. Goettingen, Math. Phys. Klasse 1, (2), 11-42 (1934). 73 Koehler, Zeit. Geophys., 6(2), 123-126 (1930). ™U.S. Coast & Geod. Surv., Spec. Bull. No. 201, 163-224 (1936). 75 Koehler, Nachr. Ges. Wiss. Goettingen, loc. cit. 914 MISCELLANEOUS GEOPHYSICAL METHODS [CuHap. 12 rock-burst investigation. Rock bursts are miniature earthquakes of the displacement type and result from the release of rock stresses. These stresses may be due to natural orogenic forces, that is, folding or faulting, or may be caused by the removal of rock material in underground mining operations. At times these rock bursts are of no small intensity; they have been recorded by seismic stations several hundred miles away. Continu- ous rock-burst records in areas subjected to faulting and mining may not only help in the interpretation of the records of distant earthquake stations, but may be expected to be helpful in predicting fault quakes, cave-ins, and roof failures. This subject is discussed further in the section on strain gauging (page 929). Statistical analyses of rock-burst records appear to indicate a triggering effect of variations in atmospheric pressure.” There may also be a parallelism with sun spot cycles and bodily tides. There- fore, the possibility of predicting earthquakes, at least those of the dis- placement type, is probably not so remote as some seismologists appear to believe. Most of the measurements of free ground vibrations published to date have been made with regular seismic station equipment. For proposed building sites, dam foundations, and the like, it is necessary to employ recording mechanical or electrical vibrographs. The vibration produced by traffic or industrial plants in the vicinity may be sufficient; otherwise, blasting will be required. However, it is much more satisfactory to use a vibrator and to record a complete response curve. In the interpretation of the field data much help may be obtained from an investigation of models of the surface formation.” If the actual geologic conditions have been duplicated with sufficient accuracy on the model (for instance, by securing data on the thicknesses and elastic characteristics of surface formations from refraction surveys), and if the elastic properties of the model material have been sealed down in keeping with dimensional analvsis, field data and model results will be in good agreement. B. Dynamic TESTING In various fields of material testing it has been recognized for some time that dynamic tests give better and more complete data on the properties of materials than do static tests. The limitations of static methods are obvious in the testing of soils in situ: with a given load, the area covered is small; the lateral and vertical compression ranges are limited; and the weight sizes that have to be used to obtain sufficient penetration become impracticable even for moderate depth ranges. On the other hand, a 76 C. Mainka, Forsch. & Fortschr., 14(28), 314-321 (1938). 77C. A. Heiland, A.I.M.E. Tech. Publ. No. 1054, Feb., 1939. Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 915 vibrator with revolving eccentric masses permits the forces to be stepped up considerably. With sensitive detectors, vertical and horizontal ranges extend to several hundred feet and, in some cases, to several thousand feet. Furthermore, the measurement of travel-time and amplitude-distance relations gives an opportunity to test formations not exposed at the surface. Vibrations recorded near a variable frequency vibrator indicate a number of parameters not obtainable by other means, such as natural frequency, damping, energy consumption, ground compaction, and phase shift between impressed force and ground vibrations. Vibrators may be applied in testing not only the ground but structures as well. As a matter of fact, vibrators were constructed first for use in structural engineering and for the dynamic investigation of bridges, trusses, framework, conveyors, skyscrapers, shaft houses, cranes, dams, and so on. Such tests were extended to include all kinds of conveyances such as ships, trucks, automobiles, locomotives, dirigibles, and airplanes. Inves- tigations of road beds and machine foundations, made in connection with structural tests, led quite naturally to their application in soil testing.” For some of these applications an agitator made of a bicycle wheel with a weight attached to its rim is quite satisfactory. This wheel is brought up to speed and allowed to run down. For more accurate work, it is better to apply a vibrator whose frequency is held constant, yet is adjustable in definite intervals. The usual construction employs two eccentrically loaded wheels or drums that are geared together and revolve in opposition. If the two cylinders are mounted side by side, the vertical components of their centrifugal forces will add and the horizontal components will cancel. By turning the entire assembly 90 degrees (so that the two cylinders are now above each other) the vertical components cancel and the horizontal components remain. For the agitation of structures, the vibrator is ap- plied in the latter position, since vibration damage to structures results generally from horizontal forces. In soil testing, the vibrator is laid flat on the ground (so that vertical forces are produced) and is weighed down with ballast. In some vibrators, four disks are arranged with their axes in the four principal horizontal directions. The disks are then geared to produce torsional forces. The total eccentric masses of vibrators range from a few ounces to several pounds and the radius arm from a few inches to about one foot. Centrif- ugal forces may thus be varied between several hundred and _ several thousand pounds. Some vibrators are so constructed that a given centrif- ugal force may be produced by a small mass on a large radius arm, or by a larger mass on asmaller arm. The simplest arrangement is to provide a 78 Koehler, Nachr. Ges. Wiss. Goettingen, loc. cit. 916 MISCELLANEOUS GEOPHYSICAL METHODS [Cuar. 12 number of tubular openings on the circumference of the vibrator drums into which cylindrical masses of various sizes can be fitted. A soil test vibrator must be capable of producing vertical forces up to 40 to 50 cycles (2400 to 3000 r.p.m.). The larger commercial vibrators weigh from a few hundred to 1000 pounds (without ballast) and are equipped with shunt- wound D.C. motors to permit accurate speed control. The smaller vibrat- ors are driven by gasoline engines or motors supplied from storage bat- teries; the more primitive models are merely brought up to speed manuaily and are allowed to run down. Undoubtedly, the greatest flexibility is obtained by a D.C. motor sup- plied from a gasoline-engine driven D.C. generator, in which case the oat Hetiland Research Corp. Fia. 12-17. Vibrator and recording truck. speed may be accurately controlled by varying the fields of both the generator and the motor. The frequency is adjusted by a tachometer and evaluated accurately by timing the vibration records. For the measure- ment of the phase shift between force and displacement it is convenient to provide an electrical impulse transmitter on one of the revolving drums. This will record the vibrator phase, together with the oscillations picked up by one or more vibration detectors. A vibrator with recording truck in the background is shown in Fig. 12-17. For certain applications it may be convenient to insert a wattmeter in the vibrator-motor circuit for the measurement of power consumption. As shown below, the power taken from the vibrator is at a maximum near the resonance point of the ground. Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 917 For testing models of buildings, bridges, dams, and the like, miniature vibrators or electromagnetic drivers are applied. If size permits, an en- tire model may be tested on a shaking table. Vibrations may be recorded with a variety of instruments. For testing larger structures and buildings, mechanical vibrographs are generally quite satisfactory. Their magnifications range from 200 in the simpler types to 1500 in the Wood-Anderson seismograph. For model experi- ments, miniature microphones of the electromagnetic or piezoelectric variety are required. In dynamic soil testing, the sensitivity of the mechanical vibrograph is not sufficient, and more delicate seismographs must be used, equipped with mechanical, optical, or electrical magnification, ranging from 10,000 to 50,000 times.” The ground vibrations may be recorded in three direc- tions, one being the vertical and the others the two horizontal directions through the station and at right angles to the base line. Although a vibrator may produce only vertical forces, the horizontal components are quite noticeable. Since, however, the maximum response in the horizontal components appears to occur at the same frequency as in the vertical com- ponent, vertical seismographs usually suffice. If a multiplicity of seis- mographs is on hand, it is better to use them at different distances rather than for different components. Vertical seismographs or detectors with electrical transducers are available in any event where seismic refraction work is combined with the dynamic tests. Lastly, it is easier to evaluate the results when vibrations from several stations are recorded on one film (see Fig. 12-19). In order to convert record amplitude to ground ampli- tude in terms of impressed force, the recording channels must be calibrated. With the larger vibrators, the regular phones used in seismic refraction or reflection equipment work satisfactorily without amplifiers. Where a large number of soil tests have to be made, it may be more convenient to record with (calibrated) amplifiers and to cut down the weight of the vibrator to make it more portable. When the variation of vibration amplitude with depth is measured, a hole is dug with a hand auger, and a vibration pickup is placed at its bottom at the desired depth or depths. In some cases, steel rods are driven into the bottom of the hole, to which the detectors are fastened. 1. Dynamic building tests. To test buildings or structures for earth- quake or other vibration damage, a vibrator is set up on, or clamped to, the actual structure or to a model thereof (model structures require a very light vibrator, see above). Usually, the vibrator is so oriented that hori- zontal forces are produced. The frequency of the vibrator is then varied 79 R. Koehler and A. Ramspeck, Zeit. Tech. Phys., 14(11), 512-514 (1933). 918 MISCELLANEOUS GEOPHYSICAL METHODS [Cuap. 12 and the response of the structure (or model) is recorded at one or several points. The records give the variation of amplitude with frequency and (when several detectors are used) the variation of amplitude with vertical elevation and horizontal direction. Buildings and other structures may have different frequencies in different directions. Different harmonics may appear for different modes of vibration (see page 912). In dynamic investigations, harmonics are more readily segregated than in free.vibra- tion records and may not even appear when outside the range of the vibrator. Evaluation of the vibration records yields resonance frequency, natural frequency, damping, and magnification for any point. These quantities are usually combined by plotting the response curve, that is, a curve giving relative amplitude (and magnification) as a function of fre- quency. Earthquake or vibration damage for a given structureis depend- ent on its response function” and therefore on its degree of tuning in respect to prevalent ground frequencies. Hence, the damage is larger if the ratio of building to ground frequency is near 1 and if damping is small. Since, in turn, the response of the ground to earthquake waves increases with the ability of layers to oscillate, earthquake damage is controlled largely by local geologic factors. This is well illustrated by the example of two Japanese earthquakes” which, though originating about 1100 km apart, caused maximum damage in virtually the same area. The vertical component of earthquake or other vibrations is believed to be comparatively ineffective; most structures are damaged primarily by horizontal motion. For the duration of a vibration, a structure is sub- jected to a strain whose magnitude depends on the vibration amplitude at the particular: point, and damage results when the ultimate stress of the building material is exceeded. This has been verified by dynamic building tests in areas where earthquakes of known intensity had occurred and where, therefore, the building amplitude (which follows from the response function of the building for an earthquake of given strength) could be correlated with the observed damage. Calculations” showed that the ultimate stress of the material actually had been exceeded where destruc- tion occurred. The importance of resonance between building and ground may be seen from the fact that for a brick house the critical ground ampli- tude (just causing damage) is 53 microns at resonance and as much as 75 centimeters off resonance. The seismic resistance of a structure may be calculated for sinusoidal ground motion and for simple modes of vibration, provided the response 80 Ramspeck, Zeit. Geophys., 9(1/2), 44-59 (1933). 81H. Martin, Zeit. Geophys., 12(7/8), 335 (1936). 82 Ramspeck, loc. cit. Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 919 function of the structure has been determined.” Seismic resistance may be defined as the ratio of ultimate stress U to the stress X corresponding to an amplitude x at a given point. For example, in a low structure where shear predominates over flexure, the stress is approximately X = uzz/H, where yw is rigidity and 2g is the amplitude at the elevation H. The build- ing amplitude z is a function of the static magnification V, the ground amplitude a, and the frequency factor f. In other words, x is dependent on the magnification function of the building. Therefore, the seismic resistance R = U/X, where U = u(2g)u/H, with (rz). as the critical build- ing amplitude at the elevation H. Since X = yra/H and rq = Vw'a(fa), is a damped frequency factor, the seis- where (fa) = V (wo? Fi By yg Fy? mic resistance becomes UH EE BGR YSU R= Vaat’ V (wt — a)? + Adal. (12-8) Determination of static magnifications appears to have been made hitherto only on low buildings. On such structures the static magnifica- tions ranged from 0.8 to 2 and the dynamic magnifications (at resonance) from 2 to 20, the high figures indicating that the buildings were poorly damped. Dynamic vibration tests are of practical value in industrial plants where large machines are used in connection with a light framework. Structures of this kind may eventually be shaken to pieces when the machine vibra- tions resonate with the building and particularly when machine, struc- ture, and ground are in resonance. It is sometimes possible to avert damage by a slight change in the speed of the machine. Koehler™ de- scribes investigations of a coal dressing plant whose vibration amplitude could be reduced 77 per cent by increasing the speed of a screening machine by only 11 per cent. 2. Dynamic ground tests. In a dynamic ground test the site under investigation is set into forced oscillation by a vibrator and the vibrations are recorded either at the source or at one or several points some distance away. The shakers are fairly heavy, cover a surface of about 10 square feet, and are arranged for reinforcement of the vertical and cancellation of the horizontal components of the centrifugal force. Vibrations are re- corded by the usual electromagnetic vertical component seismographs em- ployed in seismic exploration. Other possibilities, in respect to vibrators and detectors, are discussed on pp. 915-917. Higher frequency agitators 83 Heiland, loc. cit. 84 Zeit. Geophys., 12(4), 148-166 (1936). 920 MISCELLANEOUS GEOPHYSICAL METHODS [CHap. 12 do not belong in the category of ground tests and are discussed in connec- tion with geoacoustic methods on page 958. The reaction of the ground to the vibrator may be described by a simple expression if it is assumed that the vibrator is force-coupled to a semi- infinite medium (with a definite stiffness and velocity damping) whose displacement x is controlled only by Hooke’s law.” Let mo be the mass of the vibrator, plus whatever portion of ground partakes in the motion, wo = ~/c/m the natural frequency of the ground, w the impressed fre- quency, Co a stiffness coefficient of the ground and « a damping coefficient, and x = X sin (wt — g) the ground displacement having a maximum amplitude X and a phase shift ¢ in reference to the agitator. Then the centrifugal force referred to unit mass is , 2 Pose. (12-9) mM where m’ is the eccentric mass with a radius r on the vibrator of the mass my. The equation of motion of the ground is therefore given by é + 2e¢ + wor = F sin ut. (12-10) This leads to a maximum ground amplitude of sg IT ison et eae 5 w/ (at —)) + Seb” whose phase shift in reference to the application of the maximum force is given by xX (12-11a) 2 tang = 3 cigs (12-116) ac The power transferred to the ground is then P= ee sin 9, (12-11c) so that, by substitution of eq. (12-9) in (12-11a) and (12-116), m'ra* xX = SSS SSS (12-11d) moV (w2 _ wae SE Aico and P = Xe sin ¢. (12-11e) 8} A. Hertwig, G. Frith, and H. Lorenz, Veréff. Deut. Ges. Boden-Mechanik Heft 1, 44 pp. (Berlin, 1933). Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 921 Measurements of the response characteristics of the ground may be made (1) at the vibrator itself (for which purpose a vibration detector may be set up on the vibrator), and (2) at one or more outside points. The observations under (1) are intended to give several quantities, all as func- tions of frequency: (a) amplitude, (b) phase shift, (c) power, and (d) compaction. Lastly, the variation of natural frequency and damping of the ground with a change in mass (ballast) may be measured. Observa- tions at points removed from the vibrator determine the following quanti- ties: (a) amplitude as a function of frequency, (b) amplitude as a function of distance (and, therefore, the existence of reflections and refractions), (c) phase or travel time as a function of distance, and, finally, (d) phase speed as a function of frequency (dispersion). The variation of amplitude with frequency is measured with a detector mounted on the vibrator, or with one or several detectors some distance away. ‘The frequency response may be taken from a continuous record by getting the shaker up to top speed and allowing it to run down, or by adjusting its frequency in steps of two cycles and taking individual records for each frequency interval. The record amplitude is converted to true ground amplitude by means of the calibration curve of the recording in- strument or recording channel and is further reduced to constant impressed force by correcting for the variation of the centrifugal force with frequency. By plotting the reduced amplitude against frequency, a peaked curve (see Fig. 12-20) is obtained. The location of the peak indicates the resonance frequency; the steepness of the slope away from the resonance peak varies inversely with the damping. The damping factor e or the relative damping 7, which is equal to the ratio e/wy, may be calculated from the frequencies ahead of and past the resonance point at which the amplitude has dropped to one-half of the resonance amplitude. The natural undamped frequency is then computed from the resonance fre- quency and the damping (see Chapter 9, section Iv). Natural frequency and damping are important characteristics of the surface soil and are closely related to its bearing capacity and compaction. Soils having a natural frequency of from 25 to 32 cycles may be loaded with 2.5 to 5 kilograms per square centimeter.” From the natural ground frequency and the mass of the vibrator (plus a certain amount of ground, see below) the equivalent spring constant of the ground can be calculated. Upon repetition of vibrator experiments, it will be found that both reso- nance frequency and damping are slightly greater the second time, owing to compaction resulting from the ground vibration. The resonance fre- quency also increases somewhat with the surface of the vibrator, corre- sponding to a larger spring area, that is, to a stiffer spring. The damping % Tbid. 922 MISCELLANEOUS GEOPHYSICAL METHODS [Cuap. 12 factor is proportional to what is known in soil mechanics as the “friction angle.” Soils with large damping (or friction) factors are desirable as foundation materials since they lessen not only the amplitude and the cor- responding stress in case of resonance with extraneous vibrations, but also the range of vibratory impulses (due to increased absorption). A second quantity which may be determined from vibrator measure- ments at the source is the phase shift between impressed force and displace- ment. At low frequencies this phase shift is nearly zero, increases at reso- nance to 90°, and gradually ap- proaches 180° at the higher frequencies (see Fig. 12-18). It is possible to calculate damping from the phase-fre- quency curve (see Fig. 9-99). The variation of power with fre- quency may be measured with a watt- meter in the circuit of the vibrator motor. The power rises rapidly with frequency (see Fig. 12-18) and shows a peak at resonance, since at maximum amplitude the ground draws the great- est power. The measured value should be corrected for the no-load variation of power with frequency which can be determined by running the vibrator with balanced masses.” The compaction, or setting, of the ground is obtainable from readings of a strain gauge inserted between a tri- pod and the vibrator underneath.” os . The variation of compaction with fre- Ue shen tested paar quency runs parallel with the phase with frequency for a resonant surface Curve (see Fig. 12-18), the gradient formation (after Spath). being a maximum at resonance. Natural ground frequency and damp- ing show a slight decrease with an increase in the mass of the vibrator. The mass partaking in the oscillation includes a portion of the surface soil — and is slightly greater than the vibrator mass. This equivalent mass 87 Ibid. 88 Thid. Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 923 may, therefore, be determined by running two tests with different amounts of ballast. Although the more important soil characteristics may be obtained from measurements at the vibrator as described, it is advantageous to supple- ment these measurements with observations at a number of points a short distance away. The additional information gained thereby is, chiefly, the variation of amplitude with distance and the velocity of the elastic waves transmitted by the vibrator. Since such measurements involve a deter- mination of the variation of amplitude with frequency, it is now the more common procedure to omit measurements at the vibrator and to confine the observations to points generally arranged in a straight line through the vibrator. Several such profiles may be made, radiating from the loca- tion of the source. Heiland Research Corp. Fic. 12-19. Record of ground response test. Measuring the variation of amplitude with frequency involves the same technique as previously described, with the exception that now as many amplitude-frequency curves are plotted as there are detectors. Fig. 12-19 shows a typical record taken at constant frequency, and Fig. 12-20 is a graph giving the amplitudes as functions of frequency for the distances involved. From such curves the variation of amplitude with distance may be plotted, as is seen in Fig. 12-21. In this case the resonance amplitude was chosen for the graph; however, amplitudes at different frequencies may be plotted as well, since the variation of amplitude with distance is dependent on frequency, as shown below. In a homogeneous medium, the vibration amplitude decreases inversely with distance for space waves, and inversely with the square of the dis- tance for surface waves. Further, there is an exponential decrease due to 924 MISCELLANEOUS GEOPHYSICAL METHODS [Cuap. 12 absorption (see eqs. [9-35] and [9-37]). In a stratified medium the directly transmitted waves interfere with refracted and reflected waves because of their path and phase difference. The amplitude-distance curve is, therefore, not uniform, as in a homogeneous medium, but shows a series VERTICAL GROUND RESPONSE IN 5 DISTANCES FROM VIBRATOR PER KILOGRAM IMPRESSED FORCE -7 Cm. X10 GROUND- AMPLITUDES IN 20 25 30 35 FREQUENCY 1N CYGLES PER SECOND Fig. 12-20. Resonance curves of surface soil at various distances. of minima and maxima. Conditions for the occurrence of minima and maxima have been discussed by Koehler and Ramspeck.” If the surface 89 Degebo. Verdéff., 4, 1-38 (1936). Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 925 distance between the vibrator and a given detector is s, if a surface layer with the wave velocity v: is underlain by another layer with the velocity ve at the depth d, and if the assumption is made that the waves travel PHASE ~SPEED 10 S (MPRESSED FORCE ¥ @ KILOGRAM SECONDS x fo) PER IN TIME TU AMPLITUDE. as 5 ’ DISTANCE CURVES* ~ w GROUND -AMPLI TUDES 100 SO) 100 50 DISTANCE IN PEE Fie. 12-2k. Phase-speed and amplitude-distance curves. vertically to and from the second layer, the phase difference between the surface wave and underlayer wave is eee as s(2 io 2). (12-12) Vi Vo Vi 926 MISCELLANEOUS GEOPHYSICAL METHODS [CHap. 12 Therefore, a maximum in amplitude occurs when +w | s(2 _ \] = Qin, (12-132) Vi Vo V1 and a minimum occurs when 2 E Bs <(2 a \] Br eh (12-138) Vi Vo Vi where w is the angular frequency andi = 0, 1,2,3,4.---. It is noted that the amplitude has to be considered as a function not only of distance but of frequency as well. Taking, first, the variation of amplitude with frequency at a given distance s, we see that the ratio of two frequencies at which successive minima occur is equal to the ratio of two successive uneven numerals (or = [2i — 1]/[2i + 1]), whereas the frequency ratio corresponding to two successive maxima is equal to the ratio of two suc- cessive numbers, or i/(i + 1.) On the other hand, if the frequency f is held constant, the distance As between two adjacent minima is given by eially eat (12-13¢) ikea | ee) Similar relations may be written for the interference of the reflected with the directly transmitted waves. Measurement of vibrations at various distances from the source has the advantage that the speed of propagation of the waves may be measured. This is done by observing the time of occurrence of equiphase amplitudes, usually the troughs, and by plotting these times as functions of distance (see Fig. 12-21). The speed of vibrator waves is much less than that of first impulse (longitudinal) waves generated by explosion. The nature of vibrator waves is still a matter of speculation; it is fairly certain, however, that they are transverse waves. Ramspeck” assumes that they are Love waves. In any event, it is permissible to state their velocity of propaga- tion by an expression of the form v; = u/d, where y is the modulus of rigid- ity and 8 the density. Therefore, when vibrator measurements are made in conjunction with seismic refraction observations, all important elastic properties of the surface layers may be calculated, provided density deter- minations are available. Thus, the modulus of rigidity u, Poisson’s ratio 90 A. Ramspeck, and G. A. Schulze, Degebo Verdéff., 6, 1-27 (1938). Cxap, 12] MISCELLANEOUS GEOPHYSICAL METHODS 927 a, and Young’s modulus E follow from a combination of the longitudinal and transverse wave speeds: 1-2(2) wove. fo a NE eS a +o). -' (12-14) In homogeneous or nearly homogeneous ground the phase-speed travel- time curves are straight lines of constant slope, that is, they indicate constant velocities which in turn depend solely on the elastic properties and the densities of the formations. In stratified media there occurs a change of velocity with frequency known as dispersion. Where there is an underlayer of higher velocity, the apparent velocity will decrease with frequency, first slowly, and then more rapidly. Generally, therefore, the presence of an underlayer will not be indicated by two true velocities and a break between them, as in the longitudinal wave travel-time curves. Only in such cases where dispersion is not possible, that is, when the fre- quency is less than the overburden velocity divided by four times the depth to the interface, will there be a break in the travel-time curve. Then, velocities will be recorded that are independent of frequency. This means that for obtaining travel-time curves with true velocities, one should operate with low frequencies, since in that case no nodal point will develop at the interface and the underlayer will partake in the oscilla- tion. Simple expressions” may be written for the apparent velocity, v, measured at the surface, and for the depth, d, to the interface when there is a considerable contrast between the rigidity moduli and, therefore, the velocities v; and ve of the two layers. In that case, ia 4fvid v= Vieftd — v3 (12-15a) and vn d= feat (12-15b) 4 —=—1 Vi where ) is the wave length and f is frequency. Owing to the considerable amount of information on surface and sub- surface formations that can be obtained by comparatively simple means from dynamic soil tests, these tests have found increasing application in various engineering fields. Such applications include: determination of 1 Thid. 928 MISCELLANEOUS GEOPHYSICAL METHODS [Cuap. 12 bearing strength, compaction, rigidity and general stability of foundations, seismic resistance of foundations and dams, effectiveness of compaction in earth dams in hcrizontal and vertical direction, solidity of road beds and road surfaces, determination of the thickness of cement slabs, and the like. C. STRAIN GAUGING Strain gauging, in the general sense, involves the measurement of small displacements of mechanical parts under static or transient loading. Secondarily, strain gauging devices are useful for the recording of vibrations and for a comparison of the dimensions of machined parts with those of standards. Strain gauging finds widespread application in the fields of automotive, railroad, pipe-line, highway, and related fields of transporta- tion engineering; in the testing of all kinds of industrial machinery requir- ing an analysis of performance under transient loads and measurements of ambient pressures; and in automatic dimension control in the machining of matched parts. Application in the mechanical engineering field includes the measure- ment of strain (and usually vibrations) in airplanes, airships, locomotives, steamships; the testing of railway and trolley tracks, railway and highway bridges and beds, and transmission towers; the determination of pressure and vibrations in pipe lines; and measurement of impact and vibration stresses in all kinds of industrial machines, such as punch presses, rolling mills, steam and water turbines, internal combustion engines, elevators, mine hoists, and the like. Although most of these applications of strain gauging are rather remote from our field, geophysical problems arise where mechanical structures are tested in relation to, or in connection with, their foundations. Examples are railway and highway road beds and bridges, irrigation and flood con- trol dams, foundations for industrial machines, and similar structures. Another application of a purely geological nature is the measurement of rock displacements in faults, shear zones, active earthquake areas, mine workings, and railroad and drainage tunnels, and the investigation of rock bursts and the subsidence of the surface of the ground and the roofs of mines. Methods and instruments for the measurement of strains or displace- ments cover the entire range from ordinary length and elevation measure- ments to measurements as precise as one one-millionth of an inch. Ordi- nary procedures for measuring lengths and the regular methods of leveling are often satisfactory for observing the changes on very active faults, particularly in earthquake areas, for checking the movement of forma- tions along major faults or fissures underground, and for keeping track of Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 929 surface subsidence. Surface subsidence occurs, first, as a natural process in consequence of the leaching of salt beds, domes and other rocks or formations which may be removed by the action of subsurface waters. More frequently ground subsidence is encountered above underground workings, particularly coal mines; sometimes it results from the excava- tion of subway tunnels in cities; it has been observed in oil fields as a consequence of the removal of oil, gas, salt water, and sand from wells. An example is the Goose Creek field in Texas in which the ground subsi- dence over the center was as much as 3.25 feet in 8 years.” Subsidence may be due also to the removal of artesian water from large basins and the pumping dry of sands and sandy clays in the process of subway or building excavation. It may, finally, result from the sanding up and accumulation of sediments in large reservoirs, although the latter is a slow process requir- ing most delicate means of observation. Next in accuracy to the simple leveling devices discussed above are mechanical gauges. ‘They come equipped with more or less intricate lever arrangements and with dials for reading the displacement, or with a pen or stylus for continuous recording. The latter are useful in the surveillance of active faults, shear zones and fissures, mine roof subsidence, and tunnel movements. For it is only by the continuous and systematic study of the time variation of such displacements that we can hope to predict roof and wall failure underground and possibly the occurrence of tectonic earth- quakes. An instructive example has been published by Landsberg” show- ing that the rate of roof subsidence changed in a definite manner (ap- proximately in inverse proportion to the distance of the pillar retreat line) until a cave-in occurred. For attaining the ultimate objective, that is, the ability to predict the time at which a roof or wall is likely to fail or a fault is likely to slip, it would be necessary to study not only the time variation of the relative displacements along mine walls or faults, but to record simultaneously the variation of as many other factors as may be suspected of accumulating tensions and contributing to such failures. In addition to processes under human control, such as the removal of rock, and shocks produced by blast- ing, the following phenomena should be observed continually: natural earthquakes, rock bursts, variations in barometric pressure, variations in moisture, and possibly the bodily tides produced by sun and moon (see page 164). Most of these phenomena may be recorded by a single instru- ment and may possibly be combined with the displacement record by using a gauge that is sensitive to both displacement and vibration. It should be added that rock bursts and roof and wall displacements may be mutually % W.T. Thom, A.I.M.E. Tech. Publ. No. 17, 9 pp. (Sept., 1927). 93 A.I.M.E. Tech. Publ. No. 685, 5 (Feb., 1936). 930 MISCELLANEOUS GEOPHYSICAL METHODS [CHap. 12 related. It is possible that abrupt displacements give rise to audible vi- brations, and rock bursts of sufficient strength in turn may be responsible for the release of tension elsewhere in the vicinity. For recording roof subsidence, Landsberg” applied a simple recorder consisting of two telescoping steel tubes. The lower of these rested on the mine floor, while the upper was pressed against the roof by a coil spring and connected to the pen of a recorder supported by the base. The dis- placements resulting from mining by retreating pillars may amount to several centimeters in a day’s time. The sensitivity of metvhanical strain gauges may be increased by the addition of an optical lever. Such gauges have been described by Tucker- man.” A sensitive optical gauge can be made by combining a Martens lozenge extensometer with an autocollimation telescope (used in magnetom- eters, see Fig.:8-18a). The fixed pin of this extensometer rests on one part of the member to be tested and the lozenge, to which a mirror is attached, rests on another part a few inches away. Displacements as small as 1/250,000 inch may be detected. Interferometer gauges, while very sensi- tive, are too intricate for field applications. Compared with mechanical and optical gauges, electrical devices have the advantage of smaller dimension and possibility of remote indication and recording. These gauges are used chiefly in the testing of convey- ances, railway tracks, bridges, pipe lines, dams, and foundations. They are applicable also in the investigation of ground and roof subsidence and of rock bursts as discussed above. Generally speaking, an electric strain gauge is a device by which an electric current is controlled or modulated according to the relative position of two of its parts. The current modula- tion, in turn, may be accomplished by variations in (1) resistance, (2) capacitance, and (3) inductance. A simple resistance gauge is made from a potentiometer whose sliding contact is actuated by the magnification lever of a displacement meter (see Fig. 9-13). Another resistance gauge, known as the telemeter,” employs a stack of carbon disks held by a metal frame under an initial pressure of about 180 Ib. in’. Variations in resistance of the stack result from small deformations of the metal frame and are recorded by a Duddell- type oscillograph. The telemeter unit may be used in a water-tight cartridge for sealing into the concrete walls of dams or similar structures whose internal stresses are to be checked periodically. Because of its % Tbid., with bibliography. % T,, B. Tuckerman, Am. Soc. Test. Mad. Proc., 28(II), 602-610 (1923). 96 B. McCollum and O. S. Peters, U. S. Bur. Stand. Tech. Paper, 17 (No. 247), 737-777 (Jan., 1924). O.S. Peters and R. S. Johnson, Am. Soc. Test. Mat. Proc., 23(II), 892-901 (1923). O. S. Peters, Am. Soc. Test. Mat. Proc., 27(II), 522-533 (1927). Cnap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 931 small size, the unit would also be suited for diamond-drill holes issuing from mine drifts, cross cuts, raises, and the like, where it may be left to record variations in roof or wall stresses as mining operations proceed. With a high-speed oscillograph, these elements may also serve to record rock bursts and blasting vibrations. Several elements in suitable geomet- ric arrangement would permit the taking of travel-time records in connec- tion with blasting operations. From such records the velocity of seismic waves and their variation with time may be calculated. This will furnish data on the variation of rock pressure with time (see discussion at end of this section, page 934). Single-stack carbon gauges have the disadvantage that their current characteristics are not linear. This may be overcome by mounting two stacks in one frame, with a tongue projecting between them from the frame. The tongue is actuated by a thrust rod free to move through the - frame, the end of the rod being connected to that part of the member whose displacement is to be measured. The two stacks are arranged in opposite arms of a Wheatstone bridge containing an oscillograph in the center arm. This arrangement has the advantage of greater sensitivity and of balanced setup, since the resistance of one stack increases while the other decreases when the thrust rod moves in a given direction. The double unit is well suited for clamping to structural members of bridges, foundations, pipe lines, rails, and the like. A unique type of resistance strain gauge has been described by R. Gunn. It consists of a vacuum tube with the cathode filament between two anodes that are mounted together on a rod passing outward through a flexible diaphragm. A displacement of the rod decreases the plate re- sistance of the tube on one side and increases it on the other. The plates are connected to a balanced bridge circuit with microammeter. The magnification is of the order of 10,000. Strain gauges depending on variations in capacitance to indicate dis- placement are known as ultramicrometers.” Various circuits and methods have been proposed for the measurement of minute changes in capacity. These are: (1) the Dowling method, using a grid-tuned or plate-tuned circuit with variable capacity in a Hartley, Colpitt, or similar oscillator; %2 Rev. Sci. Instr., 11(6), 204 (June, 1940). 97 J. J. Dowling, Phil. Mag., 46(27), 81-100 (July, 1923). C. B. Bazzoni, J. Frank. Inst., 202, 35-50 (July, 1926). S. Ekeléf, J. Opt. Soc. Amer., 18(4), 337-341 (April, 1929). J. Obata, J. Opt. Soc. Amer., 16(6), 419-432 (June, 1928). H. Olken, Instruments, 5(2), 33-36 (Feb., 1932); Electronics, 3, 144 (1931). H. Thoma, V.D.I. Zeit., 73, 639 (1929). R. W. Whiddington, Phil. Mag., 40(139), 634-639 (1920). W. W. Loebe and C. Samson, Zeit. Tech. Phys., 9(10), 414-419 (1928). H. Gerdien, Wiss. Veréff. Siemens Konzern, 8, 2 (1929). H. Riegger and R. Boedecker, Wiss. Veroff. Siemens Konzern, 1, 126 (1920). S. Reisch, Zeit. Hochfrequenztech., 38, 101 (1931). G. Gustafson, Ann. Phys., Sec. 5, 22(6), 507-512 (Mar. 21, 1935). 932 MISCELLANEOUS GEOPHYSICAL METHODS [CHap. 12 (2) the Gerdien-Thoma resonance circuit; (3) the Whiddington heterodyne method; and (4) capacitance bridges. The simplest of these arrange- ments is probably the Dowling circuit which contains the variable capaci- tance in the grid circuit, the corresponding plate current variation being read on a sensitive meter provided with a bucking circuit. Obata used this method in a seismograph accelerometer and a pressure gauge. The disadvantage of this circuit is its nonlinear characteristic, the sensitivity decreasing in inverse proportion to the condenser spacing. In the resonance method a V.T. oscillator is coupled through a condenser to a measuring circuit that is so tuned as to nearly resonate with the former. The measuring circuit contains the variable capacitance, ampli- tude variations being read on a thermocouple-millivoltmeter. Several commercial machines for matched production control have been developed along this line. In Whiddington’s heterodyne ultramicrometer two oscil- lators are employed; one contains the variable capacitance (and is therefore variable in frequency), whereas the frequency of the other oscillator is fixed. In Whiddington’s setup, the beat frequency is observed directly in a detector circuit by means of a speaker. In a modification by Loebe and Samson, the beat frequency, converted into amplitude variation in a nearly resonant circuit, is then amplified and read on a meter. The capacity-bridge ultramicrometer developed by Reisch has the advantage of a linear relation between reading and displacement. It employs a movable plate between two fixed condenser plates, and stray effects are eliminated by a balanced circuit. Ultramicrometer capacitance gauges are exceedingly sensitive. It is not difficult to measure changes in length to a millionth of a centimeter. However, there is frequent interference because of stray capacitances, temperature changes, and the like. This probably accounts for the fact that these gauges are used chiefly in plants and laboratories and are not so desirable as the resistance and inductance gauges for use in the field. An inductance-bridge strain gauge is essentially a Wheatstone bridge with iron core reactors in opposite arms. The iron core coils are provided with armatures, and the gap between them remains fixed in one of the reactors whereas the other changes with the displacement to be measured. In another form of the inductance gauge there is but one armature with two coils on opposite sides, so that a displacement of the armature in- creases one gap and decreases the other.” In still another form of this bridge, two balanced armature coils are in one arm of the bridge while two balancing coils, wound on a transformer core, are in the other arm. 98 A. V. Mershon, Gen. Elec. Rev., 31(10), 526-531 (Oct., 1928); 35(3), 139-144 (March, 1932). C. M. Hathaway and E. S. Lee, Mech. Eng., 59(9), 653-658 (Sept., 1937). M.A. Rusher, Am. Ceram. Soc. Bull., 14(11)}, 365-367 (Nov., 1935). Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 933 The supply frequency of inductance bridges is usually 60 cycles, but it may be increased to 500 and 2000 cycles for certain applications. In gauges intended for thickness measurements and similar uses in controlled plant production, the indicators are rectifier meters. When time varia- tions of displacements or vibrations are to be recorded, measurements are made with oscilloscopes or oscillographs. General Electric Company has developed several commercial models for the inspection of outside and inside tolerances of machined parts, spacing of holes, and the like, and for the automatic control of machining opera- tions. (A balanced armature inductance gauge of similar construction is illustrated in Fig. 9-12). Inductance gauges are suitable for the measure- ment of strains in foundations, bridges, and dams, and for recording stresses, roof subsidence, and wall and fault displacements in underground workings. In application, the fixed and variable air gaps in the reactors are first adjusted to bring the bridge into balance. Then the variable reactor is taken apart, transferred to the member to be tested, and again adjusted for air gap length to obtain bridge balance. The magnification of inductance gauges is of the order of 100,000 and may be combined with trouble-free operation. Various seismologists have attempted to measure displacements between points at the earth’s surface. Milne” determined the motion between two piers 3 feet apart by attaching a thrust rod to one of them and recording the motion of the free end of the rod with respect to the other. This arrangement is therefore similar to the convergence recorder previously described (see page 930) operating in a horizontal instead of a vertical direction. Milne’s arrangement was modified and increased in sensi- tivity by various investigators, such as E. Oddone,” R. Takahashi,” and H. Benioff."” Benioff used two piers 60 feet apart, with a thrust rod con- nected to one of them. The free end of the thrust rod was provided with a balanced armature reluctance transducer. The currents induced by the movement of the piers with respect to each other were proportional to the displacement velocity; hence, the apparatus functioned essentially as a seismograph and not as a strain gauge. However, it could readily be con- verted into a displacement meter by an adaptation of the mductance bridge previously described. A number of the strain gauges described above, when reproduced on smaller scale, may be applied in experiments with models of proposed structures, tunnels, or underground workings. It is true that much valu- °9 Trans. Seis. Soc. Japan, 12, 63 (1888). 100 Bull. Soc. Seis. Ital., 11, 168 (1900). 101 Bull. Earthq. Res. Inst., 12(4), 760-775 (1934). 102 Bull. Seis. Soc. Amer., 25(4), 283-309 (Oct., 1935). 934 MISCELLANEQUS GEOPHYSICAL METHODS [CHap. 12 able information on strain distribution in structures can be obtained by photoelastic studies. However, the fact that only relatively thin sections can be used limits the validity of the conclusions to a single plane. If actual conditions are to be duplicated in three dimensions, it is necessary to resort to reduced scale models and test them with miniature strain gauges placed at suitable points. Attention must be given to model scale factors, and the elastic properties of the model material must be scaled down in keeping with the requisite dimensional relations. In concluding this section on strain gauging, it should be pointed out that a strain gauge will indicate merely the variation of stress or strain with time and not the absolute stress that may be present in the member to be tested. To a certain extent this difficulty may be circumvented by imbedding strain gauges into a structure in the process of construction, or by relieving the stress at suitable points after the installation of the gauges. There is a possibility of obtaining absolute pressures in rocks (7m situ) by measuring velocities of elastic waves. As was shown in Chapter 9 (see page 474), the elastic modulus and therefore the elastic wave speed of porous rocks change with pressure. The variation is not linear; it is fairly large for smali pressures but decreases for larger pressures as a limiting value is approached. It is assumed that the’ pores are first closed up by the lower pressures, after which the stress begins to work on the mineral grains themselves. Hence, the variation of elastic modulus with pressure is different for every type of rock and is dependent on porosity, moisture, crystalline structure, and anisotropy. The variation of elastic wave speed with pressure for various types of rocks has been determined recently by L. Obert." At reasonably shallow depths, where the pressure is not so great that the flat part of the pressure-velocity curve is approached, stresses in underground workings may therefore be determinable by seismic velocity observations. IV. ACOUSTIC METHODS Acoustic methods are included here in the discussion of geophysical exploration since, by definition, geophysics is concerned with the three acoustic transmission media: the earth, the water, and the atmosphere. Although we are inclined to associate the transmission of sound with the latter only, sound passes with equal and often greater ease through the media of water and solid ground. Transmission of infra-acoustic frequency earthquake waves of natural or artificial origin is usually referred to as seismic wave propagation, whereas sound transmission through air and water, ranging in frequency from single impulses to supersonics, as well 103 J. S. Bur. Mines Rep. of Invest. No. 3444, April, 1939. Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 935 as the transmission of audio-frequency vibrations through the ground, is termed “‘acoustic” transmission. With this in mind, we divide the fol- lowing discussion into (a) atmospheric-acoustic, (b) marine-acoustic, and (c) geoacoustic methods. The principal applications of acoustic methods are: (1) communication (segnaling); (2) location of sound sources (acoustic triangulation, position- finding, or sound-ranging) by measurements of time and distance; (3) deter- mination of the direction and characteristics of a source (direction-finding and nozise-detection); (4) location of intervening media (transmission meas- urements); (5) determination of distances of sound-reflecting objects (echo- sounding); (6) noise-prevention. A. ATMOSPHERIC-AcouUsTIC METHODS 1. Velocity and absorption of sound in air. Of the three possible sound transmitting media—air, water, and earth (inclusive of solids)—the at- mospheric air is, of necessity, the one most widely used and yet probably the least efficient of the three. Sound propagates in air more slowly than in liquid or solid media. If the ratio of the specific heats for constant temperature and pressure be designated by k (= 1.405 for dry air), if P is the pressure (1.013 megadynes cm ’) and 8 (= 0.29-10-°) the density of air at 0° C., the sound velocity (at that temperature) is given by fe 4/ KE, (12-16) or, with the above numerical values, = 331.8 meters per second. The velocity increases with the absolute temperature, ta., or V = 20-/ta». m-sec. ', which for centigrade temperatures t above zero is usually written ve = 331.4 + 0.66 t°. Other factors which affect the sound velocity in air are humidity, wind direction, and velocity. Near intensive sources, velocity increases have been observed. For long ranges the sound does not always propagate along straight paths through the atmosphere. From the source the sound rays may curve upward because of a decrease in atmospheric tem- perature with height, up to about 15-20 km. Temperatures are likely to remain uniform and then to increase again at heights of 30-40 km in the ozone layer where sound velocities may reach values of 350-360 m-sec’. The vertical increase in velocity results in an advance of the upper portion of the wave front and a bending back of the sound rays to the earth’s surface. For a uniform vertical velocity gradient dv/dz, the ray curvature is given by —(1/v)-dv/dz. The bending of the sound rays in the high velocity layer gives rise to the well-known “silence zones’’ in sound-ranging 936 MISCELLANEOUS GEOPHYSICAL METHODS [CHap. 12 and explosion observations and is similar in principle to the “reflection” of radio waves from the Kennelly-Heaviside layer. Another cause of ray curvature may be the increase of wind velocity with altitude. Sound is absorbed in air because of viscosity, heat conduction, and scattering on small particles. The effect of viscosity and heat conduction may be expressed by =z I, = I-e a where I is intensity at distance x and @ is an amplitude attenuation coeffi- cient, that is, the reciprocal of the distance at which the amplitude has dropped to 1/e of its initial value. If internal friction alone is considered, the coefficient ; 8a roy OF he sie (12-17) where II/d is the static mass-viscosity coefficient, v is the sound velocity, and f is the frequency. The coefficient of absorption due to heat con- duction is about one-third of that due to internal friction. The absorption increases in proportion to the square of the frequency; hence, the range of audio signals in air is much less (30 kilometers maximum for the band of 300 to 600 cycles) for audio frequencies than that of explosion sounds (which have been recorded by microphones up to 400 to 500 km at 5 to 10 cycles). However, there are so many possible interferences with sound transmission, due to variations in meteorologic factors (humidity, wind, clouds, fog, and the like) that these ranges are not always reached; sound transmission through air is, therefore, much less reliable than through water. Some of the very large ranges observed for explosions are no doubt caused by the so-called “abnormal” sound propagation, that is, repeated reflections on the (ozone) layer and the earth’s surface. For very high (supersonic) frequencies the absorption and scattering on small particles become so strong that their range is very small. The scattering effect is inversely proportional to the volume of the particles concerned and airectly proportional to the fourth power of frequency. 2. Sound transmitters. The design and construction of sound trans- mitters and receivers for atmospheric acoustic work depends entirely on the purpose for which the sound transmission is intended. When sound originates without control by the listener (explosions, gun fire, airplane propeller noise) the technical problem is, of course, confined to the con- struction of suitable receivers. In atmospheric acoustic signaling, position- finding, and echo-sounding, the transmitters vary in construction, but the emphasis is usually on the low-frequency end of the spectrum. ‘The Behm airplane echo sounder and the ‘“‘Echometer’’ for measuring the depth of fluid levels in wells employ simple gunpowder cartridges as transmitters. Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 937 In radio-acoustic atmospheric position-finding and communication, the transmitting devices are, in increasing order of range, bells, horns, whistles, sirens, diaphragm-whistle combinations, and “group” transmitters of the latter. For controlled communication, sound telegraphy, and the like, 300-600 c.p.s. appears to be the most suitable frequency band; it is more or less a compromise between a frequency to which the ear is most sensi- tive, one having a practical range, and one giving directional properties when necessary. The latter increase with the ratio of diameter and sound wave length (27/\, 2rf).™ In this frequency range, electromagneti- cally driven diaphragms combined with quarter-wave whistles or exponen- tial horns seem to be most efficient. If directional transmission is desired, a group of horn transmitters may be arranged vertically above one another. For nondirectional trans- mission, Hecht’ has designed a double diaphragm transmitter of 500-cycle frequency, about 33 cm in diameter (= half wave length to resonate the air cavity to the diaphragm), with diaphragms in horizontal position, four of these being arranged vertically (at a distance of half the wave length) above one another. The (acoustic) power is about 2000 watts and the range is of the order of 15 miles. 3. Sound receivers. In a number of applications of atmospheric acous- tics, signals are received unaided by the human ear. This is particularly true for short-range communication. The sensitivity of the ear is greatest in the frequency range of 1500 to 3000 cycles; the corresponding detectable pressure variation at the ear drum being of the order of 6-10 * dynes-cm”. The sensitivity of the ear may be increased by various mechanical and electrical devices, particularly if arrival times of sounds are to be recorded. Mechanically this may be accomplished by increasing the area of reception and by narrowing it down to the ear passage, that is, by the use of horns. More effective is a combination of such horns with diaphragms whose motion can be recorded photographically by transferring it by a bow-string mechanism to a rotating mirror (““Undograph’”’)™ or electrically by the use of transducers (carbon, crystal, reluctance, or coil microphones). Of these, the carbon microphone is least suitable. Crystal and reluctance phones are better adapted to marine use, which leaves the coil microphone as the most advantageous. It is virtually the only kind that can be used 104 Considering that the radiation from a diaphragm of radius r is confined to a cone, and designating one-half of the apex angle by a, the (approximate) relation that obtains is sin a = 0.6A/r. 106 H. Hecht, Handb. Exper. Phys., 17(2), 409 (1934). 106 This mechanism resembles that applied in the Schweydar mechanical seis- mograph (p. 609). See also C. A. Heiland, A.I.M.E. Geophys. Pros., 242 (1932). 107 Regarding arrangement of transducers, see notes on construction of hydro- phones, p. 948. 938 MISCELLANEOUS GEOPHYSICAL METHODS [Cuap. 12 when quantitative reproductions of sound intensity and phase are required (as in electrical direction-finding compensators). For detection purposes, receivers are generally arranged in groups either along a horizontal base line, along a vertical line, on the surface of a sphere, or on the circumference of a circle, all depending on the purpose of the detection apparatus. For detecting low-frequency sounds (gun re- ports, and the like) the hot-wire microphone (or ‘‘thermophone’’) is given preference over the types just mentioned. It consists of a grid of platinum wires of about 6-10 * cm thickness, heated by an electrical current, and placed in the neck of a Helmholtz resonator or in the passage between two resonators. At these points the amplitude of the air moving to and fro is greatest and produces variations in the temperature and therefore the resistance of the platinum filament. When the microphone is arranged in one of the arms of a Wheatstone bridge with an oscillograph in the de- tector arm, it is possible to obtain a linear relation between oscillograph amplitude and resistance variation and, therefore, the sound amplitude. The direction of sound is determined by the binaural effect, that is, the ability to detect (subconsciously) very small differences in arrival time at each ear. If the incoming sound makes the angle a with the connecting (base) line of both ears and if d is their distance, the corresponding phase shift is” ji zal COS a or At = cn a (12-18) a V where J is wave length and v is velocity. In other words, the directional sensitivity of the ear depends on the ratio d/\ (which also controls the directional properties of transmitters) and amounts to about 3°, or a time difference of 30 microseconds. It is obvious that the directional accuracy can be increased by a binaural device of larger base, as in airplane detectors. The direction of sound is then determined by rotating the device until the base coincides with the wave front. For airplane detection, two sets of ‘‘ears’’ (microphones in parabolic reflectors or in horns) are required, one pair rotatable about a vertical axis to determine the horizontal azimuth, the other rotated about a horizontal axis to obtain the vertical angle. If apparatus of this type is impracticable because of size, the phase shift in the sound impulses received by a pair of detectors may be ascer- tained by insertion of time-delaying arrangements. These may be me- chanical (extension tubes) or electrical (compensators). Fig. 12-22 shows a compensator employed in connection with a number of microphones 108 This relation is identical with that relating time and apparent surface velocity to emergence angle in seismology, see p. 541. Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 939 arranged on the surface of a sphere. The microphones are associated with a network consisting of an equal number of series inductances, L, and parallel capacities, C. The latter are connected by two sets of contact brushes in such a way that the time differences are balanced. Then the position of the two sets of brushes gives the direction of the sound ray in space. The delay for each filter is ~/LC. The total delay is n+/LC, if there are n receivers to the diam- eter d of the sphere. The total delay must equal the time re- quired for the sound to pass through this distance, so that'” : =nvV/Lc. (12-19) In automatic compensators the position of the contact brushes is continually adjusted to the direction of the sound, which makes it possible to aim search- lights and anti-aircraft guns automatically at the target. 4. Atmospheric-acoustic com- munication. Sound signaling in air to warn approaching vehicles and vessels is applied in every- day life more extensively than is probably realized, the automobile horn, the factory whistle, the fire bell or siren, the fog horn, bells and whistles on buoys and lighthouses and lightships being Fie. 12-22. Electrical direction compen- feat sator for acoustic airplane detection (after familiar examples. For trans- Hecht). mission of messages, special audio-frequency transmitters have been constructed (see page 937). 5. Atmospheric-acoustic position-finding and sound-ranging. By position- finding is meant the procedure of determining one’s location by distance 109 Hf. Hecht, loc. cit. 940 MISCELLANEOUS GEOPHYSICAL METHODS [CHap. 12 measurement from one or two acoustic sources of known position which transmit a controlled impulse or, as in radio-acoustic position-finding, a simultaneous radio and acoustic impulse. Conversely, souwnd-ranging is a method of locating a source by acoustic triangulation, that is, by recording its sound impulses on a number of receivers of known position. When a lighthouse or lightship transmits simultaneous light (or radio) and acoustic signals, an approaching vessel may readily determine its distance. Assuming that both impulses travel by the same path and that At is the time difference of arrival, v; the light velocity, v, the velocity of sound in air, and Av the difference in the velocities, the distance from the source is At Sia Vine ES aVgs (12-20) since Av v, = 3-10° m, whereas v, = 3-10’m. Therefore, the distance in kilometers is readily obtained by dividing 3 into the time interval (in seconds) between reception of radio and acoustic signal. Measurement of distances from two sources of known position gives the true position of the receiver. In seismic refraction work, use is made of this method to obtain the distances of the seismic receivers from the shot point by recording the shot instant by radio and the sound of the explosion by a blastophone on the same film. The object of sound-ranging is to locate enemy guns by recording the sound of their detonation. Records of arrival time are taken at a number of receiving stations spread out along a base behind one’s own lines. To minimize errors due to local variations in sound velocity, the length of the base is made as great as practicable and of the order of 15,000 to 25,000 feet. It is generally about 10,000 feet behind the lines. From six to twelve microphones are arranged at equal intervals along the lines and are connected through amplifiers to a six- or twelve-element oscillograph camera constructed like the seismic cameras used in refraction or reflection recording.” To be sensitive only to the low-frequency sounds trans- mitted by the firing of a gun and to reject other sounds produced by the activities of one’s own or enemy troops, the microphones are coupled to Helmholtz resonators tuned to about 12 cycles. The microphones are usually of the hot-wire type, although experiments with moving-coil microphones have also been very successful. Since the enemy batteries may be 15,000 to 50,000 feet away from the microphones and must be located with an accuracy of about 100 feet, the position of the microphones must be surveyed with an accuracy of 1 to 3 feet. Records must be taken with an accuracy of 1/100 of a second and 110 See p. 556. Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 941 the sound velocity must be known to about 1 per cent or better. It is in regard to the latter that the chief difficulties arise, since the effects of wind, temperature, and humidity, their rate of change in vertical direc- tion, and the corresponding curvature of the sound rays are not known. To eliminate this uncertainty as much as possible, another sound-ranging station may be set up between the front and the main base line, with microphones arranged in a circle about a point at which small charges are exploded from time to time and meteorological elements are recorded simultaneously. In this manner, the relation between sound velocity and meteorological data is established empirically. The location of the sound source is established by measuring the time differences in the arrival of the sound at the various stations 0, 1, 2, 3, and so on.” If the sound arrives at station 0 in & (unknown) seconds after its initiation at the source, in ¢, seconds at station 1, in tg seconds at station 2, and so on, circles may be drawn about station 1 with the radius V(t; — t&), about station 2 with the radius v(t2 — é), and so on, with v the velocity of sound corrected for wind velocity, temperature, and hu- midity, or determined experimentally by the auxiliary ranging setup described above. The source is the center of a circle with radius vt passing through 0 and touching the circles about stations 1, 2, 3, and so on. In practice, the source is located by the intersection of hyperbolas drawn about the receiving station as foci. To eliminate calculations, a series of hyperbolas are plotted previously on a large map with the time differences to be expected, and the source is located by interpolation. The recording apparatus and amplifiers are started by a sentry located between the front lines and the base, when he hears the sound of the gun, or they are set in motion automatically by a microphone in forward location. With some practice it is possible to identify the type of gun from the character of the record; if shell bursts from the same gun have been recorded, its range and thus its caliber can be deduced. 6. Direction-finding, noise-detection. Atmospheric-acoustic direction- finding is concerned largely with the detection of enemy scouting or bombing planes when unfavorable weather or light conditions preclude other ways of detection. The sound emitted by a flying plane is com- posed of the exhaust noise, the ship’s vibration, and the propeller noise (the latter being the most predominant), and comprises a wide range of frequencies. Most suitable for detection is probably the band from 300 to 600 cycles, corresponding to a wave length of 1 to $ meters. Since the 111 The appearance of the record is much similar to that of a seismic refraction record (see Fig. 9-91, first part of record) except that the impulses are of shorter duration. See also plate on p. 16 (article: ‘‘Sound’’) Ency. Brit., 14th ed. 942 MISCELLANEOUS GEOPHYSICAL METHODS [Cuap. 12 unaided ears have a directional sensitivity of about 3 per cent, corre- sponding to a time difference of 30 microseconds, it follows that to attain an accuracy of 3° or better, as required in plane detection, an artificial pair of ears should have a base length of six times that of the ears, or of 1.2 meters. Airplane detectors have base lengths of this order, consist of two pairs of large “ears,” and have the shape of reflectors, horns, or funnels which can be aimed independently by two operators to locate the target by horizontal and vertical angle adjustments. If such detectors are too bulky, compensators with mechanical or electrical time delay mechanisms are used in conjunction with a cluster of (coil) microphones in circular or spherical arrangement (see Fig. 12-22) and may be arranged to operate anti-aircraft batteries and searchlights mechanically or elec- trically. Noise analysis, or determination of type of source by the character of sound emitted, is often associated with direction-finding and sometimes with sound-ranging. An analogy familiar from everyday life is the physi- cian’s method of diagnosing heart and lung diseases by the use of the stethoscope. Another acoustic diagnostic procedure applied in medicine, the determination of the condition of certain organs by tapping and lis- tening to the sound with the stethoscope, is without analogy in atmos- pheric-acoustic transmission measurements. 7. Atmospheric echo-sounding. In primitive form, echo-sounding in air has been employed for a long time in the navigation of narrow channels during foggy weather by skippers, who estimate the distance to shore by the length of time required to receive the echo from the ship’s whistle. Another application of atmospheric echo-sounding is made in the Behm ground-distance meter. A pistol is fired on one side of an airplane and the reflection from the ground is received on the other side by a micro- phone. The firing of the pistol sets in motion a disk carrying a mirror which projects the image of a light source on a scale. The light passes through a small lens which is deflected electromagnetically at the instant when the sound is received by the microphone. The Behm airplane echo- sounder is not usable for distances much in excess of 500 feet and has been ‘superseded by an electromagnetic terrain-clearance indicator using fre- quency-modulated short-wave radio transmission.” Finally, atmospheric echo-sounding is applied in geophysical research concerned with the constitution of the upper atmosphere (investigation of the so-called ‘‘anomalous”’ sound propagation, see page 936) and in the measurement of depth to fluid level in oil wells."* The sound is generated in the last method by the firing of a cartridge in a chamber attached to 112 Bell Sys. Tech. J., 18(1), 222-234 (1939). 113 J, J. Jakosky, Petrol. Tech., 2(2), 1-23 (May, 1939). Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 943 the casing head of an oil well. Reflections are recorded from any kind of obstacle in the well, that is, not only from the oil level, but also from tubing catchers, liner tops, and tubing collars. These echos are picked up by a microphone and are recorded oscillographically on rapidly moving film. Because of the variation of the sound velocity with the nature and temperature of gas admixtures in the well, the lesser reflections from tube collars of known depth-interval are used as a means of calibrating the time scale when necessary. 8. Noise prevention. Noise prevention or noise reduction becomes in- creasingly important with the growth in the use of industrial machinery. In respect to vehicle traffic, noise prevention methods extend to the reduc- tion of sounds and noises from horns, engines, exhausts, automobile tires, and tram wheels; in construction work they involve decreasing the noise of riveting, and the like; in mechanical and electrical processing, these methods aim at sound-proofing and vibration-insulation of foundations. One important phase of this work is the reduction of reverberations in offices and auditoriums and the improvement in their acoustics generally speaking; another phase, of military significance, is the design of airplane, submarine, and battleship engines, shafts, and propellers in such a manner that noise and noise transmission is reduced as much as possible. B. Marine-Acoustic Mretuops 1. Velocity and absorption of sound in water. Compared with air, water is a much more suitable medium for the transmission of sound. Its velocity is 45 times as great, its absorption more than thousand times less. Like the velocity of atmospheric sound, the velocity of sounds in a liquid changes with temperature. In marine transmission, significant varia- tions occur with changes in salinity. Following are two useful relations expressing the velocity in water as a function of temperature t (in degrees C.) and salinity u in permille (at 0° C.): (1) Metric (Maurer) formula: Vm-se-1 = 1445 + 4.46t — 0.0615t? + (1.2 — 0.015t)(u — 35) (12-21) (2) English formula: Vit.-seo-1 = 4626 + 13.8t — 0.12t? + 3.73u. Unlike sound in air, sound in water is not much affected by the move- ment of the transmission medium; in other words, oceanic, tidal, and similar currents are ineffective. However, as in air, refraction and reflec- tion occur because of vertical variations in salinity and temperature. The 944 MISCELLANEOUS GEOPHYSICAL METHODS [Cuap. 12 vertical velocity variation in water is often much the same as that in air but it occurs on a smaller scale. In some experiments described by Swainson,“ the velocity decreased rapidly for the first 50-100 fathoms, then leveled off, and increased again from about 500 fathoms on down (1 fathom = 6 feet). The temperature decreased from 14° to 9° C. to 100 fathoms and stayed constant at about 4° from 500 fathoms on down. The salinity increased from 33 to 34.2 thousandths as far as about 200 fathoms and stayed constant from that depth on down. These levels change to a certain extent with the seasons. The result of such velocity variations is that the sound rays are first bent away from the horizontal and curve toward it again at greater depth. Contrary to air, the energy does not return to the surface by refraction but only by reflection at the ocean floor. Long-range transmission does not occur by the direct path but by multiple reflections on both. the ocean bottom and water surface. According to Swainson’s observations,” the direct ray was recorded up to 20 km, once-reflected waves up to 70 km, twice- to five-times-reflected waves up to 85 km (and possibly more). At that distance the travel time was about 1 minute. These ranges hold for bomb explosions and not for continuous waves. When the depth is small compared with distance (as in most marine-acoustic communication prob- lems, except echo-sounding) the time “delay” + due to the reflection is small compared with the total travel time. According to Swainson,” the time difference between the first and fifth reflections at 85 km distance was about 1 second; thus, the delay for each reflection was 4 second. Although the delay is, strictly speaking, dependent on distance (since the travel-time curves are hyperbolas, see page 557) and varies in value from one reflection to another, it is satisfactory to write s = v(t — ne) (12-22) for distance determinations from the travel time, for n reflections. The velocity of sound waves in water increases somewhat near the source and decreases slightly with an increase in frequency (in the super- sonic range). The attenuation of sound waves in water and air is governed by the same relation (formula [12-17]) as far as viscosity damping is concerned. The coefficient «/f’ is 1.45-10°* em-sec. * for air, and 8.5.10” em-sec. for water. For the latter, the attenuation is therefore about 1700 times less.” 1140. W. Swainson, ‘‘Velocity of Sound Waves in Sea Water,’’ U. 8S. Coast & Geod. Surv., Spec. Rep., Feb. 28, 1936. 115 Thid. 16 Joid. 17 T,, Bergmann, Ulirasonics, Wiley (1939). Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 945 In water, the losses due to heat conduction are negligible. Contrary to air, water is suitable for both audio- and high-frequency transmission. Theoretically, for 1000 cycles the sound intensity decreases to 0.81 of its initial value at a distance of one kilometer in air, whereas in water approxi- mately the same ratio (0.75) obtains for ten times the range (10 km) at ten tumes the frequency (10 kce.). Ultrasonic frequencies are, therefore, a highly suitable means of signaling. A wave of 100-ke. frequency travels in air but 5 m to its I)/e value while in water the same wave would travel 3.6 km, or more than 700 times the distance.”* Actually, the ranges are very much less than the theoretical values because of scattering, refrac- tion, and reflection. H. Hecht’’ places the average practical range of subaqueous (audio-frequency) signaling at 20 km with 150 km as the maximum possibility. 2. Marine sound transmitters. Sources of sound in marine transmission vary greatly with application. Their construction depends primarily on the directional characteristics desired. As pointed out on page 937, the latter depend on the ratio of transmitter diameter and wave length. Since in water the wave lengths, for the same frequencies, are 44 times greater than in air, it is seen that correspondingly greater transmitter dimensions are required to obtain the same directional characteristics as in air. Such dimensions are usually impracticable; therefore, transmitters intended for signaling are built for high or ultrasonic frequencies. Where directional characteristics offer no advantage, low frequencies are satisfactory. Hence, the frequency range of subaqueous transmitters covers the entire band from detonations to ultrasonics, depending on purpose. Detona- tions may be produced by depth bombs (as in radio-acoustic position- finding) or by the firing of cartridges (as in the Behm echo-sounder). For submarine telegraphy, a frequency is selected which is sufficiently removed from the noise produced by the propellers, shafts, engines, and the like. When transmitters are used in conjunction with direct listening devices, this frequency is usually close to the frequency for which the human ear is most sensitive. Originally, the transmitters in the audio range between 500 and 1000 cycles were simple bells or sirens driven by jets of water. They were later abandoned in favor of electromagnetically driven dia- phragm transmitters. On lightships, two or more twin-diaphragm trans- mitters are employed. They are rotated with respect to one another for uniformity of directional coverage and are mounted one above another with diaphragms vertical. These transmitters are lowered through a shaft in the vessel to a point 10 to 15 feet below its keel. A transmitter of this type (frequency, 525 c.p.s.; power, 800 watts; efficiency, 63 per cent) has 18 #. Grossmann, Handb. Exp. Phys., 17(1), 498 (1934). 19 Toc. cit. 946 MISCELLANEOUS GEOPHYSICAL METHODS [Cuap. 12 been described by Hecht.” In echo-sounding, single units may be made to do double duty as transmitter and receiver. These are then mounted on the keel of the ship with diaphragm in horizontal position. Where separate units are preferred for transmission and reception, the transmitter is on one side of the ship and the receiver is on the other side and slightly forward from the transmitter. An electrical transmitter of high efficiency, designed like a dynamic speaker, has been constructed by Fessenden.” There are two fields at each end of the electromagnet; the diaphragm is a steel plate; and the moving coil is a copper cylinder in which eddy currents are induced by two stationary windings in push-pull arrangement. The range of this transmitter is about 30 miles for telegraphy and one-half mile for speech. Another widely used transmitter of unique construction is the Hahnemann “Tonpilz.”’ Since, in a subaqueous transmitter, one part of the vibrating system is actuated in air whereas the other vibrates in contact with water, it is advantageous to employ a mechanical step-up transformer because of the considerable difference in radiation impedance between water and air. This is realized by converting the large displacement and low-pressure oscillation of the electromagnetic driver into the small displacement and high-pressure oscillation of the water-bounded diaphragm. Mechanically, the transformation is effected by coupling a heavy diaphragm to a driver of small mass by means of a solid elastic rod. Ultrasonic transmitters are less useful in position-finding and sound- ranging but are well suited for communication and echo-sounding because of their directional characteristics. Three types are in predominant use: electromagnetic, piezoelectric, and magnetostrictive. The electromag- netic transmitters follow in design the Fessenden or Hahnemann type previously discussed and cover the lower ultrasonic range (10,000 to 20,000 cycles). A transmitter consisting of six elements about 15 cm in diame- ter, mounted one above another on a vertical tube which can be withdrawn by a hydraulic lift into the ship’s hull, is described by Hecht.” An echo- sounding transceiver operating electromagnetically at a frequency of 17,500 cycles is illustrated in Fig. 12-23. The piezoelectric (crystal type) transmitters are generally used at between 30 and 40 ke., which gives ample range (10 to 20 km) and sufficient directional discrimination (about 25° to 30°, see footnote on page 937) for signaling between shore stations and ships and between ships in motion, and also for echo-sounding. Since a large radiation area would not be obtainable with thin quartz plates, 120 Thid., p. 413. 121 T]lustration in G. W. Stewart and R. B. Lindsay, Acoustics, p. 249, Van Nos- trand (1930). 122 Op cit., p. 413. Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 947 mosaics of such plates between two steel plates are used. In the Langevin- Florisson transmitter,” the quartz plates are 2 mm and the steel plates each 3mm thick. The diameter is 25 cm, the frequency 38 ke. Virtually the same transmitter has been built in England and Germany for the purpose of echo-sounding (37.5 ke., driven by peak voltages of 6000 volts, transmitting damped impulses of about 1/1000 second duration). Magnetostrictive transmitters make use of the Joule effect, that is, changes in length of a rod when it is magnetized longitudinally. The drivers are solenoids (see Fig. 12-24) or iron yokes, surrounded by coils and used with a biasing field. The armatures are nickel rods, coupled to aluminum diaphragms. Driving power is supplied by V.T. oscillators in regenerative arrangement or by high-tension generators discharging through a condenser into the field coils surrounding the rods. The latter scheme is used in the (20 to 30 ke.) echo-sounding transmitters built by — Atlas-Werke and by the Electroacoustic Company™ and in the Hughes echo-sounder (Fig. 12-24). 3. Submarine sound receivers (hydrophones). Subaqueous sound re- ceivers fall into two groups: (1) stethoscopic listening devices, and (2) elec- trical microphones. In the former, the application of the stethoscopic principle (amplification by reducing the section of a receiving chamber to that of an ear tube) is necessitated by the energy loss occasioned by the tremendous contrast in the acoustic resistivities of water and air. Were the sound to pass directly from water to air, only 0.12 per cent of the incident amount would be transmitted. A stethoscope with a 15:1 ratio of base to tube diameters raises this to 2.4 per cent,” that is, it effects a twentyfold improvement. To obtain unit yield, a 60:1 ratio in the base to tube diameters would have to be realized. This means that with the normal ear-tube size, hydrophones of impracticably large diameters would have to be built. The difficulty may be overcome by interposing another medium between air and water. Unit transmission may be accomplished if the acoustic resistivity of this medium is the geometric mean of the acoustic resistivities of air and water and if its thickness is one-quarter of the wave length of the sound in it. This has led to the adoption of listening devices with rubber shells fashioned in the form of a Broca tube, that is, a spherical receiver attached to an ear tube. On small vessels such receivers have been used on both sides of the ship, and the direction of sound has been determined by aiming the ship for equal sound intensity or phase, making use of the binaural effect. For larger vessels, mechanical or electrical 123 Tllustrated'in Bergmann, op. cit., p. 196. 124 Tilustrated in Bergmann, op. cit., p. 198. 125 Stewart and Lindsay, loc. cit. 948 MISCELLANEOUS GEOPHYSICAL METHODS [CHap. 12 compensators take the place of the rotatable receiver system. In stetho- scopic devices, mechanical compensation may be accomplished by varying the length of the ear tubes in trombone fashion, or by inserting a rotatable capsule which has variable air passages inside” and allows the direction of sound to be read directly. Greater accuracy in direction-finding is possible by the use of multiple receivers. As many as twelve to eighteen have been used on each side of the ship. Stethoscopic listening devices have been largely superseded by electrical receivers. The latter consist in the main of diaphragms provided with carbon-microphone, electromagnetic, piezoelectric, or magnetostrictive transducers. Carbon microphones have been applied mainly in inertia- coupled form as described below. Electromagnetic hydrophones are of the inductive (moving coil) or reluctance (variable air gap) variety. Representatives of the former are the Fessenden oscillator (see page 946) and the Electroacoustic Co. detector.” In this, the diaphragm carries a piston, moving in a closely fitted ring, with oil in the gap to achieve damping. Reluctance receivers are constructed very much like the reluc- tance seismographs described in Chapter 9.’% One example is the Hahne- mann Tonpilz transmitter (when used as a receiver), another the ordinary headphone receiver, and a third is the balanced armature (Baldwin or Westinghouse) speaker when suitably coupled to the diaphragm as dis- cussed below. The piezoelectric and magnetostrictive receivers are usually identical in construction with the transmitters previously described. Hydrophones may be readily constructed with available microphone or speaker units. Three arrangements are possible: (1) mounting the micro- phone to the orifice of a stethoscopic air chamber behind the diaphragm; (2) combining the diaphragm with the moving coil of a dynamic speaker or of a coil microphone, or with the armature of a reluctance phone, the magnet unit being rigidly fastened to the case; (3) suspending the repro- ducer in inertia or Tonpilz fashion from the diaphragm. The first arrange- ment lends itself best to hot-wire, condenser, electromagnetic, and other available microphones or diaphragm reproducers, but it is the least efficient of the three. The second method is best suited for velocity (inductive and reluctance) transducers and for quantitative reproduction, particu- larly in connection with compensators. The third is probably the most effective and is used with reproducers of light weight, such as crystal and carbon button microphones. 126 Tllustrated in Stewart and Lindsay, op. cit., p. 276. 127 Tllustrated in Hecht, op. cit., p. 429. 128 See p. 611. 129 Such a use of Baldwin balanced armature reproducers is described by H. G. Dorsey, U. S. Coast and Geod. Surv., Field Eng. Bull. No. 12, 212 (Dec., 1938). Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 949 Electrical receivers may be combined with electrical compensators for directional reception. The design of the delay network is the same as in the atmospheric sound compensators previously discussed (see page 939). However, determination of vertical angles is rarely required; and, there- fore, the hydrophones and the delay elements in the compensators are arranged as nearly in a circle as the ship’s outline will permit. A com- pensator for submarine detection, corresponding in construction to that illustrated in Fig. 12-22, is described by Hecht.” 4. Marine-acoustic communication. The frequencies used for marine communication depend greatly on purpose, location of the receiver, relative stability of the positions of the communicating parties, as well as range, directional selectivity, and secrecy desired. Since receivers are usually located on ships in motion, interfering noise frequencies due to engines, propellers, and the like, must be suppressed. This requirement sets the lower frequency limit at about 500 cycles. For direct reception, the upper limit is determined by the sensitivity of the ear. As a practical compro- mise, a frequency of 1050 cycles has been adopted in most merchant marines for some time. In the navy, where directional transmission is desirable, communication frequencies are higher and extend into the ultra- sonic range. Speech transmission, direct or by modulating a high-fre- quency carrier, has been successful for short distances only (one-half to one mile). Audio-frequency transmitters and receivers are generally of, the electromagnetic type. Ultrasonic receivers are arranged in groups and are mounted on tubes which may be lowered from the ship’s keel and rotated about a vertical axis. The purpose is to confine the beam to the direction of communicating shore stations, surface ships, or submarines. Because of its directional properties, acoustic communication is often su- perior to radio. When used between ships of the same fleet in combat, it is less vulnerable than radio. 5. Marine-acoustic position-finding and sound-ranging. In its simplest form, marine-acoustic position-finding consists of a determination of the bearing of two sources of sound of known position, such as buoys, light vessels, and shore stations equipped with identifiable transmitters. Strictly speaking, this method comes under the heading of direction- finding; hence, this discussion will be confined to the more quantitative methods of position-finding and sound-ranging by measurement of travel times. The distance of a ship from a source transmitting both an air and water signal at the same time, such as light vessels and buoys, may be deter- mined by application of formula (12-20). If v, is the velocity of sound in 130 Op. cit., p. 428-429. 950 MISCELLANEOUS GEOPHYSICAL METHODS [Cuap. 12 water and v, that in air, the formula gives a factor of 0.42 with which the time difference in seconds is multiplied to obtain the distance in kilometers. Capable of greater range is distance determination by the use of radio and sound signals transmitted simultaneously from shore stations and light vessels. In that case (by application of formula [12—20]) the distance in kilometers is approximately equal to one and one-half times the observed time difference in seconds. By receiving signals from two radio and under- water sound transmitters of known position, the ship’s position may be found without difficulty. Conversely, a ship firing a depth charge and transmitting a radio signal at the same time to two shore stations equipped with hydrophones may be given its position by radio. This is of con- siderable help to navigation in fog; a ship forty miles away from the transmitters may thus locate itself within about 2000 feet. A similar procedure is applied in the “RAR” (radio-acoustic-ranging) system of the U. S. Coast and Geodetic Survey to determine the position of echo-sounding vessels. From the latter, a depth bomb is fired elec- trically at the desired location, and the sound wave is picked up by two Sono-radio-buoys anchored at known positions. The buoys are equipped with short-wave transmitters which radio the instant of reception back to the surveying vessel where the radio signals are recorded on a chrono- graph. For this purpose, a hydrophone is suspended half way down the anchor line of the buoy. The phone is connected to a tuned three-stage transformer-coupled amplifier which, through a gas tube, trips the grid of a 4 megacycle (2 to 5 watt) transmitter.’ This arrangement removes the carrier between signals and makes for a longer life of the transmitter batteries. The maximum hydrophone range to trip the transmitter is 80 to 100 km; the range of the radio transmitter in terms of signal required to work the recording chronometer is about twice as great. The accuracy of the RAR system depends, naturally, on how well the velocity of the sound in sea water is known; and this in turn changes with refractions, reflections, and variations in temperature and salinity (see page 944). For a given area, velocities can be determined by RAR observations with known vessel positions obtained from geodetic triangulation or astronomic measurements. Marine sound-ranging methods are used for the location of mine ex- plosions and depth charges, and for determining the range of a ship’s shell fire. The hydrophones are placed along a base line about twelve miles long and are connected to a shore recorder similar to the type used in atmospheric sound-ranging. If the secrecy of the installation is of no 131 A. M. Vincent, U. S. Coast and Geod. Surv., Field- Eng. Bull. No. 11, 73, (Dec., 1937). A slightly different circuit is described by H. G. Dorsey, op. cit., p. 99. Cuar. 12] MISCELLANEOUS GEOPHYSICAL METHODS 951 consequence, the hydrophones are suspended from radio-equipped buoys which communicate the impulses to a shore recording station or recording vessel. Explosions of mines and torpedoes or shell hits may be located by sub- marine sound-ranging equipment up to distances of 100 km. 6. Direction-finding and noise-detection. Marine noise-detection and direction-finding are applied (1) in navigation, to determine a ship’s posi- tion by taking bearings of one or two sound sources of known position (submarine transmitters on buoys, lighthouses, shore stations); (2) in the detection of enemy craft from surface ships and submarines, and in de- tecting the approach of friendly ships to avert collisions with emerging submarines; (3) in the surveillance of straits and harbors during periods of poor visibility. With the exception of the last application, the detecting devices are mounted on board ship and therefore an immediate difficulty arises from the high noise level caused by the ship’s engines, propellers, rush of water, and activities on board ship. This interference may be partially reduced by sound insulation and electric or mechanical filtering; however, the only really effective means of separating the noises to be detected from these accidental noises is by directional hearing. Among the noises produced by other ships, most important is probably that caused by the propeller as the result of the collapse of air bubbles. This noise is so characteristic that a practiced listener may determine the number of propellers and blades, the type of engine, and therefore the type of ship to which he is listening. Other noises are produced by the ship’s engines, by pumps, and by generators, and are transmitted through the hull to the water unless special precautions are taken. The frequency range of a ship’s noises is considerable; for practical purposes, the band from 500 to 2000 is most suitable. In the early days of marine direction-finding, two receivers of the Broca type were used with a rotatable base of comparatively small length. Later this was replaced by two or more receivers on both sides of the ship, con- nected to a mechanical time-delay compensator of the trombone type previously described. This system has recently been superseded by elec- trical coil microphones with electrical compensators, as described on page 939. 7. Echo-sounding. Echo-sounding is undoubtedly the most widely used marine-acoustic method. Its advantages in speed and accuracy over the mechanical wire-sounding method are obvious. The method is more than a mere means of measuring depth. Because of the speed and completeness with which the topography of the ocean floor may be mapped, it is an aid in navigation since in many cases the ship’s position may be determined accurately from a bottom contour map. Echo-sounding has been applied 952 MISCELLANEOUS GEOPHYSICAL METHODS [Cuap. 12 in the location of shipwrecks and submarines on the bottom, the determina- tion of the character of the ocean floor, and the detection of fish shoals. Echo-sounding was tried at an early date on icebergs; Fessenden found at the time that (on account of the irregular surface of the berg under water) the ice echoes were much more feeble than the sea-bottom echoes. This may possibly be overcome by the use of high-frequency sounds and hori- zontally directed beams. In this manner ranges of at least several hundred yards may be obtained. It has been reported” that greater ranges (up to three miles) are obtainable by listening to the bursts which apparently develop in the iceberg from its cracking under water. Marine echo-sounding methods involve the principle of distance deter- mination by measuring (1) the direction of the return ray, and (2) the time interval that elapses between the initiation of a sound impulse and the arrival of the echo. The first system requires that the depth be comparable with the length of the triangulation base, that is, the length of the ship. Therefore; this method is applicable only at shallow depths, to about 100 fathoms. As originally applied, this method utilized the propeller noise as sound. A group of submarine detectors was mounted forward on the ship and connected to a compensator, whereby the direc- tion of the incoming sound could be determined. If ¢ is the angle which the sound, reflected from the sea bottom, makes with the horizontal, and if 2a is the distance of the detector group from the propellers, the depth to bottom is given by d = a tang. This method is not particularly fast nor is it very accurate. In all other echo-sounding procedures, the time interval that elapses between the initiation of a sound impulse and the arrival of the echo is measured. The reflection of a sound impulse generated by striking a bell may be perceived by the human ear. However, the intensity of such an impulse would not be sufficient to actuate an automatic indicating device, nor would this timing method be accurate enough. Large intensities may be generated by crowding the available energy into a short space of time, for example, by the detonation of an explosive, or by a condenser discharge into an electromagnetic or magnetostriction oscillator. A wide frequency range has been utilized. High frequencies, although subject to great absorption, offer definite advantages in regard to directional selectivity. In shallow water they are the only ones applicable. Since, for a depth accuracy of five feet, a time interval of 2 milliseconds must be measured, the length of the initial impulse cannot be more than 1/10 of this interval. Inasmuch as, for moderately damped transmitters, the impulse dies out after about 10 oscillations,” frequencies ranging from 10 to 50 ke. are 132 H. T. Barnes, Nature, 124, 337 (Aug. 31, 1929). 133 H. Hecht and F. A. Fischer, Handb. Exp. Phys., 17(2)., 433-4389 (1934). Crap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 953 required for shallow echo-sounding. Ultrasonic receivers and transmit- ters of the electromagnetic, piezoelectric, or magnetostrictive type, previ- ously discussed (see pages 946 and 948), are mounted on opposite sides of the ship, usually in water-filled tanks on the inside of the hull. In many installations, only one device is used for both transmitting and receiving. In regard to construction and operation, three different kinds of echo- sounders may be distinguished: (1) phase shifters, (2) dial indicators, and (3) automatic recorders. An example in the first group is the British Admiralty depth finder, in which the transmitter is a 2000 cycle diaphragm that is struck a hard blow with an electromagnetic hammer to start the sound impulse. The electrical impulses are transmitted to the oscillator three times a second from a contactor switch rotating at uniform speed. This commutator carries two segments which are connected to the re- ceiving phones and which put a short circuit on the phones except for a brief instant. The brushes making contact with the transmission seg- ments are fixed, whereas the receiving brushes may be revolved with re- spect to the former. The operator adjusts the angle between the two sets of brushes until he can hear the echo distinctly, the angular rotation then being a measure for the echo time and therefore for the depth. In one of the sonic depth finders developed by the U. 8. Navy, the above principle is reversed and the time interval between successive impulses is changed until transmitted and received impulses are heard simultaneously. This will be the case if the transmission interval is an integral multiple of the echo time. The transmission interval is controlled by varying the dis- tance of a friction wheel from the center of a driver disk rotated at con- stant speed. Further details on this method will be found in Stewart and Lindsay.” In the second group of echo-sounding devices, depth readings are taken on rotating dials or pointers that are started by the sound impulse and stopped by the echo. The earliest of these is the ‘‘microtimer” invented by Behm.” It is essentiaJly an electrically operated stop watch and consists of a disk with a steel projection which is held in the starting posi- tion by an electromagnet. When an underwater cartridge is fired, a nearby microphone picks up the sound impulse and by a relay disconnects the starter electromagnet from the circuit. The disk is then set in motion by a leaf spring which engages a projection on the outside of the disk. A second microphone, when struck by the echo, disconnects a second or brake electromagnet, thus releasing its armature which is fastened to a brake 134 Op. cit., p. 283-286. 135 Literature will be found in: B. Schulz, Ann. Hydro., 62, 254-271, 289-300 (1924). H. Maurer, Ann. Hydro., 52, 75 (1924), 64, 336-340, 391 (1926), 56, 347-352 (1928); Zeit. Ges. Erdk. Berlin, 62, 371-377 (1927), 63, 248-249 (1928); Erg. H., III, 130-218 (1928). Hecht and Fisher, loc. cit. 954 MISCELLANEOUS GEOPHYSICAL METHODS [Cuap. 12 shoe. At that instant the disk is stopped, its graduation giving the depth directly. The accuracy of this device is claimed to be 1/10,000 of a second. In the ‘“echometer’”’ designed by Hecht, a steel disk connected to a pointer is situated between two electromagnets. One of these is stationary and the other is revolved continuously by a synchronous motor. Before the sound impulse is sent, both electromagnets are energized and the steel disk is held by the stationary electromagnet in such a manner that the pointer is on the zero point of the dial. The sending of the impulse dis- connects the stationary electromagnet so that the moving electromagnet’ is free to take the disk along with it. When the echo arrives, the rotating magnet is disconnected and the stationary magnet is energized so that the disk and the pointer stop at an angular position corresponding to the echo time and, therefore, the depth. The pointer is held in this position for a few seconds, permitting a reading to be taken. It is then returned auto- matically to its starting position. Another dial-indicating instrument is the “fathometer” developed by the Submarine Signal Corporation. A modification for shallow depths by Dorsey’ is illustrated in Fig. 12-23. In this instrument the pointer is represented by a slot in a disk attached to the rotor of a synchronous motor driven by a 1025-cycle tuning fork. In front of the revolving disk is a frosted glass dial and behind it is a circular neon tube which lights up instantaneously when the echo strikes the receiver, thus illuminating the depth reading on the stationary dial. The sound impulse is dispatched by the action of a photoelectric cell which receives a flash of light from a mirror attached to the rotor when the latter passes through its zero position. Recently, the recording type of echo-sounding device has come into in- creased use. It is a simple matter to record oscillographically the reflected impulse, together with what motion may be produced by the direct wave which travels from the source to the receiver through or around the hull of the ship. Records of this kind resemble those taken in reflection seis- mic exploration.’ However, such oscillograph records are required only in connection with experimentation and research. Because of the rela- tive strength of the reflected impulse, its well-defined character, and the absence of interference from other refractions or reflections, a complete record can be dispensed with. The echo-depth recorders now used work automatically and record continuously both impulse transmission and echo depth; in other words, they trace the water surface and the bottom contour. An automatic recorder developed by the British Admiralty™® is illus- 136 H. G. Dorsey, J. Wash. Acad. Sci., 26(11), 469-476 (Nov., 1935). 137 See records in B. Gutenberg, Lehrb. Geophys., 3, 585 (1926). 138 J, §. Slee, J. Inst. El. Eng. (London) 70, 269-280 (1932). Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 955 trated in Fig. 12-24. Both transmitter and receiver are high-frequency (16,000 cycles) magnetostriction units and are mounted on opposite sides of the ship in water-filled tanks. The sound impulse is initiated by dis- charging a high tension generator through a condenser into the windings of a submarine oscillator, the transmission key being actuated by the recorder itself when it reaches the zero position. The recording unit is PHOTOELECTRIC UGHT 2 110 volts m3 f 60 cycles TUNING FORK 1025 cycle supply KEVING CIRCUIT 17.5 k.c supply 110 volts 60 cycles CONVERTOR ° 110 velts,0.¢. % SHIPS SUPPLY Ocean bottom U. S. Coast and Geodetic Survey Fig. 12-23. Schematic circuit of Dorsey fathometer. essentially a spiral drive which moves a stylus back and forth across re- cording paper impregnated with starch iodide. An imprint is produced by liberating iodine when current passes through the stylus and the paper to a metal roller beneath the paper. When the stylus is at the edge of the paper, the transmission key is closed and current passes through the stylus, thus marking the instant when the signal is dispatched. On arrival of the echo, current is again passed, thus producing a continuous record of the ocean bottom. With these high-frequency recorders it is possible to dif- 956 MISCELLANEOUS GEOPHYSICAL METHODS [CHap, 12 Transmitting key Recording fon Mahe ferentiate between the sur- face of the silt and the solid rock on the bottom of the ocean, and to pick up fish shoals, determining their depth and their concentra- tion in relation to the topo- graphy of the ocean floor HT. generator (Fig. 12-25). The ability of high-frequency echo- sounders to furnish this information in addition to m rarenntens ocean bottom contour has ey made them invaluable in commercial fishing.” Chemical recorder C. Groacoustic MrtTuHops Section of E mete eee Geoacoustic procedures are essentially short-wave (or high-frequency) seismic methods. . They are distin- guished from seismic meth- ods” in that they involve audio-frequency communi- Fig. 12-24. Automatic magnetostriction echo cAllon apg Lapeer enn: depth-recorder (after Slee). and not direct measurement of travel times. At pres- ent, geoacoustic methods are applied in mine safety, mine rescue, mine surveying, location of water pipes and water leaks, and location oH enemy sappers in trench warfare. 1. Velocity and absorption of sound waves in the ground. Since travel times are not measured in geoacoustic methods, few direct data on the ground velocities of audio-frequency sounds are available. However, there is no reason to assume that they differ from the velocities of seismic waves of lower frequencies, as discussed in Chapter 9, pages 468-472. Of the three sound-transmitting media—air, water, and earth—the latter, particularly consolidated rock, shows the highest velocities. Com- 139 QO. Sund, Nature, 136(3423), 953 (June, 1935). 140 In respect to transmission frequency, dynamic soil-testing (discussed in sec- tion III of this chapter) occupies an intermediate place between seismic and geo- acoustic methods. Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 957 pared with water and air, the ground is a-rather poor sound-transmission medium. Attenuation of audio-frequency elastic waves in the ground is much greater than the attenuation of seismic waves. Many factors are responsible, such as refraction, reflection, scattering, absorption, and damping. To begin with, more energy is lost in audio-frequency than in seismic-frequency transmission because of scattering, since the wave length of audio-frequency sounds is comparable with the dimensions of the interfering objects. In seismic exploration, the wave length of re- flected waves of an average speed of 10,000 feet per second is 200 feet at a Nughes £tho Souncer f= 16000 ~ + ; Cowtish Shoal | - } t i f es { m4 j t Sorrento pecs aoa 5 Minute *Marks . ALU? Codtish Shoal wee “Sgmineeente mam 0 ee YO y m . ” Ocean 4ottom) + Deg eS IS Johan tort ita brent Wes7TFsoeo LOFOTEN Fig. 12-25. Fish-shoal detection by sonic depth finder. frequency of 50 cycles, and the wave length of ground-roll waves of a velocity of 1000 feet per second is 100 feet at a frequency of 10 cycles. On the other hand, the length of geoacoustic waves of a velocity of 6000 feet per second is only 3 feet at a frequency of 2000 cycles. Since the intensity of sound scattered by an obstacle is proportional to the volume of the obstacle and inversely proportional to the fourth power of the wave length, it follows that high-frequency sounds may readily be scattered several hundred thousand times more than low-frequency seismic waves, other conditions being equal. This accounts for the limited range of high-fre- quency sound waves in the ground. The relative range of seismic and 958 MISCELLANEOUS GEOPHYSICAL METHODS [CHap. 12 acoustic waves in the ground is therefore comparable with the ranges of audio-frequency and supersonic waves in air. Another cause of attenuation is loss of amplitude due to internal fric- tion. In a viscous medium, the distance traveled by an elastic wave until its amplitude is diminished to 1/e of the initial amplitude is the reciprocal of the absorption coefficient, or 3v\’/8r'II, where II is the static vis- cosity coefficient, v the velocity, 5 the density, and \ the wave length. The range is thus inversely proportional to the square of the frequency. With increasing distance, the higher frequencies drop out and the lower- frequency components of the initial impulse remain. The range increases further in direct proportion to the radiation impedance (product of veloc- ity and density). Hence, the waves travel farther in firm and consolidated than in loose and unconsolidated rocks (see page 478). Leighton’™ has given the following values for distances at which the pounding of a sledge hammer could be detected with a 1000-cycle geophone through various formations: 3000 feet through hard rock, 2000 feet through coal, 400 feet through clay, and 550 feet through the mine cover. For vertical propaga- tion down to 400 feet, Howell, Kean, and Thompson obtained half-value distances of 900-cycle waves ranging from 78 to 640 feet.” It follows from the above that geoacoustic methods are well suited for the location of highly absorptive formations underground, such as clay seams, faults, and shear zones. 2. Geoacoustic sound transmitters. More than twenty years ago Fes- senden suggested the use of submarine transmitters in wells as a source of elastic waves for the exploration of mineral deposits.’ Such transmitters were not wholly successful because of the limitations of the high frequencies just discussed. Comparing 400-cycle propagation with explosion-gener- ated waves in a profile across the Hawkinsville salt dome, L. G. Howell, et al, found shorter travel times for the explosion waves, which would indicate that the latter penetrated the cap rock whereas the audio-fre- quency waves tended to travel near the surface. It is probable, therefore, that for exploration purposes the lower frequencies, such as those used in dynamic soil-testing vibrators, have better possibilities. In mine rescue work and trench warefare there is, naturally, no choice in regard to the frequency characteristics of the sound source. As a mat- ter of fact, the higher frequency components have to be utilized if the drill- ing or digging tools and associated activities are to be identified. The 141 A. Leighton, U. S. Bur. Mines Tech. Paper No. 277 (1922). 142 T,, G. Howell, C. H. Kean, and R. R. Thompson, Geophysics, 5(1), 1-14 (Jan., 1940). 143 U.S. Patent 1,240, 328. 144 Toc. cit. Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 959 same applies in the location of water leaks, whose characteristic sounds are caused by the impact of the escaping water on the surrounding formations. In underground communication and mine rescue operations it has been found that the most effective way of transmitting sounds is to strike a hard rock surface with a sledge hammer. 3. Geoacoustic receivers. The unaided ear would be a rather ineffective means of detecting earth sounds. A marked improvement may be at- tained by the simple means of using a canteen almost full of water, and by placing the ear as closely as possible to its orifice. The principle involved here is that the contrast in radiation impedance between ground and air is stepped down by the insertion of water (see page 947). Another way of detecting sounds transmitted through the earth is to resonate a mechanical detector or seismograph to the predominant ground frequency and to con- nect this detector with the ear by a stethoscopic amplification device. A detector of this kind is known as a geophone and is illustrated in Fig. 12-26. Fic. 12-26. Geoacoustic Monee (geophone) (after Teese htoi. (a) Sree (6) cap plate, (c) iron ring; lead weight in solid black. In it a lead mass weiahing about one pound is suspended between two nickel diaphragms about 7235 inch thick. The space above the upper diaphragm is about 3 neat in diameter and connects to an orifice of about ¢ inch in diameter. From the orifice the sound passes into the rubber hose of a stethoscope whose end fits snugly into the ear. Geophones are generally used in pairs for directional hearing. To obviate phase dif- ferences, the rubber hoses must be of equal length. The reduction of diameter of the geophone in its orifice results in an increase of amplitude. Since the transmission of sound from a large to a small tube is equivalent to the transmission from a dense to a rare medium, eqs. 9-34 (see page 478) apply. Substituting, for the radiation impedance, the products of velocity and density, considering the velocities equal on both sides, and setting the densities proportional to the cross-sectional areas, the transmitted amplitude is 2.S,/(S2 + Si) times greater than the amplitude of the diaphragm. For a standard geophone in which the ratio of the cross-sectional areas of diaphragm and orifice is of the order of 120, 960 MISCELLANEOUS GEOPHYSICAL METHODS [Cuap. 12 the amplitude of the air in the rubber hose is therefore about twice the amplitude of the diaphragm. Thus, the gain resulting from a reduction of the cross-sectional area is rather small. It may be increased by the use of electro-mechanical trans- ducers coupled to the geophone mass. Ackley and Ralph” have reported that the minimum audible distance could be doubled by using a standard geophone with an unbalanced reluctance transducer and a three-stage triode amplifier. Undoubtedly this sensitivity can be further increased by crystal transducers and higher gain amplifiers. Carbon microphones and hot-wire microphones have been proposed for this application but are probably not so good as crystal microphones. 4. Geoacoustic communication. Geoacoustic methods are used as a means of communication of rescue parties with entombed miners and with other parties located at the surface or in near-by mine openings. Signals are transmitted by striking the wall at short intervals with a sledge hammer or other available tool. Transmission is better in the direction of the strike of formations than at right angles thereto, and it may be cut off occasionally by faults or shear zones. Communication is possible in this manner through distances of 2000 to 3000 feet in rock and through about 500 feet of overburden. Speech may be picked up through distances of several hundred feet, although the standard geophone, being undamped, is not particularly suited to a faithful reproduction of speech. It is probable that an adaptation of the crystal microphone would be better adapted to direct speech transmission. 5. Geoacoustic position-finding and sound-ranging. From the discussion of these topics in connection with marine-acoustic methods, it will be re- called that position-finding is defined as the determination of one’s position by timing the sound from one or two sources of known location, and that sound-ranging involves the location of a source by acoustic triangulation. Both of these procedures involve the measurement of travel times and have therefore no direct parallel in geoacoustic work with present equip- ment. A related seismic application is the determination of crookedness of drill holes by measuring the travel time from surface shot points to a phone located in the hole (see page 863). Geoacoustic triangulation is possible only by an application of direction/finding methods discussed in the next paragraph. 6. Direction-finding, noise-detection. 'These methods are applied in mine rescue, mine safety, and mine surveying work for locating entombed miners, detecting and locating underground fires, determining the approach of tunnels and drifts and bringing together raises and stopes (thereby pre- “45 W. T. Ackley and C. M. Ralph, U. 8S. Bur. Mines Rep. Invest., Ser. No. 2639, Sept., 1924. Crap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 961 venting accidents in blasting through), and locating and measuring the drift of boreholes sunk from the surface with the intention of reaching a definite point of the subsurface workings. Military application includes the detection and location of enemy galleries in trench warfare and the surveillance of underground sapping activities for escaping enemy blasts and directing counterblasts. In the latter application, the object of acoustic observations is to de- tect, identify, and locate mining operations by the noise of mining tools such as hammers, picks, dnils, shovels, and other machinery. Sounds transmitted by mining tools are characteristic and permit definite identi- fication, despite the distortion occurring in the intervening media and an undamped tuned receiver. Underground fires are identified by a typical hissing sound produced by air drafts, by cracking of timber, and by the fall of rock from the mine roof. Civil engineering application of geoacoustic methods includes the loca- tion of pipes and pipe leaks. Water, gas, and oil pipes can often be found by the typical noise of the gas or liquid passing through them, that is, by the vibration set up in the pipe, although the use of an electromagnetic detector (see page 819) is preferable if the pipe itself is to be located. Leaks in water pipes can be found by the noise of the water impinging on sand, gravel, or rock in the cavity surrounding the leak, and by the vibration produced in the pipe by the water issuing from the leak. Geoacoustic direction-finding makes use of the binaural effect discussed on page 938. Two geophones are shifted in position until a line connecting them is at right angles to the direction of the sound. The phones may also be used in fixed position, when they are provided with a compensator to determine direction by adjusting the phase difference. In application of the first method, the two phones are first set out with their base approxi- mately at right angles to the direction of sound. One phone is left sta- tionary and the other is moved toward the sound source so that the sound appears to come from the right. Then this phone is moved back in the opposite direction from the base line until the sound appears to come from the left. In this manner an intermediate position can be established in which the sound comes from neither the left nor the right.“° A source is then located by making direction determinations at a number of points and by finding the intersection of the rays. Pipe leaks are usually not located by direction-finding but by following the course of the pipe and by observing changes in sound intensity. The location of a leak is indicated by the point of maximum intensity. This point may be considerably re- moved from the surface evidence of the leak, since the liquid issuing from 146 Leighton, loc. cit. 962 MISCELLANEOUS GEOPHYSICAL METHODS [Cuap. 12 it may travel along the pipe or follow subsurface cavities of an unpredict- able course. Noise measurements for the detection of leaks should be made in the early morning hours when traffic is at a minimum. Another method of leak detection developed by the Western Instrument Company requires contact between the pipe and a probe carrying a crystal pickup at its end. The pickup is oriented in two directions, one parallel with, and the other at right angles to, the pipe. Intensity of vibration is measured in both directions and also as a function of frequency if neces- sary. It is claimed that the ratio of longitudinal to transverse vibration intensity shows significant variations when a leak is approached. Geoacoustic direction-finding is not so reliable nor is it applicable at such great distances as marine-acoustic methods. Transmission is limited, not only in range but in direction as well, by rapid changes in the elastic wave speeds, particularly near the earth’s surface. When underground workings are situated in a district of complex geology, it may be quite difficult to establish consistent directions from geoacoustic observations. 7. Transmission measurements. Occasionally, valuable information may be obtained in underground mining operations from the location of faults, fissures, shear zones, clay seams, and the like. This may be done by pro- ducing sounds at a given location and observing the intensity of reception at a number of points so arranged in adjacent drifts, tunnels, or shafts that the presence and approximate disposition of sound-absorbing media may be determined. With electrical geophones, direct measurements of intensity may be made by the use of a calibrated amplifier with output meter.” Indirect measurements of intensity may be made by swinging a hammer through a predetermined arc in a mechanism especially made for this purpose. By gradually reducing the arc, the minimum transmission intensity necessary to produce an audible signal is obtained. As a rule, however, quantitative intensity measurements are not made, and the presence or absence of sound-absorbing media is ascertained by merely noting at which points the sound reception is poor or entirely absent.” 8. Geoacoustic-reflection methods. Reflection of sound waves in the ground is determined (1) by noting the direction of the return ray, and (2) by measuring the time interval between the initiation of a sound im- pulse and the arrival of the echo. Distance of reflecting surfaces has been measured underground by ad- justing the position of two geophones in a vertical plane for equal recep- tion. This is not possible at the earth’s surface, and it is necessary to use a compensator to establish the direction of the return ray. Attempts have 147 A suitable instrument (sound-level meter) is manufactured by the General Radio Company, Cambridge, Massachusetts. 148 Leighton, loc. cit. Cuap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 963 been made to locate ground-water levels and bedrock surfaces in this manner, but they have not been wholly successful. This is because the sound rays may be diverted in a quite unpredictable manner by the in- tervention of different formations. This is particularly true of the near- surface weathered layer which deflects the return ray into an almost verti- cal direction, thus virtually obliterating any significant variations in the direction of the reflected ray. A measurement of reflection travel time would undoubtedly obviate the difficulties mentioned, since it is then pos- sible to correct for the low-velocity surface layer. Unquestionably one of the reasons for the lack of progress in geoacoustic- reflection methods is the superiority of explosion-generated impulses as used in seismic reflection procedure over audio-frequency impulses. As far as principle is concerned, there is, of course, very little difference be- tween acoustic echo-sounding and seismic-reflection methods. The dif- ference is primarily one of frequency. As a matter of fact, the use of low-frequency sustained oscillations (as applied in dynamic soil testing) has been proposed for the location of shallow formations, since the seismic- reflection method, at present, cannot be used successfully for that purpose. In practice, this limitation is not too serious, inasmuch as shallow forma- tions may be readily mapped by the seismic-refraction method. 4 H & Tier ed 3 ’ what Beers a : E ; * ~ Ma r ei 4 $ ; . E 4 " , ‘ . \. F . , 4 4 ‘ 4 + : a . £ A f 4 ha ¢ , ye : + he net A 17 ‘ t 5 " » 4 + : Lf ’ . bs f CLs 5 + r ' ; 2 f * + Riek Pe | j pre . A 4 ‘ ‘ M | 7 : ‘ ¢ = > 7 5 t oT ‘ ( ; % b ‘ . = - . a ‘ A i . i ; 4 tea 4 a] . * 5 phe * ., r . ; ‘ b : SUBJECT INDEX: A Aaregranite, susceptibility of, 313 ABC system, 548, 549, 572, 576 Abdank-Abakanovicz integraph, 249 Abnormal polarization (see Polarization) Abrasives, 550 Absorption and attenuation: — coefficients (see Coefficients) -— of electric currents and radiation, 627, 652, 685, 686, 809, 811, 812, 813 ~ of radioactive radiation, 870-873, 881 — of seismic energy, 480, 492, 924 — of sound waves (see Sound, absorp- tion of —) A.C. (see Alternating current) Acceleration: — in fan shooting, 500-501 —of gravity (see also Gravitational field and Gravity), 88, 89, 454 — of ground motion, 447-449, 477, 586, 587, 590, 593, 920 — vectors, 500, 501 Accelerometer, 586, 587, 590, 598, 613 Acetylenes, 889 Acidity of soils, 647, 680 - Acoustic: — communication, 937-939, 945, 949, 960 — compensators, 938, 939, 942, 948, '949, 951, 952, 961 - direction-finding, 938, 941, 942, 951, 960-962 ~ echo-sounding (see Echo-sounding) — frequencies in acoustic methods, 866, 937, 940, 941, 945, 946, 949, 952, 9538, 955, 958 — intensity, 477-481 — methods, 9, 36, 41, 58, 934-963 — noise-detection, 941, 942, 951, 960-962 — opacity, 480 = postion nce, 937, 939, 940, 949, 960 — ranging (Gee RAR system) — receivers (see Sound receivers) — resistance, specific, 477-479, 947, 949 — transmission measurements, 962 - transmitters (see Sound transmit- ters) Sound-ranging and Acoustic (cont’d): — transparency, 480 ~ triangulation, 940, 942, 949, 950, 960 — waves (see also Sound, Seismic waves), 435-436, 943-945, 956-958 — say pea au 35, 866, 867, 942, 4 Actinium, 873 Actinon, 873 Activity, electrochemical (see Polariza- tion, spontaneous) Agitator (see Vibrator) Air: radioactivity of —, 874 sound velocity? in - , 468, 867, 935, 941, 943 Airplane: detection of —, 9, 41, 64, 941, 942 measurements in -, 7, 19, 41, 42, 363, 365, 407, 408, 813 Air-pressure correction, 10, 118, 133 Albite, density of, 80 Alluvium: density of -, 82 longitudinal wave velocity of -, 469 Rayleigh wave velocity of —, 473 resistivity of —, 664 Alpha rays and alpha radiation, 863, 864, 871-873, 882, 884, 885 Alternating current in electrical pros- pecting, 25, 619, 624, 630, 642-649, 681, 685-696, 701, 752, 760, 761, 763-765, 774 Alternator (see Generator) Altimeter, 64, 813, 942 American mining compass, 346 Ames gauges, 454 Ammunition, 63, 297, 435, 436, 624, 627, 706 Amphiboles: density of -, 80 elastic moduli of —, 467 Amphibolites: density of -, 81 susceptibility of -, 312 Amplifier: — in electrical prospecting, 27, 29,. 30, 695, 696, 701, 758-761, 765, 774, 775, 778-782, 784-786, 820, 821, 823, 824 1 Geographical names will be found in the Name and Place Index. 965 966 Amplifier (cont’d): — in Geiger counter, 864, 882, 883 seismic —, 21, 503, 552, 553, 556, 617, 618, 917 Amplitude correction, 98, 99, 117, 118 Andalusite, density of, 80 Andesite: density of -, 81 elastic moduli of —, 467 electrical anomaly of —, 755 heat conductivity of —-, 849 specific heat of —, 848 Andesite glass, density of, 81 Anglesite, density of, 77 Anhydrite, 34, 54, 291, 292 density of —, 79, 84 dielectric constant of —, 666 elastic moduli of —, 468 longitudinal wave velocity of -, 471 susceptibility of —, 310, 312 Anisotropy: elastic —, 476 electric —, 636, 643, 693, 700, 706 thermal —, 848, 851-853 Ankerite, susceptibility of, 310 Annabergite, density of, 78 Anodic zones, 680, 681 Anomalies: electromagnetic —, 766, 773, 790-809 Eltran -, 761 equipotential-line —, 697-706 gravity -, 4, 12, 146-162 magnetic -, 4, 16, 18, 19, 296, 316, 373- 378, 381-436 resistivity —, 713-744 self-potential —, 672-681 torsion balance —, 254-292 Anomalous vectors, 378, 379, 405-407, 411, 413, 417, 418 horizontal —, 378, 379 total -, 380 vertical —, 379, 380 Anorthosite, density of, 81 Antenna, 812, 813, 814, 815, 867 Anthracite: density of -, 79 dielectric constant of —, 666 resistivity of —, 658 spontaneous polarization of —, 53, 668, 677 - Anticlines (domes, uplifts), 5, 8, 12, 15, 43, 45, 70, 151, 153, 158, 160, 161, 252, 259, 262, 263, 282, 283, 296, 396, 425, 430, 431, 441, 508, 518, 547, 551, 577, 736-738, 907 electrical logging results on -, 838 electrical prospecting results on -, 735-737 magnetic results on —, 424, 425, 428, 429 pendulum and gravimeter results on -, 157-161 seismic results on -, 518, 547, 577 SUBJECT INDEX Anticlines (cont’d): torsion balance results on -, 273, 274, 283, 284 Antimonite, density of, 78 Antimony, density of, 77 Apatite, density of, 80 Aperiodic motion (see Damping, critical) Apparent velocity (see Seismic wave velocity) Approximation curves, 717, 718, 729-731 Aquagel, 491, 571 Aqueducts, 57, 58 Aquifer (see also Water), 61, 62, 743 Arago gauge, 899 Archimedian spiral, 583 d’Arcy’s law, 904 Argentite, density of, 77 Argillite, resistivity of, 662 Armorican sandstone, 706 Aromatic hydrocarbons, 889, 890, 900 Arsenides, resistivity of, 657 Arsenopyrite: d’Arsonval galvanometer, 552 density of -, 77 — ore, 704 susceptibility of —, 310 Artesian basins, 61 Asbestos, 55 Asphalt: — base oils, 888-889 density of -, 79 — deposits, 886, 887 Aspirator, 868, 877, 881 Astatic system, 301, 302, 303, 359, 364, 865, 866 magnetic, 367 Astatization: — of gravimeters, 11, 127, 128 — of seismographs, 586 Astronomic observations, 113, 168, 169 Atacamite, density of, 78 Atmosphere, unit, 452-454 Atmospheric acoustic methods, 935-943 Atmospheric electricity, 3, 370 Atomic number, 871 Atomic weight, 872 Attenuation (see Absorption) Augite: density of —, 80 dielectric constant of —, 666 elastic moduli of —, 467 susceptibility of -, 310 Augite diorite: coercive force and remanent magneti- zation of -, 316 density of -, 80 Augite syenite: coercive force and remanent magneti- zation of —, 316 susceptibility of —, 313 Austin chalk, 285 Autocollimation method and system, 177, 321, 322, 324, 930 SUBJECT INDEX Automobile, magnetic effect of, 373 Auxiliary magnet (see Magnet, auxiliary) Average velocity (see Seismic waves, velocity of) Azurite: density of -, 78 susceptibility of —, 310 B Balance: induction —, 819, 820, 822 Jolly -, 72 magnetic — (see Magnetometer) torsion — (see Torsion balance) vertical gravity gradient —, 190-192 Baldwin receiver, 595, 948 Ballistic galvanometer, 305, 306, 307, 359, 360, 361, 363, 893, 894 Ballistic metnod of measuring suscepti- bility, 306, 307 Balloon, 19, 407, 408 Barite: density of -, 79 — deposits, 50, 55, 70, 288 dielectric constant of —, 666 Barometer, 119, 123 Barometric method of measuring grav- ity, 123, 124 Barret terrometer, 628, 823 Barye, 452-454 Basalt, 73, 76, 290-292, 414, 415, 432-435, 512, 513 coercive force and remanent mag- netism of —, 316 density of -, 81 dielectric constant of —, 666 elastic moduli of —, 467 heat conductivity of —, 849 longitudinal wave velocity of —, 472 radioactivity of —, 874 specific heat of —, 848 susceptibility of —, 314, 432 Basaltic glass, density of, 81 Base correction, 17, 135, 332, 338, 339, 372, 373 Base station, 135, 338, 339, 372, 373 Basement rocks, 4, 19, 43, 46, 53, 70, 160, 283-285, 409, 421, 422, 424, 425, 427-430, 432, 441, 516, 546, 847 specific acoustic resistance of —, 479 transverse wave velocity of -, 473 Batholith, 427, 437 Bauschinger gauge, 455 Bauxite: density of —, 79 — deposits, 51, 417 Bayley-Walker extractor, 901 Beam: gravimeter, 132, 133 torsion balance —, 11-15, 85-88, 175-199 Bearing capacity, 921 Bedrock, depth determination of, 502, 625, 728, 729, 733, 734, 740-743, 756, 757 967 Below method, 155, 236, 237, 238, 268 Bending tests, 458-460 Benzenes, 889 Beryl, density of, 80 Beta rays and radiation, 871-873, 881, 882 Bicarbonates, 901, 903 Bicycle, magnetic effect of, 373 Bieler-Watson coil and method, 626, 779, 783, 784, 804, 806 Bifilar suspension, 11, 128, 130, 131, 195 Binaural effect, 938, 942, 947, 951, 961 Biotite gneiss, resistivity of, 660 Bismuth, density of, 77 Bismuthinite, density of, 77 Black sands, 5, 49, 51, 318, 416 Blasting caps, 20, 487-489, 494-496, 571 Blasting vibrations (see Vibrations, blasting) Blastophone, 503 Blueground, 56, 419 Bodily tides, 163, 164, 929 Boiling point, 847, 891, 892 Booneville dam, 435 Borax, density of, 79 Borda equation, 117 Bore holes (see Wells) Borings (see Wells) Bornite: density of —, 78 resistivity of —, 657 Bouguer anomalies, 142 Bouguer reduction, 11, 136, 137, 141, 142, 147, 152 Boulder Dam, 63 Boundaries of formations (see Formation boundaries) Bourdon tube, 366 Bow wave, 507 Bricks: density of —, 79 magnetic effects of —, 317, 374 Bridges: foundations of -, 57, 58, 60 magnetic effect of —, 373 strains in —, 928, 930, 933 vibrations of —, 441, 912, 915 Brine, 61, 867, 886 Broadcast waves (see Radio waves) Broca tube, 947, 957 Brown iron (see Limonite) Brown pendulum, 109, 110, 112 Brucite, density of, 78 Brunton compass, 352 Building materials, 54 Buildings: magnetic effect of —, 374 resonance of —, 918, 919 vibrations of -, 6, 9, 441, 911-913, 915, 917-919 Bulk density, 74, 75, 77 Bulk modulus, 446 Buoyancy, 72, 118, 133 Buoys, 949, 950 968 Buried ridges or hills, 5, 8, 18, 45, 47, 70, 161, 283, 284, 296, 422, 429, 430 Butane, 888-891, 896, 903 Buzzer, 765, 774, 775, 819 C Cables, electrical effects of, 701, 702, 766, 769, 771, 772, 776, 777, 791- 793, 796 Calcite: density of -, 8 dieleciric constant of —, 666 elastic moduli of —, 467 heat conductivity ‘of -, 848 resistivity of —, 658 - specific heat of - , S48 Calculation charts and forms: — for magnetometer, 333, 339, 405 — for pendulum, 106, 123 —for torsion balance, 200-209; 223, 225, 229-238, 242, 245, 246, 267, 268 —in electrical prospecting, 726, 727, 730-733, 769, 794, 795, 804 Calibration: ~ of electroscopes, 879, 880 — of gravimeters, 133, 134, 135 — of magnetometers, 329-332, 338, 348, 366 — of pendulums, 118-122 — of seismographs, 615-618 — of torsion balance, 194-198 Calomel, density of, 77 Calorimetric methods, 848 Camera recording and recorders, 20, 21, 110, 111, 332, 366, 503, 552-554, 556, 599, 608, 611, 614, 616, 617, 828, 912, 940, 941, 943, 950, 954, 956 Canal rays, 871, 898 Canals, 57, 58 Capacitive detectors (see Seismographs) Capacitive strain gauges (see Ultrami- _crometer) Capacity, bearing (see Bearing capacity) Capillarity, 744 Cap rock: density of —, 84 detail geophysical work on -, 501 gravity anomalies on —, 158, 274-283 magnetic anomalies on -, 423 sulfur in -, 53 Carbon: — dioxide, 894-901 — microphone, 613, 937, 948, 960 — seismometer, 613 — strain gauge, 930, 931 Carbonates, resistivity of, 658 Carboniferous formation, 538, 421, 439, 470, 473, 736 Cardan suspension, 102, 103, 110, 333, 352, 353 Cardan suspension magnetometer, 333, 352, 353 Carnallite, density of, 79 Cartographic correction, 226, 227 SUBJECT INDEX Casing depth, 835 Cassiterite: density of —, 77 dielectric constant of —, 666 susceptibility of -, 310 spate oscillograph (see Queille: aph Cathodic! protection’ 63, 372 Cavendish torsion balance, 85, 175 Caverns: location of —, 815, 816 magnetic anomalies in -, 376 Caving (see Mine caving) Cavities, in shot holes, 489, 503 Cement and cementing, 34, 858-860 Cement rocks, 51, 54 Cenco pump, 899 Centrifugal force, 89, 92, 93-96, 123, 919- 921 ' Centrifugal pump, 20, 491, 492 . Chalecocite: density of -, 78 resistivity of —, 659 Chaleopyrite: density of -, 78 — ore, 704, 804 resistivity of —, 657, 659 susceptibility of —, 310 Chalk: density of -—, 84 — deposits, 54 dielectric constant of —, 666, 667 longitudinal wave velocity of -, 471 specific heat of —, 848 Chamber, ionization (see chamber) Channels, erosional (see Placer deposits) Chanute shale, 83 Chazy shale, 84 Chemistry: — of hydrocarbons, 888-891 — of solutions, 628-639 Cherokee shale, 83 Chert, 52, 289 Chlorite, density of, 80 Chloritic slate: density of -, 81 elastic moduli of —, 467 Chromite: density of -, 78 — deposits, 50, 52 magnetic anomalies of — , 418, 422 resistivity of —, 659 susceptibility of -, 310 Chromium, 73 Chronograph, 113, 114, 950 Chronometer, 10, 103, 104, 107, 113, 116, 117 - correction, 116, 117 ° Chrysocolla, density of, 78 Cinnabar: density of -, 77 resistivity of -, 657 Circulation of drilling fluid, 856, 857 Tonization SUBJECT INDEX Clairaut’s theorem, 89, 90-96, 136, 190 ay: density of —, 74-76, 82 — deposits, 54 dielectric constant of —, 666, 667 ~ heat conductivity of —, 849 longitudinal wave velocity of —, 469 resistivity of —, 637, 658, 661, 664 specific heat of —, 848 susceptibility of —, 312 Coal: density of -, 79 — deposits, 51, 53, 287, 740, 886 heat conductivity of —, 848 resistivity of —, 658 specific heat of —, 848 ‘susceptibility of —, 312 © Coal removal, effect on gravity, 167 Coast: — effect on gravity, 166, 241, 242 — effect on gravity gradient, 241, 242 Cobaltbloom, density of, 78 Cobaltite, density of, 77 Cobalt ore, 52 spontaneous polarization of —, 668 Coefficients (see also Constants): absorption -, 480, 481, 652, 845, 936, 944, 958 anisotropy —, 700, 852 attenuation — (see absorption —) curvature —, 173, 174 dilation -, 443-445 dissipation —, 483 expansion — , 327, 328, 337, 338 - instrument -, 178- 189, 192-198 Lamé -, 445-448 mass-absorption —, 873, 881 Poiseuille —, 481-483, 936 - reflection -, 478, 712 stiffness — (see Constant, spring -) temperature, 118, 133, 196, 197, 327, 328, 331, 338, 367 terrain -, 217-225 torsion -, 85, 88, 130, 131, 177. 178, 185, 193-199, 353, 598-600 - viscosity — (see Poiseuille -). Coercive force, 307, 309, 315, 316, 401 oil: HielaiWolte —, 330, 331, 338, 363, 366,403 reception —, 30, 39, 763, 765, 773,776, 778-786, 807, 819-822, 824 Coincidence: — interval, 103-106, 108, 117-119, 121, 122, 135 — method, 10, 103-108 stroboscopic -, 104, 105, 106 Colorimetric analysis, 901 Colpitt oscillator, 931 Combustion of hydrocarbons, 895-896 Communication: acoustic —, 63, 935, 939, 946, 949, 960 radio -, 114, 115, 496, 503, 555, 809 wire -, 494, 495, 504, 555, 556 969 Commutator, 29, 304, 644, 723, 724, 826, 27, 953 Compaction, 75, 76, 915, 921, 922 Compander, 552, 554 Comparator: electrical — (see Ratiometer) optical —, 99 Compass: American mining -, 346 dial -, 17, 346, 403 dipping -— (Louis), 346. Swedish mining -, 17, 319, 320, 345, 346 — variometer, 365, 376 Wilson compass attachment, 352 Compensation: acoustic — (see Compensator) electrical — (see Compensator) — inductor, 363 Compensator: acoustic —, 938, 939, 942; 949, 949, 951, 952, 961 electrical —, 28, 30, 40; 624-626, 648, 695, 696, 726, 758, 760, 765, 766, 779, 781-785 gravity —, 87, 88 magnetic —, 301, 348, 350, 351 Compressibility, 446, 457, 458, 467, 468 tests of —, 457, 458 Compression, 442, 443 Compression (= flattening), 95 Compressional wave, 448 Concentration: — of currents (see Current concentra- tion) — of gases, 884, 885, 903, 905-907, 909 — of magnetic materials, 297, 318, 416 mechanical concentration deposits, 49, 51, 297, 318, 416 — potential (see Diffusion potential) —of radioactive materials, 864, 870, 875, 885 Condenser microphone, 552, 610-612, 948 Condenser-microphone strain gauge, 456, 931, 932 Conduction: dielectric —, 26, 640, 641 electrolytic —, 26, 633-640 electronic — (metallic), 26, 632-634 Conductive surface layers, 652, 702, 743, 805, 809 Conductivity, electrical (see sistivity), 26, 28, 622, 632-637, 639, 640, 641, 652, 655, 656, 685, 688, 721, 727-730, 741, 748, 791, 796- 800, 811 apparent ~, 721, 727-730, 800 Conductivity, heat (see Thermal con- ductivity) Conglomerate: density of -, 83 gold -, 49, 419 resistivity of —, 662 970 SUBJECT INDEX Constant: attenuation — (see Coefficients, absorp- tion) dissipation —, 485 gravitational -, 85, 86, 87, 139, 140, 393-395, 797 instrument —, 178-179, 192-198 spring —, 99, 100, 124, 449, 581, 582, 591, 595, 920 Construction materials, location of, 54, 58, 60, 434, 435 Contact metamorphism and contact metamorphic zones, 4, 6, 16, 50, 51, 297, 317, 318, 385, 412, 414, 417 Contact resistance, 642, 643, 753 Contacts, formation — (see Formation boundaries and Faults) Continuous profiling, 25, 570 Contrasts of rock properties on formation boundaries (see Formation bound- aries) Convergence recorder, 928-930, 933 Copper: arsenic —, 803 damping resistance of -, 482 density of -, 77 — deposits, 50, 51, 52, 70, 73, 74 resistivity of —, 659 — sulfate, 630, 667, 701 Corona (see Halo) Core: — analysis, 835 — orientation, magnetic, 35, 685, 866 Coring: electrical -, 8, 28, 33, 34, 41, 44, 45, 623, 625, 744, 825-840, 843 mechanical -, 47 Corrections: amplitude -, 10, 98, 99, 117, 118 auxiliary magnet —, 330, 333, 338, 339 base -, 17, 332, 338, 339, 372, 373 Bouguer -, 11, 136, 137, 141, 147 buoyancy -, 118 cartographic —, 226, 227 chronometer -, 116, 117 coast effect —, 241, 242 diurnal variation —, 18, 162, 367-372 drift —, 135 elevation -, 11, 25, 136-137, 375, 509, 572, 578 flexure —, 10, 119-122 free-air —, 11, 136, 137 — for normal values, 11, 14, 18, 141, 210-212, 377 planetary -(latitude) -, 11, 14, 18, 94- 97, 141, 210, 212, 375, 376 regional -, 141, 160, 162, 240, 241, 246, 251, 377 spread -, 23, 558-560 temperature -, 10, 17, 118, 133, 134, 196, 197, 327, 328, 331, 337, 366, 367 terrain -, 11, 14, 71, 137-140, 169, 213- 240, 375, 376 Corrections (cont'd): topographic — (see Terrain and Eleva- tion correction) — for variation in air pressure, 10, 118, 133 — for variations in gravity, 162, 166, 326 — for ek intensity variations, 336, 33 weathering -, 24, 548-549, 569, 571, 572, 576 Correlation: — of depth temperature curves, 34 — of electrical logs, 33, 825, 836, 837 — of resistivity profiles, 736, 738 - shooting, 25, 570, 578, 579 Corrosion, 6, 26, 38, 41, 42, 63, 372, 624, 631, 667, 668, 676, 679-681, 752, 754, 755 Corundum, density of, 79 Cost of geophysical work, 5, 47, 48 Coulomb’s balance, 303 Coulomb’s friction, 582, 583 Coulomb’s law, 16, 145, 293 Covellite: density of -, 78 resistivity of —, 657 Cretaceous formations: specific acoustic resistance of -, 479 vertical velocities in —, 473 Crevices (see Faults and Fissures) Critical: — angle, 506, 519, 522-535, 538, 539, 541, 542, 546, 547, 557 — damping (see Damping, critical) Crocoite, density of, 7 Crooked holes, 862, 863, 960 Cryolite, density of, 78 Crystalline rocks (see Igneous rocks and Basement rocks) Cuprite, density of, 77 Curie: — point, 317 — unit, 873 Curie - Chénéveau balance, 303 Current: alternating — (see Alternating current) — concentration, 31, 32, 766, 767, 769, 790, 791, 801 — density, 26, 630, 633, 640, 673, 674, 683, 685, 697-699, 767-769 direct — (see Direct current) - lines, 681-684 d natural — (see Spontaneous potential) Curvatures: — of interference fringes, 460 — of niveau surfaces of gravity, 12-15, 167, 169, 170-172, 174, 176, 190, 191, 210-212, 247 Curvature values, 12-15, 166, 168-170, 172, 174-178, 184, 186, 187, 189, 190, 193-195, 198-206, 208-213, 215- 217, 219, 220, 222-226, 228-231, 233, 235-238, 242-248, 251-270, 273, 276, SUBJECT INDEX Curvature values (cont’d): 277, 280, 284, 286-289, 291, 292, 394-396, 400 graphical representation of —, 244-250 integration of —, 39, 168, 169 Curvature variometer: — Brillouin, 292 — Eétvos, 13, 14, 175, 176, 178, 193 Curved-ray method, 23, 540-546, 560 Cuyuna formation, Wis., 415 Cyclodiolefins, 889 Cycloolefins, 889 Cycloparaffins, 889 Cyclotron, 354, 355 Cylinder: gravity attraction of —, 146-150 magnetic anomalies of —, 392, 396 torsion balance anomalies of -, 258, 259, 261 D Dacian formation, 836, 837 Dacite, density of, 81 Dahlblom: — magnetometer, 348, 352 — sine arm, 349, 352 Dam: — investigations, 6, 57, 58, 435, 441, 624, 733, 734, 741, 742, 928, 930 — sites, 8, 57, 58, 60, 435, 928, 930 Damping: .- air —, 583 antenna -, 815 — constant, 481, 584 critical —, 584, 585, 587, 588, 590, 603, 604, 605, 606 determination of -, 481, 616, 617, 921 electromagnetic —, 584 — of electromagnetic waves, 649, 685, 811 — factor, 586 — of ground, 911, 921 oil -, 583 — ratio, 585, 586, 588 relative —, 481, 482, 586-590, 602, 606, 607, 921 — resistance, 482, 584 — rocks, 481, 482, 483 — of structures, 36, 911, 912, 918, 919 d’Arcy’s law, 904 Darley pipe locator, 765, 818, 819 Decibel, 480 Declination, magnetic, 39, 40, 295, 355, 356, 361 Declinator, 356, 357 De Collongue deflector, 349, 351 Decomposition (see Disintegration) Deep: — sea sediments, 874, 875 — wells, 840, 841, 845, 862, 863, 866, 867, 868 971 Deflection: — of galvanometer, 304-307, 598-601, 644 — of gravimeter, 124, 128-131, 133 — of magnetometer, 300, 301, 303, 306, 321, 323, 326, 335, 336, 340, 344, 345, 348-351, 353, 356, 357, 364, 365 — of pendulum, 97-100, 581 — of rock specimen, 459, 461 - of seismograph, 58-588, 591, 593- 596, 616 sine method of -, 349, 364, 365 tangent methods of —, 349, 365 — of torsion balance, 177, 178 — of the vertical (plumb-line devi- ation), 70, 167-170 Deflectometer (see also Strain gauges), 454-456 Deflector, de Collongue (see also Magnet and Compensator), 351 Deformation, elastic, 441-449 Del Rio formation, 285 Demagnetizing: — effect of A.C. fields, 328, 372, 373 — factor, 306, 390, 393, 395, 401, 402 — influence of disintegration, 318 — influence of gaps, 315 Density, 4, 10, 15, 16, 67 bulk -, 74, 75, 77 — change with depth, 75, 76 — of combustible minerals, 79 determination of -, 70-72 buoyancy method, 72 flotation method, 72 pyknometer method, 71 by weighing, 71 factors affecting —, 72-77 — of igneous rocks, 73, 80, 81 — of metallic minerals, 77-79 — of metamorphic rocks, 81 — of miscellaneous materials, 79 mineral —, 74 natural —, 76, 77 — of ore bodies, 73 — of rocks, 70 — of sedimentary rocks, 82-84 Deposits, mineral, 49-51 Depth: — of burial, 74-76, 474-476 — calculations and determinations, 7, 11, 15, 19, 22, 23, 25, 26, 28, 29, 31, 32, 143, 144, 148-157, 251-270, 382, 384, 387, 407, 408, 439, 504, 508-515, 524, 525, 529-533, 538, 542, 544-548, 560, 572, 576-579, 671, 673, 728-734, 747, 754, 756, 766, 767, 790, 793, 794, 799, 807, 812, 818, 835, 837, 856, 867, 885, 905, 925, 951-956, 963 — control, 8, 67, 293, 437, 621, 671, 708 — of crystallization, effect on elastic properties, 474 972 Depth (cont'd): — penetration of curved ray, 542-545 — penetration of electrical energy, 619, 621, 625, 627, 683-686, 708, 736, 761, 763, 765, 773, 806, 809, 811, 812, 815, 816, 819, 824 variation of seismic and sound velocity (see Vertical variation of Beismic and sound velocity) Derricks, magnetic effects of, 375, 425 Detection coil (see Coil, reception) Detector (see also Seismegraph and Microphone): capacitive —, 20, 593, 610-612, 932, 948 electromagnetic = 593= 597, 609, 612, 862, 912, 917, 937, 940, 942, 948, 951 gas —, 35, 36, 868, 887, 892-898 inductive —, 20, 593-595, 597, 609-612, 912, 917, 937, 940, 942, 948, 951 magnetostriction, 948, 955, 956 piezoelectric (crystal) -, 20, 463, 593, 613, 937, 948, 949, 953, 960 reluctance -, 20, 595-597, 610, 611, 862, 937, 953-955 seismic —, 20-22, 35, 503, 505, 551, 552, 554, 555, 556, 593-597, 609-613, 862, 912, 917 thermal -, 58, 59 Detrusion meter, 454, 460 Devonian, 735, 736, 772, 885 apparent resistivity on Devonian an- ticline, 736 vertical velocities in —, 473 Dewar flask, 900 Diabase: coercive force and remanent magneti- zation of —, 308, 309, 316 density of -, 73, 81 elastic moduli of —, 467 magnetic effects of —, 414, 417 radioactivity of =, 874 resistivity of —, 660, 661 susceptibility of - , 308, 309, 318, 314 Diagrams, interpretation - (see Graphi- cal interpretation) Diagrams, wave front (see Wave front) Diamagnetism, 7, 299, 423 Diamond, 50, 52, 56 density of -, 80 Diatomaceous earth, 55, 74, 637 Dielectric constant: apparent —, 640, 641, 666, 667 determination of -, 649-656 phase shift method, 651 polarization measurements, 651-656 resonance method, 649-650 substitution method, 650, 651 — of minerals, 665-666 ~ of rocks and formations, 666, 667 true —, 622, 631, 633, 665, 666, 667, 811, 812, 813 Dielectric current conduction, 632, 640 Differences, method of, 23, 548, 549, 572, 576 SUBJECT INDEX Diffusion (of gases), 884, 887, 905, 906 Diffusion potential, 33, 624, 630, 631, 831-833 Diffusivity, thermal (see Thermal diffu- sivity) Dikes, 29, 5, 46, 70, 151-153, 259, 261- 264, 385, 396, 308, 399, 401, 402, 411, 414, 417-419, 429, 433, 750- 752, 865, 870 Dilation, 442, 443 Diluvial sands, longitudinal wave velo- city of -, 469 Diolefins, 889 Diorite: coercive force and remanent magneti- zation of —, 316 density of -, 80 dielectric constant of -, 666 elastic moduli of -, 467 radioactivity of -, '974 resistivity of -, 660 susceptibility of —, 313 Dip, apparent, 525, 526, 567 Dip determination,.and effect of dip: — on. apparent ‘resistivity, 722, 734, 735, 739, 740 — on electromagnetic field, 763, 767, 771, 772, 790, 791, 794, 800-803, 805 —on equipotential-line anomalies, ‘701, 06 — on geothermal data, 852, 853 — on gravity, 153, 162 — on magnetic anomalies, 384-386, 388, 398, 399, 403, 410, 411, 412, 419, 420 — on potential ratio, 748-751, 754 on reflection travel times, 563-571, 579 — on refraction travel times, 502, 504, 521-536, 538-539, 546, 547 — on Spontaneous potential, 671, 674, 675 — on torsion balance, 251, 252, 261-263, 288, 290 — in wells, 834, 865 Dip, magnetic (see Inclination) Dip needle, 17, 345, 346, 347, 356-358, 403, 413, 415, 422, 436 Dip shooting, 25, 567, 568, 570, 571, 579 Dipping needle, 345, 346 Direct current, 25, 403, 600, 601, 617, 619, 624, 631, 633, 642-645, 681, 685, 692, 723, 725, 758, 827 Directional transmission, 937, 945 Direction finding, 36, 37. 64, 938, 63, 941, 942, 951, 960-962 Dirigibles, 813 Disintegration, 16, 318, 478 Dispersion, seismic (see Seismic waves, dispersion of) Dispersion of electroscope, 876-881 Displacement current, 640, 641, 649. 685, 686, 811 ‘ Displacement recorders (see Strain gauges) SUBJECT INDEX Displacements of rocks, 928-930, 933 Disseminations, 162, 623, 628, 632, 659, 660, 677, 705, 802 Dissipation of seismic energy, 481, 482, 483 8 Dissociation, 633, 637 Disturbance vector (see Vector, anom- alous) Diurnal variation: — of gravity field, 163, 164 — of magnetic field, 41, 42, 331, 366, 367-371 Divining rod, 3 Dolerite: density of -, 76 - radioactivity of —, 874 susceptibility of -, 314 Dolomite: density of —, 80, 84 dielectric constant of —, 666 radioactivity of —, 875 specific heat of —, 848 susceptibility of —, 310, 312 Domes (see Anticlines Doublet, electrical, 672, 673, 697, 722, 723, 810 magnetic —, 19, 384, 387, 778 Drain pipes, magnetic effect of, 374 Drill casing: magnetic effect of —, 374, 375 plastic —-, 491 Drill holes (see Wells) Drill rigs, 490, 491, 842 Drill rods, magnetization of, 317 Drill, rotary, 20, 490, 491, 842, 899 Drilling mud and drilling fluid, 827- 835, 857 Dynamic magnification (see Magnifica- tion, dynamic) Dynamic response (see Frequency re- sponse) Dynamic testing: | — of rock specimen, 460-464 — of soils, 9, 36, 58, 62, 911, 914-928 — of structures, 9, 58, 62, 911, 914-928 Dynamite: — charges, placement of, 489, 490, 550, 551, 569-571 consistency of —, 486 cost of —, 486 density of —, 485 freezing resistance of —, 486 inflammability of —, 487 kinds of —, 484-485 — magazines, 487 propagation effectiveness of —, 485 rate of detonation of —, 485-486 safety of —, 486, 487 — as source of seismic energy, 7, 20, 484 Dynamo-metamorphic: — deposits, 41, 42, 49, 414- — effects, 317, 475, 476 973 E Kagleford formation, 285 Ear, sensitivity of —, 937 Earth: figure of -, 89, 95-97, 169 gravity field of — (see Gravity field) magnetic field of — (see also Total in- tensity, Vertical intensity, and Horizontal intensity), 16, 19, 293, 295, 296, 299, 301, 303, 307, 309, 316, 317, 320 mass of -, 87, 90 rotational velocity of -, 89 Earth currents, 372 Earth inductor, 40, 358-363, 366, 403, 866 Earth inductor compass, 363, 866 Karth magnetism, elements of, 295 Earthquakes, 3, 63, 317, 440 damages of -, 9, 910, 912, 913, 918 — vibrations, 36, 910, 912, 913, 918 — waves (see also Seismic Waves) 450-452 Echo, depth sounding, (see Echo sound- ing) Echometer, 867, 936, 942, 943, 954 Echo sounding, 9, 36, 37, 41, 59, 63, 64, 942, 943, 945, 946, 947, 950-957 Eclogite, density of, 81 Edwards limestone, Texas, 285 Effusion, 905 Elastic: — coefficients, 443, 445, 446 — constants (see — moduli) — deformations, 441-449 ~ moduli, 442-446, 911, 926, 927 complex -, 482, 483 — of formations in place, 911, 926, 927 laboratory determinations of -, 452-464 — of minerals, 467 — of rocks, 467 — units and conversion, 452-454 —, variation with pressure, 474, 934 — properties, factors affecting, 474-477 — waves (see Seismic waves) Elasticity: factors affecting -, 474-477 -of rocks, 4, 452-473 theory of -, 442-448 Electric (al): — anisotropy (see Anisotropy, electric) — conductivity (see Conductivity) — field, 7, 25, 26, 30, 619, 621, 622, 633, 640, 641, 652-654, 671-673, 681-692, 694, 697-699, 810-813, 815-818 -, A. C., 685-692 horizontal component of -, 652-654 normal —, 682, 683, 693, 694 potential of — (see Potential, elec- tric) quadrature component of -, 687, 690, 695, 696 974 Electric (al) (cont'd): stationary and quasistationary -, 681-684 vertical component of —, 652-654 — logging, 8, 28, 33, 34, 41, 44, 45, 623, 625, 744, 825-840, 843 detection of water flows by -, 834 dip determinations by —, 834, 835 electrode arrangements in —, 826, 827 resistance and impedance measure- ments in -, 825-831 spontaneous potential (porosity) measurements in —, 831-833 — methods, 25, 50, 51, 52, 54, 619-624 classification of -, 624-628 fundamentals of —, 619-624 operation of, 670-671, 692-695, 708, 723-726, 754, 764, 774, 779, 786, 793, 803, 806 - prospecting (see Electrical methods) — seismographs, 20, 551, 552, 592-597, 601-607, 609-613, 912, 917, 932 — surveys, 675-681, 703-706, 735-744, 755-757, 761, 771-773, 801-808 — transients (see Eltran and Transients, electric) Electrochemical: — method, 761-763 — phenomena, 622, 624, 628-633, 637, 639, 667, 668, 679, 680, 757, 761, 762, 831-833 Electrode: — arrangements, 709-711, 715, 745, 747, 752, 826, 827 — basis, 683, 711, 745, 754 — clamps, 642, 643 current — (see power -) energizing electrode (see power —) expanding electrode system, 749, 754 line -, 27, 30, 624, 693, 694, 764 mercury -, 643 nonpolarizable —, 26, 629, 630, 669, 670, 692, 725, 758, 763, 827 point —, 27, 30, 624, 682, 683, 764 polarization of —, 630, 669, 675 porous pot — (see nonpolarizable —) potential — (see search — power -, 27, 30, 682, 683, 692-694, 707, 708, 709-711, 745, 751, 752, 754, 758, 762, 764, 773, 826, 827 primary — (see power —) resistance, 642, 643, 753, 827 search -, 619, 625, 670, 671, 678, 692- 696, 701, 707-716, 745-749 secondary — (see search —) self-watering —, 695 — spacing, 670, 671, 694, 695, 708, 716, 718, 721, 726-732, 735, 736, 745- 749, 758, 763, 765, 773, 826-830, 834 Electrofiltration, potential, 33, 624, 631, 668, 831-833 Electrolytic phenomena, 629, 632, 633, 637, 757, 831-833 747- SUBJECT INDEX Electromagnetic field, 7, 25, 30, 621, 622, 625, 626, 642, 763-807, 815— 819, 821 epeorn aon of —, 685, 792, 811-813, 815, horizontal components of -, 30-32, 765-773, 776-778, 784, 735, 787— 796, 800-807, 810 in-phase components of —, 30-32, 622, 625, 626, 695, 696, 764, 765, 769, 779, 782-785, 787, 788, 792-794, 796, 797, 800-804: — of loops, 776-779 — of ore bodies, 770-772, 787, 789, 790, 791, 800-805, 807, 808 out-of-phase component of — quadrature components of —) phase differences of —, 30, 31, 769, 779, 783-789, 791, 793 polarization of —, 764, 778, 779, 783, 784, 786-789, 807, 818 quadrature components of -, 30-32, 622, 625, 626, 764, 769, 779, 782- 785, 787-789, 792-794, 796, 797, 800-805 ratios of —, 30, 31, 622, 764, 785, 786, 803, 804 vertical components of -, 30-32, 765- 773, 776-779, 784, 785, 787-789, 791-794, 796-803, 807 Electromagnetic methods, 25, 55, 619, 621-623, 625, 626, 690, 763-809 Ambronn’s method, 625 Bieler-Watson method, 626, 783-785, 806 depth range, 763 Elbof method, 626, 771 galvanic -, 7, 8, 25, 30, 764-773 horizontal loop methods, 774-805 inductive -, 5, 7, 8, 25, 26, 31, 32, 39, 45, 61,- 621-623, 625, 626, 773-809 Mason method, 626, 806 Radiore method, 626, 648, 806-809 ring induction method, 626, 648, 782, 796 Sundberg method, 626, 791-796 sat coopera method, 625, 771, 79 Miller method, 626, 772 vertical loop methods, 626, 805-809 Electromagnetic ‘radiation, 651, 652, 810-812, 871-873 Electrometer, 876-881, 898 Electrons, 353-355, 871-873, 882 Electroscope, 876-881, 898 Elements: — of earth’s magnetic field, 293, 295 resistivities of —, 657, 658 Elevation correction (see Correction, elevation) Elinvar, 10, 113 Ellipse, 653-655, 687-693, 764, 766, 772, 778, 779, 783, 784, 786, 788, 789, 818 (see 31, 32, 39, SUBJECT INDEX Ellipsoid: — of reference, 97, 167, 168 — of rotation, 91, 97, 167, 376, 381, 389, 392, 393, 700, 834 Elliptical bodies, 376, 381, 389, 392, 393, 698, 699 Elliptical polarization: — of electrical field, 653-655, 681, 685, 687-692, 693, 701 — of electromagnetic field, 690, 779, 787-789, 807 — of radio waves, 651-655, 689, 692, 818 Ellstone structure, Texas, 433 Eltran method, 30, 47, 623, 625, 631, 757-763, 817, 901, 908 Emanation: actinium -, 873 — chamber, 865, 876, 879, 880, 881 radium —, 865, 870-881, 884, 885 thorium -, 873, 877 Emergence angle, 533, 539, 541, 545, 952, 962 Emersio, 451 Emery testing machine, 457 Enargite, density of, 78 Energy, absorption of (see Absorption) Engineering: — applications of geophysics, 57-64, 297, 408, 433-436, 441, 503, 505, 624, 679-681, 706, 741, 742, 755, 765, 818-824, 866, 911-934, 956, 959, 961, 962 civil —, 6, 9, 58, 297, 433-436, 441, 503, 505, 624, 679-681, 706, 735, 741, 755, 765, 866, 911-934, 956, 959, 962 foundation —, 58, 60, 485, 441, 503, 505, 624, 741-748, 755, 911-914, 919- 931, 933 gas —, 6, 868, 869 — geology (see also — applications), highway -, 6, 8, 58, 69, 435, 441, 503, 505, 624, 735, 741-742, 743, 911, 915, 928 hydraulic — (see also Water, Pipe lines, and Engineering, founda- tion), 58, 60, 911 military -, 6, 9, 37, 42, 59, 60, 63, 64, 297, 433-436, 624, 706, 940, 942, 943, 951, 956, 958, 961 mining — (see also Mining and Mine safety), 167, 928-934 pipe line — (see Pipe lines) sanitary —, 58, 60, 911 — seismology, 441, 910-928 structural -, 6, 9, 58, 910-912, 915, . 917-919, 928-930, 934 transportation (see also Engineering, highway and structural), 58, 60 Enstatite porphyry, coercive force and remanent magnetization of, 316 Eocene. vertical velocities in, 473 975 Eétvés torsion balance (see Torsion balance) Kétvés unit, 89, 166, 170, 191, 192, 213, 216, 245, 380 Epeirogenic movements, 163, 165, 317 Epidote, density of, 80 Equilibrium, radioactive (see Radio- active equilibrium) Equipotential-line method, 26, 27, 78, 681-706 conditions for A.C. fields, 685-692 conditions for stationary fields, 681- equipment, 692-696 generators, 692, 694 interpretation in, 28, 697-703 power electrodes, 692-694 procedure, 671, 693-696 results, 703-706 search electrodes, 670, 671, 692, 694, 695 Equipotential lines, 26, 27, 39, 40, 624, 669, 670, 671, 675, 676, 681, 682, 688, 692-694, 696, 697, 699, 700- 706, 756, 817 quadrature -, 696, 701 Equipotential surfaces: convergence of —, 13, 15, 170, 172, 175 curvatures of — (see Curvature) cylindrical -, 169, 174 electrical —, 476, 682, 683, 693, 834 — of gravity, 12-15, 70, 89, 167-172, 174-176 Erosion, effect of on gravity, 165 Erosional channels, 61, 70, 292, 416, 417, 421, 439, 501, 502, 624, 678 Eruptive rocks (see Igneous rocks) Escarpments, 15, 514, 516, 517, 519, 520 Essexite, density of, 80 Ethane, 36, 888-892, 894-896, 899, 900, 902, 903, 906, 908-910 Evinrude pump, 491, 492 Ewing seismograph, 127, 580 Expanding electrode system, 747, 748, 749, 754 Explosion, instant of (see Shot instant) Explosives (see Dynamite and Blasting caps) Extension, 448, 444, 454-457 Extensometer (see also Strain gauges), 454-456 Extractors, 901 F Fan shooting, 20, 499-504, 546 — accelerations, 500-501 — equipment, 503-540 — in mining, 501-502 — in oil exploration, 499-504, 546 Faraday constant, 620, 629, 631 Faraday’s law, 642 Fathometer, 954-955 Fatty acids, 901 976 Faults, 5, 8, 15, 29, 35, 43, 45, 46, 52, 53, 61, 63, 70, 151, 152, 252, 264, 284- 286, 296, 395, 396, 425-427, 430, 432, 433, 441, 514-517, 519, 520, 624, 625, 718-721, 735, 738, 739, 742, 748-752, 754-756, 774, 805, 815, 853, 855, 862, 865, 870, 875, 883-885 Fechner balance, 193 Fechner pendulum, 109 Feldspar, 55 density of —, 80 elastic moduli of —, 467 heat conductivity of -, 848 specific heat of —, 848 Fence, magnetic effect of, 373 Fermat’s principle, 504, 533, 534 Ferromagnetic substances, 317. Field balance (see Magnetometer, Schmidt) Field strength (see Electrical fields, Electromagnetic fields, and Mag- netic fields) Fields, physical: direction of-, 39, 8&, 89, 168, 289, 621, 626 potential of — (see also Potential), 39 quasi-stationary -, 38, 681 stationary -, 38, 88, 293, 681-684 variation of —, with time, 38, 162-167 Figure eight, 684, 688 Fisher Metallascope, 628, 823, 824 Fish shoals, 64, 956, 957 Fissures (see also Faults), 60, 61, 427, 623, 738, 739, 870, 875, 883-885, 904- 907, 909, 928-930, 933 Flank formations, 274, 276, 296, 422, 423, 862 Flash box, 105, 109, 117, 120 Flattening, 95, 96, 97, 212 Flexure: — of pendulum support, 101, 121 — correction, 119-122. Flint, density of, 80 Float, 703. _ magnetic effect of -, 376 Floats, measurements on, 41, 42 Flotation method, 72 Fluctuation (see Variation) Fluid level determination, 867, 936, 942, 943 Fluorite: density of -, 79 — deposits, 50 electrical location of —, 52, 55, 735, 739 heat conductivity of —, 848 Fluorspar (see Fluorite) Flux, magnetic, 298, 299, 360, 596 electrical —, 26, 27,31 Flywheel machines (see Vibrators) Focal length, 178, 194, 321-323, 327, 328, 335-337, 340, 341, 344, 600, 608 Focal plane, 115 Focus, 106 Folding, 317, 551 SUBJECT | Fractionation, INDEX Folds (see Anticlines) Fontactometer, 881 Forced oscillations, 36, 62, 461, 481, 586- 911, 912, 917-919 Formation boundaries: concentration differences on -, 622, 631, 667, 678, 679, 831-833 density contrasts on -, 10, 67, 148, 278, 283, 285 differences in elasticity on-, 439, 441, 475, 478, 504, 548 differences in heat conductivity on -, differences of magnetization on-, 296, 390, 395, 425 resistivity contrasts on -, 28, 33, 622, seal 712, 718, 742, 765, 797, 828, Formation water (see Water) Foundation studies, 6, 8, 57, 58, 435, 441, 624, 625, 733, 741, 742, 911, 913, 914, 922, 928-930, 933. Four-electrode methods (see Resis- tivity methods and Gish-Rooney method) Fourier series, 220, 222 Fractional distillation, 891 low-temperature, 892, 898, 900 Fracture zones (see Shear zones) Frame, detection (see Coil, reception) Franklinite: density of -, 78 susceptibility of -, 310 Free-air correction, 135-137, 141 Free fall in vacuum, 123 Free oscillations, 62, 86, 97, 100, 356, 449, 461, 582-586, 598, 615, 616, 911-914 Freezing method of shaft sinking, 867 Frequency (ies) : acoustic —, 866, 937, 940, 941, 945, 946, 949, 952, 953, 955, 958 angular -, 92-100, 124, 449, 581-584, 639-641, 688 ~ bridge, 647, 774 damped (seismic) -, 584, 585, 588, 601 - and depth penetration of electric current (see Depth penetration) — factor, 587, 588, 604-606, 919 ground-(seismic) +, 452, 586-590, 593- 596, 598, 601-607, 911-913, 915, 920. high (electric) —, 619, 622, 623, 648, 685, 774, 805-809, 819, 821-823, 867 intemnedieT (electric) —, 619, 646, 647, 4 low (electric) —, 619, 645-646, 766, 774, 780, 797, 819, 823 natural (seismic) —, 36, 454, 460, 461, 481, 482 , 581-584, 586-596, 598, 600- 602, 604, 605, 607, 609, 615, 616, 617, 911-913, 915, 918, 920 of antenna, 814, 815 radio —, 619, 809, 811, 812, 814-818 SUBJECT Frequency/(ies) (cont’d): — range, in electrical methods, 25, 31, 619, 642, 685, 686, 694, 752, 763, 774, 809, 811, 812, 819 — ratio (see Tuning factor) resonance — (seismic), 461, 462, 481, 482, 588, 601, 616, 814, 815, 918, 921, 922 — response: of ground 36, 441, 493, 911, 912, 915, 918, 921-925 of rock specimen, 461, 481 of seismographs, 586-591, 593, 594, 597, 598, 601-606, 616-618 of structures, 36, 62, 441, 911, 912, 915, 919 — of seismic waves (see also Frequency, ground), 449, 452 ultrasonic — (see Ultrasonic trans- mission) Friction, 582, 583, 615 - angle, 922 G Gabbro: coercive force and remanent magne- tization of -, 316 density of -, 80 elastic moduli of -, 467 radioactivity of -, 874 resistivity of —, 660 susceptibility of -, 313 Gaede pump, 899 Gal (unit), 10, 13, 88 Galena: density of -, 77 — deposits, 417, 804 resistivity of —, 657, 659 | Galvanic-electromagnetic methods (see Electromagnetic methods) Galvanometer: astatic —, 359 : ballistic —, 305-307, 359, 360, 361, 363, 893, 894 bifilar —, 21, 552, 598, 600 . coil -, 21, 552, 598, 599, 600 — in earth inductors, 359,-361, 363 ~ in electrical logging, 826, 827 — in electrical receiving devices, 626, 644, 646, 651, 670, 671, 692, 693, er eee 762, 778, 780, 783, 814-816, — in gas detectors, 892, 893 — on Geiger counters, 864 loop-, 359, 609, 893 response of-, 600-603 seismic —, 495, 496, 504, 552, 555, 593, 595, 598-607, 617, 618 sine —, 365, 366 string -, 21, 359, 552, 598-601 tangent -, 365 — for temperature recording, 844 Gamma (magnetic unit), 16, 19, 296, 412, 414-417, 419-426, 428, 430, 432-436 INDEX 977 Gamma rays (radiation), 35, 54, 863, 864, 871-873, 876, 878, 879, 881, 884, 885 Gamma-ray well logging, 35, 42, 863- 865, 876, 883 Garnet, density of, 80 Garnet gneiss, resistivity of, 660 Gamnet schist, heat conductivity of, 849 as: — analysis, 5, 35, 868, 885-910 composition of -, 890 — constant, 629, 631 — detection, 9, 64, 866, 868, 869, 886, 887, 892-898 — detector, 64, 868, 869, 892-898 emanations of -, 35, 886, 887, 902-906 — leaks, 9, 35, 868 ~ in rock pores, 76, 887, 892, 898 — in wells, 34, 825, 842, 856, 866, 868, 869 Gauge, strain (see Strain gauge) Gauss (magnetic unit), 16, 295, 296, 298, 299, 308, 766, 793-795, 797 Gauss positions, 300, 325, 329, 336, 338, 351 Gauss tangent method, 349, 365 Gaylussite, density of, 78 Geiger-Mueller counter, 864, 876, 878, 881-884 Gems, 56 Generator, electric, 645, 692, 694-696, 724, 725, 758, 763-765, 774, 775, 781, 783, 807, 821, 823, 916, 947, 956 acoustic — (see Sound transmitter) Geoacoustic methods, 956-963 Geocentric coordinates, 92 Geochemical prospecting, 885-910 Geodetic triangulation, 168, 169 Geoid, 167, 168 Geological applications: — in engineering (see Engineering) | — in mining (see Mining exploration and Engineering, mining) — in oil exploration (see Oil exploration) Geologic bodies, 4, 7, 10, 11, 16, 38, 42, 67, 148, 144, 169, 247, 250-254, 293, 295, 377, 381, 389, 437, 439, 621, 622, 697, 707, 764 — two-dimensional -, 144-146, 150-157, 169, 243, 247, 251, 252, 254, 257-270, 385-388, 395-400, 768 three-dimensional -, 144-150, 153, 250, 253-258, 265, 266, 269, 270, 375, 381-885, 390-395 Geologic history, effect.on magnetic rock properties, 296, 315, 317, 318 Geologic structure (see also Structural studies), 4, 5, 8, 10 Geophone (see also Seismograph), 20, 58, 580, 591, 866, 959, 960, 961 Geophysical exploration: definition of -, 3, 4, 38 ~ im engineering (see also Engineering), 6, 8, 57-64 indirect -, 5, 6 major fields of -, 5, 6 measurement procedures of -—, 38-42 978 Geophysical exploration (cont’d): ~ in mining (see also Mining explora- tion), 6, 8, 49-56 — in oil (see also Oil exploration), 5, 8, 43-48 Geophysical mapping, 41 Geophysical methods, classification of, Geophysical orientation, 44 Geophysical prospecting (see Geophysi- cal exploration) Geophysical science, 3, 4, 70, 296, 440, 623 Geophysical sounding, 41 Geophysics, derivation of word, 3 Geoscope, 725 Geothermal gradient (see geothermal) Geothermal investigations (see Tem- perature measurements in wells) Geothermal methods, 840-845 ~ Gilbert (unit), 297, 298 Gimbal suspension, 102, 103, 110, 352 Gish-Rooney method, 28, 645, 660, 661, ee 709, 710, 712, 715, 720, 723-725, Glacial drift, 415, 703, 741, 756, 757 longitudinal wave velocity of - , 469 resistivity of —, 661, 664 specific acoustic resistance of -, 479 Glaciation, effect on earth’s tempera- tures, 853, 855, 856 effect on gravity of -, 165 Glaciers, 814, 815 Glass, damping resistance of, 482 Glauberite, density of, 78 Glow tube, 116, 497 Gneiss: density of -, 81 dielectric constant of —, 666 elastic moduli of —, 467 — formation, 271, 284, 288, 409, 430, 678, 679 heat conductivity of -, 849 longitudinal wave velocity of -, 472 radioactivity of -, 874 specific heat of —, 848 susceptibility of —, 312 Gold, 5, 8, 50, 51, 73, 297, 419, 704 —conglomerate, 50, 51, 419 density of -, 7 direct location of -, 5 — quartz, 29, 50, 52, 624, 754-756 Gossan, 27, 629-630, 668, 669 Gradient: — and curvature variometer, 13, 175-184 geothermal -, 844-847, 850-854, 860 horizontal -, of gravity (see Gravity gradient) magnetic —, 363, 380, 406, 407 regional -, 240, ‘241, 246, 251, 262, 281 vertical -, of gravity, 70, 136, 169, 190-192, 394 Gradient, SUBJECT INDEX Gradiometer: magnetic —, 40, 363, 364, 380 torsion balance —, 184-192, 380 vertical -, 190-192 Grain packing and porosity, 634-637 Graneros shale, 84 Granite: — building stone, 435 coercive force and remanent mag- netization of —, 316 density of -, 73, 75, 76, 81 dielectric constant of —, 666 elastic moduli of —, 467 ~ formation, 430, 502, 677, 678, 703, 742 heat conductivity of —, 849 longitudinal wave velocity of -, 472 radioactivity of —, 874 Rayleigh wave velocity of -, 473 resistivity of —, 660, 661 — ridge, 8, 18, 45, 47, 161, 284, 429-431 specific heat of =, 848 susceptibility of - -, 313, transverse wave velocity of —, 472 Ea areen longitudinal wave velocity Oo Granulite, density of, 81 Graphical correction methods, 138-140, 226-236, 243, 559 Graphical interpretation methods, 144, 153-154, 253, 256, 265-268, 389, 400, 536-539, 729-733, 768-769, 793-795 Graphical representation of data (see Plotting) Graphite: density of —, 79 — deposits, 55, 756 heat conductivity of —, 848 — impregnations, 623 resistivity of —, 632, 657, 659 spontaneous polarization of -, 668, 678, 680 susceptibility of -, 310 Graticule (correction and interpretation diagram), 138, 139, 153, 154, 229- 234" 265-267, 400, 769 Grating (see Graticule) Gravel: density of —, 838 — deposits (see also Placer deposits), 54, 277, 416, 417, 421, 439, 501-502, 733, 735, 742, 743 — pits, 377 Rayleigh wave velocity of -, 473 resistivity of —, 664 water -, 748, 744 Gravimeter, 8- 12, 39, 40, 43, 46-48, 53-55, 67, 70, TAN 123-137, 161, 162, 274, 580 Askania = 126 astatic —, 127-134 bifilar -, 130, 131 Boliden -, 125 calibration of —, 133-135 drift of —, 135 SUBJECT INDEX Gravimeter (cont’d): Isin Lindblad- Melinquist=- —, 125, 126 Mott-Smith -, 133, 134 natural frequency ‘of -, 127 recording -, 165 — results in mining, 161, 162 scale value of -, 134 sensitivity of —, 134 — survey results, 157-162 Threlfall and Pollock -, 125 Thyssen -, 132, 133 trifilar —, 131, 132 Truman -, 132 unastatized —, 124-126 underwater -, 109 Wright -, 125 Gravimetric methods, 7-15, 67-292 Gravitation, principles of, 88-97 Gravitational: — constant, 85-87, 139, 140, 797 — exploration (see — methods) — field, 11-16, 67, 88-96 time variations of -, 162-167 —methods, 7, 8, 9-15, 67-292 — pressure, 75, 476 Gravity: acceleration of —, 88, 89, 454 — anomalies: regional -, 141, 142, 160 local —, 145-162 — attraction of: cylinder, 146-150 sectors, 149 two-dimensional bodies, 150-154 — calculation from gradients, 248-250 - change with elevation, 135-137, 190 — change with latitude, 141, 211 — compensator, 87-89 corrections on -, 135-143 — field, 3, 9-16, 67, 88-96 — gradient, 10, 13-15, 70, 170, 171, 175-179, 182, 184, 186, 187, 189-195, 199, 201-203, 206, 210, 211, 213, 215, 218, 220, 222, 226- 230, 231, 233- 236, 238, 240, 244-266, 269, 270-292, 394-397, 400 graphical ‘representation of —, 244-248 Gravity: horizontal components of, 12, 39, 157, 167-169, 171, 172, 174- 176, 253, 254, 394 international formula for -, 97 — interpretation, 143-157 analytical -, 146-153 direct —, 143, 144 graphical -, 153, 154 indirect -, 148, 144 integraph methods, 154-157 979 Gravity (cont'd): isostatic correction for -, 141 — meter (see Gravimeter) — methods (see Gravitational methods) —multiplicator, 88 normal! -, 141 ~ pendulum, 10, 97-123, 135 planetary correction of -, 141, 211 regional -, 141, 142, 160 secular variation of - , 165 —terrain correction, 137-140 time variations of -, 162-167 — variation with latitude, 94-97, 141, 211 Gray seismograph, 580 Graywacke: density of -, 81 elastic moduli of -, 467 Greenstone, resistivity of, 661 Ground-distance meter (see Terrain- clearance indicator) Ground roll, 450, 452, 550, 551 Ground water (see Water, ground) Grueneisen method, 455, 456 Guillemin effect, 317 Gypsum: density of -, 79 — deposits, 51, 54, 736, 738 dielectric constant of -, 665 elastic moduli of -, 464° heat conductivity of -, 848 One ae wave velocity of -, 470, radioactivity of -, 875 resistivity of -, 663 specific heat of —, 848 susceptibility of —, 312 H Half-value point, 382, 387, 393, 673, 698 — time, 877 Halides, 901, 903 resistivity of —, 658 Halleflinta, density of, 81 Halo, 36, 903-910 Harbor investigations, 57, 58, 738 Harbor surveillance, 951 Hardness, 464 Hartley oscillator, 931 Heat (see also Temperature): - conductivity (see Thermal con- ductivity) specific —, 847, 848 Helium, 873 Helmholtz coil, 330, 331, 333, 338, 348, 363, 366, 403 - with uniform field, 363 Helmholtz resonator, 938, 940 Hematite: density of -, 78 — deposits and mineral, 51, 52, 297, 318, 414, 415, 417, 520 dielectric constant of —, 666 980 Hematite (cont'd): resistivity of —, 657, 659 susceptibility of -, 311 specular -, 50, 414, 415, 657 Hemisphere (see Northern hemisphere and Southern hemisphere) Hettangian age, 676 High frequency (see Frequency, high) High-frequency method, 31, 32, 619, 622, 623, 626, 648, 805-809 High-frequency well-surveying, 867 Highway engineering (see Engineering, highway) Hooke’s law, 442, 920 Horizontal component: — of electrical field (see Electrical field) — of electromagnetic field (see Electro- magnetic field) — of gravity force, 12, 39, 157, 167-169, 171, 172, 174-176, 253, 254, 394 ~ of ground or building vibration, 917, 918 - of magnetic force (see Horizontal intensity) Horizontal directing forces (see Curva- ture values) Horizontal intensity, magnetic, 16-18, 295, 301, 306, 320 321, 323, 325, 335-341, 344-346, 349-351, 355-357, 360, 361, 364-366, 368, 374, 378-402, 406, 409, 410, 412, 417 — determination of: by deflection, 356, 357 by oscillation, 356, 357 Hep eout a loop methods, 5 626, 648, elliptical polarization, 787-789 equipment, 774, 778-786 interpretation, 789-800 loop fields, 776-779 results, 800-806 Horizontal pendulum or seismometer (see Seismograph, horizontal) Hornblende: density of -, 80 resistivity of —, 658, 660 susceptibility of —, 310 Hornblende-gabbro, density of, 80 Hornsilver, density of, 77 Hotchkiss superdip, 175, 342-344, 379, 430 Hot wire: — gas detector, 64, 868, 869, 892-894 — microphone, 938, 940, 948 — seismometer, 613 Hughes balance, 819, 820 Hughes echo sounder, 957 Huygens principle, 506 Hydraulic engineering (see Engineering, hydraulic) Hydrocarbons: aliphatic —, 889 aromatic —, 889 SUBJECT INDEX Hydrocarbons (cont’d) : classification of —, 889 liquid -, 888, 891, 901-904, 909, 910 paraffin —, 888-892, 895, 896, 901-905 pseudo -, 36, 891, 899, 903, 909 soil analysis by -, 35, 885-910 Hydrogen, 629, 669, 891, 894, 899, 903, 905 Hydrogen sulfide, 886 Hydrometer, 72 Hydrophone, 947-951 Hygrometer correction, 118 Hygrometric observations, 61 Hyperbola, 559, 560, 561, 941 Hypersthene, density of, 78 Hysteresis: — curve, 297, 299, 300, 303, 307-309, 318, 401 elastic —, 442 magneto-mechanical -, 317, 318 temperature -, of magnetization, 317 I Ice: density of -, 79 dielectric constant of —, 665 elastic moduli of —, 467 heat conductivity of —, 848 Iceberg, locating, 9, 41, 59, 64, 952 Igneous intrusions (see Intrusions) Igneous rocks, 4, 16, 48, 55, 61, 284, 286, 296, 297, 376, 389, 401, 416-419, 422, 424, 427, 429, 432-435, 512, 513, 634, 637, 638, 656, 742, 849, 870 coercive force and remanent mag- netization of —, 316 densities of —, 73, 74, 76, 80, 81 elastic moduli of —, 467, 474, 475, 477 heat conductivities of -, 849 longitudinal wave velocities of -, 472, 474, 475, 477 magnetic susceptibilities of —, 313-315 radioactivity of —, 870, 874, 875 Rayleigh wave velocities of —, 473 resistivities of —, 634, 637, 638, 657, 660, 661 specific heats of —, 848 transverse wave velocities of —, 472, 473 Ilmenite: coercive force and remanent magneti- zation of —, 315 density of -, 78 resistivity of -, 657 susceptibility of —, 310, 314 Images: — in inductive methods, 32, 791-800 — in radio methods, 818 —in reflection seismic methods, 562, 567 —in resistivity methods, 672, 711-714, 717-719, 722, 745, 749, 751 Impedance bridge, 647 Impetus, 451 Impregnation (see Dissemination) Inclination, of formations (see Dip) SUBJECT INDEX Inclination, magnetic, 17, 39, 40, 295, 343-347, 349, 355-359, 361, .362, 364, 368, 378-380, 393, 394. 403, 418 Inclinator, inclinometer: =dip circle and dip needle, 17, 345-347, 356-358, 403, 413, 415, 422, 436 rotary — (see Earth inductor) Tiberg -, 349, 364 Incompressibility factor, 445, 446 Index curves, 807, 808 Indian magnetometer, 358 Indicator length, 581, 582 Inductance bridge, 305, 306, 932, 933 Inductance function, 758 Induction: — balance, 819-822 — factor, 792-797 — instruments (magnetic), 364, 365 - theory in magnetic interpretation, 19, 389-400 Inductive electromagnetic methods (see Electromagnetic methods, induc- tive) In-phase component (see Electromag- netic field) Instruments: gravity measuring — (see Pendulum and Gravimeter) magnetic — (see Magnetometer) rock testing — (see Density; Magnet- ism; Susceptibility; Elastic mod- uli; Resistivity; Dielectric con- stant; Radioactivity; and Thermal conductivity, determination of) _Integraph, 144, 154, 156, 157, 236, 238, 239, 249, 253, 268, 269, 270, 400 Intensity: acoustic — (see Acoustic intensity) — of electrical field (see Electrical field) — of electromagnetic field (see Electro- magnetic field) - of gravity (see Gravity field) magnetic -— (see Total intensity, Vertical intensity, and Horizontal intensity) — of radioactive radiation (see Radio- active radiations) seismic — (see Seismic intensity) Interferometer, 120, 455-457, 460, 930 Interior friction, 118, 481, 583, ’922, 936 Interpretation: analytical methods of -, 144, 146-153, 265, 381, 400, 728, 766-769, 790-791 -—diagrams, 144, 150, 154-156, 256, 258, 263-268, 388, 400, 537-539, 544. 546, 558-560, 565, 566, 726, 727, 733, 768-769, 793-795 direct —, 19-23, 26, 28, 31, 32, 67, 143, 256, 260, 263-265, 382, 384, 385, 387, 437, ’623, 673, 727-733, 793, 885 - of electromagnetic surveys, 31, 32, 766-777, 789-800 — of equipotential line surveys, 28, 981 Interpretation (cont'd): graphical methods of -, 144, 153-154, 253, 256, 265-268, 389, 400, 536-539, 729, 733, 768-769, 793-795 — of gravimeter surveys, 11, 67, 143-157 indirect -, 11, 15, 148, 144, 253, 388, 389, 395-400, 623, 671, 766-769. integraph methods of -, 144, 154-157, 253, 268-270, 400 - of magnetic results, 19, 293, 377-402 ~- by models (see Model experiments) — of pendulum results, 11, 67, 143-157 -of potential-drop-ratio measure- ments, 29, 747-751 qualitative —, 11, 15, 19, 26, 28, 31, 143, 250, 380, 623, 697, 727-728, 766 — of resistivity surveys, 726-734 -of seismic results, 20-25, 506-549, 557-567, 572, 576-579 — of self-potential surveys, 26, 671-675 - of soil and gas analvsis data, 36, 902-909 - of torsion-balance results, 15, 148, 250-270 - by type curves, 29, 252, 383-387, 623, "er: 731-733, 734, 767, 790, 791 Intrusions, 4, 8, i5, 19, 45, 51, 70, 297, 315, 381, "417-419, 421, 422, 497, 429, 430, ‘432, 433, 435, 514 Ion, 369, 829-638, 637, '639, 679, 874, 882, - concentration, 629-631, 637 - mobility, 631, 637, 639 Ionization, 637, 872, 873, 878, 898 — chamber, 35, 865, 872, 876-881, 884 Iridescent films, 886 Tron: — chloride, 303 ' -objects, 332, 333, 373-375, 404, 425 - ore, 4, 8, 16, 51, 70, 73, 74, 287, 296, 318, 376, 385, 389, 401-415, 884 coercive force and remanent mag- netization of -, 315 density of -, 73 susceptibility of -, 311, 401, 411 — quartzite, 287, 409-411 susceptibility of-, 312, 411 Ironstone, density of, 83 Isanomalics, 18, 19, 378 Isochronous pendulum, 101 Isochrons, 476, 548 Isogam, 11, 18, 141, 142, 158-161, 170, 244, 248- 252, 272, 279. Isogeothermal surfaces, 845, 852-854, , 861 Isomagnetic lines (see Isanomalics) Isomers, 891, 901 Isometric representation, 378 Isostatic: -—compensation, 165 - correction, 141 —equilibrium, 165 Isothermal (see Isogeothermal) Isotime curves, 476, 548 982 J Jadeite, density of, 81 Jolly balance, 72 measurements of vertical gradient by -, 190, 191 Joule effect, 947 Jurassic formations, 81, 291, 703, 706 K Kainite, density of, 79 Kaolin, density of, 79 Kaolinite, density of, 79 Keewatin formation, 703 Kelvin balance, 303 Kelvin theorem, 845, 846 Kennelly-Heaviside layer, 936 Keratophyre, coercive force and rema- nent magnetization of -, 316 Keuper formation, 290 Kew magnetometer, 358 Kieserite, density of, 78 Kilohm-centimeter, 633 Kirchhoft’s law, 717 Kirchhoff-Wheatstone bridge, 363 Kundelungu formation, Belgian Congo, 678, 679 L Laccolith, 428, 433 Lakes: electrical 802, 803 gravimeter measurements on -, 162 torsion balance measurements on-, 270-275 Lamé coefficients, 439, 445-448 Lamont sine method, 349, 364, 365 Landolt-Boérnstein tables, 310 Langevin-Florisson transmitter, 947 Laplace’s equation, 89, 169, 191 Larsen compensator, 30, 781, 782 Latitude variation: — of curvatures of earth ellipsoid, 211, 212 — of curvature values, 211, 212 — of gravity, 94-97, 141, 211 — of gravity gradient, 210, 211 — of magnetic anomalies, 393, 394, 397-399 — of magnetic field components, 372 - of magnetic variations, 368, 369 Lava: density of -, 73, 81 — flows, 297, 317, 318, 416, 419, 434, 435 heat conductivity of —, 849 radioactivity of —, 874 resistivity of -, 661 susceptibility of —, 849 Layered media (see Stratified ground) measurements on-, 764, SUBJECT INDEX Lead: damping resistance of —, 482 — deposits, 70, 73, 74 ~ for ionization chambers, 881 gravity Leads, power (see Power leads) Lead-zinc deposits, 50, 289, 417, 705 Leakage (see Pipe leaks) Lecher system, 648 Lejay-Holweck pendulum (see Pendu- lum) Lemniscate, 687, 688, 691 Lenticular oil deposits, 45, 47, 422, 433 Leptite formation, 162, 703, 704 Leucite, density of, 80. Level surface (see Equipotential surface) Leveling, 137, 213, 239, 571 Lightning, 309, 315, 316, 376 Light velocity, 685, ’810, 811, 940 — pice eet 70, 289, 290, 739, 740, , density of -, 79 Limestone: density of -, 76, 84 dielectric constant of —, 666 elastic moduli of -, 468, 474, 475 — formations, 46, 51, 54, 61, 76, 284, 285, 286, 289, 414, 441, "474, 475, 508, 518, 520, 547, 637, 677, 728, 729, 735, 736, 738, 7Al, 833 heat conductivity of - —, 849 fone widinel wave velocity of -, 470, radioactivity of —, 875 Rayleigh wave velocity of —, 473 resistivity of —, 637, 660, 663, 836 specific acoustic resistance of —, 479 susceptibility of —, 312 transverse wave velocity of -, 473 Limonite: density of -, 78 dielectric constant of —, 666 — mineral, 51, 318, 415, 417, 630, 668 resistivity of —, 657 susceptibility of -, 311 Lines of force (diagram), 389 Liquid hydrocarbons (see Hydrocarbons) Listening devices (see Sound receivers) Lithographic stone, 55 Loam: density of —, 82 dielectric constant of —, 666, 667 longitudinal wave velocity of —, 468 specific heat of —, 848 Loess: density of —, 82 elastic moduli of —, 468 longitudinal wave velocity a -, 468 Rayleigh wave velocity of -, Logarithmic decrement, 585, dee, 815 Longitudinal wave, 447, 448-452, 464, 466, 468-477, 498-502, 504-551, 536-569, 849, 862, 863, 866, 914 Loop galvanometer, 359, 609, 893 SUBJECT INDEX Loops: horizontal -, 31, 32, 776-779, 783, 787, 791, 793 vertical —, 31, 32, 805, 806, 807 Louis dipping compass, 346 Love waves, 450, 451, 926 Low frequencies (see Frequency) Lunar variation of gravity, 163, 164 M Mache unit, 873, 881, 884 Machine drill (see Rotary drill) Maeotic formation, 837 Magma movements: effect of -, on gravity, 165 effect of -, on magnetic anomalies, 318 Magmatic differentiation deposits, 49, 50, 52, 412, 413 Magnesite: density of -, 79 —deposits, 55 susceptibility of -, 310 Magnet: auxiliary —, 325, 326, 330, 333, 336, 338, 339, 341, 347, 349, 350, 351, 373 dipping —, 384-386, 388, 403 =magnetic doublet, 19, 384-388, 778 Magnetic: — anomalies, 4, 16, 18, 19, 296, 316, 377, 378, 381-402, 409-436 relation of-, to gravitational anomalies, 393-395, 400 — balance (see Magnetometer) — corrections, 366-377 — doublets, 19, 384-388, 778 — field (see also Horizontal intensity, Total intensity, and Vertical in- tensity), 16, 293, 295, 296, 298, 299, 302-320 latitude variations of —, 372 — of subsurface bodies, 377-402 time variations of —, 367, 372 — flux (see Flux) — gradient, 363, 380, 406, 407 — inclination (see Inclination) — instruments, 17, 18, 318-366 classification of —, 319 construction principles of -, 318, theory of —, 319-321 — interpretation: induction theory, 389, 400 pole and line theory, 381-389 qualitative, quantitative, 380, 381 theory based on both permanent and induced magnetism, 400-402 —latitude, 16, 19, 298, 295, 327, 328, 332, 338, 343, 369, 372, 380, 389, 392, 393, 394, 395, 397-399, 403, 416 — line, 19, 145, 385 ~ line doublet, 19, 385-388 - method, 8, 15, 16-19, 43, 45, 49, 50, 51, 52, 54, 293-436 983 Magnetic (cont'd): —moment, 299-303, 306, 307, 320, 321, 323, 326-330, 335-338, 340, 341, 344, 345, 348, 351, 353, 365, 374, 390, 392, 778 —needle, 17, 301, 302, 306, 320, 321, 341, 348, 344, 349-351, 357, 358, 364, 365 — objects,332, 333, 373, 374, 375, 404, 425 — observatories, 366, 367, 368, 369 — permeability, 297, 298, 299, 302, 622, 642, 685, 757, 810, 811 — pole (pole of magnet), 19, 115, 302, 320, 326, 330, 336, 348, 350, 351, 354, 374, 375, 378, 380, 381, 384, 388, 389, 390, 406-408, 552, 754, 766, 785, 792 — reluctance, 297, 298, 595 — reluctivity, 298 —rock properties (see Magnetism of rocks) — storms, 370 - surveys, 408-436 — in engineering, 433-436 — in mining, 409-422 — in oil exploration, 422-433 — susceptibility, 16, 297, 299, 301, 302, 303, 304, 305, 306, 307, 309, 374, 376, 382, 387, 390, 392, 395-402, 411, 414, 419, 424, 427, 432, 433, 865 apparent -, 390, 392 — of igneous rocks, 313, 314 — and magnetite content, 315 measurement of -: balance method, 303 ballistic method, 306, 307 inductive method, 303-306 Koenigsberger method, 301, 302, 303 solenoid-deflection method, 306 test tube method, 301 — of metamorphic rocks, 312 — of minerals, 310, 311 — of sedimentary rocks, 312 — systems, 17, 3038, 319, 320, 321, 322, 324, 325, 334, 335, 337, 339, 340, 342, 347, 348, 351, 352 temperature-compensated -, 322, 324, 325, 327, 328, 337 — theodolite, 355-358, 366 — torsion balance, 303, 355, 380 — variations, 367-372 diurnal -, 367-371 secular -, 370, 371 — vectors, 378, 379 — vertical intensity (see Vertical intensity) Magnetite, 16, 50-52, 287-290, 296, 297, 308, 309, 314, 315, 318, 409, 411-417 coercive force and remanent magneti- zation of —, 315 density of —, 78 elastic moduli of —, 467 heat conductivity of -—, 848 984 Magnetite (cont'd): resistivity of -, 657, 659 spontaneous polarization of —, 668 susceptibility of -, 311 Magnetism of rocks, 4, 16, 19, 297-318 determination of —, 300-309 factors affecting -, 314-318 — and geologic history, 315, 318 induced -, 296, 297, 299-301, 306, 307, 309, 382, 389, 390, 392-394, 400, 401, 402, 865 — and mechanical forces, 317, 318 — and mineral composition, 314, 315 — and temperature, 317 Magnetization: intensity of, 298-300, 307, 317, 318, 382, 387, 390, 393, 394, 401, 402 remanent -, 16, 19, 296, 297, 299-301, 303, 306, 307, 309, 315-317, 382, 400-402, 865 Magnetomechanics, 317, 318 Magnetometer: Ambronn -, 341 Angenheister —, 342 astatic —, 301, 302, 303, 359, 364, 865, 866 Cardan suspension —, 352, 353, 422 Dahlblom pocket -, 348, 349 earth inductor type —, 358-363 fundamental equation of —, 321 Haalck universal -, 339, 340, 341 horizontal —, 17, 301, 306, 318, 334-339, 340, 341, 349, 350, 351, 352 Hotchkiss superdip -, 17, 342, 348, 344 Koenigsberger —, 342 Kohlrausch -, 349, 350 Koulomzine -, 342 operation of, 332, 333, 338, 339, 373 Ostermeier —, 342 « Ostermeier universal -, 351, 352 prospecting -, 321-355 Rieber -, 364 Schmidt compensation —, 330, 351 Schmidt horizontal -, 17, 318, 334, 339 auxiliary magnets, effect of, 336 gravity, effect of, 337 misorientation of —, 335 operation of —, 338, 339 scale value of —, 335 temperature, effect of, 337 theory of —, 335 tilt, effect of, 336 vertical intensity, effect. of, 336, 337 Schmidt vertical —, 17, 18, 40, 48, 301, 318, 321-333, 405 auxiliary magnets, effect of, 325, 326 gravity, effect of, 326 instrument case, magnetic effects of, 373 instrument constants and correc- tions, 328-332 misorientation of —, 323 operation of -, 333 scale value of —, 323 temperature, effect of, 326, 327, 328 SUBJECT INDEX Magnetometer (cont'd): theory of —, 321-328 tilt, effect of, 323, 325 Thalén-Tiberg -, 349, 402, 405 Thomson-Thalén -, 347, 348 Toepfer —, 342 unifilar — , 301 vertical —, 17, 18, 40, 48, 301, 318, 321- 333, 341, 342, 347, 348, 351, 352, 353, 361, 364, 366 Watt -, 342 Wilson attachment for —, 352 caer any force, 297, 298, 5 Magnetostriction: — effect on rock magnetism, 317 — transmitters and receivers, 946, 947, 948, 952, 953, 955, 956 Magnetron, 353, 354 Magnification: dynamic -, 481, 587, 588, 589, 603, 604, 605, 606, 618 static —, 581, 586, 587, 588, 589, 593, 594, 595, 596, 598, 601, 602, 606, 615, 617, 912, 917, 919 Malachite: density of —, 78 susceptibility of —, 310 Manganese, 51, 52, 73, 421 Manganite, density of, 78 Manometer, 119, 899, 900 Marble: density of -, 81 dielectric constant of —, 666 heat conductivity of —, 849 Marine-acoustic methods, 943-956 Marine gravity apparatus, 101-103, 107, 109 595, Markasite: density of -, 78 resistivity of —, 657 susceptibility of —, 310 Marl: density of -, 81 longitudinal wave velocity of —, 469 resistivity of —, 637, 663 Martens gauge, 454, 930 Mass-absorption coefficient, 873, 881 Mass displacements, effect on gravity, 167 Mass spectrograph, 898 Maxwell (unit), 297-299 May sandstone, 706 McKittrick formation, 424 McLeod gauge, 899 ; Measurement procedures in geophysical exploration, 38-42 Mechanical concentration: — deposits, 49, 51, 416 effect of -, on rock magnetism, 318 Mechanical seismographs (see Seismo- raphs, mechanical) Megabar, 452-454 Megger, 644, 645, 723, 724, 725 SUBJECT INDEX Melaphyre, density of, 81 Melting point, 891, 892 Mentor beds, 84 Mercury, 738, 123, 124 Meridian, magnetic, 295, 321, 325, 334, 338, 341-342, 345-347, 350, 353, 357, 361, 363, 378, 379, 405 Metallascope, 628, 823, 824 Metal mining, geophysical methods in (see also Mining exploration), 49, 50, 51, 52 Metamorphic rocks, 48, 61, 287, 315, 410, 412, 419, 424, 439, 678, 734, 756, 848, 849, 874 coercive force and remanent magneti- zation of —, 316 densities of -, 74, 81 heat conductivity of —, 849 longitudinal wave velocities of —, 472 radioactivity of —, 874 resistivities of —, 637, 660, 661 susceptibilities of - , 312 Meteorological factors and magnetic variations, 369, 370 Meteorology, 3 Meteors, 70, 422 Methane, 36, 888-897, 899, 900, 902- 907 Mho-centimeter, 633 Mica: density of -, 80 — deposits, 55 dielectric constant of —, 666 elastic moduli of —, 467 heat conductivity of —, 848 resistivity of —, 658 Microgal, 88, 139, 150, 154 Microgauss, 622, 793-795 Microphone, 20, 866, 867 carbon -, 937, 948, 953, 960 coil -, 20, 937, 940, 942, 948, 951 condenser -, 20, 932, 948 crystal —, 21, 937, 948, 949, 953, 960 hot wire —, 938, 940, 948, 960 magnetostriction —, 946-948, 952, 953, 955, 956 reluctance -, 20, 937, 954, 955 Microtimer, 952 Military engineering, 6, 9, 37, 42, 59, 60, 63, 64, 297, 433-436, 624, 706, 940, 942, 943, 951, 956, 958, 961 Millerite, density of, 78 Milligal, 10, 88, 101, 104, 106, 110, 113, 117, 118, 123-127, 129, 130, 132-137, 141, 148, 158-162, 164, 165, 170, 248, 249, 272, 274, 283 Mine: — caving, 36, 63, 914, 928-930, 933 — safety, 9, 956, 960, 961. —workings (see Underground workings) 985 Mineral composition, effect on, of: elastic rock properties, 474 rock density, 73 rock magnetism, 314 Mineral density, 74 Mineral deposit, classifications, 49, 50, 51 Minerals, resistivities of, 657, 658 Minette, 51 Mining: acousticemethods in —-, 37, 956-963 — compass, 17, 320, 345, 346, 403 electromagnetic methods in -, 31, 52, 55, 626, 771-773, 800-809 equipotential-line method in -, 27, 52, 624, 703-706 --exploration, 6, 17, 19, 23, 49-56, 70, 161, 162, 286-292, 297, 404-422, 439, 501-5038, 505, 623 gravitational methods in -, 52, 53, 54, 55, 161, 162, 286-292, 520 magnetic methods in - , 17, 19, 49, 51, 52, 54, 56, 297, 404-422 ~ operations, effect on gravity, 167 potential-drop-ratio method in -, 29, 52, 625, 755-757 radioactivity methods in -, 35, 884, 885 radio methods in -, 32, 627, 813, 816, 817 resistivity methods in -, 28, 52-55, 625, 739-741 seismic methods in -, 21, 23, 49, 50, 53, 54, 55, 439, 501-508, 505, 520 self-potential methods in -, 26, 52, 53, 624, 675-679 strain gauging in -, 36, 63, 928-934 Mint, 63 Mirror device, 115, 116, 496, 616 Mississippian formation, 735, 736 vertical velocities in -, 473 Model experiments, 41, 42 electrical —, 28, 623, 700, 701, 734, 735, 771, 800, 801, 802, 812 gravimetric -, 88 magnetic —, 19, 402-404 seismic —, 62, 911, 912, 914, 917 — for strain measurements, 63, 933 Moduli, elaeue, 442-446, 467-468, 911, » 9 } dissipative —, 483 measurement of —, 452-466 Moisture, effect on, of: density, 74, 76 dielectric constant, 641 elastic rock properties, 475 high-frequency and radio fields (see also Near-surface interference), 655, 806, 809, 815 rock resistivity, 634-639 thermal properties, 847, 848, 849 Moll galvanometer, 841 Molybdenite: density of -, 78 — deposits, 50 resistivity of —, 657 986 Moment: electric —, 672, 697 magnetic — (see Magnetic moment) Monacite sand, 55 Moon, effect of, on gravitational field, 162-164 Motor generator (see Generator) Muaslira series, 678 Mud: density of -, 74 drilling — (see Drilling mud) — volcanoes, 886, 887 Muscovite, dielectric constant of, 666 N Nacatoch formation, 432 Nagelflue, heat conductivity of, 849 Nagyagite, density of, 77 Naphthalenes, 889 Naphthenes, 889, 890 Natural density, 76, 77 Natural earth currents and potentials (see Spontaneous potential) Natural frequency (see Frequency) Navarro shale, 285 Navigation, 9, 64, 940, 942, 949, 951 Near-surface interference, 31, "745, 763, 764, 808, 809, 815, 817 Negative potential center, 26, 27, 668, 669, 671, 675, 677 Nephelite, density of, 80 Nephelite basalt: density of -, 80 susceptibility of -, 314 Nephelite-syenite, density of, 81 Nephrite, susceptibility of," 313 Neutron, 872 Newtonian potential, 145 Newton’s law, 16, 85, 87, 89, 144, 145 Nickel: damping resistance of —, 482 magnetostrictive properties of -, 317, 318, 947 Nickel ores, 50, 73, 289, 310, 385, 415, 416 Nicollite, resistivity of, 657 Nitramon, 485, 486, 490, 571 Nitrates, 54 Niveau surfaces of gravity (see Equipo- tential surfaces of gravity) Noise: detection of -, 9, 35, 58, 59, 63, 64, 935, 938, 941, 942, 948, 951, 958, 960-962 prevention of -, 36, 37, 935, 943 Nomographs, 202, 203 Nonastatic gravimeters meters, unastatized) Nonmetallic mining, geophysical ex- ploration in, 52-56 Nonpolarizable electrode trode) (see Gravi- (see Elec- SUBJECT INDEX Norite: coercive force and remanent magneti- zation of -, 316 density of -, 80 elastic moduli of —, 467 radioactivity of —, 874 Rayleigh wave velocity of -, 473 susceptibility of —, 313 transverse wave velocity of -, 473 Normal: — electrical field, 683, 693, 694, 697 - electromagnetic field, 766, "770-773, 776-779, 801 - equipotential lines, 682, 683, 693, 697, 699 - geothermal gradient, 847 — gravity, 141 — gravity gradient, 210 — magnetic field, 377 — potential differences, 670, 678 — ratio (P.D.R.), 746, 747, 754, 756 — travel-time curve, 499, 500 Northern hemisphere, 211, 212, 293, 295, 375, 416 Nucleus, 870-873 O Observatory, magnetic, 2, 3, 362, 366-369 Obsidian: density of -, 81 elastic moduli of -, 467 heat conductivity of -, 849 Oceanography, 3, 42 Oerstedt unit, 298 Oertling balance, 193 Ohm-centimeter, 633 Ohm-foot, 633 Ohm-inch, 633 Ohm-meter, 633 Ohm’s law, 632, 633, 683 Oil: composition of —, 890 direct location of -, 5, 9, 338, 45, 47, 825, 831, 837, 856, 884, 886-888, 894, 902-910. — exploration, 4, 5, 19, 25, 33, 43-48, 70, 157-161, 272-286, 422-433, 439, 441, 498, 499, 503, 6238, 736-739, 755, 761, 805, 817, 825, 835-837, 856-858, 862, 864, 867, 884, 886- 888, 892-906 cost of —, 47, 48 reconnaissance and detail methods in -, 45 — formations, resistivity of, 665, 830 geothermal effects of -, 842, 848, 856, 858 radioactivity of —, 35, 864, 876, 884 — in rock pores, 76, 830 — sand: radioactivity of —, 864, 876, 884 resistivity of —, 665, 830, 8321, 837 — seepages, 886, 887 SUBJECT INDEX Oil (cont'd): —in wells, 34, 830, 831, 837-839, 842, 856, 858, 864, 867, 884 Olefins, 889 Oligoclase, density of, 80 Olivine: density of -, 80 elastic moduli of —, 467 Olivine diabase, susceptibility of —, 314 Olivine gabbro: density of -, 80 susceptibility of —, 313 Olsen testing machine, 457 Optical systems: — in displacement meters, 455, 456, 930 — in gravimeters, 127, 129, 132, 133, 134 — in magnetometers, 301, 321, 322, 332, 334, 342, 357 —in pendulums, 101, 102, 105, 107, 109, 111, 112, 115-120 — in seismographs, 599, 608, 615 — in torsion balances, 193, 194, 199 Ordovician, 46 vertical velocities in -, 473 Ore bodies, location of: — by direct and indirect methods, 4, 5 — by electromagnetic-galvanic meth- ods, 30, 31, 50-52, 789-791, 800-809, 813, 815 — by equipotential-line methods, 26, 50-52, 703-706 — by gravimeter, 50, 161, 162 — by magnetic methods, 19, 50-52, 296, 297, 409-422 — by potential-drop-ratio methods, 29, 751, 754, 756 — by radioactivity methods, 35, 51-52 — by resistivity methods, 28, 50-52, 739-740 — by seismic methods, 21, 50, 51, 439, 502, 520 — by self-potential methods, 25-27 — by torsion balance, 50-52, 286-292 Ore deposits, classification of, 49-51 Ores: densities of -, 73 resistivities of —, 659 Orogenic movements, effect on grav- ity, 165 vibrations caused by -, 914 Orpiment, density of, 78 Orsat pipette, 897 Orthoclase: density of +, 80 elastic moduli of —, 467 Oscillations (see Free oscillations and Forced oscillations) Oscillator, test (see Shaking table) Oscillograph, 21, 30, 115, 457, 494, 496, 497, 503, 552, 553, 598-600, 610, 614, 651, 758, 762, 898, 940, 943, 954 cathode ray —, 30, 651, 652, 759, 760° glow-tube -, 116, 496 987 Osmotic potential tential) Out-of-phase components: — of electromagnetic fields, 31, 32. 622, 625, 626, 764, 769, 779, 782— 797, 800-806 — of potential fields, 624, 686-690, 692, 694, 701, 702 — of radio fields, 653 Overburden: density of -, 82 elastic moduli of —, 468, 475 Rayleigh wave velocity of —, 473 Overhang, 35, 862 Overshoot, 585, 616 Oxidation, 668, 669, 860 Oxides, resistivity of, 632, 657 Ozokerite, 886, 887 density of -, 79 P (see Diffusion po- Pallograph, 580 Parafin hydrocarbons, 888-892, 895, 896, 901-905, 909 Paramagnetism, 7, 299, 423 Partitioning method, 710 Peat: density of -, 79 resistivity of —, 637 specific heat of -, 848 Pegmatite, 50 Peg models, 378 ' Pendulum, 8, 9, 39, 40, 43, 47, 67, 70, 97-123 air-pressure correction for —, 118, 119 amplitude correction for -, 99, 117, 118 — apparatus, 108-113 Askania -, 110, 111 astatic —, 99, 100 bronze -, 108, 118 Brown -, 110, 112 coincidence method for -, 10, 103-107 companion -, 120 fictitious —, 101, 102 — on fixed support, 97-98 — support, flexure of, 101, 119-123 — instrument corrections, 116-123 invar —, 108, 118 inverted —, 10, 99, 100, 113, 127 isochronous -, 101 Lejay-Holweck -, 10, 99, 100, 112, 113, 129 mathematical —, 97-98, 580-581 — measurements in submarines, 101, 102, 107, 109 minimum -, 108 — on moving support, 101-103 — observation methods, 103-108 operation of —, 103-123 — period, 10, 97-104, 117-119, 121, 122, 135 physical -, 99 quartermeter —, 108 988 Pendulum (cont’d): quartz -, 10, 108, 118 reference —, 103 reversible —, 99 — rods, 108 — survey results, 157-162 suspended -, 99, 100 time transmission -, 10, 103-116 Vening Meinesz -, 109-110 Penetrating radiation (see Gamma ra- diation) Pennsylvanian, vertical velocities in, 473 Peridotite: density of -, 80 — plugs, 56, 418 susceptibility of -, 318, 314 Period: — of gravimeter, 124, 125, 127, 130, 132, 134 -— of ground motion, 449, 452, 586 —of pendulum, 10, 97-104, 117-119, 121, 122, 135 ~ of seismograph, 581, 588, 585, 586, 591. — of torsion balance, 86, 178, 195-197 Periodic motion, 449 Permeability: — for liquids and gases, 743, 835, 836, 869, 902, 904, 905 magnetic- (see Magnetic permeability) Permeation, 904, 905 Permian, vertical velocities in, 473 Petroleum (see also Oil): composition of -, 890 density of -, 79 dielectric constant of —, 665 heat conductivity of -, 848 Petrologic composition (see composition) Phantom horizon, 579 Pharmacosiderite, density of, 78 Phase: ~ of ground motion, 449 — logs (seismic), 576, 577 ~— shifts, phase differences: — in directional hearing, 942, 948, 949, 953, 961 — of elastic and dissipative moduli, 483 — in electrical prospecting, 28, 31, 32, 622, 624-626, 639, 640, 649, 650-654, 686-688, 691, 692, 695, 696, 702, 752, 753, 764, 766, 769, 779, 784-793, 803, 804, 806, 807, 810 — of ground and seismograph, 587- 590, 618 — of ground and vibrator, 915, 916, 920-922 — of pendulum, 107 — of temperature variation, 861 — speed, 921, 923, 925-927 Phlogopite: elastic moduli of -, 467 susceptibility of -, 310 Mineral 938-939, SUBJECT INDEX Phone (see Geophone and Seismograph) Phonolite, density of, 81 Phosgenite, density of, 77 Phosphate, 54 density of -, 79 Photoelastic studies, 934 Photoelectric cell, 112, 113, 115, 116, 366, 869, 954, 955 — well logging, 869 Photographic recording (see Recording) Phyllite: density of -, 81 heat conductivity of —, 849 susceptibility of —, 312 Physical properties of rocks (see Rock properties) Pickup (see Detector) Picrite, density of, 81 Pipe leaks, 6, 9, 61, 64, 866, 868, 956, 959, 961, 962 Pipe lines: corrosion of -, 6, 26, 38, 41, 42, 63, 372, 624, 631, 667, 668, 676, 679, 680, 681, 752, 754, 755 location of —, 33, 57, 58, 68, 297, 436, 624, 627, 765, 818-824 magnetic efiects of —, 333, 373-405, 436 Pitchblende, 35, 854, 875, 884 Placer deposits, 5, 8, 21, 26, 49, 51, 70, 291, 292, 297, 318, 416, 417, 419, 421, 439, 501, 502, 624, 628, 667, 675, 677, 678, 735 Planetary variation (see Latitude vari- ation) Planimeter, 154, 155, 236-238, 268 Plastic shot-hole casing, 491 Platform (see Scaffold) Platinum, 50, 52, 297, 416 Platinum wire, 197, 701 Pleistocene to Oligocene, vertical veloci- ties in, 473 Plotting: — of dynamite test data, 923 — of electrical data, 26, 670, 695, 696, 702, 729, 733, 754, 771, 784 — of geothermal data, 844, 345 — of gravity data, 11, 141, 143 — of magnetic data, 18, 19, 377-380 — of seismic data, 21, 501, 502, 504, 505, 509, 510, 586-538, 546, 576, 579 — of torsion-balance data, 15, 244-250 Plumb-line deviations (see Vertical, deflection of) Poisseuille coefficient, 489, 481-488, 936, 958 Poisson’s ratio, 4384, 448-446, 449, 454, 457-460, 463, 468, 474, 926, 927 Poisson’s theorem, 393 Polar: — gravity, 96 — radius, 95, 210, 212 | Polarity, magnetic, 16, 19, 296, 316, 320, 339, 380 ’ Sqr ae SUBJECT INDEX Polarization: abnormal -, 19, 48, 296, 316-318, 380, 401, 405, 419, 425 dielectric -; 640 electrode -, ” 630 electrol; ytic —, 639, 640, 757, 761-763 elliptical -, 626, 651-655 magnetic -, 16, 19, 296, 316, 318, 320 — potential, 625, 628, 630, 631, 632, 639, 640, 643, 762, 763 — of radio waves, 651-656 spontaneous -, 628-630, 668-669, 671- 675, 678, 762 Poles: earth’s geographic -, 88, 210-213, 326 — of magnets, 19, 115, 302, 320, 326, 330, 336, 348, 350, 351, 364, 374, 375, 378, 380, 381-384, 388-390, 406-408, 552, 766, 767, 785, 792 Polybasite, density of, 7 Pontian formation, 836, 837 Pore volume, 76 Porosity, 33, 62, 74-76, 474, 624, 630, 631, 634, 743, 830, 835, 836, 849, 864, 865, 869 — and grain packing, 634-637 — determination in wells, 831-839 Porous pots (see Nonpolarizable elec- trode) Porphyrite: density of -, 81 radioactivity of —, 874 Porphyritic glass, density of, 81 Porphyry: density of -, 81 dielectric constant of —, 666 heat conductivity of -, 849 specific heat of -, 848 Position-finding, 36, 63, 64, 935, 939-940, 949, 950, 960 Potash, 51, 54, 70, 274, 740 Potassium, 864, 870, 873 Potassium salt, density of, 79 Potential: electric -, 7, 8, 25-30, 39, 298, 621, 624, 625, 628-633, 645, 671-675, 681-684, 693, 694, 697-699, 701, 707-715, 718- 720, 745, 746, 748, "752, 757-760, 762, 828, 831, 881, 882 electrode -, 628-630 — gradient, "39, 88, 298, 621, 629, 633, 670, 673, 674, 681, 683, 707, 754, 756 — of gravity, 39, 89- 94, 170, 394, 797, 99 logarithmic -, 145, 150, 253 magnetic -, 39, 298, 381, 390, 393 - methods, electrical, 25-30, 39, 58, 619, 621-625, 667-764 Newtonian -, 145, 253 -ofa physical field, 39 -ratios, 29, 621-623, "746-750, 752-757 second derivative of -, 39 self — (see Spontaneous potential) 989 Potential (cont'd): spontaneous — (see Spontaneous po- tential) vector potential of electromagnetic field, 792 Potentil- drop-ratio method, 29, 40, 60, 61, 621, 622, 623, 625, 711, 744-757 equipment ‘for -, 752-753 interpretation of - , 147-750 procedure in -, 752-755 results of —, 755-757 theory of -, 745-751 Potentiometer, 27, 29, 34, 359, 363, 365, 670, 678, 695, 696, 723-726, 761, 820, 827, 844 Pottery, 317 Power (vibrator), 922 Power leads, electrical effects of — (see Cables, electrical effects of) Power lines, 328, 372, 404 Power stations, 333, 372, 680 Pre-Cambrian: density of -, 81 — formations, 284, 285, 410, 480, 432 resistivity of -, 661 Precious stones, 56 Pressure: air and gas -, 110, 118, 119, 128, 124, 133, 856, 880, 891, 899, 900, 905, 929, 935 , — of drilling fluid, 631, 832, 842, 857 — gauge, 119, 899, 900, 932 gravitational - (see Gravitational pressure) hydrostatic —, 445, 457 rock -, 474, 477, 914, 931, 934 solution — (see Solution pressure) units of measurement of -, 452, 453 Probes (see Electrodes, search) Productivity, 33, 831, 837, 839 Propagation: — of radio waves, 810-818 — of seismic waves, 22-25, 447-452, 474-483, 497-499 — of sound waves, 935-936, 943-945, 956-958 Propane, 888-891, 896, 899, 902, 903, 908 Prospecting, 3 Proton, 872 Proustite, density of, 77 Pseudohydrocarbons ‘(see Hydrocarbons, pseudo) Psilomelane, density of, 77, 78 Pumice stone, 74 Pyknometer, 71 Pyrargyrite, density of, 77 Pyrite: density of -, 73, 78 ~ deposits, 52, 73, 290, 292, 623, 704— 706, 802, 804 elastic moduli of —, 467 resistivity of —, 657, 659 990 SUBJECT INDEX Pyrite (cont'd): spontaneous polarization of -, 630, 668, 669, 676 susceptibility of —, 310 Pyrolusite: density of -, 78 resistivity of —, 657 susceptibility of —, 310 Pyreoxene: density of —, 80 elastic moduli of —, 467 Pyroxenite, density of, 80 Pyrrhotite, 8, 51, 73, 289, 297, 309, 317, 415, 416, 676, 704, 802 density of -, 73, 78 — deposits, 289 magnetization of -, 310, 314, 317 resistivity of —, 657, 659 spontaneous polarization of —, 668, 676 Q Quadrature component (see Electro- magnetic field, quadrature com- ponent of) Quartz: density of —, 73, 80 dielectric constant of —, 665 heat conductivity of —, 848 resistivity of —, 658, 661 specific heat of —, 848 susceptibility of —, 310 Quartz-diorite, density of, 80 Quartz-porphyrite, density of, 81 Quartz porphyry: density of -, 73, 81 radioacitivity of —, 874 resistivity of —, 660 Quartz sand: density of -, 83 — deposits, 55 heat conductivity of —, 849 specific heat of —, 848 Quartz veins, 29, 50, 52, 624, 754-756 Quartzite: elastic moduli of —, 467 longitudinal wave velocity of —, 472 radioactivity of —, 875 Quartzitic slate: density of -, 81 elastic moduli of —, 467 Quasi-stationary fields (see quasi-stationary) R Racom (see Ratiometer) Radiation: electromagnetic -, 651, 652, 810, 811, 871-873 — impedance, 477-479, 959 penetrating —, 35, 54, 863, 864, 871-873, 876-879, 881, 884, 885 radioactive — (see Radioactive radi- ation) Fields, | Radio-acoustic position-finding, 63, 937, 940, 949-951 Radioactive: — gases, 35, 870-875, 880, 885 — ores, 9, 35, 51, 52, 854, 865, 875 — radiations, 35, 863-865, 871-873, 878- 885 — waters, 61, 870, 873-875, 881, 883, 884 Radioactivity, 9, 35, 51, 52, 54, 870-876, 878-881, 883-885 effect of -, on earth temperatures, 853, 854 equilibrium in -, 873, 876 measurements of —, 9, 35, 42, 51, 52, 55, 61, 876-883 — methods, 9, 35, 51, 52, 54, 55, 61, 870-885 operation of —, 876-881 — of rocks, 873-876 -well logging, 35, 42, 863-865, 876, 883 Radio frequencies allotted to geophys- ics, 496 Radio methods, 32, 58, 63, 623, 627, 628, 809-818 Radio receivers, 114-116, 496, 497, 815- 819, 823, 824 Radio signal transmission: — in pendulum work, 10, 106, 113-117 — in radio-acoustic ranging, 950-951 — in radio methods, 812-818 — in seismic prospecting, 20, 496, 497, 503 Radio transmitters, 114, 115, 116, 496, 497, 812, 815-817, 819, 823, 824 Radio waves: attenuation of —, 811, 812 elliptical polarization of — (see Elliptical polarization of radio waves) Radium, 870, 871-874, 877, 878, 884 — emanation (see Emanation, radium) — ore 9, 35, 51, 52, 854, 865, 874, 875 Radon (see Emanation, radium) Railroad: — construction, 6 — investigations, 6, 57, 58, 915, 928 magnetic effects of —, 372, 374, 404, 405, 680 Ramann effect, 898 RAR system (see Radio-acoustic posi- tion-finding) Ratio bridge (see Ratiometer) Ratio compensator (see Ratiometer) Ratiometer: electromagnetic —, 30, 31, 753, 754, 764, 779, 785, 786, 789, 803, 804 potential -, 30, 31, 40, 752-755, 785 Rayleigh wave, 450, 451, 452, 473, 551 Rays: alpha — (see Alpha rays) beta — (see Beta rays) gamma — (see Gamma rays) seismic — (see Seismic waves) SUBJECT INDEX Realgar, density of, 78 Rebound observations, 463-464 Receivers: acoustic — (see Sound receivers) seismic — (see Detectors, seismic) — in electromagnetic methods, 31, 32, 763, 765, 778-786 sound — (see Sound receivers) radio — (seé Radio receivers) Record, seismic (see Seismogram) Recording: — echo sounder, 943, 950, 954, 956 — gravimeters, 164 = peencenreterss 18, 41, 42, 332, 366, 370 — pendulum, 102, 105-107, 109, 110, 113, 115 — seismographs, 20, 21, 41, 42, 503, 581, 591, 598, 599, 607, 608, 610-616, 912, 917 — sound-ranging devices, 940, 941 — strain gauges, 41, 42, 929-931, 933 — torsion balance, 14, 86, 177, 193, 194, 199 — well-logging devices, 34, 827, 828, 843, 844, 864, 867, 869 Red beds, 736, 738 Reef, 51, 419, 420 Reference: — coil, 784 — lead, 695, 696, 759, 760, 781 — level, 136 — pendulum, 106 — signal, 760 — transformer, 695, 696, 781, 783 Reflection, seismic, and seismic reflec- tion method, 7, 8, 20, 23, 24, 35, 40, 48-48, 53, 61, 487, 440, 441, 450-452, 478-480, 484, 486, 488-490, 492, 493, 505, 549-579, 862, 921, 963 average velocity determinations in -, 23, 568-569 calculations in —, 23, 572, 576-579 — on dipping beds, 562-568 — equipment, 20, 21, 551-556 field practice in —, 25, 569-576 — on horizontal beds, 557-561 Reflection factor, 478, 711-716, 718-722, 726-732, 745-749, 813 Reflection of radio waves, 812, 817, 818 Reflection of sound waves, 867, 935, 942-944, 951-957, 962, 963 Refraction, seismic, and seismic refrac- tion method, 4, 7, 8, 20-24, 35, 40, 43-46, 48, 53, 55, 58, 61, 437, 440, 441, 450-452, 475, 478, 480, 487, 489, 4938, 504-549, 550, 551, 568, 862, 863, 921, 940, 963 arc Mapping in — (see also Fan shoot- ing), 546-548 curved-ray interpretation in -, 23, 540- 546 991 Refraction (cont'd): — for dipping beds, 521-523 — for horizontal beds, 506-514 method of differences in —, 23, 548-549 — for steps and domes, 514-520 vertical-ray interpretation in -, 533- 536 wave-front interpretation in —, 536-540 Refraction of equipotential lines, 700 Refractive index, 480 Regional: — gradient, 240, 241, 246, 251, 262, 281 — gravity variation, 141, 160, 162, 281 — magnetic field, 377 Relaxation time, 585, 586 Reluctance: — detector (see Seismograph) magnetic — (see Magnetic reluctance) Reluctivity (see Magnetic reluctivity) Remanent magnetization (see Mag- netization, remanent) Residual magnetism (see Magnetism, residual) Resistance: acoustic —, 477-479, 947, 959 contact — (see Contact resistance) ~— coupled amplifier, 21, 552, 780, 882 freezing —, 485, 486 -, resistor, rheostat, 300, 360, 361, 456, 494-495, 600, 633, 634, 636, 639, 642-648, 650, 670, 671, 683, 693, 708, 723-725, 745, 752, 753, 760, 761, 774, 779, 780, 785, 824, 825, 827, 843, 844, 850, 868, 893, 930, 931, 938 seismic —, 62, 918, 919 — thermometer, 843, 844, 850 water —, 485, 486 Resistivity: apparent —, 28, 642, 708, 715-744, 756, 828-830, 835-839 determination of —, 642-649 — by A.C. methods, 645-648 — by D.C. methods, 643-645 — by high-frequency methods, 648, 649 — of igneous and metamorphic rocks, 660, 661 — of impregnations, 659, 660 — mapping, 28, 625, 708, 825 — methods, 25, 28, 29, 39, 45, 53, 55, 60-63, 621-623, 625, 707-744, 761, 825 electrode arrangements in —, 709-711 equipment for -, 723-726 interpretation in —, 727-735 procedure in —, 723-726 results of —, 735-744 theory of -, 711-723 — of minerals, 657, 658 — of ie formations, 665-830, 831, 835- — of ores, 659 — of rocks, 4, 642-649, 656-665 992 Resistivity (cont'd). — of sediments, 661-664 — sounding, 28, 625, 708 temperature coefficient of —, 639 — of water, 61, 62, 631, 633, 636-638, 658 ~ in wells, 33, 34, 41, 42, 825-831, 835- 839 Resolving power, 39, 40 Resonance: electrical —, 649, 650 — frequency ‘ (see Frequency, reso- nance) — radiation, 898 — of rock specimens, 461, 462, 481, 482 483 — of structures and ground, 36, 911, 918, 919, 921 — of seismographs, 587-589 Response (see Frequency response) Restoration coefficient, 463-464 Reversible pendulum, 99 Rhyolite, density of, 73, 81 Rhyolite glass, density of, 81 Riefler clock, 86 Riehlé testing machine, 457 Rigidity, modulus of, 445-448, 460, 483, 592, 926, 927 Ring hee method, 626, 648, 782, 83, 796 Road beds, 57, 441, 928 magnetic effect of -, 374 Road materials, 54, 58, 60, 434, 624, 742 Rock bursts, 914, 928, ‘929, 931 Rock density (see Density) Rocking mirror devices, 454-457, 930 Rock prorereee D hysical, 4, 5, 20, "Al, 437 —, contrasts on oundaries (see Forma- tion boundaries) -, densities, 70-84 electrical —, 628-667 magnetic —, 297-318 radioactivities of —, 873-878 seismic —, 441-483 thermal -, 848-849 Rock resistivity (see Resistivity) Rock salt, 51, 54, 291, 292, 736, 738, 740, 851, 860 density of -, 79 dielectric constant of -, 666 elastic moduli of -, 467 heat conductivity of —, 848 longitudinal wave velocity of -, 471 resistivity of —, 658 specific acoustic resistance of -, 479 susceptibility of —, 310, 312 thermal conductivity of -, 848 Rock saw, 642 Rock temperatures (see Temperatures of rocks) Roof failure (see Mine caving) Rotary drill, 20, 490, 491, 842, 899 Rotation of the earth, 89, 163, 367 SUBJECT INDEX Bante damping resistance of, 479, Rutile, density of, 78 8 Safety: — of dynamite, 485-487 mine — (see Mine safety) Saline waters, 54, 638, 658, 816, 833, 867, 888, 929, 943 Salinity, 60, 869, 943 Salt (see Rock salt) Salt anticlines, 45, 158, 273, 274, 423, 736 Salt domes, 4, 5, 8, 15, 21, 33, 35, 43-47, 53, 54, 70, 158, 159, 275, 282, 295, 422-425, 441, 499-501, 518, 579, 738, 739, 805, 806, 817, 851, 852, 860, 862, 894, 929 acoustic measurements on -, 958 electrical results on -, 738, 739, 805, 806 gas and oil analysis results on -, 894, geothermal investigations of -, 851, 852, 856 gravity maxima on -, 158, 278, 281, 282 gravity minima on -, 158, 159, 275, 276, 277 leaching of -, 929 magnetic results on-, 423, 424 pendulum and gravimeter results on -, 158, 159 radio field strength measurements on -, 811, 817 seismic results on —, 275, 282, 500, 501, 518, 579, 862 torsion balance results on -, 274-283, 291, 292 Salt mines, 54, 274, 291, 292, 811, 817 Saltpeter, density of, 79 Salt water (see Saline waters) Sand: density of -, 74, 76, 83 — deposits, 54, 55, 742 dielectric constant of —, 666, 667 grain arrangement of -, ’ 634-637 heat conductivity of -, "849 longitudinal wave velocity of -, 468-470 oil — (see Oil sand) porosity: of —, 74, 637, 832 radioactivity of -, 864 resistivity of -, 637, 664, 833 specific heat of -, 848 susceptibility of ~ -, 312 water — (see Water sand) Sandstone: coercive force and remanent magneti- zation of —, 316 density of -, 75, 83 dielectric constant of —, 666 elastic moduli of —, 468 — formations, 55, 284, 285, 289, 290, 424, 427 SUBJECT INDEX Sandstone (cont’d): heat conductivity of -, 849 longitudinal wave velocity of -, 470 radioactivity of —, 875 resistivity of —, 637, 662, 663 specific heat of —, 848 susceptibility of —, 312, 424 Sapper, detection of, 9, 64, 956, 961 Sassoline, density of, 78 Saturation current, 873, 880, 881 Saturation effect, 622, 698, 707 Saugus formation, 424 Sawtran method, 761 Scaffold, 7, 19, 20, 41, 407, 408 Seale factor (see also Model experi- ments), 800 Seale value and sensitivity: — of electroscopes, 876-879, 881 —of galvanometers, 601, 603, 617, 670, 780, 841 — of gravimeters, .11, 125-127, 130, 131, 134, 135 — of magnetometers, 17, 300, 322, 323, 325-330, 335-338, 341, 344, 345, 303, 367 — of pendulums, 10, 99, 100, 101, 104 — of radio methods and apparatus, 814, 822 — of seismometers (see Magnification) — of thermometers, 841, — of torsion balances, 13, 172, 198-199 PeAbUeriie (see Seismic waves, scattering o Schist: density of -, 81 dielectric constant of —, 666 longitudinal wave velocity of -, 472 resistivity of —, 660 susceptibility of -, 312 Schmidt balance (see Magnetometer, Schmidt) Sea, measurements at, 41, 101, 107, 109, 365, 945-956 Sea level, reduction to (see also Bouguer reduction), 136 Search coil (see Coil, reception) Search electrode (see Electrode, search) Secondary electrodes (see Electrode, search) Secular variation: — of gravity field, 165 — of magnetic field, 370, 372 Sedimentary: — formations, 16, 19, 48, 46, 55, 74-76, 278, 280, 283-285, 296, 312, 316, 318, 389, 409, 410, 419-427, 429, 430, 439, 441, 474-476, 508, 512, 518, 520, 540, 547, 551, 677, 678, 706, 736, 738, 740, 743, 772, 805, 833, 836, 846, 847-849, 851, 862, 875, 904, 906, 908, 909, 929, 960 — iron ores, 51, 52, 414 — ores, 439 ~ rocks (see Sediments) 993 Sedimentation: effect of -, on gravity, 165 — and subsidence, 929 Sedimentation deposits, 49, 51, 52 Sediments and sedimentary rocks: clastic —, 474 density of -, 74-77, 82-84, 278, 280, 283-285 factors affecting elastic of -, 474, 475 longitudinal wave velocities of -, 468-471, 474-476 magnetic properties of —, 16, 19, 43, 46, 55, 296, 312, 316, 318, 389, 419-426, 865 radioactivities of —, 864, 874, 875 Rayleigh wave velocity of -, 473 resistivities of —, 637, 661-665 specific acoustic resistances of —, 479 specific heats of -, 848 thermal conductivities of —, 847-849, 852 Seismic: — arc mapping, 546-548 — detector (see Seismograph and De- tector) — equipment, 20, 21, 503, 504, 505, 551- 555, 616-618, 862, 912, 915-917 — fan shooting, 499-504 — instruments (see also Seismograph) 20, 21, 503-505, 551-555, 579-618, 862, 912, 915-917 — intensity, 477-481, 497, 498 — interpretation: curved ray -, 540-546, 560, 565 — in fan shooting, 499-502 —in reflection shooting, 557-567, 572-579 — in refraction shooting, 505-549 vertical-ray —, 533-536 wave-front —, 536-540 — methods, 7, 8, 19, 437-618, 910-928 method of differences, 23, 548, 549, 572, 576 operation of —, 489, 490, 498-505, 514, 522, 525, 546, 548-551, 555, 568- 576, 615-618 — records, 22-24, 451 573-575, 913, 923 -— reflection methods (see also Re- flection), 479-618 — refraction methods (see also Re- fraction), 549-579 — resistance, 62, 918, 919 — unrest, 913 waves: absorption of — (see Absorption) dispersion of —, 480 497, 921, 927 longitudinal - (see longitudinal waves) reflection of — (see Reflection) refraction of — (see Refraction) scattering of -, 479, 480 spreading of —, 479, 480 transverse — (see Transverse waves) properties 994 Seismic wave velocities, 22-24, 44, 439- 441, 448-452, 454, 464-466, 468-480, 497, 498, 500, 501, 504, 505-550, 557-571, 578, 862, 863, 948; 944, 956 apparent -, 440, 521-524, 526, 528, 529, 541, 542, 545, 550, 564, 927, 935 average —, 23, 24, 25, 42, 441, 568-570 differential —, 465, 473, 476, 568, 862, 863 factors affecting —, 474-477 horizontal —, 464 vertical —, 465, 473, 476, 568, 862, 863 Seismic well shooting, 23, 34, 35, 465, 568, 862, 863 Seismogel, 485 Seismogram, 22-24, 451, 573-575, 913, 923 Seismograph (see also Detector): Ambronn -, 612, 613 Askania -, 609 Benioff —, 595, 614 calibration of —, 615-618 capacitive —, 20, 552, 610, 612, 931, 932 classification of —, 579-580 crystal —, 20, 613 damping of —, 583-586 electrical —, 20, 551-552, 592-597, 601— 607, 609-6138, 615, 912, 917, 932 electromagnetic -, 20, 551-552, 592- 597, 601-607, 609-610, 917 Ewing -, 580 forced oscillations of —,-586-591 free oscillations of —, 581, 582 friction in -, 582, 583 Galitzin —, 580-584 Gray -, 580 horizontal -, 127, 129, 130, 163, 168, 580, 917 hot wire -, 613 1.G.E.S. -, 610 inductive —, 551, 592-595, 609-611 mechanical —, 591, 592, 607-609, 917 Milne -, 580 Mintrop —, 607-609 pallograph —, 580 piezoelectric —, 613 pressure type -, 612, 613 prospecting —, 581, 607-615 Rebeur-Paschwitz —, 580 reluctance —, 552, 610, 611, 862 Schweydar -, 580, 609 series —, 550 station —, 581, 583, 589, 590, 615 Tanakadate —, 580 theory of —, 580-591 transients, effect on —, 589-591 vertical —, 127, 132, 551, 580, 917 Vicentini —, 580 well detector —, 568, 862 Wenner -, 584, 614 Wiechert —, 484, 580, 583 Wood-Anderson -, 580, 584, 614 Zoellner —, 580 Seismology, 3, 440 engineering —, 441, 910-928 SUBJECT INDEX Seismometer (see Seismograph) Self-potential method, 8, 25-27, 39, 53, 58, 63, 619, 621-624, 667-681 corrections in —, 675 electrodes in —, 669, 670 equipment in -, 669, 670 interpretation in —, 671-675 procedure in -, 670, 671 results of —, 675-681 Senarmontite, density of, 78 Sensitivity (see Scale value) Series detectors, 550 Serpentine, 55, 76, 405, 422, 432, 433 coercive force and remanent mag- netization of —, 316 density of -, 80, 81 heat conductivity of —, 849 resistivity of —, 658, 660, 661 susceptibility of —, 310, 312 Shafts, 57, 58, 407, 740 Shaking table, 616, 617, 618, 917 Shale: density of -, 76, 83, 84 — formation, 24, 34, 51, 162, 284-286, 419, 420, 441, 474, 676, 677, 706, 735, 736, 738, 772, 836, 864 longitudinal wave velocity of —, 470 resistivity of —, 661, 836, 837 susceptibility of —, 312 Shallow wells, 862, 865, 866, 868, 880, 887, 889 Shear: — modulus, 445 — stresses and strains, 442, 446, 448 — zones, 742, 754-756, 884, 885, 904-907, 909, 928-930, 933, 958 Shell limestone, density of, 84 Shepard tester, 725 Ships, measurements on, 41, 42, 945-956 Shoestring formations, 45, 47, 422, 433 Shooting, technique of, 483-490, 503, 551, 570, 571 Shot-hole drilling, 490-492, 571 Shot-instant transmission, 465, 493-497, 508, 555 Shots, placement of, 489, 490, 503, 550, 551, 569-571 Siderite: density of —, 78 dielectric constant of —, 666 — ore, 50, 287 resistivity of —, 658 susceptibility of -, 311 Side-wall sampling, 47, 869 Siemens compensator, 843, 844 Silence zones, 935, 936 Silica content: effect of =, on elastic properties of rocks, 474 effect of —, on rock density, 73 effect of —, on rock magnetism, 314 Siliceous lime, density, 81 SUBJECT INDEX Silt: density of -, 74 resistivity of —, 664 Silver: damping resistance of —, 482 density of -, 73, 77 — ore, 50 Sine galvanometer, 365, 366 Sine (deflection) method, 349, 364, 365 Skin effect, 681, 685, 686, 757, 758, 801, 811 Slabs: magnetic anomalies of —, 397 torsion balance anomalies of —, 256, 257 Slate: conductive —, 659, 660, 705 density of -, 81 graphitic —, 678 heat conductivity of —, 849 longitudinal wave velocity of —, 472 magnetic -, 50, 419 radioactivity of —, 875 resistivity of —, 659-661 specific heat of —, 848 susceptibility of —, 312 Slope: electrical (surface potential) effect of ~, 722, 748-749 gravity anomaly of -, 151i, 153 magnetic effect of —, 376, 397 seismic effect of —, 521-533, 538, 547, 562-568 torsion balance anomalies of -, 259, 260, 261 Smaltite, density of, 77 Smithsonite, density of, 78 Snell’s law, 504, 533, 541 Snow, density oi, 79 Soapstone, 55 Sodium chloride, 26, 638 Soil: acidity of —, 680 density of -, 82, 83 dielectric constant of —, 666, 667 longitudinal wave velocity of —, 468 radioactivity of —, 874 Specific acoustic resistance of —, 479 specific heat of —, 848 Soil air, radioactivity of, 874 Soil analysis, 5, 35, 45, 47, 885-910 operation of —, 900 Soil condenser, 649-651 Soil gas (see Gas) Soil-resistivity bridge, 646, 647 Soil-testing methods (dynamic), opera- tion of, 921-923 Soil wax (see Wax) Solar tides, 163, 164 Solution deposits: autogenetic —, 49, 51 heterogenetic —, 49, 50 Solution pressure, 26, 629, 630, 668 995 Sound: absorption of —, 935, 936, 943, 958 directed transmission of -, 937, 945, 946, 949 — frequencies (see Acoustic frequen- cles) — intensity, 477-481 propagation of —, abnormal, 936, 942 — range in: air, 936, 937 earth, 957-958, 960 water, 940, 944, 945, 951 — ranging, 9, 36, 37, 41, 42, 59, 63, 64, 940-942, 949, 950, 960 — receivers, 937, 938, 947-950, 953-956, 959, 960 reflection of —, 867, 943, 944, 952, 957, 962, 963 refraction of —, 943, 944, 957, 963 shot-instant transmission by -, 494, 503 — transmitters, 936, 937, 945-947, 949, 950, 952-956, 958 — velocity in: air, 867, 935, 940, 941, 943 earth, 468-472, 956 water, 943, 944, 949, 950 Sour dirt, 886, 887 Southern hemisphere, 211, 212, 293, 295, 412, 416, 418-420 Soxhlet extractor, 901 Space wave, radio, 651, 652 Spectrograph, mass, 898 peecute porate (see Hematite, specu- ar Specularite (see Hematite, specular) Sphalerite (zincblende, zinc sulfide): density of -, 74, 78 — deposits, 52, 804 dielectric constant of —, 666 resistivity of —, 657, 659 Y Sphere: displacement of equipotential lines by -, 697-700 gravity anomaly of —, 146 magnetic anomaly of —, 390, 391, 392 resistivity anomaly of -, 723 self-potential of —, 672-674 torsion balance anomaly of —, 254-256 Spinel, density of, 78 Spontaneous: - polarization (see Spontaneous po- tential) — polarization method (see Self-poten- tial method) — potential, 26, 33, 619, 621, 623, 624, 628-631, 667, 668, 676-681, 825, 831-839, 869 Spring: — constant, 99, 100, 124, 449, 461, 581, 582, 591, 595, 596 — sediments, 875 — water, 60, 61, 875, 881, 883, 884 Stakes (see Electrode, search) 996 SUBJECT INDEX Static magnification (see Magnification, static) — methods of measuring gravity (see Gravimeter) Station factor, seismic, 913 Steel, damping resistance of, 482 Steel objects, effects of, 332, 333, 373- 375, 404, 425 Step outs in seismic récords, 567, 568 Stethoscope, 948, 959 Stibnite: density of -, 78 resistivity of —, 657 Storms, magnetic, 570 Strain and stress relations, 442-447 Strain gauges, 454-456, 928-934 carbon -, 930-931 electrical —, 456, 930-933 inductance -, 932, 933 mechanical —, 454, 929, 930 optical -, 455-457, 930 , telemeter —, 930, 931 ultramicrometer —, 931-932 Strain gauging, 9, 36, 41, 42, 58, 62, 911, 928-934 Strain recorder (see Strain gauge) Stratification and physical anisotropy (see Anisotropy) Stratified ground, investigations of, 20, 22, 28, 32, 44, 53, 60, 61, 150, 416, 417, 419, 437, 476, 621, 622, 624, 625, 626, 699, 700, 707, 738, 740, 744, 747, 748, 751, 774, 790-800, 804-806, 828-837, 852 Stratigraphic: investigations (see Stratified ground) — traps, 907 — variations (shallow) (see Near-sur- face interference) Stresses: mechanical -, 16, 442-447 normal —, 443-445 shearing -, 446, 447 tangential —, 446, 447 ultimate —, 918, 919 units of measurement of —, 452, 453 Stringers: magnetic —, 376, 404, 414 self-potential anomalies of —, 676, 677 String galvanometer, 359, 609, 610, 613 Stringocephalus lime, 772 Stroboscopic coincidence method, 104- 106 Structural studies: — by electromagnetic methods, 623, 626, 771-773, 791-800, 804-806 — by equipotential-line methods, 624, 706 — by gravity methods, 70, 158-161, 290-292 — by self-potential methods, 678 Structural studies (coni’d): — by torsion balance, 70, 273-288, 290-292 — by well logging, 804-806, 836, 837, 853, 864 Subaqueous (see Underwater) Subdrift topography (see Bedrock depth determination) Submarine: detection of —, 9, 41, 59, 64, 949, 950-952 measurements in -, 41, 42, 101, 107, 109, 947, 949, 951 — signaling, 484, 945-949 — transmitter, 484, 945-947 Subsidence, 36, 63, 914, 928-930, 933 Substitution method, 644, 646, 650, 651 Subsurface bodies (see Geologic bodies) Suess balance, 193, 194, 201 Sulfide: nickel —, 52 — ores, 4, 8, 34, 35, 50-52, 162, 417, 624-626, 632, 642, 668, 675, 704, 705, 739, 802-804, 809, 817 resistivity of —, 657 zine — (see Sphalerite) Sulfur: density of ~, 79 — deposits, 53, 70, 740 dielectric constant of —, 665 resistivity of —, 658 Sun: effect of -, on gravitational field, 162-164 magnetic field of -, 317 Sundial, 346 Superdip, Hotchkiss, 17, 342-344, 379, 430 Surface anomalies (see Near-surface interference) Susceptibility: electric —, 640 magnetic — (see Magnetic suscep- tibility) Suspension: bifilar -, 11, 130, 131 gimbal -, 102, 103, 110, 352 - of torsion balance, 175, 184, 186, 187, 196-198 trifilar —, 11, 128, 131, 132 Zoellner —, 191, 192, 580 Swedish mining compass (see Compass) Syenite: density of —, 80 dielectric constant of —, 666 magnetic anomalies of -, 417 radioactivity of —, 874 resistivity of —, 660, 661 specific heat of -, 848- Syenite-porphyry: coercive force and remanent magne- tization of -, 316 susceptibility of -, 313 Sylvanite, density of, 77 ——=- = he SUBJECT INDEX Sylvite: density of -, 79 susceptibility of -, Synclines, 15, 61, 151, 153, 161, 252, 259, 262, 263, 396, 400, 772, 773 T Tage interpretation method, 726-731 Tale: density of -, 80 — deposits, 55 Tangent galvanometer, 365 Tangent method, 349, 365 Tank experiments, 701, 734, 735 Tank farms, magnetic effects of, 374 Tanks, water, 912 Taylor seismograph, 609 Taylor shale, 285 Telemeter, 930, 931 Telescope, zenith, 113 Tellurides, resistivity of, 657 Temperature: — coefficient of resistivity, 639 — coefficient of torsion wire, 197 = correction for pendulum, 118 effect of -, on gravimeters, 133, 134 effect of —-, on magnetometers, 326-328, 331, 337, 338, 366, 367 effect of -, on rock magnetism, 16, 317 effect of —, on torsion balance, 197, 198 — gradient (see Gradient, geothermal) low -, 899 ~— measurements in wells, 9, 33, 41, 42, 47, 837-862 — of rocks, 839, 844-853 transient —, causes of, 853-860 _ ae diurnal and annual, 860- 2 Tension tests, 457 Terraces, 45, 70, 514, 516, 517, 520, 521, 529 Terrain: — corrections and effects, 11, 14, 71, 137-140, 169, 213-240, 375, 376, 509, 551, 622, 623, 702, 703, 763, 771, 808, 809, 815, 860, 861 — in relation to geophysical operations, 64, 813, Terrain-clearance 817, 942 Terrestrial magnetism, 3 Terrometer, 628, 823 Tertiary formations, density of -—, 82 Test block (see Shaking table) Testing methods: — for density, 71, 72 dynamic -, 914-928 — for elasticity, 452-466, 927 — for electrical properties, 642-656 — for magnetism, 297-309 — for radioactivity, 876-883 — for thermal properties, 849-951 well —, 825-869 Tetrahedrite, density of, 78 indicator, 997 Thalén-Tiberg magnetometer, 349 Thenardite, density of, 78 Theodolite, magnetic, 355-358, 366 Thermal conductivity, 847-853, 860 Thermal detection, 9, 64 Thermal diffusivity, 846, 847, 860, 861 Thermal gradient (see Gradient, geo- thermal) Thermocouple, 840, 841, 843, 850 Thermoelement, 844 Thermometer: bimetallic —, 843 Bourdon tube -, 366 — carriers, containers, 841, 842 maximum -, 841, 842, 843 mercury —, 321, 334, 840, 841 overflow -, 841 resistance —, 840, 8438, 850 thermocouple — (see Thermocouple) Thermonatrite, density of, 78 Thermostat, 133 Third curve, 829 Thomson-Thalén magnetometer, 347, 348, 351 Thorium, 870, 872-874, 877 Three-dimensional geologic __ bodies, 144-150, 153, 250, 253-258, 265, 266, 269, 270, 375, 381-385, 390-395 Tides, 163, 164 effect of —, on gravity, 165, 166 effect of —, on torsion balance, 166 Time constant, 757, 758, 760-762 Time gradient, 557, 558, 564-566 Time signals (see also Transmission of time signals and Shot-instant transmission), 106, 113-115 Time variations of gravitational field, 162-167 Time variations of magnetic field, 367- Timing, time marking, 20, 464, 465, 552, 555, 614, 615 Tin, 51, 73 Titanite, density of, 78 Titano-magnetite, 314 Tonpilz, 946, 948 Topaz, density of, 80 Topographic correction (see Terrain cor- rection) Topography (see Terrain) Top soil (see Soil) Torsion balance (Kétvés) 8, 9, 11, 13, 40, 45-48, 52, 53, 55, 61, 170-292 Askania —, 193-195 Bamberg -, 193 Berroth -, 191 calculation of results, 199-210 Cavendish -, 85 — coast effect, 241-242 — corrections, 210-244 — equations for three positions, 180 — equations for four positions, 181 — equations for five positions, 183-184 998 Torsion balance (cont'd): Fechner -, 193 Gepege -, 194 graphical representation of data, 244— 250 Haalck -, 186 Haff -, 194 Hecker -, 186 interpretation: — diagrams (Barton), 266, 267 — diagrams (Numerov), 265 — integraph (Askania), 269-270 — method (Below), 268 — of results, 14, 15, 215-270, 393 Kilchling -, 189 magnetic —, 303, 355, 380 — in mining, 286-292 Nikiforov -, 194 Numerov -, 187 Oertling —, 193 — in oil exploration, 272-286 operation of —, 206-210, 239-240 principal equation of —, 178 principle of —, 13-15, 170-178 — regional gradient, correction for, 240-241, 246, 251, 262, 281 — results, 270-292, 409-411 rotating —, 189 Rybar -, 194 Schweydar —, 194 sensitivity of —, 198, 199 Suess -, 193, 194 Tangl -, 194 — terrain corrections, 71, 75, 213-240 theory of —, 175-192 tilt beam —, 13, 194, 195 Tsuboi -, 193 —underground corrections, 242-244 Z beam -, 194 Torsion coefficient (see Coefficient) Torsionless position, 14, 177, 178, 179, 184, 199, 200, 204, 206 Torsion tests, 460 Torsion wire, che 13, 177, 178, 194-198, 342 calibration of -, 195-197 Total intensity ’ (magnetic), 16, 293, 295, 319, 342-344, 364, 379-390, 400, 418 Tourmaline, density of, 80 Trachyte: density of -, 81 heat conductivity of —, 849 radioactivity of —, 874 Transceiver, 497, 955 Transducer, 552, 591, 593, 595, 933 Transformer: differential —, 696, 820 reference —, 695, 696, 781, 783 Transients: electrical — (see also Eltran methods), 30, 625, 757-763 seismic —, 587, 588, 590 SUBJECT INDEX Transmission: — constant, 594, 595, 602, 603, 606, 617 — factor, 811 — of time signals and shot instant, 10, 20, 106, 113-117, 465, 496, 497, 503, 504, 950, 951 Transmission and reception points, spac- ing of, 7, 19, 437, 621-623 Transmitters: coil —, 821-824 —in beh aarti prospecting, 774— 78 radio —, 114-116, 496, 497, 812, 815-817, 819, 823, 824, 950, 951 sound —, 936-937, 945-956 Transportation, 6, 44 Transverse: — waves, 447, 448, 450-452, 472, 473, 913, 926 — wave velocities, 472-474, 913, 927 Trap rock: ° density of —, 75 heat conductivity of —, 849 resistivity of —, 661 Travel time, 4, 20, 22, 44, 484, 494, 497, 498, 500, 502, 504-507, 509-517, 519, 521-525, 527, 528, 533-536, 541-544, 546-549, 556-572, 576, 578, 579, 863, 940, 941, 944, 952 Travel-time curve, 441, 451, 499-502, 504-512, 514, 516-522, 525-529, 531, 534, 537-542, 544-546, 557, 560, 561, 863 Treasure finders, 33, 63, 818-824 high-frequency —, 629, 821-824 low-frequency —, 627, 819-821 Trifilar suspension, 11, 128, 131, 132 Trolley lines, 372, 680 Tuning factor, 481, 587-589, 590, 601, 602, 604-607 Tuning fork, 555, 615, 618 Tungsten, 50, 52 Tunnel investigations, 6, 14, 57, 58, 63, 376, 404-407, 741, 863, 928-930, 933, 959-962 Turbidity, 897 Twin-pendulum method, 101, 102, 121- 123 Two-dimensional geologic bodies, 144- _ 146, 150, 157, 169, 243, 247, 251, 252, 254, 257-270, 385-388, 395-400, 768 relation of -, to three-dimensional bodies, 257, 258 U Uley graphite, 756 Ultramicrometer, 125, 931, 932 Ultrasonic transmission, 945-949, 952, 953 Unconformities, 5, 551, 864 Unconsolidated formations, 23, 61, 74, 452, 468, 474-476, 663, 664 SUBJECT INDEX Underground: — measurements, 14, 19, 41, 54, 242-244, 291, 292, 404-407, 411, 413, 739, 811, 816, 817, 863, 884, 928-933, 959-962 — openings, 14, 36, 242-244, 292 — workings, 14, 36, 62, 405, 815, 845, 855, 860, 863, 928-930, 933, 958-962 Underwater: — gravimeter, 109 — pendulum apparatus, 101, 103, 109, 110 — resistivity surveys, 738 — sound receiver, 947-956 — sound transmitter, 945-956 Undograph, 937 Uraninite, density of, 77 Uranium, 35, 51, 52, 870, 872-875, 880 V Vacuum, free fall in, 123 Vagabondary currents, 63 Valentinite, density of, 77 Vanadinite, density of, 77 Vanadium, 51, 52 Variation: annual temperature —, 860-862 artificial magnetic —, 372 diurnal magnetic -, 41, 42, 331, 332, 366-369, 371 diurnal temperature —, 860 — of gravity field, 162-167 — recording, 18, 41, 42, 63, 164, 331, 332, 366-372, 755 secular —, 370, 371 stratigraphic (shallow) (see surface interference) Variometer: gravity — (see Torsion balance) magnetic — (see Magnetometer and Observatory) Vector potential (see Potential) Vectors, anomalous, 378-380, 405-407, 4ll, 413, 417, 418 Vehicles, measurements in, 41, 42 Veins, 29, 50, 52, 150, 162, 259, 260, 264, 287, 385, 395, 396, 413, 624, 625, 729, 740, 749-751, 755, 774, 803, 816, 883, 884 Velocity: apparent — (see Seismic wave velocity, apparent) average — (see Seismic wave velocity, average) bar -, 461, 463, 482 differential — (see Seismic wave ve- locity, differential) light — (see Light velocity) phase — (see Phase speed) seismic — (see Seismic wave velocity) Sound — (see Sound velocity) vertical — (see Seismic wave velocity, vertical) Near- 999 Vertical: — balance (see Magnetometer, Schmidt . vertical) — component (see Vertical component) deflections of —, 70, 167-170 — electrical drilling (see Resistivity sounding) —gradient of gravity, 70, 136, 169, 190-192 — gradiometer (see Gradiometer) — intensity. 16-18, 295, 302, 320, 321, 323, 326-328, 335-337, 339-341, 344, 345, 348, 378-402, 405-412, 414-417, 420, 423, 425-429, 431, 432, 434-436 — loops (see Loops) —Mmagnetometer (see Magnetometer, chmidt vertical) — ray interpretation, 533-536, 549 — shooting, 23, 557, 560 ~ seismograph (see Seismograph) —variation of seismic and sound velocity, 23, 474, 476, 533, 540-546, 560, 565, 935, 936, 943, 944 — velocity (see Seismic wave velocity, vertical) — velocity gradient (see Vertical varia- tion of seismic and sound velocity) Vertical component: — of gravity, 88, 124, 164, 168 — of ground and building vibration, 20, 551, 918 — of electrical field (see Electrical field) — of electromagnetic field (see Electro- magnetic Feld) -— of magnetic field (see Vertical in- tensity) Vibration: acoustic — (see Acoustic waves) blasting —, 36, 911, 913, 931 bridge —, 912, 915, 917 building -, 6, 36, 911, 912, 918, 919 dam -, 912 — damage, 9, 910, 911, 913 — detector, 866, 867, 916 earthquake -, 36, 912, 918 flexural —-, 912, 919 forced —, 36, 62, 461, 481, 586-591, 911, 912, 917-919 free —, 62, 86, 97, 100, 356, 449, 461, 582-586, 598, 615, 616, 911, 912-914 frequency of — (see Frequency) ground -, 912-914, 919-925 industrial —, 36, 910 pipe -, 866, 867, 982 — recording, 36, 58, 912-928 — of roads, 6 — of rock specimens: longitudinal vibrations, 462-463 torsional vibrations, 461-463 shear —, 912, 919 — testing, 9, 36, 41, 911 torsional -, 912 1000 Vibration (cont'd): traffic -, 36, 41, 42, 913 Vibrator, 20, 36, 484, 911, 915-917, 919-927 Vibrographs, 581, 912-917 Villari effect, 317. Viola lime, 46 Viscosity, 481, 631, 639, 736, 905, 958 Vitrophyre, density of, 81 Vivianite, density of, 73 Volcanic rocks: densities of —, 73, 81 deposits of -, "416, 419, 424, 434, 855 elastic moduli of -, 467 magnetic properties of —, 313-318 resistivities of —, 659 Volcanism, 3 effect of -, on geothermal data, 853- effect of —, on gravity, 165 Volcanoes, mud, 886, 887 Volcanology, 3 Voltmeter, vacuum tube, 31, 617, 626, 778 Volume control, automatic, yA 552 Volumetric method of measuring grav- ity, 124 WwW Wall failure (see Mine caving) Walters Arch, Okla., 161, 430 Warfare: aerial —, 59, 63, 64, 941, 942 chemical -, 59, 64 land —, 59, 68, 64, 940, 958 marine -, 59, 63, 64,-949, 951 Washburn-Bunting method, 835 Water, 5, 6, 8, 47, 58-62, 76, 433, 475, 633, 636-639, 641, 743, 744, 57, 812, 817, 830- 840, 842, 847, 853- 858, 866, 869, 870, 873-875, 881, 883, 884, 886-888, 895, 896, 899, 900, 906, 934, 935, 943-956, 959, 963 bromine -, 886, 887 cavern -, 60, 61 connate —, 60, 62, 631, 638, 830-833 resistivity of —, 638, 832, 833 — content (see Moisture) dielectric constant of —, 633, 665 direct location of —, 5, 61, 812, 834, 836, 857, 866, 869, 883, 959, 961, 963 = encroachment, 858 fissure —, 60, 61, 623, 735, 738, 739, 875, 885, , 9 08 — flows "(see ‘also Pipe leaks), 834, 854, 857, 858, 866, 869 ground -, 60, 61, 62, 743, 744, 812, 963 dielectric constant of — , 655, 665 resistivity of —, 638, 655 heat conductivity of —, 848 iodine —, 886, 887 — leak (see Pipe leaks) — level,*changes in, 165 location of -, 47, 60, 61, 62, 433, 624, 625, 743, 744, 812, 830-840, 856-858, 866, 867, 869, 883, 959, 961, 963 SUBJECT INDEX Water (cont’d): a ey wave velocity of -, 468, meteoric -, resistivity of, 638 mine -, resistivity of, 638 movement of (see also Pipe leaks and Water flows), 631, 667, 906, 961 radioactivity of — (see Radioactive waters) resistivity of —, 61, 62, 631, 633, 636- 638, 655 river -, resistivity of, 658 saline — (see Saline waters) —sands, 636-638, 744, 830, 831, 833, 834, 836, 838, 857, 858 soil -, resistivity of, 658 sour —, 886, 887 spring -, 60, 61, 875, 881, 883, 884 stratigraphic location of -, 61, 743, 744, 756, 757 ee location of -, 61, 433, 748, surface -, resistivity of, 658 —in wells, 34, 830-840, 842, 853-858, 866, 869 Wave front, 506, 507, 536-539, 623 Wave-front diagrams, 536-540 Wave length, 652, 655, 810-818, 881, 927, 937, 938, 945, 957 Waves: acoustic — (see Sound waves) elastic — (see Seismic waves) longitudinal - (see Longitudinal waves) Love — (see Love wave) radio — (see Radio waves) Rayleigh — (see Rayleigh waves) seismic — (see Seismic waves) sound — (see Sound waves) Wax, 36, 886-888, 899, 901, 903, 904, 908, 910 Weathered layer, 23, 474, 475, 499, 533, 534, 540, 548, 550, 571-573, 576, 578, 862 longitudinal wave velocity of — 474, 475 Weathering: effect of —, on density, 74, 75 magnetic effect of —, 318, 376 Weathering correction, 24, 548, 549, 571- 578, 576, 578, 579, 862 Weathering deposits, Bl Weight: determination of -, 71 falling -, as seismic energy source, 483-484 Well casing: magnetic effects of —, 374, 375, 425 plastic —, 491 Wellington shale, 83 Well surveying, 863, 866 , 468, SUBJECT INDEX 1001 Well testing, well logging, 6, 9, 33, 45, | Wood: 825-837 density of -, 79 acoustic —, 866-867 fossil -, 876 electrical —, 825-837 Woodbine sand, 835 gamma ray -, 876, 883 density of -, 83 gas detection —, 868, 869 Wulfenite, density of, 77 geothermal -, 837-863 peeved -, get x photoelectric -, ti radioactivity —, 863-865, 876, 883 X rays, 871-873 seismic —, 862, wee aes Y rature — = cos ata Young’s modulus, 100, 438, 439, 443, 445, deep — (see Deep wells) 446, 454, 457-461, 463, 464, 465, 467, shallow — (see Shallow wells) 468, 474, 475, 482, 483, 485, 591, Well shooting, 23, 34, 35, 465, 568, 862-863 849, 927 Wenner-Gish-Rooney method (see Gish- Z, Rooney method) Wertheim effect, 317 Z beam torsion balance, 193, 194 Wheatstone bridge, 29, 363, 613, 644, 645, | Zeiss galvanometer, 609, 893 745, 827, 843, 844, 868, 931, 932, 938 | Zeolitization of lavas, 51 Wiedemann balance, 303 Zine, 73 Wilson balance, 303 Zincblende (see Sphalerite) Wireless communication (see Radio) Zincite, resistivity of, 659 Wire transmission, 10, 20, 114, 465, 494- | Zine sulfide (see Sphalerite) 497, 504 Zircon, density of, 80 Wolframite: Zoeliner suspension, 191, 192, 580 density of -, 77 Zoisite, density of, 80 resistivity of —, 657 Zones, contact metamorphic (see Con- susceptibility of —, 310 tact metamorphism) NAME AND PLACE INDEX A Aachen, Germany, 422 Abana mine, Quebeg, 417, 739 Abraham, M., 648 Ackley, W. T., 960 Adams, C., 429 Adams, F. D., 457, 458 Adams, L. H., 458, 465, 467, 468, 477, 844 Adirondacks, 51 Africa, 50, 56, 419, 678, 679, 812 Aguerrevere, P., 363 Ahrens, W., 434, 435 Alabama, 51, 430 Alabama Hills, Calif., 472 Aland, Finland, 314 Alaska, 51, 416 Alberta, Canada, 468, 469, 470, 756 Aldredge, R. F., 722 Aldrich, H. R., 413 Alexander the Great, 886 Alexanian, C., 427, 848 Algeria, 660, 663 Alleghany County, N. C., Allen dome, Texas, 278 Allen, T. L., 472 Allschwill, Alsace, 427 Alps, 370 Amagat, E. H., 458 Amarillo, Texas, 47, 284, 429, 430, 432 Ambronn, R., 79, 306, 341, 612, 613, 625, 666, 691, 841, 863, 880, 884, 885 American Askania Corporation (see As- kania) Amu-Darya River, U.S.S.R., 886 Anadarko basin, 161 Anadarko, Oklahoma, 371 Anderson County, Kansas, 433 Angenheister, G., 342, 365, 469, 471 Ansel, E. A., 536, 538, 539, 540. Anse La Butte dome, La., 424 Antonov, P. L., 905, 909 Appalachian Mountains, 50 Apsheron (Peninsula), U.S.S.R., 738, 886, 909 Aquagel, 491, 571 Arad, Hungary, 283 fuel Mountains, 160, 161, 284, 430, Ardmore Basin, Oklahoma, 161 Arizona, 50, 659 Arkansas, 50, 51, 52, 56, 417, 418 740 160, Arsonval, d’, 552 Asia Minor, 310 Askania, 10, 13, 17, 109, 110, 111, 115, 116, 126, 157, 178, 187, 193, 194, 195, 198, 199, 208, 222, 238, 240, 269, 322, 324, 326, 329, 331, 332, 334, 356, 357, 358, 362, 609, 892, 893 Athy, L. F., 75 Atlanta area, Arkansas, 910 Atlas Powder Company, 484, 485, 487, 488 Atlas Werke, 947 Aubure, Alsace, 427 Aurand, H., 369 Australia, 53, 468, 469, 470, 472, 660, 705 Austria, 471 Ayvazoglou, W., 201 Azerbeijan, U.S.S.R., 160 B Babylon, Asia, 886 Bacon, R. H., 363 Bagratuni, Armenia, 422 Bahnemann, F., 412, 419 Bahurin, J., 310, 311, 312, 390 Baicoi-Tintea dome, Rumania, 277 Baird, J., 748 Baku, U.S.S.R., 160, 738, 886, 909 Balachany, U.S.S.R., 160 Balaton Lake, Hungary, 271, 312 Balcones fault zone, Texas, 805 Baldock, England, 666, 667 Bamberger, M., 876 Banat, Rumania, 287 Banos, A., 386 Barber’s Hill dome, Texas, 424 Barnes, H. T., 952 Barnett, S. J., 365 Barrell, J., 77, 80, 83, 84 Barret, W. M., 304, 305, 306, 375, 403, 404, 423, 424, 426, 628, 816 Barsch, O., 469, 470, 472, 493 Barton, D. C., 44, 79, 82, 84, 135, 241, 248, 266, 267, 278, 280, 281, 282, 283, 285, 470, 471, 499, 500, 501, 863, 888 Bastrop County, Texas, 432 Bauer, L. A., 365 Bavaria, 660 Bazzoni, C. B., Beckham els Ou 430, 432 Bee County, Texas, 426 373, 374, 428, 432, 1003 1004 Beekmantown, Ont., 84 Behm, A., 936, 942, 945, 953 Béhounek, F., 875, 884 Beienrode, Germany, 79, 83, 84, 291, 292 Belgian Congo, 660, 884 Belle Isle dome, La., 278 Bellinzona, Switzerland, 312 Belluigi, A., 767, 769 Benioff, H., 593, 595, 614, 933 Benthen, Germany, 423 Berezniaky, U.S.S.R., 278 Berg, J., 345, 349, 405 Berggiesshuebel, Saxony, 406, 412 Bergmann, L., 944, 947 Berlage, H. P., 127 Berroth, A., 96, 109, 114, 119, 130, 133, 191, 355 Beuerman, W., 468 Beyer, G., 308, as Beyschlag, F be Bibi Eibat, U. g 8. R., 160, 738 Biddle, James G., Company, 725 Bielgorod, U.S.S.R., 409 Big Lake field, Texas, 909 Birnbaum, A., 291 Bjurfors, Sweden, 704, 705 Bjurliden, Sweden, 704 Black Forest, Germany, 884 Blankenburg, Germany, 884 Blau, L. W., 827 Blondeau, E. E., 817 Blue Ridge dome, Texas, 278 Bock, R., 363 Boeckh, H. v., 273, 274, 283 Boedecker, R., 931 Bogoiavlensky, L. N., 881, 884 Boliden, Sweden, 125, 704, 803 Bonner Springs, Kansas, 83 Boreslau, Poland, 310 Born, A., 874, 875 Born, W. T., 465, 467 Borne, G. v. d., 884 Borough, W., 346 Bourdon tube, 366 Bowen, A. R., 890 Boyer, 660, 661 Brammer, E. B., 365 Brankstone, Gealy, and Smith, 83, 84 Brazil, 50, 312, 314, 433 Brazoria County, Texas, 760, 761, 910 Bridgman, P. W., 457, 458 Brillouin, M., 292 Bring, G. G., 311 Brinkmeier, G., 423 British Admiralty, 953, 954 British Columbia, 51, 416 Brockamp, B., 469, 471, 472 Brown, Hart, 130 Bruckshaw, J. MecG., 783, 784 Bruner field, Texas, 805 Briix, 310 Bryan, A. B., 132 Buchanan field, Texas, 433 NAME AND PLACE INDEX Buchans mine, Newfoundland, 705, 756 Bucovul anticline, Rumania, 277 Bukhara, U.S.S.R., Burbank pool, Calif., 856 Burma, India, 886 Burrows, L. A., 488 Bush City, Kansas, 433 Butte, Mont., 659 Buwalda, J. P., 469, 472, 473 C Caddo-Shreveport uplift, 432 Caldwell County, Texas, 432, 805 Caldwell deposit, Ontario, 290, 292 California, 5, 46, 50, 51, 370, "416, 421, 424, 427, 430, 432, 468, 472, 473, 475, 512 Cambridge Instrument Company, "599, 609, 610 Cameron, G. H., 880 Canada, 5, 50, ‘422, 561, 659, 702, 705, 803, 809, "884 Canal field, Calif., 910 Caribou, Colo., 226, 287, 288, 289 Carlheim-Gyllenskéld, V., 311, 390, 411, 412 Carlsbad, N. M., 51 Carnegie Institute, 358, 362, 365, 579 Caspian Sea, 160, 275 Caucasian foothill zone, U.S.S.R., 736, 37 Caucasus, U.S.S.R., 160, 282 Ceceaty, de, R. P., 470 Cedar Lake field, Texas, 910 Chapel, C. E., 824 Charnwood Forest, England, 312 Charrin, P., 660 Cheltenham, Md., 368, 371 Chile, 54 Chimaira, Lycia, 886 Christiansen, C., 851 Cienaga, Colombia, 677 Clark, R. P., 278, 279, 282, 424, 500 Clemens dome, Texas, 278 Clifford, O. C., 374 Clinton, Alabama, 51 Cloos, E.,.816 Coalinga, Calif., 424 Coffin, R. C., 428 Colbert, L. O., 97 Coles-Levee field, Calif., 910 Collingwood, D. M., 312, 432 Collinsville, Illinois, 82 Colombia, S. A., 678 Colorado, 50, 51, 52, 284, 416, 430, 468, 470, 471, 664 Colorado School of Mines, 301, 735, 786 Columbia County, Arkansas, 910 Connecticut, 664 Conroe field, Texas, 280, 425, 426 Cooper, W. R., 639 Cornwall, England, 311 Courtier, W. H., 416 Crary, A. P., 541, 740 NAME AND PLACE INDEX Criner Hills, Okla., 284, 430 Crosby, T. B., 741 Crossley, N. J., 82 Cuba, 51 Cuba, N. Y., 886 Curtis, 658 D Dacian field, Rumania, 665 Dahlblom, Th., 348, 349, 352, 407 Dale field, Texas, 432, 433 Dana, J. D., 77, 78, 80 d’Arcy’s law, 904 Beeey pipe locator, 765, 818 Das, A. K., 878 Davenport, Okla., 890 Daventry, England, 667 Davies, R., 283 Davis, R. O. E., 646, 647 Dead Sea, 886 DeFord, R. K., 428 Degebo, 920, 926 De Golyer, E. L., 48 Denmark, 469, 471, 472 Dennis, L. M., 895, 901 DeQuervain, A., 580 Derbyshire, England, 311 Deussen, A., 665 Deveaux, P., 469, 470, 472 Dewar flask, 900 Diaz Lake, Calif., 469 Dieckmann, Th., 772 Dix, C. H., 862, 863 Dixon, P. C., 868 Djerba Island, Africa, 470 Dominguez dome, California, 425 Don Leet, L., 465, 467, 472, 473, 541 Dorsey, H. G., 948, 950, 954, 955 Dorsey, N. E., 361, 362 | Dossor, U.S.S.R., 276, 279, 286 Dove, H. W., 819 Dowling, J. J., 931, 932 Ducktown, Tenn., 51 Duddell oscillograph, 552, 598, 930 Duesseldorf, Germany, 421 Dunston, mn E., 44, 887 Du Pont Powder Company, 484, 485, 486, 487, 488 E Eads, Colo., 371 Eagle Harbor, Mich., 662 East Texas field, 910 Ebert, A., 435, 436, 660, 706, 765 Eblé, L., 470 Eby, J. B., 278, 279, 282, 424, 430, 500 Edge, A. B., and Laby, Tr. H:, 290, 291, 3, 416, 419, 421, 468, 469, 470, 472, 502, 548, 609, 610, 613, 657, 658, 660, 670, 675, 695, 705, 753, 755, 756, 783, 788, 805, 808 Edinburgh, Scotland, 286 Egbell, Czechoslovakia, 158, 281, 283 1005 Egersund, Denmark, 310 Egloff, G., 48, 890 Fisenerz, ‘Austria, 310 Ekeldf, a 931 Eklund, E., 287, 802, 803 Elba, Island of, 310, 311 Elberfeld, Germany, 421 Elbof Company, 626, 766, 771 Electroacoustic Company, 947, 948 Ellsworth, E. W., 421 Emba, U. 8.8. Rs 158, 275, 279, 738, 739 England, 839, 947 England, J. L., 125 EKétvos, R. v., 11, 14, 70, 87, 88, 169, 175, 178, 191, 193, 194, 218, 219, 271, 273, 281, 283, "284, 286, 355, 389 Erdmann, C., "658, 662, 663, 664 Errington, Ontario, 413 Esperson dome, Texas, 280, 281, 283, 424 Eureka field, Texas, 908, 910 Kurope, 452 398, 403, 408, 413, 660, 739, Eve, A. S., 811 Ewing, M., 471, 472, 473, 541, 658, 740 F Failing, Geo. E., Supply Company, 490, 491 Bree ore body, Ontario, 289, 415, Falun, Kansas, 84 Fannett salt dome, Texas, 278, 279, 424 Fanselau, G., 363 Faust, L. Y., 462, 463, 473, 476 Feldman, C. B., 650, 651, 658, 654, 818 Fennoscandia, 165 Fessenden, R., 484, 946, 948, 952 Fichtelgebirge, Germany, 316 Filipesti anticline, Rumania, 277 Fischer, F. A., 952, 953 Fisher Research Laboratories, 819 Flathead County, Montana, 662, 663 Fleming, J. A., 358, 666 Floresti, Rumania, 277, 280 Focken, C. M., 791 Forberger, K., 427 Fort Bend County, Texas, 200, 805 Fort Collins, Colo., 283 Fox oil field, Okla., 241, 284 France, 53, 470, 473, 639, 666 Frankenstein, Germany, 310 Franklin, N. J., 310 Franklin Furnace, N. J., 659 French, R. W., 857 Friedl, K., 803, 806 Fritsch, V., 815, 816 Frosch, A., 864, 865 Frih, Gu 920 Fuchs Brauns, 76, 77, 78, 79, 80 ues ee 06 da, E., rive Fulton, Mo., 82, 83 Fushun colliery, Japan, 288 1006 G Gaines County, Texas, 910 Gal (unit), 10, 13, Galileo, G., 88 Galitzin, B., 439, 440, 580, 584, 586, 602, 604, 615, 617 Gall, 1p! Cr 696, 701 Gamburzeff, Gun , 270, 287, 390, 400, 411 Garber field, Okla. 425 Gard (dept. i France, 676 Gassmann, F. aor 525, 526, 527 Gavat, I. , 277, 28 Gella, Ni 894 Gelliondale, Australia, 290 Gellivaara, Sweden, 311 General Electric Company, 933 General Radio Company, 962 Geoffroy, M. P., 285, 424, 660, 663, 676 George, P. W., 80, 84, 289 Gepege balance, 194 Gerdien, H., 931, 932 Germany, 47, 53, 83, 468, 470, 472, 663, 666, 839, 909, 947 Gerolstein, Germany, 310 Ghitulesco, M., 277, 280 Gibbons, C. H. , 454 Gibraltar, 469, 470, 472 Gibson, R. E. , 458, 465, 467, 468, 477 Gibson County, Ind., ’910 Gilchrist, L., 659, 660 Gillingham, W. ate 830, 831, 856, 869 Gish, O. H., and Rooney, W. J., 28, 645, 660, 661, 664, 709, 710, 712, 715, 720, 723, 724, "725, 758 Glasgow, Scotland, 82, 83 Goettingen, Germany, 884 Golden, Colo., 327, 335, 417 Goldstone, iE, 468, 470, 579 Goose Creek field, Texas, 907, 929 Gorgoteni field, Rumania, 836, 837 Gotthard Switzerland, 312 Graf, A., 100, 126, 194, 198, 366, 766, 782, 893, 804, 909 Graham oil field, Okla., 241, 284 Grand County, Utah, 851 Grand Saline salt dome, Texas, 852 Greenwich, England, 96 Griesser, Re 390, 392 Griffin, Ind., 910 Grime, G., 461 Griswold, D., 740 Grohskopf, J. G., 415, 417, 433 Grossmann, F., 945 Grozny, U.S.S.R., 158, 282, 665, 736, 737, 832, 837, 839, 890 Guewenheim, Alsace, 427 Gulf coast, 5, 44, 79, 82, 84, 274, 278, 279, 281, 282, 283, 424, 425, 470, 499, 513, 886, 907 Gulf Oil Corporation, 126, 127 Gulgong field, Australia, 291, 419, 502 Gunn, R., 931 NAME AND PLACE INDEX Gustafson, G., 931 Gutenberg, B., 451, 469, 472, 473, 480, 525, 913, 954. Guyod, il 845, 858 H Haalck, H., 123, 124, 140, 186, 234, 235, 303, 339, "340, 349, 375, 390, 392, 393, 398, 399, 401, 405, 410, 411, 423, 765, 766, 773 Haanel, K.., 345, 347, 348, 388, 403, 408 Haas, if oO; 853, 856 Hack, F., 655; 656, 818 Haeno, g., 610 Haff balance, 194 Hague, B., 582 Hahnemann, W., 946, 948 Halliburton Oil-Well Cementing Com- pany, 827 Hamilton County, Kansas, 84 Hammer, S., 138 Hancock, Mich., 661 Hannibal, Mo., 84 Harbou integraph, 249 Harding, R. L., 467 Harris County, Texas, 908, 910 Hartley, 10, 126 Harvey Radio Laboratories, Inc., 497 Harz Mountains, Germany, 308, 309, 310, 312, 313, 314, 315, 316, 414, 660, 884 Hastings, Texas, 910 Hathaway, C. M., 932 Hawkins, J. E., 786 Hawkins, R. H., 658, 664, 740 Hawkinsville salt dome, Texas, 805, 806, 958 Hawtop, E. M., 852 Hayford, J. F., 169 Hazard, D., 358, 362, 363, 365, 366, 368 Hazeldean, Ontario, 81, 83, 84, 285, 432 Heald, K. C., 840, 856 Healdton field, Okla., 284, 375, 425 Hecht, H., 927, 939, 945, 946, 948, 949, 952, 953, 954 Hecker, O., 123, 186, 194, 241 Hedberg, H. D., 74, 75, 76, 81, 82, 83, 84 Hedstrom, H., 749, 755, 791, 796, 800, 802, 803, 804 Hee, A., 610 Heiland, C. A., 58, 125, 198, 217, 222, 232, 303, 312, 328, 334, 352, 353, 379, 416, 423, 424, 429, 468, 470, 473, 551, 593, 607, 616, 617, 743, 862, 914, 919, 937 Heiland Research Corporation, 21, 24, 554, 555, 556, 599, 611, 670, 782, 868, 916, 923 Heine, W., 694, 702, 703, 767, 771 Helmert, F. R., 146, 190, 241, 242 Helmholtz, H. v., 644 Henderson, L. H., 742 Hercules Powder Company, 484, 486, 487, 488 Herdorf, Germany, 311 NAME AND PLACE INDEX Herodotus, 886 Herroun, HE. F., 311, 315 Hertwig, A., 920 Hess, V. F., 880 Hessen, Germany, 422 Hettenschlag salt dome, Alsace, 424, 738 Heyl, P. R., 85, 86, 175 Hey Tor, Devon, 315 Higasinaka, H., 265, 286 Hobbs field, N. M., 428, 910 Hoffmann, C. R., 853, 856 Hola Bight, Norway, "957 Holanda mine, Spain, 703 Holmdel, N. i 666, 667 . Holst, ine 271 Honolulu, 368 Hoover, H., Jr., 898 Hope mine, B. C., 676 Horne mine, Quebec, 771, 772 Horvitz, L., 899, 900, 903, 904 Hoskins mound, Texas, 278, 281, 282 Hotchkiss, W. O., 17, 342, 343, 379, 403, 413, 430 Houghton County, Mich., 661 Houston, Texas, 894 Howell, i G., 735, 751, 863, 865, 958 Hoyt, Ne 126, 127 Hubbert, M. Ke 735, 738 Hubert, F., 484, 489 Hugo, Colo., 571, 572 Hull, A. W., 358, 354 Hull, Texas, 665 Hull-Gloucester fault, Canada, 284, 285 Humble field, Texas, 907 Humble Oil Company, 11, 132 Hummel, J. N., 634, 635, 698, 699, 715, 716, 717, 718, 723, 764, 791, 810, 812, 813, 827, 828, 829, 830, 879, 884 Hungary, 169, 273, 283 Hunkel, H., 659, 660, 678, 679 Huntington Beach, Calif., 890 Hunton limestone, 46 I Idaho, 660 Ide, J. N., 462, 463 Ilfeld, Germany, 884 Illinois, 50, 52, 661, 739 Imhof, H., 194, 195 Imperial Geophysicai Experimental Sur- vey (see also Edge and Laby), 548, 610, 613, 695, 752, 753, 804, 805, 806, 809 Independence, Kansas, 83 India, 165 Ingersoll, L. R., 841, 850, 856 Ireland, G. A., 610 Irthlingborough district, England, 311 Irvine field, Kentucky, 84 Ishimbaev field, U.S.S.R., 909 Ising, G., 127, 128, 129, 130, 131 Iskin, U.S.S.R., 276, 279 1007 J Jabiol, M., 470 Jackson, Miss., 46, 432 Jacobsen, L. g), 582 Jakosky, J. J., 416, 422, 434, 807, 867, 942 Jameson, M. H., 748, 749 Japan, earthquakes i in, 018 Jeans, J. H. an Jena, Games 468, 470 Jennie, W., 118 Jenny, W. P., 379, 404, 424, 425, 429 Joachimstal, Czechoslovakia, 854, 875 John, W., 427 Johnson, E. A,, 302, 363 Johnson, J. B., 454 Johnson, N. G., 485 Johnson, N. H., 735 Johnson, R. S., 930 Johnston, J., 458, 844 Jolly, J., 190, 191 Jones, J. H., 283, 501, 546, 547 Joplin, Mo., 659 Joyce, J. W., 324, 413, 809, 811, 812, 821, 822, 823 Jueterbog, Germany, 469, 471 Jugoslavia, 661 Jung, K., 87, 138, 139, 140, 154, 155, 156, 164, 165, 193, 211, 227, 229, 230, 232, 236, 237, 238, 249, 255, 256, 258, 260, 261, 262, 263, 264, 265, 266, 268, 427 K Kadina, Australia, 413 Kaibab Plateau, 434 Kaiser, H. F., 883 Kala field, U.S.S.R., 909 Kallmerberg, Sweden, 411, 413 Kansas, 47, 80, 84, 284, 430, 470, 471 Karadagh, Asia, 314 Karcher, J. C., 758, 827 Kaselitz, F., 238 Kassel, Germany, 82, 314 Katanga district, Belgian Congo, 678, 680 Kean, C. H., 958 Kegel, W., 414 Keilhack, K., 72, 413 Kelly, 8. F., 434, 677, 738 Kelvin River, Scotland, 292 Kern County, Calif., 910 Kettleman Hills, Calif., 425, 890 Keuffel and Esser, 436 Keys, D. A., 403, 408, 413, 660, 739, 811 Kihlstedt, F., 751, 752, 755 Kiirunavaara (see Kiruna) Kilchling, K., 189 Kimberlite, 419 Kinney County, Texas, 433 Kircher, A., 839 Kirchhoff, G. R., 363, 717 Kirsch, G., 873, 876 Kiruna, Sweden, 50, 311, 408, 411, 412 1008 Klipsch, P. W., 760, 761 Knaebel, C. H., 683, 684 Koch, H. W., 91 Koehler, R., 913, 915, 917, 919, 924 Koenigsberger, J. G., 880, 885 Kohbrausch, F., 349, 350, 351, 352 Kohl, E., 423 Kohlhorster, W., 880 Kokubu plain, Japan, 284 Koulomzine, Th., 342 Krahmann, R., 419, 420, 423 Krasulin, 422 Kristineberg field, Sweden, 704 Krivoj-Rog, U.S.S.R., 290, 311, 312 Krjukowa, U.S.S.R., 409 Krugersdorp, South Africa, 420 Krusch, P., 73 Kumagai, N., 292 Kummersdorf, Germany, 469 Kursk, U.S.S.R., 51, 52, 287, 311, 315, 401, 409, 410, 411 Kurtenacker, K. S., 742 L LaCoste, L. J. B., 127, 612 Lahee, F., 428 Lahn-Dill district, Germany, 414 Lake Superior, 51, 52, 364, 413, 416, 419 Lancaster-Jones, E., 741 Landes (dept.), France, 53 Landsberg, H., 929, 930 Lane, A. C., 75, 855, 885 Lane-Wells Company, 827 Langsele Lake, Sweden, 162 La Rosa field, Texas, 910 LaRue, W. W., 862 Lasarefi, P., 287, 409 Laubmeyer, G., 890, 894, 907, 909 Laylander, K. C., 416 Leadville, N. S. W., 804, 805 Lebong Donok mine, Sumatra, 755 Lee, E. S., 932 Lee, F. W., 659, 660, 661, 709, 710, 725 Leeds and Northrup, 670 Leicestershire, England, 312, 315 Leighton, A., 958, 959, 961, 962 Leimbach, G., 867 Leine Valley, Germany, 468, 473, 884 Leitrim, Ontario, 81, 82, 83, 84, 285 Lejay-Holweck, 10, 99, 100, 112, 127, 129, 130 Leningrad, U.S.S.R., 272 Leonardon, E. G., 664, 665, 741, 832, 835, 848, 857, 866, 869 Leopoldsdorf fault, Austria, 282, 427 Lester, O. C., 474, 475 Levi-Civita, T., 791, 792 Leyst, E., 409 250, 301, 302, 310, 311, 312, 313, 314, 370, 372, 376, 377, 390, 392, 646, 648, 657, 658, 663, 665, 755, 766, 782, 783, 791, 796, 840, 852, 184, 198, 256, 288, NAME AND PLACE INDEX Liddle, R. A., 433 Limagne-Graben, France, 285 Lindblad, A., and Malmquist, D., 10, 125, 126, 134, lene Lindgren, W. Lindsay, R. Be 478, 481, 946, 947, 948, Link, E., 884 Littfeld, Austria, 310 Little Fry Pan, Texas, 433 Littleton, N. H., 733 Loebe, W. W., 931, 932 Loehnberg, A., 664 Loewinson-Lessing, F., 308 Lofoten Islands, Norway, 957 Logan, J., 278 Logan, K. H., 632 Lomakin, A. AG 880. 881, 884 Long Beach field, Calif., 360, 861 Long Point dome, Texas, 278 Lopez, Texas, 910 Lorenz, H., 920 Lorraine, 51, 662, 663 Los Angeles, Calif., 468, 470, 473 Louisiana, 430, 470, 471, 579 Love, A. E. He 442 Lowy, H., 657, 666, 867 Lubiger, F., 133 Liibtheen-Jessenitz salt dome, 274, 276 Lucien field, Okla., 429 Ludwiger, H. V., 696 Lueneburg, Germany, 423 Luettich, Belgium, 421 Lukow, Bohemia, 310 Lumberton, Missouri, 371 Lundberg, H., 287, 402, 408, 422, 625, 659, 701, 704, 756, 757, 771, 800, 802, 803 Luyken, K., 365 Lynton, E. D., 424, 425, 426, 427, 432, 865 M Mache, H., 876 Maikop field, U.S.S.R., 884 Maine, 467 Mainka, C., 914 Malagash, Nova Scotia, 79, 82, 83, 84, 292 Malamphy, M. C., 218, 312, 314, "433 Malgobek, US. S.R., 909 Mammoth Cave, Ky., 811 Manhart, T. A., 735 Maracaibo, Venezuela, 665, 837, 838 Marafael, Venezuela, 517 Maros Valley, Hungary, 158, 273, 274 Martin, H., 105, 106, 470, 590, 918 - Martin, J. N., 489 Martin, M., 830, 831 Masjid-i-Suleiman, Persia, 508, 518 Mason, M., 626, 806 Massachusetts, 467 Matuyama, M., 265, 284, 286, 287 Maurer, H., 948, 953 Maurin, C. H., 470 Maxwell, C., 634 rd TS ee i atin: aD a, NAME AND PLACE INDEX McCann, D. C., 869 McCarthy, G. sea 430 McCollum, B., 476, 632, 862, 930 McCutchin, in A., 854 McDermott, E., 550, 758, 907, 908, 909, 910 McLean County, Ky., 83 McLintock, W. F. P., 80, 82, 83, 286, 288, 289, 292 MeNish, A. G., 364, 365 Mecklenburg, Germany, 423 Meggen, Germany, 772 Meisser, O., 108, 109, 242, 248, 291, 292, 468, 470, 471, 524 Melton-Mowbray district, England, 311 Menstrisk Lake, Sweden, 162, 287, 802, 803 Mershon, A. V., 932 Mesopotamia, 886 Meteor Crater, Arizona, 422 Mexia, Texas, 890 Mexia-Luling fault, Texas, 285 Mexico, 46, 47, 240, 433 Meyenheim, Alsace, 738 Meyer, G., 414, 415 Michigan, 346, ‘413, 659, 661, 662, 885 Midcontinent, 5, 283 Midwest Refining Co., 369 Millcreek, Okla., 371 Miller, A. H., 79, 81, 82, 83, 84, 284, 285, 290, 292 - Millikan, R. A., 880 Millom,. Cumberland, 520 Milne, J., 580, 933 Mineville, N. Y., 660 Mintrop, L., 494, ” 505, 607, 608, 609 Mironov, 3. 286 Mississippi, ’430, 470, 471 Missouri, 50, 414, 659, 660, 663 Missouri River, 82 Mitkevitch, V., 308 Moffat tunnel, ‘Colo., 860, 861 Moll, H., 423 Monroe, 'La., 46 Mons, Belgium, 421 Monument field, N. M., 910 Moore’s field, Texas, 805 Moss Bluff dome, Texas, 278, 500, 501 Mott-Smith, L. M., 128, 133, 134 Moureaux, Th., 409° Mueller, r. 884, 885 Muenster, Germany, 421 Muenster Arch, Texas, 161, 284, 430 Muenster-Bulcher Ridge, 284 Mueser, E., 772 Miiller, Max, 626, 761, 762, 767, 770, 774, 775, 778, 779, 780 Murray, G. H. , 830, 831 N Namur, Belgium,’ 421 Nash, H. E., 489 Nash’ dome, Texas, 277 1009 Neher, H. V., 882 Nemaha ridge, Kansas, 47 Nernst, W., 870 Netcong, N. J., 666 Nettleton, L. so 71 Nevada, 50, 416 Newfoundland, 422, 660, 705, 756, 757, New Jersey, 51, 346, 664 New Mexico, 46, 50, 428, 430, 470, 471, 736, 738 New South Wales, 705 New York, 51, 659 Nicar, 430. Nickopol, U.S.S.R., 422 Niederhaslach, Alsace, 427 Niederlausitz, Germany, 740 Nienhagen-Haenigsen salt dome and field, Germany, 274, 907, 909 Nikiforov, P., 194, 287 Nineveh, 886. Nippoldt, A., 351, 358, 365, 376, 383, 384, 385, 386, 387 Nischne Tagilsk, U.S8.S.R., 310 Nitramon, 485, 486, 571 Nocona field, Texas, 284, 429 Norgaard, Ge 130 Norman, G. W. H. ., 292 Normandy, 660, 663, 706 North Carolina, 430 North Dakota, 430 Northumberland, England, 314 Norway, 310, 315 Nottinghamshire, England, 311, 312, 314 Novacesti anticline, Rumania, 277 Nueces County, Texas, 910 Nujol, 584 Numerov, B., 109, 187, 227, 229, 230, 265, 271, 272, 273, 274, 278, 279, 282, 286 Nunier, W., 782 O Obata, J., 931, 932 Oberg field, Germany, 907, 909 Oberharz, Germany, 311, 312, 314 Obert, L., 934 Oddone, E., 933 Oklahoma,. 46, 47, 430, 467, 468, 470, 471 Oklahoma City field, "425, 836, 853, "854, 890 Oldau-Hambuehren, Germany, 275 Olken, H., 931 Oltay, K., 169 Ontario, 50, 310, 467, 473, 661, 664, 740 Oregon, 854 Oribuiansky, U.S.S.R., 409 Oriental mine, Newfoundland, 705, 756 Oslo, Norway, 298 Ostermeier, i AB 342, 349, 351, 367, 677, 678, 863 Otavi, S. W. Africa, 310 Ottawa, Canada, 285 Owen, J. E., 465 1010 Owens Valley, Calif., 469 Oxnard, Calif., 432 Oxus River, U.S.S.R., 886 Pr Page, L., 98, 442 Palestine, 664 Parana, Brazil, 312, 314 Paris, ay, 681 Parsis, 88 Ede Calif., 369, Ps Paso Creek, Calif., Patriciu, V., 884 Payne County, Oklahoma, 910 Peachbottom vein, North Carolina, 740 Pearson, T. M., 757 Pechelbronn, Alsace, 856 Pennsylvania, 470, 471, 473 Pentland ae Aeatand, 286 427 Petrowsky, A. "672, 813, 815, 817, 818 Petsamo, Finland, 314 Pettus area, Texas, 426 Phemister, J., 80, 82, 83, 286, 288, 289, 292 Pico formation, 512. Pierce Junction, Texas, 158, 894, 907, 909 Piltchikow, 409 Pirson, S. J., 400, 559, 565, 567, 570, 729, 904, 905, 906, 909 Pittsburgh, Pa., 165 Plainview, Texas, 371 Ploesti, Rumania, 277 Plutarch, 886 Pockels, F., 314, 316 Pohl, 665 Poincaré, J. H., 90 Poldini, E., 660, 663, 672, 677, 680, 733 Pollock, I. A., 10, 125 Poole, 666 Port Barre salt dome, La., 423, 424 Portland cement, 858, 859 Port Lincoln, Australia, 756 Portobello fault, Scotland, 286 Potsdam pendulum, 109, 123 Potter County, Texas, 430 Prahova River, Rumania, 277 Prey, A., 90 Pugh, W. E., 328, 468 Pullen, M. W., 632, 643, 646 Puzicha, K., 306, 307, 308, 310, 311, 312, 313, 314, 315, 316, 414, 415 Q Quebec, 50, 659, 660 Queensland, Australia, 705 Quervain, de, A., 580 Quiring, H., 287 Quitaque, Texas, 371 NAME AND PLACE INDEX R Radiore Company, 626, 648, 806, 807 Raleigh, Sir Walter, 886 Ralph, C. M., 960 Ramann effect, 898 Ramsey Field, Okla., 158, 159, 910 Ramspeck, A., 468, 473, 917, 918, 924, 926, 927 Rand area, South Africa, 50, 56, 419, 845 Randolph, Oklahoma, 371 Rankine, H., 508, 518 RAR system, 950 Ratcliffe, J. A., 650, 651, 652 Raven Pass anticline, Calif., 424 Rayleigh wave, 450, 451, 452, 466, 551 Reagan County, Texas, 909° Rebeur-Paschwitz, E. v., 580 Refugio County, Texas, 910 Reich, H., 74, 77, 78, 79, 80, 81, 82, 83, 84, 309, 421, 422, 435, 469, 470, 471, "472, 493, 657, 849 Reinoehl, C. O., 415, 417, 433 Reisch, S., 931, 932 Reitz, ie 380 Renfrew County, Ontario, 292 Renison-Bell field, Tasmania, 416, 804 Reutlinger, G., 594 Rhoen, Germany, 471 Richards, T. C., 456, 460, 465, 468, 473 Richland, La., 46 Richland County, S. C., 82 Richter, C. F., 470, 472, 473 Ricker, N. Be 609 Riddell, W., 407 Rieber, ie 364, 468, 469, 472, 475, 476, 512 Riegger, H., 931 Riverside area, Texas, 910 Rixmann, F., 492 Roberts, D. C., 866 Robinson Deep mine, South Africa, 845 Rodd, 409 Roess, J., 463, 464 Réssiger, M., ea 312, 314, 353, 414, 415 Roman, I., 248, 363, 519 Rooney, Wet: (see Gish, O. H.) Rosaire, E. E., 761, 817, 899, 901, 903, 904, 907, 908, 910 Ross and Kerr, 79, 82 Rostagni, A., 791 Rothelius, Ee 403 Rouyn, Quebec, 771, 772 Rubens, H., 666 Rubey, W. W., 75 Ruecker, A. W., 318,314 Rugby, England, 666, 667 Ruhr district, Germany, 167, 421 Rilke, O., 829 Rumania, 47, 276, 277, 280, 837 Rusher, M. A., 932 Russell, W. L., 83 Russia, 416, 417, 813 Rutherford, E., 871 NAME AND PLACE INDEX Rutherford, H. M., 540 Rybar, Stephen, 171, 194, 287 Ss Saar, Germany, 53 Sain Bel ore body, France, 676, 860 Saint Charles County, Mo., 82 Saint Quirinus Spring, Bavaria, 886 Sakhalin, U.S.S.R., 886 Sakurazima Volcano, Japan, 284 Salt Creek, Wyoming, 853 Saltikowsky, U.S.S.R., 409 Salzgitter, Germany, 423 Samson, C., 931, 932 San Andreas fault, California, 425, 426 San Gabriel dam, Calif., 472 San Joaquin Valley, Calif., 4382, 469, 476, 845 San Pedro, Brazil, 433 Sandy Point oil field, Texas, 760, 761 Sapulpa, Okla., 853, 854 Sasvar dome, Czechoslovakia, 281, 283 Sauerland, Germany, 772 Savage, J. L., 859 Sawtelle, G., 886 Saxony, 50, 316, 422 Schaffernicht, W., 131 Schilthuis, R. J., 835 Schidtz, O. E., 241 Schleusener, A., 133, 134, 135, 165, 166, 167, 169, 198 Schlumberger, C. and M., 33, 53, 160, 658, 660, 662, 663, 665, 680, 681, 700, 706, foeletat. tat, 138, 109, (41, 752, 755, 757, 763, 827, 828, 832, 833, 834, 835, 836, 837, 838, 839, 844, 859, 866 Schmehl, H., 104, 109, 118, 121, 123 Schmerwitz, G., 127, 191, 192, 602 Schmidt, A., 131 Schmidt, Adolf, 17, 301, 318, 321, 324, 325, 326, 332, 333, 334, 341, 342, 347, 348, 349, 350, 351, 358, 367, 379, 405, 406, 423, 665 Schmidt, O. V., 507, 510, 511, 517, 527, 529, 531 Schmidt, W., 665, 666 Schneeheide salt dome, Germany, 159, 277 Schober, R., 884 Schroeder, R., 435 Schuh, F., 423 Schulz, B., 953 Schulze, A., 926 Schumann, R., 282, 287 Schwarz, M. v., 72 Schweydar, W., 194, 219, 222, 224, 240, 273, 276, 469, 471, 505, 580, 609 Scotland, 80, 82 Seblatnigg, H., 53, 79, 82, 83, 274, 276, 289, 290, 412 Segeberg, Germany, 423 Seismogel, 485 Seismos Company, 159, 277 1011 Seminole field, Okla., 665 Sergijevsky, 409 Sermon, T. C., 363 Shaw, H., 184, 198, 263, 264, 288, 520 Shell Oil Co., 430 Shepards-Mott dome, Texas, 280, 282 Shuvalovo Lake, U.S.S.R., 271, 272, 273, 275 Siegen, Germany, 311 Siegerland, Germany, 287, 311, 884 Silesia, Germany, 53, 422 Simmsboro area, 424 Simplon tunnel, 292 Sifieriz, J. G., 54, 469, 470, 471, 472, 612, 613 Sitka, Alaska, 368 Skeeters, W., 138 Skellefte district, 802 Skye, Scotland, 313 Slee, J. S., 954, 956 Slichter, L. B., 310, 315, 401, 411, 415, 540, 800 Slotnick, M. M., 201, 202, 203, 541, 560 Smirnow, I. N., 409 Smith, F. E., 363 Smith, G. H., 485 Smith-Rose, R. L., 641, 651, 666, 667 Smyth, H. L., 396, 413 Snarum, England, 310 Snelgrove, 422 Snell, F. A., 476 Soest, Germany, 421 Sohon, F. W., 593, 615 Sokolov, V. A., 894, 895, 896, 897, 898, 899, 900, 905, 907, 909 Solikamsk, Urals, 158, 274, 278 Sollenau fault, Austria, 427 Somers, G. B., 425 Sorrel Mountain, England, 312 Soske, J. L., 369, 370 Soule, F. M., 363 Sour Lake, Texas, 907 South Africa, 50, 56, 419, 845 South Carolina, 430 South Dakota, 430 South Liberty-Dayton dome, 280, 283 Spain, 53, 54, 469, 470, 471, 472 Spath, W., 922 Sperenberg, Germany, 469, 471 Sperry-Sun Co., 865 Spicer, H. C., 845, 847 Spindle Top dome, Texas, 277 Spraragen, L., 432, 433 Stary Oscoe, U.S.S8.R., 409 Stassfurt, Germany, 51 Statham, L., 759 Stearn, N. H., 342, 344, 346, 413, 415, 417, 418, 419, 430, 433 Stefanescu, S. 8., 55, 782, 796, 800 Stehberger, K. H., 354 Steiner, L., 312, 390 Sweden, 162, 703, Texas, 1012 NAME AND PLACE INDEX Steinhaus, W., 318 Stepanoff, A., 201 Stern, W., 666, 740, 814, 816 Sterneck, R. v., 108, 109 Steward, W. B., 856, 869 Stewart, G. W., 478, 481, 946, 947, 948, Stockholm, Sweden, 97, 402 Stokes, G., 90 Stormont, D. H., 899 Stratton, F., 413 Striberg, Sweden, 307 Strong, J., 882 Stschigry, U.S.S.R., 409 Stschodro, N., 306, Bil 315 Stutzer, F., 304, 310, 311, 315 Submarine Signal Corporation, 954 Subterrex Company, 899, 908 Sudbury, Ontario, 50, 52, 310, 415 Sugerland dome, Texas, 279 « Sumatra, 755 Sund, O., 956 Sundberg, K., 287, 402, 408, 625, 626, 636, 637, 638, 639, 643, 657, 658, 659, 660, 661, 664, 701, 702, 729, 771, 786, 791, 794, 795, 796, 800, 801, 802, 803, 804, 805, 806 Surachany, U.S.S.R., 160 Suwa mine, Japan, 706 Swainson, O. W., 944 Swanson, C. O., 413 Sweden, 315, 402, 659, 661, 702, 705, 771 Swedish American Company, 753, 754 Swick, H., 108, 109, 121, 123 Swift, W. H., 461 Switzerland, 310, 312, 663 Swynnerton, Scotland, 80, 288 Au Tage, G. F., 721, 726, 727, 728, 729, 730, Takahashi, R., 933 Takumati oil field, Japan, 286 Tampico region, Mexico, 46 Tanakadate, A., 127, 580 Tang! balance, 194 Targoviste, Rumania, 277 Tasmania, 416, 705 Tattam, C. M., 743 Teddington, England, 666, 667 Tegern Lake, Bavaria, 886 Tehuantepec, Mexico, 47 Ten Section field, Calif., 910 Terek anticline, U.S.S. sae 282 Tetschen, Czechoslovakia, 314 Texas, 46, 47, 312, 420, 470, 471, 890 Texas Body and Trailer Company, 487 Thalén, R., 384, 402 Theodorsen, Th., 820, 821, 823 Thom, W. T., 929 Thoma, H., 931, 932 Thompson, R. fe 958 Thompsons, Utah, 851 Thomson, W., and Tait, P. G., 442 Thornburgh, H. R., 536, 537, 540 Thornton, N. M., 658, 849 Thoulet’s solution, 72 Thuringia, Germany, 310 Thyssen, v., Stephen, 11, 127, 132, 133 Tiberg, E., 349, 379, 405, 406 Tim, U.S.S.R., 409 Tintea, Rumania, 665 Tishomingo, Okla., 471, 472 Titi Lake, Black Forest, 271 Toepfer, O., 342 Tokyo, Japan, 706 Tolman, C. F., 60 Tomaschek, R., 131 Tomball field, Texas, 280 Tompkins, F. A., 614 Tonkawa lime, 836 Transvaal, South Africa, 419 Traversella, Switzerland, 315 Trinidad, B.W.1I., 886 Tri-State district, 52, 289, 417 Trubiatchinski, N., 422 Truman, O. H., qe 128, 132, 609 Tschernaja Rieschka, U.S.S. R., 739 Tsuboi, C., 193 Tuchel, H., 79, 82, 83, 84 Tuckerman, L. B., 930 Tulsa, Okla., 854 Turcev, A., 311, 314, 315 Turkiana field, U.S.S.R., 909 Turley, B., 402 Tuscon, Arizona, 268, 270, 271 U Uhlich, P., 402 Uljanin, W., 363 Undograph, 937 U.S.S.R., 416, 417, 813 Bolted States, 46, 54, 141, 142, 346, 408, 5 U. S. Bureau of Mines, 934 U. S. Bureau of Reclamation, 859 U.S. Bureau of Standards, 820, 890, 930 U. S. Coast and Geodetic Survey, 97, 108, 109, 110, 112, 113, 122, 142, 148, 358, 362, 370, 371, 372, 377, 486, 579, 912, 913, "944, 948, 950, 955 U.S: "Department of Agriculture, 646 U. S. Geological Survey, 841 U.S. Navy, 953 U. S. Weather Bureau, 843 Ural River, 275 Urals, 50, 52, 310, 311, 312, 315 Urie, Switzerland, 312, 313 Uvalde County, Texas, 433 Vv Vacquier, V., 370, 371 Vajk, R., 286 Vancouver, B. C., 676 Van den Bouwhuijsen, J.N.A., 841, 855 Se ee ee NAME AND PLACE INDEX Van Orstrand, C. E., 839, 841, 842, 843, 846, 847, 849, 851, 852, 853, 854, 858, 860, 861 Van Weelden, A., 161, 374 Venezuela, 76, 84, 472 Vening Meinesz, F. A., 101, 102, 106, 107, 109, 110, 119, 123, 149 Ventura Basin, Calif., 432, 473 Vicentini, 580 Victoria, Australia, 705 Vienna, Austria, 287 Vienna Basin, 282, 427 Villanueva del Rio, Spain, 53 Villanueva de Minas, Spain, 53 Ville, Germany, 740, 773 Vincent, A. M.;, 950 Vladicaveas, U.S.S.R., 736, 737 Vogt, J. H. L., 73 Volga River, U.S.S. R., 275 W Waldenburg, Germany, 312 Wall Creek sand, Wyo., 853 Walnut Creek fault, Calif., 425, 427 Walther, H., 482, 483 Wantland, D., 416 Wasco well, Calif., 845 Washburn, H., 898 Washington, 664 Washington, D. C., 660, 661 Watson, H. G., 781 Watson, R. ips 735 Watt magnetometer, 342 Weatherby, B. B., 462, 468, 465, 470, 471, 472, 473, 476 Weaver, W., 683, 707, 708 Webb, R., 866 Weber, Richter, and Geffcken, 114 Wefensleben, Germany, 423 Wegel, R. L., 482, 483 Weiss, O., 315 Wenner, F., 28, 584, 598, 602, 614, 644, 709, 710, 712, 715, 720, 723, 725, 758 Werra Valley, Germany, 316, 468, 473 West, S. S., 760 Western Electric Company, 613 Western Instrument Company, 866, 962 1013 Westinghouse, 456, 457, 948 . Westphalia, Germany, 53 West Texas, 856 West Wits area, South Africa, 420 Whiddington, R. W., 931, 932 White, F. W. G., 650, 652 White, G., 758 White, W. T., 135 White Creek syncline, Calif., 424 Wichita Mountains, 160, 161, 430, 431 Wiechert, E., 127, 129, 484, 580, 583 Wietze, Germany, 158, 274, 907, 909 Wilcox, S. W., 743 Wildbad, Germany, 884 Williams, L. H., 425, 426 Williamson, E. D., 458, 465, 467 Wilson, E., 310, 311, 312, 314, 315 Wilson, H. A., 589, 590 Wilson, J. H., 283, 349, 352 Winkelmann, A., 389 Winterswijk, Holland, 855 Wisconsin, 413 Witwatersrand, 50, 51, 419, 420 Wolcken, K., 878 Wolf, F., 291, 292 Wood, H. O., 469, 470, 472, 473 Ween seismograph, 580, 584, 4 Woodhull field, N. Y., 909 Wright, F. E., 101, 120, 125, 149, 150 Wyckoff, R. D., 164 Wyoming, 430 MX Yoost field, ao ay 433 Yorktown, N. des Yosemite Valley, Calif., 472 Z Zeehan field, Tasmania, 416, 808, 809 Zeller, W., 591 Zenneck, J., 653 Zillingdorf, Austria, 287 Zinnwald, Germany, 310 Zirbel, N. N., 197 Zisman, W. 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