PT Pech tom cap Ep Ses Om bore inn erp a Fo tows fb is SiR OA ak Wetec “ Mt na ehh a e Sealer an ae Ma a tem © a ba nkidiomretiond psi —— aba Ad ree Weg e rer rt err JOA Ai Emin ttn Meter Neth rine Sets meen erie che AAT Sa Ns Se ake yok aay ae Ne AT Se = take emo me hom PL es Ree - at aiRafar ney biter hen oe Sherry ae RR Wr Pare NAVAL POSTGRADUATE SGRQOL Monterey, California iii oT A COMPARISON OF TWO ACOUSTIC PARABOLIC EQUATION TRANSMISSION LOSS MODELS FOR COMPATIBILITY WITH THE WAVENUMBER TECHNIQUE IN THE DETERMINATION OF SOURCE DEPTH by Joe Lane Blanchard II March 1984 Thesis Advisor: A. B. Coppens Approved for public release; distribution unlimited : egos feq-ae UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) a READ INSTRUCTIONS REPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM isle ar 4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED A Comparison of two Acoustic Parabolic Master's Thesis Transmission Loss Models for Compatibilit March 1984 Determination of Source Depth 7. AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(s) Joe Lane Blanchard II PE 63785N, NORDA 9. PERFORMING ORGANIZATION NAME ANO AOORESS 10. PROGRAM ELEMENT, PROJECT, TASK AREA & WORK UNIT NUMBERS Naval Postgraduate School N6846283WR30089 Monterey, California 93943 on 29 APRIL £983 11. CONTROLLING OFFICE NAME ANO ADDRESS 12. REPORT DATE Naval Postgraduate School March 1984 Monterey, California 93943 [oe NUMBERICr GAGES » MONITORING AGENCY NAME & ADORESS/(if different from Controlling Office) 1S. SECURITY CLASS. (of thia report) 1Sa. DECLASSIFICATION/ DOWNGRADING SCHEDULE 16. OISTRIBUTION STATEMENT (of thia Report) Approved for Public Release, Distribution Unlimited 17. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report) 18. SUPPLEMENTARY NOTES 19. KEY WORDS (Continue on reverae aide if neceseary and identify by block number) Parabolic Wave Equation, Underwater Acoustics, Implicit Finite-Difference, Split-Step Fast Fourier Transform, Wavenumber Technique, Source Depth Determination, Acoustic Propagation, ASW, Lloyd Mirror 20. ABSTRACT (Continue on reverse side if necessary and identify by block number) mae Brock version Of the Split-Step Fast Fourier meensform (SSFET) and the Jeager version of the Implicit Finite Difference (IFD) acoustic parabolic equation models are compared with a Lloyd mirror interference pattern in the Gange domain. The SSFFT displays the inability to place the Peansmassion loss nulls at the correct ranges. It is also Baap le to utilize bottom loss information correctly. . The Oe ene. DD , an rs 1473s EDITION OF 1 NOV 65 1S OBSOLETE UNCLASSIFIED Senza ET O1S16601 SECURITY CLASSIFICATION OF THIS PAGE (When Data Enters il! 2'ee7T Sun 1 ati > a aie wee i. io see Mae Tek Ts bee Te5 Fay y » Hodeve) of ‘mcr? a tl ous 11s ae ‘he hee ct a SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) IFD produced nulls at the correct ranges; however, it inserted an unaccepable amount of noise except when small (1 m) vertical grid steps were used and the pressure release bottom was placed at extended depths. In shallow water cases, the IFD is able to properly represent the pressure information. Each model is explored in the wavenumber domain by use of a "Wavenumber Technique" (WT) model with emphasis on source depth determination. The source depth may be determined by measuring the distance between the equally spaced nulls in the wavenumber representation. Neither acoustic model was able to provide accurate source depth information when the null spacings were compared to a known source-depth determination curve. Since the null Spacings were not uniformly spaced, this was to be expected. Some specific problem areas in the models were identified by the use of the WT. S/N 0102- LF- 014-6601 ————_—_—____—_-:”:”:_—_X_X—_X—n— 2 SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) ego > sgolews Sct © wae. ACKNOKLEDGEMZNT Pewoubd Like: “to express my deepest appreciation to Dr. Ne Bs Coppens for his guidance in analytical processes and fundamentals of acousitcs. His understanding and encourage- Ment provided the sound basis for this research effort. Dr. Coppens' knowledge of the subject matter combined with the ability to communicate this knowledge from many different perspectives is a unique talent recognized his students. menpn Go R. Dumlap, ~ USN (Ret) was very supportive and Sreouraging during my entire thesis research effort. ag appreciate his assistance with this project and his contin- uing work with the Environmental Acouctics Research Group. mewouldy irke to” thank the personnel of the Wek. Church Bomputcer Center and especially Ur. D. Nac and: Mr ) y maw j } é = —_ Lf i." = ke ae S. ova otatoabaeg Saas heer wis plebom ok + seize) oF gueg 4924803 wis Re . a 4 accessible. Eo waGtidLae yy “aGoustwe parabolic, equation models provide the complex envelope function (U) which must be multiplied by the Hankel function in order to obtain the complex pressure. The acoustic wave iS written in the forn P=UHS(k rye ut (eqn 2.5) where the reference wavenumrer is defined by Ko= - (eqn 2.6) and BeUGs, Zz) (eqn 2.7) is the solution to the appropriate parabolic equation. The complex pressure is corrected for volume attenuation and Fourier transformed to attain the spectral density. A plot displaying the results graphically with the horizontal wave- Humber on the x-axis and the normalized spectral density on the yr-axis is constructed and the spacings between the nulls measured. Figure 2.4 {from Ref. 2] is an example of the NT for a source and receiver in the same type of water mass. Since the Lloyd mirror field in the wavenumber domain is given by [Ref. 2] E(k) = ae elie Ze) (eqn 2.8) A) uolverps silodeisy wi . Sngt deady (UG) aokasaye” je oe edj-4istdo of ashaG fh gue Sion 943 al nezrtizy as oyeu = 1" ee fy Dae Ff : j~ ‘sivets yew pores, soLsu loa @ an alternative formulation [Ref. 2], which produces evenly spaced nulls, is obtained by converting the horizontal wave- number to beta BsAke = ke ails By using beta instead of tne horizontal wavenumber, the distance, delta beta, between any two nulls can be used to ascertain the source depth by maze (egn 2.10) as illustrated in figure 2.5. The application for implying tne method of images, in isospeed cases, to describe the erfects of a perfectly flat pressure release boundary can be justified by inspection. Therefore the parabolic equation can be used to produce the DPoyd's mirror effect and surface decoupling 1S not an issue, cf. Chapter 4 of Brekhovskikh [Ref. 7]. When the WT is implemented, care must be exercised to ensure that the complex pressure contains an adequate number Seepoints to describe the shortest periodicity in the pres- Sure ficid. Phas will preclude the possibility of aliasing in the wavenumber domain. The ceal and imaginary elements of the pressure signal must be modified so that the signal begins and ends with zero values. Piss WOdLeLeation 2's hecessary because the pressure signal must represent a repetitive oscillaticn for the transform. The complex pres- Pime array is zero-filled beyond the data in order to gemerate an array which has the length of a power of 2 for eae Fast Fourier Transform (FFT). The horizontal wavenumber increment is generated within the computer code by 18 4 7 = (insve eeaphoz is bade ale i ~evev Lodooriaon ody ead oY: oe “t siaccised Et 36 Teac be > SeeV doh .&7eq 6F ob ,¢ d TET 223 Wdea od? d ae | (a? ol SOR, 72bhlegs * _, = = ee | a4 -84 aJ? eile ows fe al 7 96a) aa rs ._¢ eae se 7 > i) ge 223 D>D G24 2 ee . ~ ‘ bis bs ui jodeveateg) i i 4 jeaeeaQ civ abee Bam at) eoeced” Gee 22 20 t9al i cee ye sol1g2ugiag es 4 -4> @& 56 is -. + (1V9) cmedegeye - 2 ee seheot Syke ee 90x — | eee he =k. 1 2m SPT 4) feqn 2. 11) 13 “(6161 ‘zoeneyT word) ZH OG 2e 3Nnd3NnO JM FO oTdurxy (W/L) HASIWAN SAVM €2°0 120 610 LL'0 St'0 £1°0 aay "I me Sa A at yt” aie ASVO YAAVTNI WANYLOAdS YAEGWNNAAVM IWLNOZIYOH AO ACNLINOVIN tia 200° v00° Z oanfty (W) WNYLOSdS — X 4O 3GNLINDYW 900° eRe ane — JATHOSIAOH FAO SOUTHIDAN | MUA OS9S FIOMUMAVAY a +4 > “OAIND UOTzeUTMI930q YYdeq soANOS G°Z eanbtry (W/T) SNTOUdS ULI o90°0 =9S30°0 = 0SN"0 SOO: OFOs SEO"OS USO) SZ0°OSz0"0 Ss S10"0-—Ss OO"O~—s SoD 0°0 0° 0002 0° 000% WOLLINOOHL 0°0003 III. ACOUSTIC MODEL ANALYSIS A. PARABOLIC EQUATICN The elliptical wave eguation can be approximated bya parabolic equation (PE) when it is assumed that the envelope function varies slowly with range. A detailed nathematical @escription of the PE from an acoustic point of view is presented by DeSanto [Ref. 8 and 9] and a simpler but less general description can be found in Coppens [Ref. 10}. The parabolic equation has the forn 2 = + 2)k (LY) + (k?-KE)U =O (ean 3-1 Z where it is assumed that the pressure has the form of equa- elon 3.2, Pree 2) Sp) (eqn 3.2) S(t) represents the primary radial dependence of the field in terms of an outward propagating cylindrical wave of the form [Ref. 4] (act Se ao ules) (eqn 3.3) If it is assumed that the range of interest is many wave- lengths from the source; then the asymptotic form of the Hankel function (equation 3.4) can be used [Ref. 11]. 22 - eo oe es. ers UCL SEU ES SHRM | ot 22 onde GS ae 60062 #21. Yiue we, , H61) 2 4/ eo e (kor -1/4) wikohns= 3 (egn 3.4) Two PE models, the Brock version of the Split-Sterp Fast Fourier Transform (SSFFT) and the Jeager version of the Implicit Finite Difference (IFD) were investigated for compatibility with the WT in determination of source depth. Be SSFFT 1. Cansmission Loss Comparison with Lloyd LEEOL — == To analyze sound waves in the wavenumber domain, we needed a model to fprovide the pressure as a function of range. Initially the SSFFT model [Ref. 4] was selected . This model generates successive values for U as a function of range with the helr of the algoritha U(rear, 2) = e@Jarke(n?-1)/2 (eqn 3.5) FRalech ojark? e JAPK2Ke FE T(U(r 7) This model was a natural choice since it was the model used in the preliminary study dealing with the determination of tae source depth by the WT [Ref. 3]. However, Zt Soon became apparent that this model's inherent weaknesses would require the consideration of another nodel if ocean botton interactions were to be studied. These weaknesses, and their impact upon the WT, will be discussed shortly. The SSFFT is a range dependent acoustic wave model which, for this analysis, will be operated in a range inde- pendent manner. in othe xs words, only one sound speed profile will be used, the water mass will be assumed homoge- neous, and the bottom flat. TO) facriitate Che study of the SSFFT model, the source code of the nodel was modified to generate the variables required for follow-on programs to 23 i®el ape) t xe 7 - : ’ 5 ae 3 ,ele-s. gt of3 36 Oo Aerator 7H4 48h war bas : ' Lizesvr} i1S6@ (easy $0. aan, Ta % 29 d0i-cdbepesss af Se ae ~ - alhahy 28) ge fi sever bassgoegy 207 Oelver® Veg is ~liagg 2 ts tenep e4 af? Qeiw f ‘ae ‘ "LU ; e 2 . e F ” al > | aren al - ie ie nd “v ots ,»Fommiad iid 422 sossod ene - eho? mosepe 8 ore pee 7 = n Seeamstorm the pressure information and then display the results graphically. LA copy Or tae, source code Listing for Gach program is provided in appendices A, B, and C. These programs were then linked by Job Control Language (JCL) so that the WT graphics were an automatically executed. A ieese rina t tne SSEPL was made tor 100 (nz, 500 mn source and receiver depths, 0.019 km range step, fully absorbing botton, 2000 m water depth, and an isospeed profile at 1500 n/sec. These values were chosen so that a comparison could be made with the theoretical Lioyd mirroc Beansmission loss (figure 2.2). Tre output was displayed as a@etransmission loss curve (figure 3.1). From equation 2.4, meemerccation o£ null number 1 (R1)’ should be 33.33 km and Hib: number 2 (R2) should be at 16.67 xn. The’ SshriLr placed fieadt approximately 38.3 km and R2 at 17.1 kno. Since the model kept the frequency, source depth, and receiver depth constant, then this equates to a reference sound speed of 1305 and 1462 m/sec respectively. ft 2S “apparent fhatwa’s the range decreases the error is reduced which indicates the Bossibility of a problem in the range step section of the model which leads te the introduction of a systematic and increasing deviation of the calculated sound field from that Meedicted by the classical Lloyd's mirror interference pattern. Th2 “washing out" of the interference pattern for Bamges less tian about 2 km is a cesult of the particular appeoximation of a point source used to initiate the program, which is tc be expected. Ratner regular fluctua- tions develop beyond about 30 ka; from the geometry of the Sase, it is plausible that this arises from interference with bottom reflected signals. 3 Veta sete hae bh “03 (a.jali shes sO tigs Gem rr, toe S48 wens faegge i. oi Jegdees dew “tia ~ ; iq = we - ‘co gow 838 aap Se ae ua - ie ~stetotvus 445 'o.6 2d39geh wees in se &£ (002 se ot -o¢e%e 6% :v ohas at Sa (43) waad /iU3 tee, @oin $eGix / “32 off S % ta62 4 eal = ves O Ss w o Thee iadae *sHhutoeds TTNN TOF TepoWn LAASS Jo 4sa] Lee omnbtg (WY) JONUY | | a NM uw) ON O5S/W O86°66bI O99dS ONNOS JONIWIIY £990 900702 HILOIM Huda 4TH W/980, OlXTZ2Z°Z 4309 NOLLUANSLLY “HW 610°O “YONIT JSNUY ‘HW 0070002 HLdIO NOLUM ZH O0°OOT XAONGNOTNA “HW ZO°OOSG = HWLdIO NGAIZOIN “W OO"D0S Hdd JOYNOS Anotner test was made using the same inputs as above except that the source and receiver were nmaoved to a depth of 1500 2 ({tigure 3.2). Since the half beamwidth is 2) degrees and fme bottom is £ully absorbing, the shortest range at which a Peace reflection cculd occur is’ approximately 8.2 kn; beyond this range, surrace reflections should be spaced in accordance with equation 2.4. The nulls beyond 8.2 km do occur at the correct ranges; however, there are slow nodula- tions of the overall transmission loss signal. These siow modulations are another indication that the bottom is not mally aksorbing as had been specified as input to the progran. 26 J¢acta efor es # - wall to. ndaquh oe €S fave “vm tgs atpes (5 el rae” rs intew 9 089 2aad76ge oad ; -_ rewige ei Fees ib6> At 2608 sielgey ous Line UOTPOPISIUL woxgqog WOT TSpOW Laass po Soar, zee oanbty (WA) JONUY Ok AS 7h Sh ESecGme OPN ES 7p SC (| S2tz— az O3S/W O66°66hI O39dS GNNOS JONIYIIIY “990 000°02 W/80, OX EZ2°Z 4900 NOILUNANSLLY “Wy 610°0 STAI Sl Saal al Sez "YONI GINUY ‘HW 00° 0002 ZH OO°OO! AONANOIY “W BI°OOST HLdIO YIAIIOIN ‘W OO*OOSI HLOIM WU48 41UH H1ddO 441M HLdI0 JIYNoOs (80) SSO7 NOISSIWSNYYL 2) ee 2. kT Analysis ine wi. Cutpue trom the SSFFT model 1s in Eng units, which is a probiem when comparing different nodels. However, for this investigation the problem was minimal. As expressed by equation 2.6, the reference wavenumber for 100 hz with a reference sound speed of 4921.26 ft/sec (1500 msec) is 0.1277 1/ft. After correction of the reference wavenumber for arrange increment of 62.3 it and the 2048 points used to represent the wavenumber spectrun, ene Maximum beta value should be 0.1243 1/ft which agrees reasonably well with the maximum beta vaiues in figures 3.3, 3.4, and 3.5. Contrary to theory the nuils are not equaily Seaced and the expected delta beta vaiue of 0.00192 1yit (Equation 2.10) is net represented by any of the null spac- ings. Stamey [Ref. 3], observed tne same non-uniforn Spacing of beta nulls. The reason why the source depth is not represented by any of the nuli spacings may be traced to the improper null placement in the raage domaiz. The Lack @£ egual spacing between the nuils must be attributed to something else, possibly the pressure wave was improperly represented as a continuous Signal or numerical errors exis W2Zthin the source ccde. Whatever the reason for this difference, it must Le resolved before the SSFFI can be used ie e epth. with the WI to determine the source dep 28 ~ ° 4 ret = I~ iv 'Qavwgerls lua 3aq@ ,o2cege Of scale oak : £6 hagas vos oad Ge si. yee rs i7 "sI97OM ONG 7 SDINOS YITM 3OTa LM Ladss (14/1) HLA SISWANSAUM GD WOIS bOI O SOTO RUT O OO elt bit O SELES) BIL 0 elo Gial Senses Pay eet toe 1) DESY La er ere a See Seren ee) Pate ens eee L Mean seas 1 ttt bot JaS/ TIVSe Neer O99dS ONNOS JONIMIWIY “* 14/1 MOLLE 1 “0 l 1. VAVANAVA AW k €°e¢ armnbty bel 0 VV 0°0 IWWYON 8c°0 “Q "14/80 , OIMB9E"C 4900 NOILUANGLLY “°L4 6S°bZ91 HLd30 QIGId ‘*L4 89°19S9 ZH 00° 001 KONINODY 6° LS Sb OSI HiAgG Ya lagsy ~ se ce ORS MIAWAN GAHM JOBAIAY HLdd0 MGLYM HLdJO JoYNOS it sl0) b(°O Oo - Si gas) @ Wed lo r 4 oO) Cd oa oe 2 "S1979M OOOL Fl AATADAY YTA YOTA IM Laass (L4/1) ULI YASWANTAUM OD WIS OTTO SHILO OBIT O S610 OOZI'O SOZI"O O1Z1°O SIZIO O221"O S2Z1-0 OLZ1°O SEZI"O OFZI"O SbZI*O OSZI'O SSZI"O Teer et il toyed ear yarenl L a reared Ener yl Presence Ererercerta | : A Nee NOSE NG/ VAVAUAVAVA' J4S/°L4 92° 1e6b O399dS ONNOS JONIYIIGY “* 14/1 UILZe | Q ,.O1*89E°2 4909 NOITLUNNSLIY ‘*14 6S°bZ91 fee aarnbty HLd30 O1314 “*L4 89°19S9 ZH OO°NOL = AONSNOINS “°L4 O1182S HLddO YQAIBOIM ‘°L4 2b°ObS1 Y4UWAN SAUM 39UYIAU H1d90 YILYM HLd30 3OyNOS ¥I0 9T°0 mo ae =) om EE Ww —¢ 4 ~< °"SI39379N QOS 72 BOINOS YRTA AOTd LA LAASS (14/1) ULIG YIEWANSABM G31WOS O811°O SBII°O O611°O S6I1°O OOZI*O GOZO OIZI"O SIZI"O O2Z1°O SZZ1"O O£Z1°O SEZI°O UbZ1°O SbZI°O OSZ1°O SSZI‘O 1 re Enarer ered Eero ARAAAK G-e Srnb Ty O3S/" 14 92°1@6b GIIdS GNNOS JONINGAIY “* 14/1 O1* 222° 1 = NGWAN BAUM 39UNGAY J ,.O1x892°2 4509 NOILUANGLLY “°L4 15° 192 HLd30 QUG14 “14 89°19S9 ZH ON'OOL =AONANOAN f° 14 ATI82S WLI WIATGOIYN {°Ld 29° bz9z HLdd0G YaLUM H1d30 3OYNOS 21°O o1°o 80°0 30°0 r0°0 z0°0 000 ALISNSINI WWYLI3dS O3ZITWWYON yI°O 91°0 ra oe 7 Vie te See IFD the IFD nodel [Rref. Az 4 which was jnstalles and ssted inf September 4983 at NPS [ kef- 13] was the next nodel hosen as a sound source for the Wide This decision “ids made ecause the IFD was capable of properly handling the oceab orton qnteractions and was the only othet Acoust Te Vee nodel in cresidence at NPS- a copy of the source eoae Lasting cs provided rel appendix De The IFD also presented probiens which will be discussed further. The same initial test ran useé with the SSFFT was ysed with the IFD- Since the IFD requires more pottom jnfornation,s addit ional pesting we- nerformed in order to obtain 4 fui Ly apsorbing potton. Figure 3216 LS = trates the environment as seen DY the IFD model. The densities in the water maSS,y sediments and a6 ti- ficial attenuatiob layer were set to 4 constant of 1.0 and the attenuation in the sediment was adjusted until the elim qnation of bottom jnterfrerence was observed. Figure 324 2S an example of the IFD ¢transmissioa loss output for a 500 source/receiver depth, #@4 water depth or 2000 He an uprer surface of the artificial attenuation layer at 3000 , and a lower pressure release surface at 1G00 Gs 22° bottom atten fieron used to produce figure 3.7 was 0.00 16 sa/wavelengt he 17) ine) i eas ao lissen? Ge ao Dee ‘ : ; - . 7 <0 [Et eee -422 “Qae ang - si Ask isforg Fe slices. é Vine @d> gee Lia 06 £ wr 3 . 7 os we 1° sats L a fia ae « lh ,eOLes Ul # giase ao 32 ‘4 +L seeh inl 2 6te 3 “. hegemen [vited SO uit Ge water sediment “~upper surface of artificial attenuation layer b= ange = ee pressure release surfaces Figure 3.6 IFD Environment. PASS ae S2etwe 7sqEgu - Si 7a tie if *SSOTJT UOTSSTUSUPIZE GAL Lee Sanh ta (WI) JaNba GaOEe O° SC OO Go Si OOH eee Sere Se eee) OS 0°O rap) @ Oe eee "SSOT UOTSSTUSUPIT paTte%4eqd ddl (WA) JONUY as O° bs Oa OES ee ae = sail = 4 g°€ aanbty 0° OF! 0°08 0°001 0°021 SoU} NULLEdbated (a0) GOS 0° OF bee ie *"SSOTJT WOTSSTUSUPIL BJ39IZ SSTON CAL 6° E£ ainbt gq CW) JONVA Was OF OR OSC ie SS eee | See :/ oe 0°O0¢ GES theese ictinen ite O° OT Coo POronT "toe! O° OF1 SSO'1 NOILYS9bd0ud 0°09 0° 0% (€Q) 36 i a r qn" 0 0 - fie by “4, TO ; Dee 1, 7 y 0°OF *SSOJT UOTSSTMSUPTZ IOJLM MOTTRUS (WH) GONGY O°Ss 0°O£ g°sz -d4I 0°02 OLce Sanbtd OAS 0°Ol O08iggqci0C! +210 10Zi seo" Ops SSO) NOI LY¥9bdO0dd 0°09 0° OF (9d) Mmmerocation of the nulls in figure 3.7 coincide with those predicted by equaticn 2.4 if the higa frequency noise is fapereda Out by either a running average process or low pass d@mgatal filter. A careful examination of the transmission Weegee curve (figure 3.8) reveals the real problem, which is the long wavelength noise near tae wavelength of interest. fme Long wavelength noise will cause erroneous spikes on the Meeplots after being Fourier transiormed. Continued anal— Mumemeecevealcd that -the noise could be eliminated if the thicknesses of the artificial attenuation layer and the bottom pressure release suriace are chosen so that they are at least twice the water depth. Phe, choice of a ‘small Memtical grid step will reduce the thickness reguired for Hee pressure release surface, but this version of the IFD Meegram 75 limited to 5000 vertical grid points due to soft- ware restrictions. FLgGUre 3.9 iS ,a transmission loss curve Obtained from a 500 m Source/receiver depth, a 2000 m water Bepth, a400) wm upper level artificial attenuation layer, and an 8000 m bottom pressure release surface. Comparison mmergures 3.1 and 3.9 with the classical Lioyd's mirror Peansmission loss (figure 2.2) shows that the shape of the curve beyond 30 km is greatly improved with the IFD. The Mumber of vertical grid steps was 5000. When the IFD is used in a sShallcw water situation and at 25 Z, the noise Mees not appear to be present. Figure 3.10 is a plot of the Beagsmission loss for a signal at 25 hz, with the sou Beceiver depth at 50 m, the bottom sloping up from 350 t M, and an artificial attenuation layer and pottom pressure Bebease surface located at 750 and 1000 om, respectively. Miesnoise which was so evident in tigure 3.7 is absent fron the shallow w«sater case. Producing tne noise free curves Tequires excessive computer time except for shallow water Cases. 38 > as Seeds Adee EL 2@i0g {3tsype24 | S35¢ #0L se 2mooTy s a ree lgengys £2.30 cokt sedge oe ep | ‘SUL o gg ise4 ed) ’ , io ~@o. SP gy. gap zane ie ZF a” “0 ettas J1fy emioe f ‘#20 legasz ze lizg6? | - S8lca of Si + Jip hegesas edd (i108 sagehdg & --ide ogy “Ss lite (ee os “2-32 «ec OF og be 7 Je, pj =)-) ere Ott» To reduce the amount of the pressure information and Wee preserve the detaiis, the IFD tests were conducted between 10 and 40 km in range. The reference wavenumber for eae test input with the [FD was 0.4189 1/m which, after Correcting for a range increment of 7.5 m with 4096 pocints, produced a beta maximum of 0.4188 1/n. Pagures. S46 11, Ss. 12, and 3.13 indicate agreement with the beta maximum and a Metta beta of 0.00628 1/m can be found among the null spac- ings. When the vertical grid step is reduced in size, the Saeout Signal contains more information of finer detail. The finer detailed information will, if noise is present, Beagduce more clutter on the WT depiction (figure 3.13). in Numerous WI depictions a peak was observed at the nininun and maximum waveaumbers. Stamey believed that the right and left intensity maxima corresponded to beam elevation angles of 0 and 30 degrees, respectively. He further stated that the left maxima also may be reiated to algorithmic inaccura- eves [Ref. 3]. The "U-shaped phenomenon" observed during Seamey's investigaticn of the SSFFI, is present with the IFD and the nulls are not equally spaced. 3:3 oat “@l3e02¢%al Sivaweee" at ines =i13vV 87264 - $975'94 1389 + ie | taf 6 ox! 5£300 eae .62313388 626 Lf £3 a0 JG ted ITs ee | 7 i, - vb thee OF ©¢ 2Aae kJ eaevags to sileg/g@ -dazg pta9 TeoOTPISA JEzZOM GL (W/1) W138 YGOHNAGAUH ORS ov°0 sO as"O st°0 oc-0 $1°0 ——"s sustpsen08 7999 LOT pe As EE ME > vey 4a0InN0S 19700 00S ore wo e°0 ot 60°0 vb ALISNGINI WYLISES OFZ] WON ort a he 6°01 or “ddI LLce aeanbta *daysg pTiI9 TROTFASA Tayou Gs rE (H/T) UL38 Y2SHNNGABM OF WOS os"0 st°0 or-0 si'0 oro *aDmNOS 39 jEeN 00S -ddI ZTL°E BaANHTyY OFS (Ops Ok Ok O72) Ont. 1Gic oberg ALISNSINI WylI3dS C3Z] WHYON o’6 60°98 o°o! ,or™ °daqys pti) TeROTFZISA TAISEN Q°Q “edINOS AazON ECOG (W/T) W138 YGRRINGAUM COWOS sb'0 +0 S&'0 oxo zo ora sto eI" so 8 e8"0 One Ont 076 ove o"9 0% Os) | O*S ALISNGINI WaloseS 032] WHYON Pe GR Re | NG a oN ES 0°83 0°61 “ddI epee aanbry “2 fhe reason for the "U-shaped phenomenon" appears to be related to noise in the envelope function field which is further amplified when the Hankel function is inserted to obtain the conplex pressure. Using a low pass filter and increasing the vertical grid step size appear to reduce the 'problen. tier giTe Seo, che mulls occur at 33.30 and 33.39 | km men a Single null should exist at 33.33 km. This condi- tion or noise produces the most devastating erfects by | masking the desired density spectrun. A narrow band pass | filter would probably solve this problem in the short tern but eventually the IFD will require further study to elini- Mate the noise. When the shallow case is used in the WT (igure 3.14), the "U-shaped phenomenon" is absent and the mull locations are more distinct. However, in the shallow Water case, the bottom interaction produces high frequency anterference but the null Spacings occur near the expected Value for the source depth (0.0628 1/m). 43 wd es sasege Wl * G2 dotuwy Brady Peer a : : are _ ©? ietuuaal af ois ; “") . “Si-42 saaq wal 4 ‘P0s8T lean : oar Of Feeter geile yore hasty 75 ITSO eifne ody | "0" SE-EL gh mies i fvoda &; Li & <.. o°s Om (019 Ors 08 0S ALISN3INI WeLI3dS J3Z1 WRYON uy 0? ot 0°0 0.1 -0.5 -0.4 “0.3 -0.2 -0.1 0.90 -0.6 =027 -0.8 HORIZONTAL WAVENUMBER 1 meter Vertical Grid Step. Shallow Water WT, ERD Figure 3.14 I¥. CONCLUSIONS iwo EalLabolic equation models, the SSFFT and IFD, were used to predict sound fields for comparison with the Llo Mirror interference fattern in the range domain and then in the wavenumber domain. In the range domain, th SSFFT mapEoperily handled the location of pressure nulls and displayed bottom interference. While these weaknesses in the SSFFI were absent in the IFD, the inadvertent and dele- terious insertion of noise was extensive. In tae wavenumber domain, the noise in the IFD was prohibitive in ail but the deep sediment and shallow water cases. The IFD produced results which were ccmparable with the SSFFI when the noise Was not a factor. The range step and the bottom attenuation aegorithms of the SSFFI should be reviewed in order to correct those problems described above. in the 25D, . the noise problem will require further investigation. ii tie problem in the iFD is not corrected, this model will be severely limited. With the guidance provided by Lauer [Ref. 2], the wavenumber domain can provide tne detailed information needed tO gusackiy correct inconsistencies observed between acoustic models. Therefore, the WT should be investigated further to ensure that any soitware weak- messes are eliminated and a thorough understazding of the process is assured. Experiments in the operational environment should be Planned to test the WT with actual sound sources. The ship- board experiment could be easily accomplished since the WT Can be iaplemented on micro-computers if the pressure infor- maewen 1S provided from an outside source. fhe WI, if it is going to be considered as a method to determine source depth, appears to have three major shortcomings: 45 | ‘sc wi* alae Celle 2269) 763 “~A4e7 ei LBS eae ~ ae ty i 2 20s I 1. A clean CW Signal with phase information is essen- tial, which will require quadrature demodulation and extensive filtering. 2. Prediction models are required which will provide equally spaced beta nulis so that software can be developed to automate the process. 3. High resolution processing equipment is necessary because the change in beta spacing for shallow sound sources is small (figure 2.5). 46 a “neues 1 noltametas ¥ £5 Luctale beast sieke np % 4 itv 43id¢ pel ines ame ‘tebe | ‘i508 +203 Ee elfnn ‘aie y nest 29 wr & Soeeee ¥ vee Pei leeenge wt 2 abd af i cs) efed £4 apap ae 3at ilege aio APPENDIX A: SSFFT SOURCE CODE (AT NPS) ZH ok=) =) HAsO HaagH4 (ro) cHakl a D> AS f Me Owag ta =) “oO ss fool @) oO fx eS h a2} & OURAN M 4 4 ND} (4 G4 AD Ao wa NH foe t-—-] Up] et) e fea] Nau = & = Ae HH -OmMN © onHoe oz ~ 4 [7 <2 (oS) . =) Hao Awe NO ag 4 HAHN Ne WN Zz OW AQWnetee . Nop) NO = ez) SSS Wany = ee mA ck, BA So NW He co fy AQVO 4 eof) oe = ou OHHAOHN »& nN VO PHS i=) Cy Ge Meqg4jyaAngeg 2zaaza De WH Om aUROZTH . BAHN aH A 2 Haeatg gy VU SD HS = SBM GMOHOZDWH = yZz=zO BH HW A aa MAHHOBAHSHGO OF He FD HAW DYHSO = APaAg ln el sn I ia] nN HOHOHSE UO YO BAN MHAZMQGEAGQHH= io] ZDHRPRHO Ga Fey eye N AH SAH EHet eee 2 HaHMN > 2 HoD< =) T=\olo}=) BNeEDRA Om moO DHmMDAGOUNA » Sa HDeXt 1b ahat csi eee Li -2 lpi 9s] hon Q Q ae COCO PH SP SRM ae tH atHHEe Se A [oa] ion] aaa tyke ry Sy SOAS HOszr & < = a _ oue ee A “Oh Ae ; bs eS ¥ Se ; aes oe salient 2 Spa in . oo a Ww SS AH mG = aa es (S) -~ De row] cg OmrS = HH ©) NOUHO id) fa¥) ue e iQ YQ Ww We ~~ | =>) ica] f= oS) uw o ~ 29) SG) ee) aa = t Ne Moo = Hi az HHO 4 AORN iy ity) aes wA OWS a 4H joa) i] VAs . OHM yO Oo re te ix) AM = mam RAH fy 4) ed wy eyes al orl aloe} U = O xa ido ~w2 SS WQ (oe ee) Ne OH o NO HF NaDw OOOH OQ AN mo =A 4= * ~~ HH YU HHS HHH y = wey 124 BH NAH - 4 jotgariertés) wa Zo Bb ~ >= yet NN NWN top) eS HW RH aga . O Ei TZN HY ARADO icp) SS | ° | aN» He Hy mea Oe WY HOHHO OD AAHH en Oo of = WN Zur i B= . ores) yea 2 An, H (Pej S) 4 trl 6 2 Fo AR GA BMAVULOURQ Am A = OOS + @ HH ye tH hb «<< "2 eS CON (@) ©) =2O CGH FF He OQ = wn GS ~ SESHOHS AHNOCOS Qy Cen ° R Qa mm UN TE j=) H fy ° oS isa Eyes [aa CH ] ¢ 4 = ? y e omy id) _ “_ fy GH | . — war-a NA N Az e (oe fea) Co) Neg Oty Qn fee] e ray I) Ky a Jy & le Seem yo (2) on) AG 0G YN HR ey wets) Ofmm aa im =nNoe fy - 3 fowges >) (pai YQSH = Hoenn mH BOW em eH aN cod Qoayo OH Hae as) aOW oJ co 1 aA N icp) Ss He HSH AH A mae “AA Om GN HN at PhS? Ee) ia] ea ete a) ET oe ew = e e eG retin SO) 4 NN HOQANO LOOD fx ob r= 2Ore Si WH am mM maOaHMA = GHO an as MOSAOHR SE AUS oO H ole) AB A rmmasuan HEY mH —) OO Qea= ma Q AY HoH =xnO « az NZO RSSHWNOH SQD a@ 4 fry 20RD CHHODrA mk} Hag wtO™~AH™H | ay eS ae HOH SG OHA —©@) == nAMa 2 OO kMO ma oO WG BHEe YN we am a! ORR mH 41 By BHO Q mH — OWmaaAo Of mo QH ot POE” QHae =] a] HSerean HOH -@z DBD BH ae WORHHH ONm DD 9G HA smn fmm WH N A Be (Ss) = jon) fy 0 Fy OG Fe ee mwa = ie) — Se Sas tH GH QH OMe BH OF WHA a en) HaDmamp « Of ho OHS ORG ale) a=) OArPU YN wD SS ee ee) Seo 6 ZS BAONAG GHA aae ~HN s © “— WQH® om wHO =H Wy Hoe ees VBYHHHAG HS Ho eye) TMan=w 2H NH Gm = Om met BAHODPH MOm NH WwW “KO a WOHHA «es men Ore Bet AD New SMO > se CAM NN Qwecm m2 CHO «x hen o) Aho Dp UNHARNQ ~ BNWNDs i) A) “tise! Eyes oe se Onamg— 48 BsomyHna Ei — 2S) zHAY> . NH “a Qe OF Z2eUeHx& ZuUHDH » e mB2ZeH nn Newest He DYyqO a oo} a TH eH ASS HOt Na om Eee HQ oO —& WH ey BAAS eQ «x © he ZHSBane HNDROWHEH FB fy mat Om 24 Syeq =) Pfani=2)-—fespe> | ea IO a “NASH moO MN SMQ an Hr stOOR ORK mHa FO wd FOP Hy eO FED & WH oh Ci> =u nNHOas Hog feat 4 DD QOH et Oy Uae I H BHO FOWAaD a= ~ 2H 2 a—Dooarmmy = Ol HieSSomMeaeS ZAQ USB One A G& IS ect SEeNZ& ss HAO N D ° ® OnIRa e Q HY HYZaRO OOH aww “YQSHAaA HoH = A 14 fa Ne HQ Smears ZA eis oe? I on es) oity ithe ee HORRH=a Yq Ne & fa ewfood— ica) eet ott eK uh NOW ’ e BYQeIM|g ena -_— = 1 ODI AS © 2eObh ect eN& MMU A H e Og>ys= 1oz eH ZH » QU~NR e 0Q ’ Sten | eS n°

* * Zz ro) YU VYVVUOVVUVYNVOVV VO VVOUVUVONVVVVU YUUUVUVU VU UVUU UDO UUUUUUU0U0U 49 in i ee me ee ee ne ee te ee es ee we ee ee ae eae ae ae Jus alo iep) ° e isa) a pay = 4 O HY ©) ° jen) Cy pap) tel ie Nn aot) Q Ons (=) O OF i eGo cj te 4 oy Sau _~ UMmON ise] Ltt N tr Sno al DOV 4 OHM Hi Gy +f Co oh @) 4 Am A SS ZAwe YN eH OW f& = ° ayo KH cl A; UO = S G mows wn muIGaa A me 2) aa ica] HY a} OH Ww fr] ica] faye OG HY ea] a Omnvom eo) mean 4 ae, NQ Hans Q = BHO O ema Op) i HB el HOU ‘e) tS rary ey Zittiey ey = WS wSoey =} f=) BUH ise) j=) Dm io {els} x Oyjana Qy aOR mH maaaa a MH oH =a Hi wm gu yy ° 4 Q OOa H ma fy He am an fy of =ywWaQ ZY oH S) YN » Ax waNno SH vo Aa a> OW Nee Oe A WN SS Hy MaHN an = AH OQ SH HO HW BQ 2NH HH MN Fa} On YAH A cK HH Gf oy Ha NAVUFM HX DP O Oye 2x6 OFa6Gq a 4 HUH au AZH OL = FH AnmMaY aa qm z e) TMC) = BHoOW Ot N 2 no ™m™ 2AnyH fi « OH HHP a = fF 4 He =) la am (4 = A = op) i] ay 4 iy NH WM faa) 1 i] nt = = et =) x ~ - ! Um te ow m1 wm ea] et) et ip i} wa aA a4 nN = eo @ WH x (o) oH we =r |e es poe <2 > ‘ ! Se) =a HH (yeh mfaln ) Ay = = Ba Qy sa ial or> seo ow a = ea Or A Yh ep) onl 2) fae VYUVVOVV VV VOVVVOYUVVVVYVV VV VV VU VUVVOUYUVOUUUUUUVUUUUUU UU 50 ——— a A es t27urag er Ca ack 3) " .¢ ish Ylistariie wtOen oH WY fy ° H =| 4 () x a4 = te ~ tae) | (UR x AQ =x ez Wha eH je) HOUN ial fu =aat icp) 2 ge eS) =a NDMNS ES c HOH Ne om nm HO O# EH HM BAe HAHAH KY Onan GM cot Qa 2 Ons =, fQ SS Pax mete He NOOR HHO HH NH RP H NWOS Ant fee oto} HQ HNO Il of Oa e ny =) ee == Go we SPYRO mana HH moO UMOAgZ QOL ian SBAW4Q Bea . oN Sea AnD 4 © OSG 2aezq & GH qagH= OU SS © Bano . aS ° ’ Be & =o oS, > = H A a WN e . Nw <2 eS Narsh { WO oO wv AHN moO ’ s] oetetG Qh = ey | A Be Mm Na n = mn on 4 4 ee as) <= xc > MO toma} fxq a as a *] =S eS > ) » wt COS OE AGN bard ad wee" be J ed SQ . Ff ns AnD YQ eo sH O el @ Of SIN A Rm NEG Hee = ions teense OHA = He NKR aoa: = Ss (tH = sw” » 4 QA N= eed 22 | a ws GHOA H bees ~wt ON D> ~ Ae DSR Aids f =3tF4 UUHO « oe OF ay = SS 2 asf AANS?A Sane No ff ~. RASA = wor eH = FOAHS ASAaak nN fe = RAOMw “i, wel Cr a © 6 SS OQ weit » fey iH 4 HeHAOoOm & r=) SO .FH nme % mM REINS HA Oeae™M —e fe et SBuawzwe « el ety Gm WM - -9W COPY Hee G 2 OQ AN PRAHNBY Pmorwn,s, e 2 = ROR © OanNats G&G SPpOoO~ AAGRODZO™=HaG A ao SMR Uf » =» NAN RPHSAS NON WN GG eae Nad RP NANA ENR 2 GNF e PYARAYNPNHUD NX ko RO ANSE St et me = Rom. ke OOO HO BH AE SE DRHOetHHmROGUWO AASADZOMANRNSY man PNNPNA NAN ON NA — w NY SS S'S) ee NT S2ZASZmzmzamzaszeayszyamaaey RMIYVMAVIYVVVYVY BO YVOUHA wh sa 2 - - eR + ta a be 3 H ae 3 ima STS TS TOTS) O a FORTRAN UNITS. DEFINE OVO Nor Wo Ota HH a ee ee ee ee ees ae eee we ee we _ vy varbaiaee ’ *a9% 124836 e ‘ “» uw $k ayfdvar i: READ INPUT CATA. ,LPRNI, NPE, SPH, L PLOY, FACT, DAIN, LELAGU I FLAT T5 ZS AT (8F10.2) READ (LC, 920) DMAX, RMAX, DR,CD1,CD2, CLMIN, DCL (Le, 920) )e 25,6, 2f Aan, CO,VABoF 1, ND) C) (D(T) ,T > wW tala] my ep) _ O ~~ oS r4e4 HH Sa yO —_— oO jean) Sy fx —™ SHH H @ = n 4 Ar. ~~ ca] jee) He ZOU + + “> Mes (Sek) irl f4co WWW @ @; OW ey A jee a4 i , ny Le) ~~ —_~t x QA AetnAzo Hae Hii THe NAR RAHN ae Ss H=SOnf obOs) eis NW RV mie Sas eer Ham VAoogo ast ONGC a OOS 4 me mMOmmO Beano Ox Amey me RAUNYU Re Rm BHAARWD ASAw& UL —- N oo = A e— ite) n o>) Ww om ~~ Wwy@ wor Ww SOOVQOOOVO OMO) ENON DIN SOK Kp: Ort OVO Bye} CCMPUTE TRANSHISSION LOSS. REWIND LT OVUUO YO AM, NL,D,DMAK, XMAX, IFLAT, NWARN) ar] 4 CALL PETL(ZS,B Aura 8) .5) N TERMINATED AT RANGE STEP ® we c Z nN —~— = Wm NS Cc lop Feo} So © (eKee) ie) no —S| Beg x hea tO) Ho moO x See UO we) Ov. KO) op ON NS) ee a R INS wm HW ~ A RR NS Oo we wa 4 t Lo A SF ae fm &F We) a 1 =) < Oy A KR == J ep) A & . WY wy CH e be we R a A FR KR RQ AR ia) eH mR KF 52] | A wR by} H4 FH tt Y x A >< = oS fF Qe eH eH KF . boas ee 2 He (eS) BAH Ho H RAHA =z Zt HH fm) FAOHR Ho 4 a SS = nH A >) FRU! D SU Sp) TONE MONO SMS MONE eS) e ff) ay pe} < cal = my ON ica) iS) (S) He 4 Oo 46 WwW ey One ed Hw oo eC) Es Oy) ch me Cl es, O EA Tie AE) Oe en Ett = GM Wm aN Asie AES ete Ea a) Sie et alee tsa) Se PU TS) ns AH eB ew PWT MN3-oeF H ON WM) or RD) EOHO LG ER ONT) OS OIL OM &SO™) AS HH SO wR Od ee ed be ee 18] Se FeO ~Hiees™~ AAESNSYNESNEN2H4 Il AN ROH HH Hee Be meg RHA eet ayctHHo™~ RoHS ASS HSM a RSH OHHH FS ROMEO RVGBROmONetO ROSS SHS wewHeag e o “o ON] OA ese Op Ree bn 10.8) Gye 9) OX) eee “~ ~ ~~ had UO 1) GRAPHICS DISSPLA YOUU SHSHSSHSSSFESS FISTS SSLESSHEISESSHSDSSLES PSS SISSS aC Bs pPwFe Own ZtA ath Rm hsiey I rt MA “SS —- Le hoe 2 AH “A FBDOH OF Oo Gass be a | DS Le here “TAH All »= AD sa Sans ND) FAHY NBS wa” AH ® FAN DSO Sia 27,20 F Gent) BH Oy Az SOW tHe Het RHA S6HH=S A BHHE 6GH2zG CO ASEH ZOM NN * ot - tH we & - (ony hazy OOK) oF + N F wR non Oo O O NOS 35) BET 1 N H SiN ns, 2 CONTROLS, sl ik ok DESK sOines DAP LOSS Ar ON OUTINE OF -_ = _ O fw ~~ ) ARO ROmMHAHR 22 H @aoo PDA YAWAAw OR FAR GUH a He Ay fry SdmgmH AQA~: MAOH mH AA SWORRA Yama PXeYy GW AWHoO Soe SS yOwWR fly POH OUMHHDe qoaex SH Saud OO Se DOH GaHWH QFE SZOSS Sn QVVUVVVVOUVVVSOVVO0O UO E : a } : > > “Past 7 — -_ = x éKO .e8TTA, OU 4zaN UGAIED ,QA0H Fi (Use T tere ere eee © Qa ipw4e STVGt lc! s DCUND: VELOCITY “PROPLILE BOMwAaOAy SBASaupa2aHn PReoOHOm= ORBAN GH ORM SPACE fry TER COLUMN SORBING LAYER ram =a THE TRANSFORM DEPTH INCREMENT ea] Oo Qygmtae7yaeas 42aa a BORA WOH ARHA NDS NDANOVUGAZVUVA OZDOOCRHUNG mM YSSH] NN WAOQhH Oo SHA AD WR am “MAOH QSAR ZH P2ZQocet =x Oo JA SHON BY Q OHPRANS0QOSHAWOUUmMmOA ANUSF aw fD S224 AQ OSeyaSsy 25 ot HY ONWA Bem we Nin eee AHA SBUAUD UEGORROO AAH MOOS FPHHaOm Mma HH Ba mo HOW AH Be SaaS SHA ASRONGHNG OF YB THyeyyo ZBZHAH SR NO GCHAR yeanHoeH SQ HOt QDORNH TRANS TSeONNN SERA eODOTr ketone DpoDePOwEs ec we oop ely lh - pe oi = uo om Oe ae) MESSAGE COUNT UM estan SA PLE aN O 1 NG = wo te) SRYURQSOUIHM BG Z2NQU0QUL=EE2Hhmzm Wey oH [oe} CUTPUT EDULE: OULTP JAUTICAL MILES) SS (DB) » 4 CIPROCAL RANGE KANGE SSION L 4 i PYRO NS OO GSeWHORAH 2DAS2@2 04ND oH MAXIMUM TRANSFORM SIZE CONVERSION FACTOK FT/NAUTICAI MILE RR KE NM AX LCCAL VAKTIAELES FNM CCNSTANTS = O — lm _ = fe eo) jew 1S) EH Su i") Qa Lee GG at jaar fy HQ Ss) YH aA o a ma | cot “« FIELD PRINT PLOTTER FLD TELAT, NWARN) ND, D,DMAX,RMAX, (2S, BEAL 20) , BUFO (21) EEL E [att dl EEN ADDED TO ENABLE DISSPLA GRAPHICS VAVENUMBER TECHNICUE ,ALGEN (100), UD,NBOTM DESSESEPSELESETSISSHSISHHSSLSSDHLEESS , ) PRS (2049),GA DA Sl SHHSSHHHISSHSHSHSLFESEISSSHSHESHSHE SHS LESS ESSS BH WOOOCROHE RHONNS AA ROS oS RAN EGEROURG @& =\Q8@\z< FYNORAARNOX HORAKHRHES HORE) & 1, D2, DED, CD (120) 20) eed De 101) ee ed :UF/ NOUT,RNM,T CO,H, &K,F,F NC Z 4105) @ £ (20) /NE f R KE NB, BR a E if al Y PSNSBZeHSSAHyYSzzzzz FOBZOOFOCOSG OO0000 BlOQSSeS SOBA TVsS==Tf2= BAlSTVHATSSOqKeVTsAypTS=as ROR VUORUODHOVUQUUO FPOOVUVYUFHOU BMOUYULUUU0O ~= Cisits 57 FOe29 SASS SO7 WIS he 07, {/ 048,6070.1 TRANSFORM SIZE. 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NWN CIHRIN we Quk4 Hw bog es mn Aa, aN > ®» wie Se HH +t Ho OW es ao = So i i BUN WONG Ce eet |) ) p> aa a >) = rm. lee io) ES) eae) (erat ia) Be 2k A= o~ on | BS OF QS MONRH OF Prynwrasem ue 4 Oc — = BUR Dia HH PCtOne > : : - ‘SDasartss PO te | | ee hs ee i. Isa tndoe? 36 3feD"; ces ted Bi LADS YRIST Sei UF eid Epos ° reek Gt > saa5 i 77a8. cme aye mone Ses 2 oh ai te os, a ‘e vn ” eesti BAZ «AE 2 £8 et mie r i ae . eee ss 4 . - = io U LIB GLE PAS © & c £ f ~ ‘ oJ t re * r ' a * . ) A it eos sazE iy Jeo a 14 - * bo uo? SeteG : af Agi a Sie JacgeL,. E. Cc er 2 a 2 Parabolic ua S 2B It te 2ECEe solution “detno Phcorporatias Exact —- {nts S Conditions, Naval Postgraduate School, September 983. 148 eas 79"" 4 loc BIBLIOGRAPHY Pammssten, RoA., “Low-frequency surtace interference effects in long-range sound PEO eds et Obs Jc) AGCouUStT. Soc. Al., V- peepee 76-683, January 1 31. Brigham ES0.4., Lhe? fast OUrZer Transform, Prentice-Hall ine., 1974. ae PuGekeetak., SuUcChaL;GRSNs, cand Spoftford, C.W., "Modifying Piece sounde Speed) Profile to improve the Gcuracy of the Parabolic- Equation aecuasguels UeeAsOlace OOC. Alley Ve 62, Be 2439-552, September, 1977. Clay, sG-s. and H- Medwan, Acoustic Oceanography: Principles and Applicatiogns, John Wiley andmsons, 0977 = DiNapoli RokaeaendsnkeLe . Deavenport, "Theoretical and Numerical Grean'situncet#on) field solution in a plane multi- we ncamedaum!, Ss S9ghcousts Soc. Ams, ve 67, pe 92-105, January 1980. Hamming ReWe, Digital Filters Second Zdition, Prentice-Hall tne, 1977. Naval Undersea Center Technical Report TP 488, Low-Frequency Propagation Efrects for Sources or Reclievers Near the Ocean ce y.S.AlS "Pedersen, D.F. CObGOn. © and De. Whawe, mlm ULL reo ae: eptember 1975. : : Donald, Mechanics of Underwater Noise, Pergamon Press, ELC Water Sound, Second Edition, Gere k, Rade; 4 lon in the Sea, Derense Advanced Research Proj 149 a od (98 ial rt | 10. 11. 12. INITIAL DISTRIBUTION List Defense Technical Information Center Cameron Station Alexandria, VA 22314 tTPorary, Code "0 142 Naval Postgraduate School Monterey, A 93943 Chairman (Code 68Mr) Department of Oceanograp Naval Bee Nats Schoo Monterey, CA 93543 Chairman (Code 63Rd) Department of Meteorology Naval Postgraduate School Monterey, CA 93943 h i? PEOL.s A.B. eo dens (corde 61:Cz) Department of Physics Naval Postgraduate School Monterey, CA 9394 Prof. C.k. Dunlap (Code bepartmnernt of Oceanogra Naval Postgraduate Scho Moaterey, CA 9394 is "Serle B 598-B Michels lanc Q Monterey, CA 9 i: e 35943 hard hn Rd 3°40 Derector Naval C Naval On»servator 34th and Massachusetts Avenue Ni Wasnrncton, DC 20390 R u ceanography Division y Ccmmander ; Naval Oceanography Command NStLl Station Bay oe. Louis, MS 39522 Ccmmanding Orficer Le Naval Oceanograrhic Office NSoL Station Bay (St. Louis, NS 39522 Ccmmanding Officer Fleet Numerical Oceanography Center Monterey, CA 93940 pounen diag DEEL Cee ; ava cean Researc n evelopment Activity TAtint Co 2 an) ae Nett station Bay see Louis, MS 39522 No. Copies Z do 1e5 13 “htt eae st ceee § hati ae _ + 13. 17. 18. 19. 20's 21. Ccmmanding Officer ; Naval Environmental Prediction Research Facility Monterey, CA 93940 Chairman, Oceanography Department U.S. Naval Acaden Annapolis, MD 21402 Chief of Naval Research 800 N. Quincy Street Ariangton, VA 22217 Office of Naval Research (Code 420) Naval Oc2zan Research and Development ACrAavaty . 800 N. buinc Street AElangton, VA 22217 Seventaric Izaison Offtice Office of Naval Research SC€cripps Institution of Oceanography La Jolla, CA 92037 Library CIECESE P.0.BOx 4303 2 San Ysidro, CA 92073 Ccmmander : x pecan Faphie Systems Pacific Ox Pearl Harbor, HI 96860 Ccmmander ({aAIR-370) Naval Air Systeuzs Command Washington, DC 20360 Ccmmanding OfE1 CEL ' Acens Ur R.B. Lauer, Code 323 Naval Ocean Research and Development AGCAVETY | NODS ocation oe bayveste LOUIS, MS 39522 151 o £9 seligoms >> EGE | .. ‘esate ag ws =6 ” ’ bee on ,200 gar est), 205370 ‘Thesis B54843 Blanchard Creal A comparison of two acoustic parabolic eq- uation transmission loss models for compa- tibility with the Wav- enumber Technique in the determination of source depth. | | | | | | | f two acoustic parabolic e | | 3 2768 002 13535 | I} tH | DUDLEY KNOX LIBRARY A comparison o [Pee PP are rey rae CU wea, LI ROT EY PAID FY EO eo. FE Yitapipnect PI EP Mp pr ye yD wows or UEb ene eye Ver Weve eS Seeks be ho at a aa ae AS is SPirrge ve oe eee