SYSTEM TO DETECT AND REDUCE WIDE-
ANGLE SEISMIC REFLECTIONS AT SEA,

BY
Stuart Kaufmann Edleson

United States
Naval Postgraduate School

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SYSTEM TO DETECT AND REDUCE

WIDE-ANGLE SEISMIC REFLECTIONS

AT SEA

by

Stuart Kaufmann Edleson, Jr

September 1970

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System to Detect and Reduce

Wide-Angle Seismic Reflections

At Sea

by

Stuart Kaufmann Edleson, Jr.
Lieutenant Commander, United States Navy
B.S., Iowa State University, 1962

Submitted in partial fulfillment of the
requirements for the degree of

MASTER OF SCIENCE IN OCEANOGRAPHY

from the

NAVAL POSTGRADUATE SCHOOL
September 1970

:braby .

lval postgraduate schooe

)nteeey, calif. 93940

ABSTRACT

A simple system was designed to collect wide-angle reflection
records in order to investigate the interval sound speeds of the sedi-
ment layers in the ocean. The system consisted of a frequency
modulated receiver, a cut-to-channel Yagi antenna, and a sonobuoy,
used in conjunction with a precision sonic profile recorder and a
triggered sound source. A computer routine for reducing the data was
obtained and modified for compatibility with the system and use on the
IBM 3 60/67 computer. The system was designed to be both inexpensive
and simple to use without any loss of accuracy.

TABLE OF CONTENTS

I. INTRODUCTION 9

II. BACKGROUND 11

III. THE WIDE-ANGLE REFLECTION METHOD 12

A. THE THEORY 12

B. THE MATHEMATICAL MODEL 14

1. Forming the TA Plot 14

2. Determination of Interval Sound Speed 20

a . First Layer 22

b. Second Layer 25

C. THE COMPUTER PROGRAM 32

1. Data Reduction 33

2 . Trial Solutions 3 6

IV. INSTRUMENTATION 3 8
A. THE WIDE-ANGLE REFLECTION SYSTEM 38

1. The Sonobuoy 3 8

2. The Receiver System 46

V. CONCLUSIONS 53

APPENDIX A: DIGITIZING THE WIDE-ANGLE REFLECTION 54
RECORD

APPENDIX B: ROUTINE FOLLOWED BY HONDO I COMPUTER 5 7
PROGRAM

APPENDIX C: HONDO I COMPUTER PROGRAM 66

APPENDIX D: SAMPLE DATA 79

APPENDIX E: RESULTS 80

LIST OF REFERENCES 85

INITIAL DISTRIBUTION 86

FORM DD 1473 87

LIST OF TABLES

I. Comparison of Solutions of SLOW I and HONDO I 34
Computer Programs

II. Comparison of Results of Various Trial Solutions 37

III. Sonobuoy Frequencies 40

IV. Sonobuoy Characteristics 42

1 Ct

f^y a.-/^f.

u

LIST OF FIGURES

1. Wide-angle Reflections 13

2. Ray Paths and TA Curves for Rays Reflected from 15
a Horizontal Surface

3. Ray Paths and TA Curves for Rays Reflected from 19
a Plane Dipping Surface

4. T Reflection from the Second Layer 2 7

o

5. Multiple Reflections 35

6. System for Collecting Wide-angle Reflections 39

7. AN/SSQ-5 7 Sonobuoy 41

8. Releasing the Bottom Plate of the AN/SSQ-5 7 Sonobuoy 44

9. Bottom Plate Retaining Clips 45

10. Removing the Rotochute Assembly 4 7

11. Yagi 11-element Antenna 49

12. Power Gain vs. Frequency Curve 51

13. Antenna Patterns for Yagi Antenna at Various 52
Frequencies (Relative to 175 MHz)

14. Digitizing the Data 55

15. Relating Direct Travel Time to Corresponding 60
Reflected Travel Time

ACKNOWLEDGEMENTS

The author wishes to extend his sincere appreciation to his
advisor, Professor Robert S. Andrews, who originally suggested the
topic and provided immeasurable assistance in delimiting the scope of
the problem. My appreciation is also extended to Mr. Robert C.
Smith of the Research Administration Electronics Laboratory at the
Naval Postgraduate School for his assistance in building and testing
various electronic components reguired in the course of the study; to
Mr. Robert E. Houtz at the Lamont-Doherty Geological Observatory of
Columbia University whose correspondence provided invaluable
assistance in developing the system and writing the computer program;
and to Dr. Roland von Huene and Mr. Harry Hill, both of the Marine
Geology Division of the U.S. Geological Survey, Menlo Park, for
their technical advice and various eguipment and services they made
available for testing and evaluating the system. My special thanks
are due to Miss Dianne Williams whose love and moral support aided
the study considerably.

I. INTRODUCTION

The objective of this study was to develop a simple yet in-
expensive system for collecting wide-angle reflection data. This
system would be used in conjunction with normal-reflection profiling
equipment normally carried on board oceanographic survey vessels.
The study involved testing an inexpensive radio receiver to be used to
receive a signal transmitted by a sonobuoy with enough clarity that
the signal could be recorded on a precision seismic graphic recorder.
The study also involved testing and launching five sonobuoys and in-
vestigating modifications which can be made to the sonobuoys to
enhance the success of the system.

A further objective of the study was to provide a method for re-
ducing the data collected by the system and obtaining the mean sound
speed existing between successive reflectors (called the interval
sound speed of the layer defined by an upper and lower reflector) and
the thicknesses of the corresponding sub-bottom layers. This required
modifying an existing program to read the data and compute the results
on the IBM 360/67 digital computer using FORTRAN IV language.

This paper presents a short discussion of the background and
purpose for developing a system for collecting wide-angle reflection
data and obtaining a program to reduce the data and determine the in-
terval sound speeds. A theory of wide-angle reflections is offered,
together with a mathematical model used to develop the equations and

suggest a method of solution. The computer program is discussed,
including the method of digitizing data from a wide-angle reflection
record. The radio receiver, antenna, and radio sonobuoy used to
develop the system for use in conjunction with normal-reflection
equipment is discussed. In the last section, conclusions and sug-
gestions for further work on the subject are offered.

10

II. BACKGROUND

The geological structure and composition of the sub-bottom
layers in and around Monterey Bay are presently known to only a
limited extent. Sufficient depth recordings have been made to enable
drawing a detailed relief map of the sea floor; and shallow cores and
grab samples have been analyzed for determination of the composition
of the sediments in the first few meters . But knowledge of the deeper
layers has been restricted to only subjective analysis involving the
extrapolation of the immediate terrestrial structure from wells and out-
crops and correlating the data with normal-reflection seismic profiling
data. Unfortunately, normal-reflection profiles measure only the
travel times and relative intensity of the vertical reflections. Without
knowledge of the sound speed-depth relationship, only a guess can be
offered as to the actual sub-bottom structure. A knowledge of the
sound speed-depth variation is essential to a quantitative evaluation
of the sediment layers and to a geological interpretation relating sound
speed to type of material, age, and consolidation (Le Pichon, Ewing,
and Houtz, 1968) .

The system developed for collecting wide-angle reflection data
along with the computer program to reduce the data can provide in-
formation on the sound speed-depth relationships and the layer thick-
nesses .

11

III. THE WIDE-ANGLE REFLECTION METHOD

The characteristic feature of the wide-angle reflection method is
the measurement of the travel times of longitudinal waves which have
been reflected at boundaries separating media of different acoustic
impedances (the product of sound speed and density) . From measure-
ments of reflection times it is usually possible to determine the depths
and dips of the reflection horizons and the speed of the seismic wave
(Jakosky, 1949).

A. THE THEORY

The system was developed based on the theory that a sound pro-
duced at source S (Fig. 1) will reach the hydrophone of the sonobuoy B
by three different ray paths as shown; l_ the direct ray which travels
just below the surface of the water, 2_ the sound reflected from the
water-sediment interface, and 3^ the sound waves reflected from the
various sediment layers that may exist below the ocean floor. If the
distance separating the sound source and the hydrophones is steadily
increased while the source emits sharp sound pulses at regular intervals,
the time difference between the arrivals of the direct and reflected
sound waves will change depending on the sound speed-depth variation
within the sediments. A record of time differences is used to compute
the thicknesses and interval sound speeds of the various layers and
obtain the sound speed-depth relationship.

12

Figure 1. Wide-angle reflections

13

B. THE MATHEMATICAL MODEL
1. Forming the TA Plot

For the purpose of forming an elementary concept of the
reflection method and to illustrate the formation of the wide-angle re-
flection records, it is useful to first consider a simple case of a
single layer of homogeneous isotropic material of uniform thickness H.
It follows from this case that the ray paths will follow straight lines.
A further assumption may be made that the lower surface reflects the
sound wave in accordance with the physical laws of optics so that the
angle of reflection is equal to the angle of incidence. Also it will be
assumed that the path taken by sound passing from one media to another
having a different sound speed is refracted in accordance with Snell's
Law.

Figure 2 illustrates a single layer model with a water

medium of depth H and average vertical sound speed V. The theoretical

travel time on the record for a vertically-propagating sound wave when

the sound source and sonobuoy are at the same point S in the ocean is

referred to as T . Thus T defines the origin of the record at which
o o

point the direct travel time is zero. The source sound wave will
propagate downward through the water to point A and then be reflected
back to the sonobuoy in time

T = ^~ , (1)

o V

14

10 p-

Figure 2 . Ray paths and T/X curves for rays
reflected from a horizontal surface

15

If an anology is made to the laws of geometric optics, the

ray paths may be conveniently handled by utilizing the concept of

images . The travel time to the theoretical image point 0' is equal to

the time for the reflected ray to return to the sonobuoy. Therefore,

when a mathematical model is constructed, the reflected times can be

considered as the time required for the sound to travel from any shot

point S. to the image point 0' at a sound speed of V.
1

At shot point S , a sound wave travels to point B where
it is reflected upward to the sonobuoy. This wave is referred to as
the reflected ray from the first reflector. The direct ray travels hori-
zontally from the source to the sonobuoy at S. Again using the concept
of images, the reflected ray path S B S is equal to the assumed path
SB 0' (path length R ) and the travel time becomes

Ti-f-- <2)

where T is the travel time of a reflected ray. From the geometry of
the triangle SB A

1 cos,0.

16

Equation (2) then becomes

Tl VcosjeT ' (4)

where 0 is the angle of incidence measured from the vertical.
The direct ray arrives at the sonobuoy at time

xi

Di= v ' (5)

where D is the travel time of a direct ray, X is the separation
between the shot and the sonobuoy, and V is the sound speed.

In general, the separation X can be related to the depth H
and the length of the reflected ray path by use of the Pythagorean
Theorem; i.e.,

2 2 2

X =R -4H , (6)

where R is the distance from the shot point to the image point 0' .

As successive shots are fired while steadily increasing
the separation, the record of the direct travel times results in a straight
line on the TA plot shown in the upper half of Figure 2 . From Equation
(5) it can be seen that the slope of this line is the reciprocal of the
water sound speed. The record of the arrival of the reflected rays form
a hyperbola asymptotic to the direct travel time line at large values

17

of X. Equation (6) can be combined with the relation

R

V

where T is the travel time of the reflected ray and V is the sound speed
to obtain the equation of a hyperbola

T = y- (X2 +4H2)1/2. (7)

For a bottom with a slope shown in Fiqure 3 , it can be
shown that an additional term is introduced into the above equation
The equation for the reflected travel time for such a model is

T = ~ — (X2 + 4H2 + 4HX sin 9) l/2 (8)

where 9 is the angle of slope of the bottom. The sign of the additional
term is negative if the bottom dips in the direction opposite to that
shown in Figure 3 .

If a mean sound speed between the sea surface and any
sub-bottom reflector is considered, it will be realized that the record
of reflection times from that reflector will also form a hyperbolic trace
on the T/X graph in accordance with Equation (7) , with V equal to the
mean sound speed between the surface and the reflector and H equal
to the depth to the reflector. The mean sound speed V can be calculated,
but it provides little information for determining the sound speed -depth

18

Figure 3 . Ray paths and T/X curves for rays

reflected from a plane dipping surface

19

relationship. The sound speed that is required for determining this
relationship, however, is the interval sound speed of the layer defined
by an upper and lower reflector.

2 . Determination of Interval Sound Speed

The determination of the interval sound speeds by reflection
measurements is an old geophysical problem (Clay and Rona, 1965) and
techniques for reducing the data go back a number of years (Green, 1938)
The method of determining the interval sound speeds between successive
reflecting layers from wide-angle reflection data is presently quite well
known and has been described extensively in the literature (Dix, 1955).
Its use at sea has been discussed by Houtz and Ewing (1963), Knox
(1965), Clay and Rona (1965), and Le Pichon, Ewing, and Houtz (1968),
among others. The method used in this paper follows the technique
introduced by Le Pichon, Ewing, and Houtz (1968) and is the method
used in the computer program of Appendix A.

The water layer is assumed to have a known sound speed-
depth profile, with the horizontal sound speed at the surface V dif-
ferent from that of the sounding speed (the sound speed integrated
over the depth H of the water layer) .

It is further assumed that the dip of the bottom is known.
The dip of any sub-bottom layer will be considered here to be the angle
between the upper and lower reflectors defining the layer. Dip is con-
sidered positive if the distance between the two reflectors increases

20

in the direction of separation between source and receiver. The dip
of the water layer illustrated in Figure 3, for example, is positive.

Assuming such a dip and using a mean water sound speed
equal to the sounding speed V , Equation (8) can be rewritten as

T2 = ~~ — (X2 + 4H2 + 4HXsin9) , (9)

and Equation (1) becomes

*o= f- ■ <10>

Since the direct travel times are a function of the hori-

zontal sound speed V , Equation (5) becomes

D= -f-. (11)

h

Substituting Equation (10) and (11) into Equation (9) and

rearranging terms , an equation relating the reflected travel time to the

direct travel time is

T2=T2 + (— 71— )2D2+2T (-r— )Dsin9. (12)

o V, o V

If V is replaced by the mean vertical sound speed of the material con-
tained between any two reflectors, called the interval sound speed

V. , , Equation (12) will relate the reflected travel time within the
l+l

layer to the direct travel time at the surface corresponding to the

21

reflected time. The subscript i+1 indicates the sound speed for the
i-th sub-bottom layer. The wide-angle reflection records, however,
relate total reflected travel time to total direct travel time.

The technique used to solve for the interval sound speed
involved reducing the travel times for effects of the upper layers in
order that the reduced values have the form of Equation (12) . An
iterative method is then used to reduce the effect of dip by eliminating
the curvature term /S of Equation (12); i.e. ,

V

0 = 2T (-TT— ) sin 0. (13)

o Wl

Finally, a least-squares line is fitted to the reduced

2 2 2
(T - T )/D data and the coefficient
o

V

i+1

is determined. From this, the interval sound speed is readily
determined.

a . First Layer

The water between the surface of the ocean and the
sea floor is considered here to be the first layer. It is assumed that
the dip of the sea floor 9 is known and the sounding speed V, can be
determined with good accuracy.

Knowing V and 9 and knowing the reflected travel
times as a function of the direct travel times from the T/X data, the

22

solution of the first layer involves computing the thickness of the water

layer H and the horizontal sound speed at the surface V .
1 h

If data are obtained close to T , a fourth-order

o

least-squares polynomial is fitted to the T/X data,

2 3 4

T = a +a,D + a0D + a„D +a„D , (14)

o 1 2 3 4

where the a's are coefficients of the polynomial. At reflected travel

time, T , the direct travel time D is zero; the reflected travel time,
o

also being the minimum travel time for the reflected wave, is equal

to the coefficient a ; i.e.,

o

T =a . (15)

o o

The fourth-order curve is then extrapolated, obtaining the minimum

reflection time T .
o

Care must be used with this method because the
least-squares fitting technique does not constrain the fourth-order

curve beyond the limits of the data . A more reliable but less accurate

2 2
method is to fit the T /X data to a linear least-squares line of the form

T2 =b + b0D2. (16)

o 2

2

Again it can be shown that the coefficient b is equal to T . Thus,

o o

T is obtained by extrapolating a straight line instead of a curve as

was done in the case of the fourth-order polynomial.

23

The computer program used to reduce the T/X data

decides which of the above two methods will be employed to solve for

T . Three-tenths of a second direct travel time was considered the
o

maximum allowable distance from which the curve could be extrapolated
using the fourth-order polynomial.

Having computed T and knowing V , the depth of the
layer H, is computed using Equation (1) .

The curvature term in Equation (12) is small compared

to the other two terms and, therefore, little error is introduced by

assuming V, /V, equal to unity. This assumption is used to define a
h 1

correction term to be applied to Equation (12); i.e.,

* = T 2 + 2T (1) sin 9 (17)

o o

The reduced travel times T are then computed for each data point using

r

the relation

T 2 =T2 - * . (18)

r

Combining Equations (12) and (18), the expression for T becomes

V
Tr2= (-^L~ )2D2, (19)

24

where T is a reduced travel time with the effects of both the dip and T
r o

eliminated. The horizontal water sound speed V is then found by fitting

2 2

T and D to a least-squares first-order line of the form
r

Tr2=ClD2, (20)

and solving for the coefficient c, . Knowing V, , Equation (19) can be

solved for V, ; i.e . ,
h

VMci • «21>

The separation X is then computed using Equation (5),

X = DVL (2 2)

h

b. Second Layer

The second layer is, in fact, the first layer of sedi-
ments for which an interval sound speed is desired. The record of
reflected travel times from the lower interface of the second layer T
forms a hyperbola similar to that of the first layer. In the first layer
the interval sound speed V was known and the separation X was com-
puted for each point. In the second layer, the interval sound speed V
is unknown, but the reduced direct travel time can be deduced by reducing
the effects of the first layer on the travel times of the second layer.

25

The thickness of the second layer H9 is computed

using assumed values for the interval sound speed V_ and dip 9 of

a a

the layer. These values are referred to as the trial solution for the
second layer. The trial solution is based on the apparent dips read on
the normal reflection profiles, converted to true dips using trial sound
speeds. The exact value of these trial sound speeds are not critical,
so long as they are consistent with the dips entered.

In Figure 4, an assumed ray path is drawn as the

dashed line SBC. This ray is perpendicular to the second reflector; i.e.,
to the lower interface of the second layer. From Snell's Law

sin J2f - (— sin &2) . (23)

The distance the ray travels in the first layer SB is

therefore

- Hl

SB= ~—7 , (24)

cos J3

and the time T in the first layer

Tl= -f- , (25,

where V and H are both known

26

Figure 4. T reflection from the second layer
o J

27

To obtain the reduced minimum travel time T for the

°2

r

second layer alone, the minimum measured time to the second reflector

T (obtained fitting the data to a least-squares polynomial) must be

°2
reduced by the time the sound traveled in the first layer T ,

T = T - T. . (26)

°2 °2 l

r

The length BC is obtained using the trial sound speed

V2 '

a

BC = V0 T . (2 7)

2 o
a 2
r

The length AB is the distance the direct ray will travel
corresponding to the distance SB the reflected ray travels in the first
layer. AB is computed from the expression

AB - H tan#, (2 8)

and the depth of the second layer H below the shot point S at reflected

travel time T is
o

H = BC + AB sin 9 . (29)

H is a first approximation for the thickness of the second layer,

28

Since V was computed for the first layer, Equation (14)

can be written as

T = dQ + d1 X + d2 X2 + d3 X3 + d4 X4 , (30)

where

and

X = DVU ,
h

a.

1
d.

1 Vh

Differentiating with respect to X, the horizontal
separation, Equation (30) becomes

dT 2 3

^ = dx + 2d2X + 3dgX + 4d4X° . (31)

It can be shown (Clay and Rona, 1965) that the angle of emergence
at the sea surface 0+9, is related to the derivative by

sin (0 + 9 )

iLL _ i (32)

dX V * { }

The data from the T/X graph is fitted to a fourth-order
least-square polynomial and the coefficients of Equation (30) determined

29

The angle (j2f+9) is computed for each data point by combining Equations
(31) and (32) to give

sin Oaf + 9 ) = V1 (d + 2d2X + 3d3X2 + 4d4X3) . (33)

Knowing the dip of the first layer 9 , 0 is easily obtained.

From 0 , and using the sounding speed V , the travel
time of the second reflected ray within the first layer is computed. This

is then subtracted from the total reflection time to obtain the reduced

i
reflected travel time T , the time the reflected sound from the second

r
reflector travels within the second layer. Similarly, a reduced direct

travel time D is obtained and from Equation (5) , the reduced separation
r

X . Thus, the effects of the first layer are eliminated for each point and
the problem reduced to a single layer case.

The effect of dip is removed in a way similar to that
used for the first layer. Equation (17) becomes

2 Xr

*=r + 2T (— - ) sin 90 , (34)

°2 °2 V2 2a

r r a

where

X = VUD , . (35)

r h r

and the subscript 'a' indicates the assumed values of the trial solution
of V and 9 . The reduced times corresponding to the flat layer case T„

30

are obtained from

T2 = T2 - * . (36)

r r

The reduced values are then used to compute the co-
efficients of a straight line equation of the form

T2 = k + k X2 , (37)

2 o 1 r

r

where k should be zero because ty in Equation (36) eliminates T

°2

, r

and

k, = —7— , (38)

V2

and V can be readily computed. The dip 9 is then corrected by

Li L*

a

V2
tan 02 = — tan 92 . (39)

2 a

The solutions for V and 9 then replace the original
trial solutions and the process is iterated a second time. A final
solution is obtained for V , 9? , and H„ and the computations move on
to the next layer.

Thus, in the first layer, knowing the sounding speed
V and the dip 9 , and having the record of reflected travel times T
verses direct travel times D , the value of the water depth H and

31

horizontal sound speed V were computed. In the second layer, the
problem was reduced to finding the interval sound speed V and the
thickness H by eliminating the effects of the first layer and then re-
ducing the effect of dip using a trial solution. In each successive layer,
the problem is first reduced to a single layer case by eliminating the
effects of all upper layers using the computed values of thicknesses
and interval sound speeds of those layers, and then the effect of dip is
subtracted using an iterative process and a trial solution.

This method is both fast and accurate. The time to
reduce the data from a typical station is usually less than 20 seconds
on the IBM 360/67 digital computer and the theoretical accuracy obtained
is better than 1 part in 10,000 if the proper dips are entered (Le Pichon,
Ewing , and Houtz , 1968). The primary advantage of this method is that
there is no requirement that the layers be parallel, but rather, they may
be dipping with respect to one another.

C. THE COMPUTER PROGRAM

The HONDO I program used to reduce the wide-angle reflections
is listed in Appendix C. It was adapted from a similar program used at-
Lamont-Doherty Geological Observatory (LGO) of Columbia University
(Houtz, personal communication) and follows the mathematical technique
just presented of solving for thickness and interval sound speed of
successive sub-bottom layers. Certain modifications were necessary
to make the program compatible with the wide-angle reflection system

32

developed and for use in conjunction with the IBM 360/67 digital
computer at the Naval Postgraduate School (NPS) using FORTRAN IV
language. A thorough description of the routine followed by the program
is presented in Appendix B.

Sample data were included with the LGO program and modified
accordingly (Appendix D) to be used with the HONDO I program. The
corresponding results (Appendix E) were compared with those obtained
using the IBM 1130 digital computer at LGO and the original form of the
program, SLOW I. No significant difference was observed between the
two solutions. The results from both programs are given in Table I.

1 . Data Reduction

Instructions for entering the data on IBM cards are included
on the first page of the HONDO I program list. A more delicate part of
the data reduction consists of selecting and tracing the major reflectors
from the precision seismic graphic record made during the field profiling.
Here special care must be taken to avoid multiples that can occur and to
use only those traces representing the events from true lithological re-
flectors . The difference between true reflectors and multiples is shown
in Figure 5. It was assumed that the interval sound speed increased
with depth. The apparent reflection times from multiples at a given
separation are greater than those of the corresponding true reflector
because the multiple travels longer in the lower speed layer than the
true reflector. Note also, the T/X trace of the multiple is nearly parallel

to the true reflection from the same reflector. Results that are not

33

Table I

Comparison of Solutions of SLOW I
and HONDO I Computer Programs

SLOW I HONDO I

Layer (LGO) (NPS)

FIRST LAYER:

Reflection Time 5.216 5.216

(seconds)
Sound Speed 1.490 1.490

(km/sec)
Propagated Error +.0023 +.0023

(km/sec)
Depth 3885.9 3885.9

(meters)

SECOND LAYER:

Reflection Time

5.805

5.805

(seconds)

Sound Speed

1.797

1.7861

(km/sec)

Propagated Error

+.0608

+.0597

(km/sec)

Thickness

529.22

526.28

(meters)

THIRD LAYER:

Reflection Time

6.250

6.250

(seconds)

Sound Speed

1.770

1.7875

(km/sec)

Propagated Error

+.0951

+.0952

(km/sec)

Thickness

379.83

398.16

(meters)

34

x ^I'c,^

UJ

UJ

>

<

SURFACE

T

SEPARATION X

»\?rr \\ " \ /',

REFLECTOR

B

REFLECTOR

REFLECTED
MULTIPLE

RAYS

REFLECTOR

Figure 5. Multiple reflections

35

consistent with the local geology present another indication that multiples
were present and traced. After the true reflectors are determined, the
wide-angle reflection record is digitized in accordance with the pro-
cedure outlined in Appendix A.
2 . Trial Solutions

As discussed previously, the trial solutions are obtained
from normal profiling records. The trial values of interval sound speed
and dip for each successive layer are entered on IBM cards in accordance
with the instructions listed in Appendix C. If the interfaces are hori-
zontal, there are no corrections for dip in the computations and the values
for interval sound speed are unimportant. If the interfaces are not hori-
zontal, inaccurate estimates of the sound speeds lead to only small
errors in the first iteration and become negligible by the second iteration.
However, dips entered which are inconsistent with the trial interval sound
speeds may result in large errors. The error caused by entering such
inconsistent values was investigated and the results given in Table II.
The true solutions were those values computed using the data as given
in Appendix D. The values computed in Case A were obtained assuming
a trial sound speed 0.1 km/sec greater than the given data for both the
second and third layers. For Case B, the trial sound speeds were un-
changed, but the dips of the second and third layers were entered as
+ 1.0°. It can be seen from Table II that the error introduced by incorrect
sound speeds is small, but entering dips inconsistent with the trial sound

36

speeds causes significant error. Furthermore, the computer program
will not detect such errors but will compute values consistent with the
dips entered.

Table II

Comparison of Results of
Various Trial Solutions

Computer Sound Speed (km/sec) Propagated Error (+km/sec)
Second layer Third layer Second layer Third layer

True Solution:

1.7861

1.7875

0.06

0.10

Case A:

1.7861

1.7875

0.06

0.10

Case B:

1.5756

1.3724

0.07

0.08

The total time to compute the results (Appendix E) from the sample
data (Appendix D) was 16.36 seconds on the IBM 360/67 digital computer.
The accuracy of the results is considered to be better than 1 part in 10,000
if the correct dips are entered. The propagated error gives no indication
that the correct dips were entered or that the computed values represent
the true interval sound speed. Only by subjectively analyzing the results
can gross errors be realized.

37

IV. INSTRUMENTATION

A. THE WIDE-ANGLE REFLECTION SYSTEM

The system for recording wide-angle reflection data is shown
schematically in Figure 6. The profile recorder, timer switch, sound
source, amplifiers and filters are those components normally carried
on board oceanographic survey vessels for collecting normal-reflection
seismic profiles. For collecting wide-angle seismic reflections, a
sonobuoy system was developed to be used in conjunction with the on-
board components. The sonobuoy system included a radio sonobuoy, an
antenna, and a radio receiver. The system was developed with emphasis
on simplicity and low cost; however, the two were not always synonymous

1 . The Sonobuoy

The sonobuoy, launched while the ship was underway, per-
formed as a self-contained station for detecting the sound pulses reaching
that point in the ocean by various paths as shown in Figure 1. The
pressure pulses were received by the hydrophone suspended below the
sonobuoy by a thin wire. The pulses were converted to electrical signals
and transmitted to the ship by the VHF radio transmitter contained in the
watertight compartment of the sonobuoy. The sonobuoy transmitted on a
pre-set frequency indicated by the channel number painted on the case.
Table III lists the 31 sonobuoy channels available and the corresponding
frequencies. The transmitter and acoustical amplifiers are powered by
the sea-water-activated batteries located in the base of the housing

38

Figure 6. System for collecting wide-angle reflections

39

and become active within seconds after the sonobuoy contacts the water
The sonobuoys used were of the AN/SSQ-23A, AN/SSQ-41, and
AN/SSQ-57 types. Figure 7 is a drawing of an AN/SSQ-57 sonobuoy
as it would appear in the water showing the antenna and hydrophone
package. The characteristics of the various types of sonobuoys used
are listed in Table IV.

Table III

Sonobuoy Frequencies

Channel Frequency Channel Frequency
MHz MHz

1

162.25

17

162.625

2

163.00

18

163.375

3

163.75

19

164.125

4

164.50

20

164.875

5

165.25

21

165.625

6

166.00

22

166.375

7

166.75

23

167.125

8

167.50

24

167.875

9

168.25

25

168.625

10

169.00

26*

169.375

11

169.75

27*

170.125

12*

170.50

28*

170.875

13

171.25

29

171.625

14

172.00

30*

172.375

15

172.75

31*

173.125

16*

173.50

* crystals available for radio receiver

40

transmitting
antenna

timer
switch"

21

rubber cord and
transmission wire

(28.9m)

water line

dampener —

preamplif ie r
hydrophone

lead shot

and dye

support
y net

SCALE 1 '• 10

Figure 7. AN/SSQ-57 Sonobuoy
41

Table IV

Weight,
Kg

Channels

Time Selection,
Hours

Depth of Hydrophone,
Meters

Transmitter Power,
Watts

Sonobuoy Characteristics
AN/SSQ-23A
8.11

1 - 16

18.2

1/2

^N/SSQ-

-41

AN/SSQ-57

9.02

9.02

1 - 31

1 - 31

1 or 3

1 or 8

8.2 or i

30.1

28.9

Each sonobuoy has a water-soluble scuttling plug located
above the center of the housing. When the plug dissolves, water enters
the watertight compartment and the buoy sinks. The floating period of
the sonobuoy is a function of water temperature, with the plug dissolving
more rapidly in warmer water. In no case, however, is the floating
period less than 8 hr nor more than 20 hr in the case of the AN/SSQ-5 7
type (Naval Air Systems Command, 1967).

The plug was sealed with waterproof tape when a study was
conducted investigating modifications to be made to the sonobuoy for
recovering and re-using it on subsequent stations. The study revealed,
however, that the rubber gaskets used to seal the water tight compartment
were not intended for long use and that small amounts of sea water entered

42

the compartment after only 3 or 4 hr of immersion. This was learned after
a considerable amount of sea water was found inside one particular
sonobuoy after it was in the water for about 12 hr. On another occasion,
a sonobuoy operated successfully for 3 hr in the water before it was
recovered. The salt water batteries were removed immediately to prevent
any electrolysis or heating damage and the buoy was washed in a mild
solution of soap and water. Later, however, it was found to be inoperable
due to corrosion of the electronic components inside the watertight case.
In each case, the scuttling plugs were sealed. Considering this, and
also considering the problem of trying to recover 18 to 90 m of hydrophone
wire, which had a strong tendency to kink, it was decided that the cost
of using one sonobuoy per station was far less than the complications
which would incur and the time involved to recover and re-use a sonobuoy.

The sonobuoys were launched by hand from the fantail of a
ship. A screwdriver was used to bend the ends of the retaining ring on
the bottom of the sonobuoy and release the bottom plate (Fig. 8). In
some cases, the small screw used to secure the ring was removed and
the entire retaining ring removed. Once the ring was removed, the
bottom plate and hydrophone package were free to drop out of the sonobuoy,
but were held in place until the sonobuoy was launched. The bottom
plate serves as a weight to pull an aluminum protective housing away
from the hydrophone package once the sonobuoy is in the water. For this
reason, the clips (Fig. 9), which secure the plate to the housing, are not

removed .

43

Figure 8. Releasing the bottom plate of the
AN/SSQ-5 7 sonobuoy

44

i ; :

;jJBBB^^55?5S~5i-^

I 70.5

**v

1

1

Figure 9. Bottom plate retaining clips

45

The next step was to release a second retainer ring
located around and near the top of the sonobuoy. Considerable caution
was warranted here as this ring allowed the rotochute assembly to fall
free and pull a small white lanyard releasing the spring-loaded transmitting
antenna. The antenna erects with sufficient force to cause injury. Once
it was safe to do so, the retaining ring was released by lifting a small
U-shaped pin (Fig. 10) and the rotochute assembly gently removed. A
slight tug given on the lanyard tripped the antenna retainer clip allowing
the antenna to extend to its full operating position shown in Figure 7.
The sonobuoy was then ready to be launched.
2 . Receiver System

A radio receiver and antenna system was used to receive
and amplify the VHF signals transmitted by the sonobuoy. The radio
used for this was a Japanese-made Realistic Patrolman pro-2 solid state
VHF receiver. The decision to use this radio was based mainly on its
availability at the time the study was started and the fact that its frequency
band covered that of the entire sonobuoy range. Also of importance/ and
in keeping with the idea of simplicity and economy, the pro-2 was small,
easy to carry, simple to operate, and relatively inexpensive ($99.00).
The pro-2 radio receiver is a self-contained unit operated
on normal 110-V AC. An internal speaker was used to monitor the signals.
The signal was tuned by manual control for maximum volume. Crystal
operation was available, but did not appear to increase the quality of
the signal. The crystal did, however, provide a means for tuning the

46

Figure 10. Removing the rotochute assembly

47

receiver without a signal present. With the proper crystal in place, the
radio was simply tuned for maximum background noise. Crystals for the
seven sonobuoy channels indicated in Table III were purchased from
Radio Shack Warehouse, 2 615 West 7th Street, Fort Worth, Texas.

The pro-2 receiver had two locations where the signal was
available for recording. The signal taken from the speaker jack on the
front panel of the cabinet was found generally to be highly distorted by
the audio amplifier section of the receiver. The tape-out jack on the
back of the cabinet provided a signal of rather low voltage, but when
amplified it was found to be relatively undistorted . The results were
further verified by using an oscilloscope to observe the wave form of
the signal from each jack. A pure tone was transmitted from a signal
generator and received by the radio. The signal at the tape-out jack
was clear and undistorted while that of the speaker jack was either
distorted at high volume settings or was lost in the amplifier noise at
low settings .

An 11-element Winegard Yagi antenna (Fig. 11) was used
with the pro-2 radio receiver for receiving the signal transmitted by the
sonobuoy. The Yagi was purchased when the ground plane dipole antenna
(salvaged from a used sonobuoy) failed to provide sufficient power gain
for receiving the signal from the sonobuoy except at very small separation
distances .

48

Figure 11. Yagi 11 -element antenna

49

The antenna patterns for each antenna were recorded over a
range of frequencies covering the sonobuoy range (Fig. 12) . It can be
seen from this graph that the Yagi was quite frequency-dependent and
at lower frequencies did not produce better results than were obtained
using the dipole antenna. Figure 13 shows the antenna pattern for the
Yagi at various frequencies. The dipole antenna pattern was omni-
directional over the entire sonobuoy frequency range. It was decided,
therefore, that only higher frequency sonobuoys would be used and
special attention would be given to insure that the Yagi antenna was
pointed in the direction of the sonobuoy.

A 300/50-ohm impedance matching transformer was attached
at the antenna to couple the 300-ohm antenna to the 50-ohm shielded
cable. All external connections were covered with alternate layers of
tape and electrical coating to prevent salt spray from damaging the system
A stainless steel pipe, 7-m long and 3.75 cm in diameter, was used for
an antenna support.

The entire wide-angle reflection system weighed less than
10 kg per sonobuoy and was quite transportable; the whole system can
be carried in the backseat of an automobile. It took only a few minutes
to set up the equipment aboard ship. The system was simple to use,
requiring little more than to launch a sonobuoy and to tune the receiver.

50

XI

X>

>

<

<

o

LlI

o

Q_

-\^ilP_vvitiL Gf?QiJtlD_EL^NiL

/

160

170

180

FREQUENCY (MHz)

Figure 12. Power gain vs. frequency curve

51

175 MHz

170 MHz

5_

165 MHz

160 MHz

Figure 13. Antenna patterns for Yagi antenna at

various frequencies (relative to 175 MHz)

52

V. CONCLUSIONS

It was found from this study that the Realistic pro-2 radio receiver,
when used with a Winegard Yagi antenna, could adequately receive the
VHF signal transmitted by a radio sonobuoy and at sufficient distance to
conduct wide-angle seismic reflection profiling. It was further found
that the signal received with this system was distorted by the audio
amplifier section of the radio. An undistorted signal was available at the
tape-out connection on the back panel of the pro-2 receiver cabinet, by-
passing the audio amplifier section.

It was concluded after becoming familiar with three types of radio
sonobuoys that, when used normally, they were quite simple to operate;
but any modifications that were possible required a considerable amount
of preparation in order to use the sonobuoy for more than one station.

Magnetic tape recordings have been made of the signal received
using the sonobuoy system and the sample set of data from LGO demon-
strated that the HONDO I computer program adapted for use with the
system was able to reduce wide-angle reflections and obtain the interval
sound speeds and corresponding thicknesses of sub-bottom layers.

It is concluded, therefore, that the system developed can be used
to collect wide-angle seismic reflection data and that the HONDO I
program can be used to reduce the data.

53

APPENDIX A
DIGITIZING THE WIDE-ANGLE REFLECTION RECORD

If T is marked on the record (the instant when the sonobuoy and
o

sound source are together), this point becomes the origin. Otherwise,
the direct travel time line, called the direct line, is extended to intercept
the X-axis, thus defining the origin. A plastic overlay is placed over
the record so as to include the origin and all direct and reflected traces
within the millimeter-size grid etched on it.

Figure 14 shows a sample record with a direct line and one reflected
trace. The origin of the grid does not coincide with the origin of the
record, but rather the entire data is included under the grid. Below the
record are sample values read from the record, including the two points
A and B used to set the time scale. Points A and B are selected anywhere
along the T-coordinate and are a measure of the distance in millimeters
from the origin of the grid in the T-direction only. The time DDD rep-
resents the known time interval between the two points.

The values from the direct line are recorded in eight-digit integer

form. For example, a point located at 12 7.9 mm from the grid origin on

the X-scale and 148.9 mm on the T-scale is recorded as 12791489. The

X-scale is the vertical scale and represents the first four digits, while

the T-scale is horizontal and represents the last four. From two to six

points can be used to represent the direct line. The reflection traces

are digitized similarly, except that as many as 90 points can be used.

The program can handle up to 10 reflecting horizons.

54

UK) e^-r-r-r

E
E

x

<

<
a:
<

UJ

130

120

110

100

7-r l-=r 1^M=

3

! I ' =

1

==r=~.Y£*£;

- — — *&M

35^- — — -

• ^.p -^

^~si

100

i . i ■ L_L

|_i_J_ . .

DDD

— f -H-

-

B

rri:

4-4-

i in

j_^j_

_j_i.

■f-f+-1

M-

m

110 120 130

TIME-AXIS (mm)

140

150

Direct line:
Reflected line:

Point A:
Point B:
DDD:

11101049 12791489 12931056 13781248

11041373 11291382 11531395 11811414 12801438
12281458 12501480 12611493 12811060 13001095
13111120

110.0

140.0

3 seconds

Figure 14. Digitizing the data

55

At times, the sound pulse is detected at the sonobuoy after the
recorder completes a cycle. This occurs when the separation between
the sonobuoy and the sound source becomes large enough so that the
travel time for a particular sound wave is greater than the sweep rate
of the recorder. An example of this is shown in Figure 14 where the
trace goes off the bottom of the record and continues on the top during
the next cycle. In this case, the shift is taken care of v/ithin the
program .

56

APPENDIX B
ROUTINE FOLLOWED BY HONDO I COMPUTER PROGRAM

The computations begin in the MAIN routine by reading from the
first card in the data deck the station identification, ADEN1 and ADEN2 ,
and the number of layers or reflections observed, NREF, for the particular
station. Subroutine TRIALS is then called to enter the valves for the trial
solutions which include trial sound speeds V from the second card in the
data deck and the trial dips W from the third card. Only NREF values are
taken from each card and blank spaces are read as zero. As an example,
for the sample station DIANNE (Appendix D) , the card representing the
trial dips is blank; therefore, the trial dip for each of the three layers
is zero. The technique of reading zeros from blank cards is used through-
out the program to control the exits from particular subroutines. For this
reason, it is extremely important that a blank card follow the cards con-
taining the digitized data pairs for the direct trace and for each reflected
trace, and that an additional blank card follow the data from the last
layer of the last station investigated. This additional blank card causes
the program to exit the computer and completes the job. The blank card
after each set of data points tells the computer that there are no more
points for that particular trace.

The fourth card in the data deck is also read by TRIALS. The card
contains the value of the computed sounding speed W for the water layer.
This value will replace the value read in as a trial speed for this layer.

57

Thus, the first number in the array labeled V is the actual value used for
the sounding speed VV of the first, or water, layer. Also, the dip read
for the first layer is not, in fact, a trial dip; but rather it represents the
actual value determined for the sea floor. For this reason, the values
entered for the first layer of sounding speed W and dip W must be those
values computed from observations made at the time the data were col-
lected.

Values for V and W are transferred back to MAIN through COMMON.

The program is returned to MAIN and the main loop for NREF layers
begins by setting the integer L equal to 1 for the first layer. MAIN then
calls both subroutines READS and INTERP in succession.

For the first layer, READS enters the values from the fifth data card
representing the constants which appear in Figure 14. They include two
arbitrary points on the time scale A and B, the time in seconds represented
by the distance between them (DDD) , the seconds required for each sweep
of the recorder (SPS) , and finally, DELAY, which is a provision to include
any time delay which might occur between the shot and the start of the
recorder sweep. READS uses A, B, and DDD to scale the time axis in
seconds. SPS is used to add the appropriate number of seconds to each
point of the trace if the trace is continued at the top of the record during
a scale shift.

Once the time axis is scaled, READS then enters the digitized data
points from the direct travel time trace. These points are converted to DX
in millimeters and DY in seconds from the origin.

58

Next, READS enters the digitized points from the first reflected
time trace and converts these points to RX and RY (in millimeters and
seconds, respectively, from the origin).

Subroutine COUNT is called from subroutine READS to count the
number of non-zero data points found on each card. The total number of
points for any reflected time trace is summed on II and carried via
COMMON to other locations in the program. ND is the number of points
used to compute the direct time line.

All values entered in READS are transferred to MAIN and then to
INTERP through COMMON.

INTERP interprets RX in millimeters for DD in seconds of direct
travel time corresponding to each reflected travel time RY. This is
accomplished by computing the slope of the direct time line, DELXY,
and multiplying it by the millimeters of separation between RX and the
origin DX1 as shown in Figure 15. RX is then reset equal to DD at each
point on the reflected trace. Thus, RX becomes the travel time corresponding
to each reflected travel time RY. RX and RY are transferred to MAIN
through COMMON as U and S respectively. In MAIN, the direct travel
time corresponding to the first reflection time recorded is compared with
the minimum allowable separation for considering a fourth-order polynomial
fit to the data, DMIN . DM1N is equal to 0 . 3 sec. If the direct time is
less than DMIN, subroutine LSFIT is called and the data are used to
compute a fourth-order polynomial using a least-squares technique. If
the data are not obtained at or near vertical incidence and the minimum

59

T

= DELXY

DD = DY1 + (RX - DX1)* DELXY

Figure 15. Relating direct travel time to

corresponding reflected travel time

60

reflection time is greater than DMIN, the data are squared and a linear
least-square polynomial is computed in subroutine LSFIT. In either case,
the data are extrapolated to T using the resulting polynomial equation,,
the minimum reflection time is obtained, and the depth is computed using
the sounding speed.

Subroutine LSFIT also computes the theoretical reflection time

corresponding to the measured direct time by solving for the equation of

2 2
a line fitted to the T A data-.

Back in the MAIN routine, the corrective term CON to be applied
to the travel time is computed and subtracted from the total time for
each point. Thus, the reduced times R and D are squared and LSFIT is
called to fit the values to a linear least-squares line and compute the
horizontal sound speed from the coefficient X(2) .

This completes the computations for the first layer, having obtained
the depth and horizontal sound speed. These results are printed and the
program returns setting L equal to 2 .

In successive layers, the program begins by calling the subroutine
READS. The digitized data for the particular layer is read and converted
to millimeters of separation and seconds of travel time from the origin.
Subroutine INTERP is called, interpreting millimeters of separation for
seconds of direct travel time as was done in the case of the first layer.
Now, however, the horizontal sound speed is known and the separation
can be converted to distance in kilometers by an equation equivalent to

61

Equation (5). The values of reflected times and corresponding values of
horizontal separation are returned to MAIN through COMMON as S and U
respectively.

In MAIN, the horizontal separation for the first point is compared
with the minimum allowable separation for considering a fourth-order
polynomial, DMIN. In this case, DMIN is 0.45 km, obtained from the
product of an assumed horizontal sound speed of 1 . 5 km/sec and a
minimum allowable separation. time of 0.3 sec. If the first point is less
than DMIN, the data are used in the subroutine LSFIT to compute the co-
efficients of a fourth-order least-squares polynomial. If the first point
is greater than DMIN, the values are squared and used to compute a
linear lease-squares equation, again in subroutine LSFIT. As was done
for the first layer, the data are extrapolated to obtain the minimum re-
flection time for the particular layer being considered.

The derivative of the fourth-order polynomial with respect to the
horizontal separation is used to compute the angle of emergence
ZM {0 + 9 in Fig. 4) using an equation equivalent to Equation (33). If
the minimum reflection time was previously computed using a linear fit
to the data, subroutine LSFIT is called a second time to compute the
coefficients of the fourth-order polynomial fit. ZM is a function of the
slope (dT/dX) of the fourth-order curve. The curve is not restrained
beyond the first and last points and its slope may become erratic there.
For this reason, the angle of emergence is not computed for the first
and last points .

62

Subroutine TUPPER is called and the thickness of the layer being
considered is computed using the trial solution of interval sound speed
and dip. The technique follows that given in the previous section for
the first layer, using an equation equivalent to Equation (29).

Subroutine TUPPER uses the emergence angles to compute travel
times TT in the layers above the layer for which a solution is sought.
TT is computed using the previously-solved values of interval sound
speed and dip for the upper layers. The corresponding values of hori-
zontal separation are found in a similar way. The travel times and
separations are transferred to MAIN as TR and DR respectively.

MAIN reduces the measured values of reflection time S and
horizontal separation U to obtain D, the reduced value of horizontal
separation, and R, the reduced reflected travel time. D is also adjusted
for the sum of the dips of the upper layers by dividing by C, the cosine
of the sum.

The reduced D and R corresponds to a single layer case as shown
in Figure 3 .

The travel time for each point is finally reduced to that of a flat-
layer case by subtracting equations equivalent to Equations (10) and (15)
The value R in the computer program is now the reduced time squared for
the flat-layer case. The value D is also squared and the subroutine
LSFIT is called to fit a line to the reduced values. The second coef-
ficient X(2) of the linear equation obtained from the subroutine LSFIT is
then used to compute the interval sound speed.

63

The dip of the layer W is corrected using the relation

V
tan W = - tan W ,
V a

a

where the subscript 'a' indicates the values for the assumed trial

solution.

This solution then replaces the original trial solution and the
computations go back to computing a new thickness and start the second
iteration. Upon completion of the second iteration, the solutions for
the layer are printed and the routine starts a new layer.

The results are tabulated and printed for each layer in succession.
A sample list of results for the theoretical station DIANNE are included
in Appendix E .

The first line gives the station name, layer number, and number

of points used by the programs to compute the results. The number of

points considered may be less than are digitized due to rejection of

points occurring before T or those resulting in negative reduced times.

o

The first three columns of figures below the heading represent squared
values of reduced separation and reduced reflected travel times cor-
responding to a flat-layer case. For the first layer, the square of the
separation listed under the column labeled X2 , are in seconds squared,
whereas, for each of the following layers, they are in kilometers squared

The columns labeled T2 MEASURED and T2 COMPUTED are the
reflection times squared corresponding to the separation in the first

64

column. The measured values are those values read from the reflection
curves and reduced to the flat-layer case. The computed values are
from a least-squares curve fitted to the reduced data. The fourth column
is the difference between the measured and computed values of the

reduced reflection times .

2
The variance cr of the data is computed from

<r = T^ Lj Ct - Tc ) ,

where N is the number of points, T the observed times, and T the

c

computed times. The standard deviation is the positive square root of
the variance.

If many reflection profiles were to be taken at the same location,
the variance of the interval sound speed about the mean can be calculated.
However, with only a single set of data, the variance cannot be calculated
in this way. Instead, the techniques used to compute the variance, or
propagated error, for each interval sound speed is based on the variance
of the coefficients for each point compared to those coefficients obtained
with the least-squares fit.

65

APPENDIX C. HONDO I COMPUTER PROGRAM

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

cc cc

cc cc

CC HONDO I CC

CC cc

CC PROGRAM TO SOLVE FOR THE DEPTH, DIP AND INTERVAL CC

CC SOUND SPEEDS WITHIN THE SUBSURFACE LAYERS. CC

f C <C "

CC THIS IS ACCOMPLISHED BY SOLVING THE WIDE ANGLE RE- CC

CC FLECTION PROFILE BY REDUCING EACH LAYER TO A SINGLE CC

CC FLAT LAYER CASE. CC

CC CC

CC ORIGINAL PROGRAM WAS PREPARED BY CC

CC XAVIER LE PICHON OF L AMONT-OOHERTY GEOLOGICAL OBSER-C2

CC VATORY OF COLUMBIA UNIVERSITY. THE PRESENT PROGRAM CC

CC WAS ADAPTED FOR USE ON THE IBM 360 BY S.K. EDLESON CC

CC LCDR,USM AT THE NAVAL POSTGRADUATE SCHOOL, MONTEREY, ZC

CC JULY, 1970. CC

CC CC

CC CC

CC CC

CC THE FOLLOWING INPUTS CC

CC ARE REQUIRED: | CC

CC i cc

CC CARD COLUMNS * CC

CC CC

CC cc

CC 1 1-8 STATION IDENTIFICATION CC

CC 14-15 NUMBER OF LAYERS (RIGHT ADJUSTED) CC

CC CC

CC 2 1-10, ETC TRIAL SOUND SPEEDS FOR EACH LAYER IN CC

CC KM/SEC. MORE THAN ONE CARD MAY BE CC

CC USED , BUT IN NO CASE CAN THERE BE CC

CC MORE THAN TEN LAYERS. CC

CC cc

CC 3 1-10, ETC TRIAL DIPS (DEGREES PLUS OR MINUS) CC

CC cc

CC 4 1-10 COMPUTED SOUNDING SPEED IN KM/SEC CC

CC CC

CC 5 1-6 ANY REFERENCE MARKING ON R-TIME SCALE. CC

CC (ENTERED IN MM AND TENTHS, I.E. 102. 4MM CC

CC 7-12 ANOTHER MARK ON R-TIME SCALE. CC

CC 13-18 NUMBER OF SECONDS BETWEEN ABOVE TWO CC

CC MARKINGS CC

CC 19-24 NUMBER OF SECONDS PER CYCLE CC

CC 25-30 TIME DELAY BETWEEN RECORDER AND SHOT CC

CC CC

CC 6 3-10, DIGITIZED DATA PAIRS READ OFF D-LINE. CC

CC 13-20, FIRST FOUR NUMERALS ARE MM S 1/10 *10 CC

CC 23-30, FROM X-TIMF SCALE AND SECOND FOUR THE CC

CC 33-40, SAME FROM THE R-TIME SCALE: I.E. IF A CC

CC 43-50, POINT IS (102.4, 237.1) IT IS ENTERED ACC

CC ETC. 10242371. USE AS MANY CARDS AS NEEDED. CC

CC EACH POINT MUST BE GREATER THAN 100.0 CC

CC cc

CC 7 BLANK (DON'T FORGET BLANK CARDS, THEY CC

CC ARE IMPORTANT) CC

CC CC

CC 8 1-8 STATION IDENTIFICATION CC

CC 11-15 NUMBER OF LAYER THE FOLLOWING DATA CC

CC REPRESENTS (RIGHT ADJUSTED). THIS CARD CC

CC IS REQUIRED FOR EACH LAYER CC

CC CC

CC 9 3-10, ETC DIGITIZED DATA FROM ONE LAYERS R-LINE, CC

CC ENTER SAME AS D-LINE DATA CC

CC CC

CC BLANK CARD REQUIRED BETWEEN EACH LAYER CC

CC AND TWO BLANK CARDS ARE REQUIRED AFTER CC

CC THE LAST LAYER OF THE LAST STATION. CC

CC CC
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

66

HONDO I
MAIN ROUTINE

IMPLICIT REAL*8( A-H,0-Z)

DIMENSIONTO( 10) ,HH( 10) ,V( 10) ,W( 10) , SW ( 1 0) , XXXX ( 2 5 ) ,
1CW( 10) ,TW( 10) ,D< 90), R( 90),ZM( 90 ) , P( 5,6 ) , X ( 5)
DIMENSION U( 90), S( 90 ) , DX ( 25 ) ,DY ( 25 ) , T I ( 90 ) , DDL ( 10)
COMMON TO,HH,V, W,TR,DR, SW,CW,TW,D, R, ZM , P , C , SVN, VH
COMMON X, TIT, U, S, XXXX, DY , DXO , DYO , YSCAL , SGN
COMMON M,IND,KO, IXXXX
EQUI VALENCE(WW,DMIN)
C READ IDENTIFICATION AND NUMBER LAYERS STATION

1 READ(5,110) ADEN1 ,ADEN2,NREF
110 F0RMAT(2A4,2X,I5)

IF (NREF.EQ.O) GO TO 9999
C EXIT OUT OF ROUTINE IF NREF IS ZERO. REQUIRES LAST
C CARD BE BLANK. *****nojE**** LAST TWO CARDS IN
C DATA DECK MUST BE BLANK.

10 CALL TRIALS ( KW , ADEN1 , ADEN2 , NR E F » VV , PERC E )
C MAIN DO LOOP FOR NREF LAYERS
C READ IDENTIFICATION LAYER
DO 12 L=1,NREF

401 CALL READS(L,ADENlt A0EN2tIREFTSPS)

CALL INTERP ( PERCE , ADEN1 , ADEN2 , I REF , L , SPS )
C FIT CURVE TO DATA TO OBTAIN T-ZERO AND LATER
C DIFFERENTIATE FOR ANGLE OF EMERGENCE
C IND IS AN INDEX USED IN LSFIT SUBROUTINE
C U IS NUMBER OF SECONDS OF DIRECT TRAVEL TIME CORRES-
C PONDING TO S SECONDS OF REFLECTED TRAVE TIME.

402 IF(L-l) 930,931,930

C CHECK FOR DATA TO BE FITTED TO 4TH ORDER POLY: I.E.

C DATA MUST BE COLLECTED BEFORE .45 KM OR .3 SEC SEPARAT

C ION. U(l) IS SEPARATION FOR FIRST DATA POINT.

930 DM I N = 0.45
GO TO 932

931 DMIN-0.3

932 IF (U(l).LE.DMIN) GO TO 3
923 IND=-1

DO 90 K=1,K0
C R AND D TAKE ON DIFFERENT VALUES CORRESPONDING TO
C REFLECTED AND DIRECT TRAVEL TIMES RESPECTFULLY

R(K)=S(K)**2
90 D(K)=U(K)**2

CALL LSFIT (1,L)

T0(L)=DSQRT(X(1) )

IND=1

IF(L-1)2,2,3
C IF FIRST LAYER COMPUTE THICKNESS AND VH BY T2/X2

2 C0N=2.*T0(1)*DSIN (W(l))
HH( 1 )=V( 1)*T0( 1) /2.

DO 200 1 = 1, KO
C BRING BACK TO FLAT LAYER CASE
R(I )=S( I )**2+C0N*U( I )
200 D( I )=U( I )**2
IND=1

CALL LSFIT (1,1)
VH=DSQRT( X(2) )*V(1)
GO TO 32

3 DO 92 K=1,K0
R(K)=S(K)

92 D(K)=U(K)

CALL LSFIT (4,L)
C COMPUTE COEFFICIENTS OF THE DERIVITIVE FOR OBTAINING
C THE EMERGENCE ANGLE ZM

X(2)=X(2)*V( 1)

X(3)=X(3)*2.*V( 1)

X(4)=X(4)*3.*V( 1)

67

921
920

922

30

31

C

c

c
c
c

c

c

c
c
c

3601
300

X(5)=X< 5)
CHECK = D
IF (CHECK
T0(L)=X( 1
IF (L.LT.
FIND ANGL
FIRST AND
K0=K0-1
IND=1
DO 30 1=2
ZM IS FIR
ZM( I l=X(2
ZM( I )=DAR
ZM I S NOW
D( 1 J=-1.D
TI ( 1)=0.
IND=-IND
C0N=2.*DS
IK = 0

DO 300 1=
COMPUTE T
CALL TUPP
IK = 1

REDUCE SE
NOTE THAT
D( I )=U( I )
REDUCE RE
R( I ) =S ( I )
TI ( I ) = TIT
NOTE TIT
CORRECT S
RECALL C
D( I )=D( I )
ELIMINATE
I F ( D ( I ) ) 3
REDUCE TO
R(I )=R( I )
D( I )=D( I )
CONTINUE
SOLVE FOR
KW=1 FOR
KW=2 FOR
GO TO (5,
IND=1
CALL LSFI
VV=V(L)
CHECK FOR

3101 V(L)=DSOR

C RESET ANG

TW(L)=TW(

W( L)=DATA

C COMPUTE N

CALL TUPP

C IF IND NE

IF( IND)31

32 WW=W(L)*0

WRITE (6,1

IF(L.GT.l

DOL( L) =V(

WRITE(6,1

105 FORMATt «
1T45, 'METE

GO TO 12
69 DOL(L)=V(
WRITE( 6,1

106 FORMAT? «
1T45, 'METE

104 FORMAT ( '
IV ' , • T
IV ' t ' P
1T45, 'KM/S

*4.*V( 1)
( D-DMIN

.GT.O.O) GO TO 920
)

2) GO TO 2

E OF EMERGENCE ZM FOR EACH POINT EXCEPT
LAST

tK0

ST THE SINE OF THE ANGLE

)+X(3 )*U( I )+X(4)*U( I )**2+X(5)*U( I )**3

SIN(ZM( I ) )

THE ANGLE IN RADIANS.
20

IN(W(D) /V(L)

2tK0

RAVEL TIMES IN UPPER LAYERS

ER (L»ZM( I ) tIK)

PARATION U TO SEPARATION FOR L LAYER ONLY

D IS IN KM
-DR

FLECTION TIMES S FOR TIMES ONLY WITHIN L
-TR

IS T-ZERO. REFLECTION TIME FOR LAYER L ONLY.
EPARATIONS FOR DIPS OF UPPER LAYERS:
IS THE COSINE OF THE SUM OF THE DIPS.
/C

POINTS WITH NEGATIVE REDUCED D
00,3601,3601

FLAT LAYER CASE
**2+C0N*D(I )*TI< I)-TI ( I )**2
**2

SOUND SPEED
HORIZONTAL LAYERS:
DIPPING LAYERS.
6) ,KW

T (1,L)

IMAGINARY SPEED
100,3101,3101
TU./XC2) )

LE ACCORDING TO NEW SPEED
L)*V(L) /VV
N ( T W ( L ) )

EW THICKNESS HH.
ER (L,ZM(2),0)
GATIVE RESTART PROCESS

I572957795131D02
04)V(L) ,TO(L) ,SVN,WW
) GO TO 69
L)*T0(L)*500.0

05) DOL(L)

',« DEPTH OF SEA FLOOR ' , T26 , » = « , F8 . 2 ,
RS' )

L)*(TO(L)-TO( L-l) )*500.0

06) L,DOL(L)

',' THICKNESS OF L AYER ■ , I 3 ,T26 , • = ' , Fl
RS« )

',' INTERVAL SPEED' ,T26,' = ' ,F8. 4, T45, 'KM/SEC
-ZERO REFLECTION T I ME ' ,T26 , » = » , F8 . 4, T45 , • SEC
ROPAGATED ERROR ', T26 ,' = + V + ' , T28 , '_ » , Dl 5. 7,
EC'/' ',' DIP OF LAYER' ,T26, •= ',F7.4,

.2

68

12 CONTINUE
WRITE(6,
111 FORMAT ( '
1T37TF7.3
GO TO 1
3100 WRITE(6,
3200 FORMAT ( '
9999 WRITE(6
9000 FORMAT(
STOP
END

)

11) VH

SPEED
KM/SEC

i

OF SOUND AT WATER SURFACE ='

3200)L

SPEED
9000)
1« )

NEGATIVEtREMOVE LAYER',13)

69

SUBROUTINE TRIALS

C READ TRIAL SPEEDS AND CORRESPONDING DIPS IN DEGREES:

SUBROUTINE TRIALS ( KW , ADEN 1 , ADEN2 , NREF , VV , PERCE )
IMPLICIT REAL*8( A-H,0-Z)
DI MENS I ONTO ( 10),HH(10),V(10),W(10)
COMMON TO,HH,V,W
10 READ(5T107)( V( I ) ,1=1, NREF)
READ ( 5,107) (W( I ) ,1=1, NREF)
107 FORMAT(8F10.5)
KW = 2
WT=0.
DO 6000 1=1, NREF

6000 WT=WT+DABS(W( I ) )

C SET KW = 1 IF LAYERS ARE HORIZONTAL:
C USED IN HONDO I .

IF (WT-l.D-10) 6001, 6001, 6002

6001 KW=1

6002 WRITE(6,103)ADEN1,ADEN2,NREF

103 F0RMATUH1,' STATION ' ,2A4, ■ NUMBER LAYERS ',13/

WRITE(6,600)
600 FORMAT!//' TRIAL SPEEDS AND DIPS '/)

WRITE( 6,500)
500 FORMAT( '0' ,8X, 'TRIAL' ,3X, 'TRIAL1/' ',

1T2, 'LAYER' ,3X, ' SPD. ' ,4X, 'DIP V «, ,

IT 10,' KM/ SEC, 2X, • DEGREES ■/' + ' ,
1T2,5(«'),3X,6('«),2X,7('_')/)
DO 555 1=1, NREF
555 WRITE(6,888) I,V(I),W(I)
888 FORMAT(« « , I 3 , F 1 1 . 4 , F6. 2 )
C CONVERT ANGLES TO RADIANS
DO 1300 1=1, NREF
1300 W( I )=W( I )/0. 5729577951 31 DO 2
C READ MAIN CONSTANTS
READ( 5, 105) VV, PERCE

105 F0RMAT(2F10.5)

C VV IS SOUNDING SPEED
V( 1)=VV

IF (PERCE. GT.0.1D-10) GO TO 1105
1100 PERCE =1.0
1105 WRITE(6,106) VV

106 FORMAT('0',' SONIC SOUNDING SPEED =',F6.3,' KM/SEC)
RETURN

END

70

SUBROUTINE READS

C THIS SUBROUTINE READS DIGITIZED TABLE OUTPUT OF

C D-LINE AND R-CURVES. CONVERTS RY AND DY TO SECONDS

C RX AND RY ARF TRANSMITTED TO HONDO I BY COMMON AS

C U AND S RESPECTFULLY.

SUBROUTINE RE ADS ( L , ADEN1 , ADEN2 , I REF , SPS )

IMPLICIT REAL*8( A-H,0-Z)

DIMENSION RX( 90),RY( 90 ) , DX ( 25 ) , DY ( 25 ) , I T ( 16 )

DIMFNSIONTO( 10 ) , HH ( 10) , V( 10 ) , W ( 10) , SW( 10 ) ,
1CW<10) ,TW( 10) ,D( 90), R( 90),ZM( 90 ) , P ( 5 , 6 ) , X ( 5 )

COMMON TO,HH,V,W,TR,DR,SW,CW,TW,D,R, ZM , P , C » SVN , VH

COMMON X,TIT,RX,RY,DX,DY,DXO,DYO,YSCAL,SGN

COMMON Mt IND,I I ,ND
C IF THE FIRST LAYER, READ IN THE D-POINTS IN ORDER TO
C SCALE THE REFLECTED TIME SCALE

IF(L-l) 1,1,3
1 11=0

READ(5,1002) A , B , DDD, SPS , DELAY

1002 F0RMAT(5F6.0)
READ(5,889) ( I T ( I ) , I = 1 , 12 )

889 FORMAT (6(2X,2I4) )
INDEX=1
IT( 13)=0
0X0= IT(l)
C COMPUTE YSCAL EQUAL TO NUMBER OF SECONDS OF RECORD
C PER MILLIMETER OF MEASUREMENT OF THE REFLECTED
C TIME SCALE

YSCAL=DDD/(A-B)
DY0=IT(2)

20 CHECK = IT(3)-IT(1)

IF (CHECK. GT. 0.0) GO TO 22

21 SGN=-1.
GO TO 5

22 SGN=1.
GO TO 5

3 11=0
INDEX=2

READ (5,1003) ADEN1 , ADEN2 , I REF ,IR,DREF

1003 F0RMAT(2A4,2X,2I5,F10.3)

4 READ(5,1004) ( I T ( I ) , 1= 1 , 16 )

1004 F0RMAT(8(2X,2I4) )
IF( IT( 1) )5,6,5

5 CALL COUNT( IT, N, 3, 15, 2)

C CONVERT Y TO SECONDS AND X TO MM FROM ORIGIN
DO 204 1=1, N, 2

201 XX=IT( I )
YY=IT( 1 + 1)
11=11+1

GO TO (202,203) , INDEX

202 DX( I I )=(XX-DXO)*SGN
DY(II)=YSCAL *(DYO-YY)
ND=II

GO TO 204

203 RX( I I ) = (XX-DXO)*SGN

C CHECK FOR R BEFORE FIRST D AND ELIMINATE
IF(RXUI)) 205,206,206

205 11=11-1
GO TO 204

206 RY( I I )=YSCAL*(DYO-YY)+DREF + DELAY
5886 FORMAT( • ' ,D15.T)

204 CONTINUE
GO TO 4

C FOR THE FIRST LAYER, BOTH THE D-POINTS AND THE

C REFLECTION POINTS MUST BE READ IN. IF "INDEX" IS

71

C EQUAL TO ONEt THE D-POINTS HAVE NOT BEEN READ YET

6 GO TO (61t65)t INDEX
C ADD NUMBER OF SECOND PER SWEEP (SPS) TO
C DY IF DATA IS CONTINUED AT TOP OF RECORD

DO 64 1=2 , I I

CHECK = DY(I )-DY(I-l)+SPS/2.0

IF (CHECK. GE. 0.0) GO TO 64

DO 63 J = I T 1 1

DY(J) = DY(J) + SPS

CONTINUE

GO TO 3

RETURN

END

61

62
63
64

65

72

SUBROUTINE COUNT

COUNTS THE NUMBER OF NON-ZERO ENTRIES PER CARD:

SUBROUTINE COUNT ( K , M, I STAR , I STOP , I NT )

DIMENSION K( 1)

DO 2 I=ISTAR,ISTOP,INT

IF(K( I ) ) 2,1,2

M=I-1

GO TO 3

M=ISTOP+INT-l

RETURN

END

73

SUBROUTINE INTERP

C THIS SUBROUTINE INTERPOLATES D'S FOR R'S.

C RX-U AND RY=S TRANSMITTED TO HONDO I BY COMMON

C ADD NUMBER OF SECONDS PER SWEEP (SPS) TO

C RY IF DATA IS CONTINUED AT TOP OF DATA

C

c

C

c
c
c

7

8

9

60

50
51
52

53

54
55

101

SUBROU
IMPLIC
D I MENS

1CW( 10)
DIMENS
COMMON
COMMON
COMMON
DO 9 I
CHECK
IF (CH
DO 8 J
RY( J )
CONTIN
J=l

INTERP
DO 5 5
IF ( 1-1
IF(RX(
IF(ND
DX1=DX
DY1=DY
COMPUT
IN ORD
EACH P
J = J+l
DELXY=
DELXY
GO TO
DD

RX( I } =
RX( I )
CORRES
IF NOT
IF(L-1
RX( I ) =
CONTIN
WRITE(
FORMAT

1T38, '
RETURN
END

TINE

IT R

IONT

,TW(

ION

TO,

X,T

M, I

= 2,1

= RY

ECK.

= 1,1

= RY

UE

INTERP (PERCE,ADEN1,ADEN2,IREF,L,SPS)
EAL*8( A-HtO-Z)
0(10) ,HH( 10) ,V<10) ,W( 10) , SW(10)

PtCt
SGN

10), D( 90), R( 90),ZM( 90),P(5,6),

RX( 90),RY( 90) ,DX(25) ,DY(25)

HH,V,W,TR,DR,SW,CW,TW,D,R, ZM,

IT,RX,RY,DX,DY,DXO,DYO,YSCAL,

ND,II,ND

I

( I )-RY(I-l)+SPS/2.0

GE.O.O) QO TO 9

I

(J) + SPS

X(5)

SVN,VH

OLATE D FOR R.

1=1,11

) 50,52,50

I)-DX( J)) 53,53,51

-J) 53,53,52
( J)
( J)

E SLOPE OF D-LINE BETWEEN EACH POINT
ER TO LINEARLY INTERPOLATE BETWEEN
DINT

(DY( J)-DY1)/(DX( JJ-DX1)

IS SLOPE OF D-LINE BETWEEN J AND J+l POINTS

50

=DY1+(RX( I )-DXl)*DELXY
DD*PERCE

IS NOW THE SECONDS OF DIRECT TRAVE TIME
PONDING TO RV( I ).

THE FIRST LAYER, CONVERT D'S TO KILOMETERS
) 55,55,54
RX( I )*VH
UE

6,101)ADEN1,ADEN2,IREF,II

(■IS1 STATION ',2A4,» LAYER NUMBER', 12,
NUMBER OF RE ADI NGS • , I 3// / )

74

SUBROUTINE LSFIT

C SUBROUTINE TO FIT T/X DATA TO FOURTH-ORDER LEAST-

C SQUARE POLYNOMIAL OR FITS T2/X2 DATA TO A LINEAR LEAST

C -SQUARE LINE:

C
C

9001
6000

6001
6002
1001

9002
6003

6004
6005
1000

1010

1020

1200
1021
1210
1201
1002
1022

1006

SUBROU
IMPLIC
D I MENS
1CW(10)
DIMENS
COMMON
COMMON
COMMON
R CORR
D CORR
IN = LL
I N0= I N
NQ=INO
KN=INO
DO 100
DO 100
P(M,N)
DO 100
I F ( D ( I
IFCM+N
TX-1.
GO TO
TX = D( I
P ( M , N )
CO NT IN
P(M,NQ
DO 100
IF(D{ I
IF(M-1
TX = R( I
GO TO
TX = D( I
P(M,NQ
CONTIN
DO 101
DO 101
P ( M , N )
DO 102
DO 100
11=1+1
KK=K+1
A1=DAB
A2=DAB
IFCA1-
DO 120
AA=P(K
P(KK, I
P( I, II
IF( Al-
DO 120
P(KKTN
CONTIN
CONTIN
SOLVE
DO 100
I=NQ-K
11=1+1
X( I)=P
IF(I-I
DO 106

,VH

REFLECTED
REFLECTED

TIMES
TIMES

+ 1
+ 1
-1
0
1
= 0

1
) )

-2

60

)*

= P

UE

) =

0

) )

)6

)

60

)*

) =

UE

0

0

= P

2

2

M=l, INO
N=ltM

I=ltKO

1001 ,9001,9001

)6000, 6000, 6001

02

*(M+N-2)

(M,N)+TX

0.
1=1, KO

1000,9002,9002
003,6003,6004

05
*(M-1)*R(I )

P(M,NQ)+TX

N=1,IN0
M=1,N
( N , M )
K=1,KN
1 = 1, K

S(P( 1,1) )

S(P(KK,I) )

A2) 1020, 1021, 1021

0 IIN=I,NQ
K, UN)

1 N ) = P ( I , I I N )
N) = AA

l.D-30)1002, 1002,1210
1 NM=II,NQ

M) = P(KK,NM)-(P( I ,NM)*P(KK, I )/P(I ,1 ) )

UE

UE

MATRIX

5 K=1,IN0

( I,NQ)

NO) 1006,1050,1050

0 KX=I I ,INO

75

1060 X( I ) = X( I )-(P( I ,KX)* X(KX)J
1050 A1=DABS(P( I t I ) )

IF ( A l-l.D-30) 150 0,1500, 1005
1005 X< I )=X( Il/Pf 1*11

A=IN+1

IF( I N-D1701, 1701,4
1701 IF(IND)4 ,4 ,21
21 DD0=0.
0K = K0

IF (L.EQ.l) GO TO 69
WRITE(6,696)
696 FORMAT( '0' ,3X, 'ALL VALUES ARE REDUCED VALUES')
WRITE< 6,501)

501 FORMAT(' ' ,1 .X, 'X2' ,8X, 'T2' ,8X, 'T2« ,11X, 'DIFF
1'/' ' ,T13, 'MEASURED' ,2X, 'COMPUTED

1' /'♦'J IX, 8('_«),2(2X,8('_')), IX, 14 («_')/)
GO TO 502
69 WRITE(6,500)
500 F0RMAT(,0,,1X,»X2',8X,'T2',8X,'T2',11X,'DIFF
1'/' ' ,T13, 'MEASURED' ,2X, 'COMPUTED
l»/«+',lX,8C '),2(2X,8('_')), IX, 14 (»_')/)

502 DO 1061 K=1,E0
RR = 0.

IF(D(K) ) 9003, 9004, 9004

9003 0K=0K-1.
GO TO 1061

9004 DO 106 2 1 = 1, I NO

IF( I-l )6006, 6006, 6007

6006 TX=X( I )

GO TO 1062

6007 TX=X( I )*(D(K)**( I-l) )
1062 RR=RR+TX

DK=R(K)-RR
DD0=DD0+DK**2

WRITE (6, 1700 )D( K) ,R(K) ,RR,DK
1700 F0RMAT(3F10.6,D15.7)

1061 CONTINUE
STU=OK

C COMPUTE STANDARD DEVIATION:

C STANDARD DEVIATION IS EQUAL TO THE SQUARE ROOT OF THE

C VARIANCE.

DDO=DSQRT(DDO/(STU-A) )
WRITE(6, 1802)DDO
1802 FORMAT('0',' STANDARD DE VI ATI ON « ,T 26 , • = ' , D 1 5 . 7
1,T45, ' SEC**2« )
STD=DDO
VA=1./X(2)

WRITE(6,1900)X(2),X( 1)
1900 FORMATt' ',' SLOPE OF T2/X2 L I NE • , T26 , ' = • , F9 . 5 , '
1'/' ',' T-ZERO INTERCEPT' ,T26, ' = «,F9. 5)
C SET STD EQUAL TO VARIANCE.
STD=STD**2
D11=0.
D21=0.
DO 6 M=1,K0
IF(D(M) )6, 9010,9010
9010 D2=D(M)**2
D21=D2+D21
D11=0(M)+D11
6 CONTINUE

D211=0K*D21-D11**2
SX=STD/D211
C COMPUTE THE VARIANCE OF THE INTERVAL SOUND SPEED.
SVN=OK*SX
SVN=SVN*VA**4
SVN=DSQRT(SVN)
GO TO 4

1500 WRITE(6, 1501 ) I ,1

1501 F0RMAT(2HP(, 13, 1H, ,13, 24H)=0, PROBLEM UNDETERMINED)
4 RETURN

END

76

SUBROUTINE TUPPER

C THIS SUBROUTINE IS USED TO REDUCE THE EFFECTS OF THE

C UPPER LAYERS BY COMPUTING THE TRAVEL TIME IN THESE

C LAYERS. THE COMPUTED TIMES ARE TRANSMITTED TO HONDO I

C WHERE THEY ARE SUBTRACTED FROM THE TOTAL TIMES TO

C OBTAIN THE REDUCED TIMES.

C NOTE THAT TI IS TRANSMITTED TO HONDO I AS TIT.

SUBROUTINE TUPPER (L,ZZ,IK)

IMPLICIT REAL*8( A-H,0-Z)

DIMENSICNTO( 10),HH<10),V(10),W(10), SW(10),X(10),
1CW( 10) ,TW( 10) ,0( 90), R( 90),ZM{ 90 ) , P ( 5 t 6 ) ? XX ( 10 )

DIMENSION RX( 90),RY( 90 ) , DX ( 2 5 ) ,DY ( 25 ) , Y ( 5 )

COMMON TO,HH,V,W,TR,DR,SW,CW,TW,D,R, ZM,P,C,SVN,VH

COMMON YtTI ,RX,RY,DX,DY,DX0,DYO,YSCAL,SGN

COMMON M,IND,KO
C CHECK IF FIRST POINT

IF( IK)9990, 9990, 9991
C FIND THICKNESSES ,COMPUTE SIN COS TAN

9990 DO 1000 1=1, L
SW( I )=DSIN(W{ I ) )
CW( 1 )=DCOS(W( I ) )

1000 TW( I ) = SW( I )/CW( I )
C=l.

IF(L-1 )1003, 1003,1002

1002 L1=L-1

ww=o.

DO 1001 1=1, LI

1001 WW=WW+W( I )
C=DCOS(WW)

C FIND ANGLE OF REFRACTION IN UPPER LAYER CORRESPONDING
C TO RAY REFLECTED NORMALLY FROM LOWER INTERFACE OF
C LAYER CONSIDERED

1003 I=L
Q=W( I )

IF(L-1 ) 11,11,10

10 Q=DARSIN( ( V( I-l)/V( I ) )*OSIN(Q) )+ W(I-l)
1 = 1-1

IF( 1-1)11,11,10
C FIND ANGLE OF INCIDENCE Q AT UPPER INTERFACE OF 1-1
C LAYER.

11 Q =Q-W(I )
U=0.

TT = 0.

12 IF( I-L) 13, 14,14
C COMPUTE HH(I )

13 HC = HH( I )-U*DSIN( W( I ) )
SIX=DSIN(Q)
COX=DC0S(Q)

C COMPUTE HORIZONTAL SEPARATION FOR 1-1 LAYER(U).

U=U*CW(I) +HC*SIX/COX
C FIND ANGLE OF REFRACTION XW FOR NEXT LAYER UP FOR
C ANGLE OF INCIDENCE Q FROM LAYER BELOW

TT=TT+HC/( V( I ) -COX)

XW = DARSIN(V( I + 1J*SIX/V(D)
C FIND ANGLE XW MAKES WITH UPPER INTERFACE Q. Q BECOME
C NEW ANGLE OF INCIDENCE ON UPPER INTERFACE.

Q=XW-W( 1+1)

1=1 + 1

GO TO 12

14 HC=(TO( I) /2.-TT)*V(I )

C GET THICKNESS OF LAYER OF LAYER BEING CONSIDERED
HH( I )=HC+U*SW( I)

9991 1=0

C COMPUTE ANGLE EACH RAY LEAVES SURFACE WITH RELATIVE TO

11

c

c

924
9250

9253

9252
926
92 8

21

24

252

26

261

262
27

3
30

VERT
XX(1
1 = 1 +
IF(L
SIX =
IF(S
COMP
POIN
SIXW
XW = D
XX( I
GO T
I = L +
X(L)
1 = 1-
IF( I
X( I-
GO T
MAIN
TT = 0
U=0.
1 = 0
1=1 +
HC = H
SIX=
COX=
HK = H

u=u*

TK=H
TT = T
IF(L
I = L +

HK = H
COMP
TR = T
DR = H
TI

PP = U
1 = 1-
RR = H
COX =
HK = R
PP = P
TK=(
TT = T
IF( I
DR = D
TR = T
IF( I
TR = T
DR = P
RETU
DR=-
TR = 0
TI=0
GO T
ENO

IC
) =
1
-I

DS

IX

UT

T:

= V

AR

+ 1

0

1

= x
1

-1
1)

0

c

.0
0

1

H(

DS

DC

C*

CW

C/

T +

-I

1

K/

UT

K

K

THE LAYER FOR EACH

AL

ZZ + Wd)

) 9252T9252,9250

IN(XX( I ) )

-V( I )/V( 1+1) )9253,30,30

E THE ANGLE OF ENTRY INTO

( I+1)*SIX/V( I )

SIN(SIXW)
)=XW+W( 1 + 1 )
924

X(L)

)21,21,928

= DARSIN(DSIN(X( I )+W( I ) )*V( 1-1) /V(I ) )

926

OMPUTATION

I )-U*SW( I )
IN(X(I ) )
OS(X( I ) )
(SIX/COX)
(I) +HK
< V( I )*COX)
TK
)252,252,24

DCOS(W(L) )

E REDUCTION TO REFLECTIONS TR

AND SEPARATIONS DR

=(HC/V(L) )*2

1

H(
DC
R*
P/
RR
T +
-L
R +
R +
-1
T-
P-
RN
1.

PP*TW( I )

XX(I )-W(I ) )

N(XX( I ) )/COX

I )+HK

(I) )/(COX*V(I ))

I )-

0S(

DSI

CW(

*CW

TK

) 262,261,261

HK

TK

)2T

TR

DR*

,27,26
C

D20

0 3

APPENDIX D. SAMPLE DATA

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ID

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(OHO

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79

APPENDIX E. RESULTS

STATION DIANNE NUMBER LAYERS

TRIAL SPEEDS AND DIPS

TRIAL TRIAL
LAYER SPD. DIP
KMZSE.Q P_£G_R£E,.S

1 1.5000 0.0

2 1.6000 0.0

3 1.7000 0.0

SONIC SOUNDING SPEED = 1.490 KM/SEC

80

STATION DIANNE LAYER NUMBER 1 NUMBER OF READINGS 46

X2 T2 T2 DIFF

. M£Mli££D_ C_QMPLJI£D_

0.159342 27.293261 27.364615 -0. 71 354500-01

0.470273 27.599118 27.672436 -0. 733 1 8700-01

0.739195 27.818630 27.938668 -0.12003810 00

0.965480 28.127409 28.162689 -0. 3528046D-01

1.244668 28.415657 28.439085 -0 . 23427620-01

1.508562 28.683037 28.700339 -0 . 1 730136D-0 1

1.825360 28.951670 29.013968 -0 . 6229822D-0 1

2.024092 29.266656 29.210712 0.55944300-01

2.357128 29.515341 29.540416 -0.25075170-01

2.648469 29.856153 29.828843 0.2 7309710-01

2.956782 30.130211 30.134071 -0.3 8606780-02

3.282065 30.474544 30.456101 0.18442 590-01

3.546797 30.705186 30.718184 -0.12998660-01

3.781881 30.959897 30.950917 0.89794500-0 2

4.065679 31.285595 31.231876 0.53719080-01

4.359744 31.612999 31.523000 0.89999030-01

4.619971 31.918542 31.780623 0.13791840 00

4.978674 32.178226 32.135738 0.42488410-01

5.256501 32.462718 32.410785 0.5193 2650-01

5.638670 32.796208 32.789131 0.70762530-02

5.934096 33.131402 33.081603 0.49798690-01

6.135238 33.371869 33.280732 0. 91 13680D-01

6.600064 33.758426 33.740908 0 . 1 75 1772 D-0 1

6.919376 34.049804 34.057026 -0.72220400-02

7.246231 34.342435 34.380612 -0.38177070-01

7.524372 34.660864 34.655971 0.48933970-02

7.807751 34.956103 34.936515 0.19587900-01

8.038226 35.227839 35.164684 0. 631 542 8D-01

8.449623 35.575206 35.571966 0.32391690-02

8.689317 35.899287 35.809262 0.90024190-01

9.116848 36.224837 36.232516 -0.76792580-02

9.428513 36.551857 36.541063 0.10793660-01

9.809425 36.855026 36.918165 -0.63139040-01

10.067556 37.184872 37.173714 0.11157250-01

10.527353 37.541734 37.628912 -0.87178410-01

10.794704 37.797678 37.893588 -0. 9590993D-0 1

11.065407 38.183226 38.161583 0. 2 1 64246D-01

11.408500 38.441344 38.501244 -0.59900000-01

11.756831 38.778199 38.846091 -0.67892650-01

12.181743 39.142608 39.266752 -0.12414450 00

12.325056 39.430125 39.408632 0.21492850-01

12.614197 39.797577 39.694881 0.10269670 00

12.980338 40.113893 40.057359 0.56534470-01

13.351717 40.457981 40.425022 0.32959170-01

13.880447 40.803539 40.948463 -0.14492400 00

14.033398 41.150566 41.099885 0.50681820-01

STANDARD DEVIATION = 0 . 6389933D-01 SEC**2

SLOPE OF T2/X2 LINE = 0.99000

T-ZERO INTERCEPT = 27.20687

INTERVAL SPEED = 1.4900 KM/SEC

T-ZERO REFLECTION TIME = 5.2160 SEC

PROPAGATED ERROR = ± 0.232 87260-02 KM/SEC

DIP OF LAYER = 0.0 DEGREES

DEPTH OF SEA FLOOR = 3885.94 METERS

81

STATION DIANNE

LAYER NUMBER 2 NUMBER OF READINGS 30

X2ALL VALUES ARE REDUCED VALUES

mi ill in mm

m i;ii l | ill

8:iJSR! i:¥Ml M S: ! P'":8i
8:l!SB 8:8 SJ S:M1 ! :S: !»" 8:8i

0.226165 0.084194 o'n^inf 0-12393950-01

8:13188 8: : :f ||llg=Sl

8:ilt?io3 8:11 1! S-'fllfff 8:||^BII2g=Si

0.415052 0 u?qfin S"1?712Z "0.17595640-02

8:^?is o°: : M piinnui

Utim I giifjfg 8:gl2il§?8:8i

i.oooui 8:i§III2 8:i?^8§ :8:iai$!I8=8i

fJS^g? ?iy^V?KE : 0.82838^0-02 SEC**2

PRRv°^NsTPEliePT : • '

T-ZER0 REFLECTION TIME = S «n« KM/SEC

PROPAGATED ERROR - +5,S0|Lo/„n SEC

DIP OF LAYER I ±n 0. 59694770-01 KM/SEC

THICKNESS OF LAYER 2 Z §26.28 g|^fS

82

STATION DIANNE LAYER NUMBER 3 NUMBER OF READINGS 32

ALL VALUES ARE REDUCED VALUES
X2 T2 T2 DIFF

tt£A_S_U_R£D_ C_CjMTdlJI£D_

0.027340 0.002257 0.006382 -0 .41 25055D-02

0.025440 0.003936 0.005787 -0.18 513660-02

0.026635 0.003679 0.006161 -0 . 24820900-02

0.030224 0.006926 0.007284 -0. 35 80794D-03

0.035604 0.014095 0.008968 0 . 5 1267460-02

0.045221 0.010986 0.011978 -0. 9923697D-03

0.055817 0.015926 0.015294 0.63107240-03

0.070666 0.022306 0.C19942 0.23640830-02

0.084917 0.027209 0. C24402 0 . 28075970-02

0.099064 0.034296 0.028830 0.54662720-02

0.119355 0.036131 0.035180 0.95065110-03

0.139051 0.041973 0.041344 0. 62868050-03

0.154577 0.052730 0.046204 0 . 65267710-02

0.175825 0.055410 0.052854 0. 2556720D-02

0.194427 0.058062 0.058675 -0. 6 138641 D-03

0.217424 0.066329 0.065873 0.45612860-03

0.233800 0.066879 0.070998 -0 . 4 1 19449D-02

0.244261 0.079904 0.074272 0.56317190-02

0.255025 0.082052 0.077641 0. 44 1 1 1040-02

0.265551 0.077297 0.080935 -0.36382140-02

0.268851 0.089557 0.081968 0.75 890490-02

0.270837 0.081146 0.082590 -0 . 14438620-02

0.266871 0.074851 0.081348 - 0. 6497 523D-02

0.256989 0.072681 0.078256 -0. 5574773D-02

0.246093 0.072250 0.074845 -0.25951320-02

0.231927 0.072446 0.070412 0.20346890-02

0.214524 0.070957 0.064965 0. 5991575D-02

0.189585 0.054853 0.057160 -0 . 23070990-02

0.155604 0.039932 0.046525 -0 . 6592660D-02

0.123375 0.026457 0.036438 -0.99813210-02

STANDARD DEVIATION = 0 .4465388D-02 SEC**2

SLOPE OF T2/X2 LINE = 0.31297
T-ZERO INTERCEPT = -0.00217

INTERVAL SPEEO = 1.7875 KM/SEC

T-ZERO REFLECTION TIME = 6.2508 SEC

PROPAGATED ERROR = + 0. 95201 1 8D-01 KM/SEC
DIP OF LAYER = 0.0 OEGREES

THICKNESS OF LAYER 3 = 398.16 METERS

83

SPEED OF SOUND AT WATER SURFACE = 1.483 KM/SEC

84

LIST OF REFERENCES

1. Clay, C. S., and P. A. Rona , 1965. Studies of seismic reflections
from thin layers on the ocean bottom in the western North Atlantic.
J. Geophys. Res. 70: 855-869.

2. Dix, C. H., 1955. Seismic velocities from surface measurements.
Geophysics 20: 68-86.

3. Green, C. H., 1938. Velocity determination by means of reflection
profiles. Geophysics 3: 295-305.

4. Houtz, R. E., and J. I. Ewing , 1963. Detailed sedimentary
velocities from seismic reflection profiles in the western North
Atlantic. J. Geophys. Res. 68: 5233-5258.

5. Jakosky, J. J., 1950. Exploration Geophysics . Trija Publishing
Company, Newport Beach, California, 1195 p.

6. Knox, W., 1965. A deep-ocean sedimentary velocity function.
J. Geophys. Res. 70(8): 1999-2001.

7. Le Pichon, X., J. I. Ewing, and R. E. Houtz, 1968. Deep sea
sediment velocity determination while reflection profiling.

J. Geophys. Res. 73(8): 2597-2614.

8. Naval Air Systems Command, 1967. Handbook operating
instructions, Sonobuoy AN/SSQ-57 . NAVAIR 16-30SSQ57-1 , 7 p.

85

INITIAL DISTRIBUTION LIST

No. Copies

1 . Defense Documentation Center 2
Cameron Station

Alexandria, Virginia 22 314

2. Library, Code 0212 2
Naval Postgraduate School

Monterey, California 93940

3. Professor R. S. Andrews 5
Department of Oceanography

Naval Postgraduate School
Monterey, California 93940

4 . Department of Oceanography 3
Naval Postgraduate School

Monterey, California 93940

5. LCDR S. K. Edleson 2
USS NIAGARA FALLS (AKS-3)

FPO San Francisco 96601

86

Security Classification

DOCUMENT CONTROL DATA -R&D

/Security classification ol title, body of abstract end indexing annotation must be entered when the overall report is classified)

i Originating activity f Corporate author)

Naval Postgraduate School
Monterey, California 93940

2«. REPORT SECURITY CLASSIFICATION

UNCLASSIFIED

2b. GROUP

3 REPOR T TITLE

System to Detect and Reduce Wide-Angle Seismic Reflections at Sea

4 DESCRIPTIVE NOTES ( Type ol report and, tnclusi ve dates)

Master's Thesis; September 1970

5 AU THORISI (First name, middle initial, laal name)

Stuart Kaufmann Edleson, Jr.

6 REPOR T D A TE

September 1970

7a. TOTAL NO. OF PAGES

87

7b. NO. OF REFS

ta. CONTRACT OR GRANT NO

b. PROJEC T NO

9a. ORIGINATOR'S REPORT NUMBER(S)

Bb. OTHER REPORT NOISI (Any other numbers that may be aa signed
this report)

10 DISTRIBUTION STATEMENT

This document has been approved for public release and sale; its distribution is
unlimited.

II. SUPPLEMENTARY NOTES

12. SPONSORING MILITARY ACTIVITY

Naval Postgraduate School
Monterey, California 93940

13. ABSTRACT

A simple system was designed to collect wide-angle reflection records in order to
investigate the interval sound speeds of the sediment layers in the ocean. The
system consisted of a frequency modulated receiver, a cut-to-channel Yagi antenna,
and a sonobuoy, used in conjunction with a precision sonic profile recorder and a
triggered sound source. A computer routine for reducing the data was obtained and
modified for compatibility with the system and use on the IBM 3 60/67 computer. The
system was designed to be both inexpensive and simple to use without any loss of
accuracy .

DD ,Fr»"..1473 (PflGE"

S/N 0101 -807-681 1

Security Classification

i-31408

Security Classification

key wo r o s

Seismic wide-angle reflection technique at sea

Sonobuoy; use in conjunction with wide-angle
seismic profiling

DD ,F„r.,1473 <back

S/N 0101-807-6821

Security Classification

A- 3 1 409

Thes i s

122448

E239

Edteson

c.l

System to detect

and reduce wide-angle

seismic reflections

at sea.

Thesis 122448

E239 Edleson

c.l System to detect

and reduce wide-angle
seismic reflections
at sea.

thesE239

System to detect and reduce wide-angle s

3 2768 001 90331 3

DUDLEY KNOX LIBRARY