dudu

NAVAL Pp

r. SCHOOL \ 93343

NAVAL POSTGRADUATE SCHOOL

Monterey, California

THESIS

THE IMPLICIT FINITE-DIFFERENCE (IFD)

ACOUSTIC MODEL

IN A SHALLOW WATER ENVIRONMENT

by

Mark E. Kosnik

June 1984

J.V.

Sanders

Thesis Co-advisors : C.R.

Dun lap

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4. T\TLE (and Subtitle)

The Implicit Finite-Difference (IFD) Acoustic Model in a Shallow Water Environment

5. TYPE O? REPORT & -ERIOD COVERED

Master's Thesis

June 1984

6. PERFORMING ORG. REPORT NUMBER

7. AUTHORS

Mark E. Kosnik

8. CONTRACT 0 R GR*NT NUMBERS;

9. PERFORMING ORGANIZATION NAME AND ADDRESS

Naval Postgraduate School Monterey, California 93943

10. PROGRAM ELEMENT, PROJECT TASK AREA 4 WORK UNIT NUMBERS

II. CONTROLLING OFFICE NAME AND ADDRESS

Naval Postgraduate School Monterey, California 93943

12. REPORT DATE

June 1984

13. NUMBER OF PAGES

128

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18. SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on reverse aide It necessary and Identity by block number)

Pressure Amplitude, Trapped Normal Mode Propagation, Shallow Water Acoustics, Ocean Modeling

20. ABSTRACT 'Continue on reverse side If necessary and identity by block number)

An implicit finite-difference (IFD) computer model was developed by Jaeger to solve the parabolic equation. The model preserves continuity of pressure and the normal component of particle velocity at the ocean bottom where there is an interface between media with different sound speeds and densities. This feature was implemented to make the model more accurate

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in a shallow water environment. The IFD performance in a shallow water environment is analyzed. The IFD results are compared with those of two other models and analyzed in light of basic physical reasoning. In addition, a single sloping ocean bottom is modeled in an experimental tank so that the measured pressure field can also be compared to IFD model results.

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The Implicit Finite-Difference (IFD) Acoustic Model in a Shallow Bater Environment

ry

Mark E. JtcsniJc

lieutenant, United States Navy

E.B.A., Uiiversity Cf Notre Dame, 1973

Submitted in partial fulfillment of the requirements icr the degree cf

MASTER OF SCIENCE IN METEOROLOGY AND OCEANOGRAPHY

frcm the

NAVAI POSTGRADUATE SCHOOL June 1984

AESIBACT

Ac implicit fini t€-diif erence (IFD) computer model was developed ty Jaeger to solve the paracolic equation. Ihe model preserves contiruity cf pressure and the norial ccmio- cent cf particle velocity at the ocean bottom where there is an interlace between media with different sound speeds and densities. This feature was inplemented to make tie node! more accurate in a shallcw water environment. Ihe IFD performance in a shallcw water environment is analyzed. The IFD results are compared with these of two other models and analyzed in light of basic physical reasoning. In addition, a simple sloping ocear bottom is modeled in an experimental tank so that the treasured pressure field can alsc be compared to IFD model results-

DUDLEY KNOX 1 IBRARY

IJn&J TE SCHOOL

MONTEREY, CALIFORNIA 93943

SABLE CE CONTENTS

I. INIBCEUCIION 10

II- 1EI IJD COMPUTER MODEL 12

A. EACKGEOUNI 12

£. 1HE CCMPUIEfi MODEL 13

C- H.CDEL PECEIEMS/MCEIEICATIONS 14

E. MODEL VEEIIICATICN 18

1- Comparison with Jaeger Model Bun 18

2. Comparison with Jensen and Kuperman

Model fun 19

2. Comparison with Coppens, Humphries and

Sanders Model Run 23

4. Comparison with Physical Seasoning .... 30

5. Verification Sunmary 40

III. IAECEATOEY MEASUREMENTS 42

A. EACKGEOUNI 42

E- EXPEEIMENT5L DESIGN 42

1. Ihe Tark 42

2. Signal Genera ting/Beceiving Eguipmert . . 44 C- 2EASUEEMENI PBOCEBUBES .47

IV. MCDE1 RESULT CCMPAEISCNS HUH LAEOEAIOEY

MEASUBEMENTS 53

A. 1NTROEUCTICN 53

E- IHE GENEEAI ANALYSIS 53

C. IHE DETAIIED ANAIYSIS 64

1. CCNCIUSIONS/EICCMMENIAIICNS 75

A. CONCLUSION 75

1. Perf ojiance ox tie IED Licdei 75

2. Mcdeling/tieasureiiieiit Procedures 76

£. EEC0M8ENEA1ICNS 76

APPENEIX A; REVISEI HZ PBCGFiK LISTING 78

APPENEIX E: TI CONTCCB PLOT PECGEAfl LISTING 113

APPENEIX C; RUNNING IfiE CONTOUR PLOT ON I HE NPS

COMPUTES 115

A. INTROIUCIKN 115

E. COPYING TEE FILE fCE USE 115

C. EONNING TEE FBOGBAtf 115

APPENEIX E: SOUECE IEPTK SENSITIVITY ANALYSIS .... 117

£IBIICCB*EBS 125

INIIIM EIS1RIBUIION IISI 127

IIST CF FIGURES

2.1 Jaeger1 s Deet-to-S hallow Water Case 19

2.2 Jensen and fluperman Sloping Bottom Case .... 20

2.3 III and JKM Comparison at a Range of 2.5 Klj . . 22

2.4 III and JKM Comparison at a Range ox 5.0 Km . . 23

2.5 III and JKM Comparison at a Range of 7.5 Km „ . 24

2.6 III and JKM Comparison at a Range of 10.0 Kq . . 25

2.7 III and JKM Comparison at a Range of 12.5 Ke . . 26

2.8 10 Degree Sinple Sloping Bottom Case . . .... 29

2.9 IFE and CHS£ Comparison at the Apex 31

2.10 IFI TL Contours (dn) from the Source to 604

Meters 33

2.11 IFE TL Contours (db) fiom 600 to 1350 Meters . . 34

2.12 III TI Contours (di>) from 1350 to 2100 Meters . . 35

2.13 III TL Contours (db) from 1550 to 2300 Meters . . 36

2.14 Normal Mode fropogaticn in a Wedge Shaped

Ocean 39

3. 1 Experimental Tank Set Up 43

3.2 Electronic Equipment Schematic 46

3.3 Fulse Length Analysis at 3. OX 49

3.4 Pulse Length Analysis at 10.4X 50

3.5 Fulse Length Analysis at 10.4X 51

4.1 Comparison cf Results at 1.0X 54

4.2 Comparison cf Results at 2.1X 55

4.3 Ccnparison cf Results at 3.1X 56

4.4 Comparison cf Results at 4.2X 57

4.5 Comparison cf Results at 5.2X 53

4.6 Comparison ci Results at 6.2X 59

4.7 Ccnparison cf Results at 7.3X - . 60

4.8 Comparison ci Results at 3.3X 61

4.9 Comparison ci Results at 9.4X 62

4. 10 Comparison ci Results at 10. 4X 63

4.11 Ccuparison ci Results at 0.7X 65

4-12 Comparison cf Results at 0.8X 66

4.13 Comparison ci Results at 1.0X 67

4.14 Comparison ci Results at 1.3X 68

4.15 Comparison ci Results at 1.5X 69

4.16 Comparison ci Results at 1.7X 73

4.17 Ccuparison ci Results at 1.9X 71

4.18 Ccaparison ci Results at 2.1X 72

4.19 Ccaparison ci Results at 2.31 73

£.1 Source Sensitivity Analysis at 1.0X 119

E.2 Measurements with Scurce Deptn ox 5, 7, and

9 Cm 120

E.3 Measurements with Source Depth of 11, 13,

and 15 Cm 121

£.4 Measurements with Source Depth of 17, 19,

and 21 Cm 122

E-5 Measurements with Source Deptn of 23, 25,

and 27 Cm 123

E.6 Measurements with Source Deptn of 29 and 3 1

Cm 124

ACKBOHIEDGEHSMTS

lie author thanks ICCS James Nelson, USN, for his advice and assistance in developing irany of the graphics ^letting programs. Appreciation is also due LI Patrick LeSesne, ISCG, for his nary long hcurs sptnt assisting in the lancratcry wnile ccjipiling the experimental data. Thanks are alsc due to Prcfesscr Calvin lunlap for his review of the thesis.

lie author also expresses his appreciation to Dr. Aian E. Cc;:j:ers for his advice and clarification given tc the theoretical aspects cf the thesis. finally, the author thanks Er. Janes 1. Sanders for his time and efnent in assisting in ail aspects of research and thesis preparation, fiithcut the knowledge, patience, and advice of the Cczjens and Sanders team this thesis sculd not have been possitle.

I- M11CEUCTI0N

A variety of acoustic models exist to predict transmis- sion Jess. Each of these models contain inherent strengths and weaknesses. All have shown poor results in a shallow water environment due to difficulties at the ocean ret torn where there is an interface between media of different sound speeds aid densities.

Since its introduction (Hardin and Tappert, 1973) , the paratclic wave equation has been a widely accepted means cf soluticn for acoustic propagation. The earliest programs used a split-step Fourier transform algorithm to solve the paratclic eguation (II) . Several other solution techniques have teer developed primarily to overcome difficulties that cccur when the Fourier transform encounters an interface ietween different media (Lee and Botseas, 1982 and EcDaniel and lee, 1S62) .

In alternative solution technique that uses an implicit finite-difference (III) algorithm was developed hy lee and PapacaJcis (1979). Iris method incorporates appropriate interface conditions and allows solutions in shallow water. Starting with the IFI algorithm, Jaeger (1983) developed a computer mcdel to predict transmission loss and acoustic pressure rased en user specified bottom topograph} aid a single scund speed profile. This computer model uses the mathematical treatment of the horizontal and sloping inter- faces developed by ecEaniel and Lee (1982) and lee and McDaniel (1S83). It also utilizes several design features and aetlcds incorporated in an earlier coirputer program developed tv Lee and Eoteas (1S82), and a P£ computer iiodel developed tv 3rcck (1578).

10

Tie IJrE program preserves continuity of pressure and continuity cf the ncimal component of particle velocity at an interface .between nedia having different scund speeds and densities. This feature makes the program unconditionally stable and better able to handle the bottom boundary conditio!.

Since its development, the IFD program has cot neen rigorously tested. This thesis analyzes the program's performance in an idealized shallow water environment. The environment includes a simple sloping sand bottom beneath an isospeed water field. Ihe analysis begins by comparing the IFD's predictions vith predictions froii Jecscn and Kupernan's (1980) PI model and Coppens, Humphries and Sander's (1S84) image model. The analysis also includes a comparison of the ncdel' s estimated transmission less contours with expectations based on simple physical reasoning. Finally, the thesis describes an attempt to node! a shallow sloping bottom in an experimental tank. Tne tank contains a sand bottom sculptured with a ten degree slope, laboratory measure meets cf the pressure field are taker at a frequency cf 100 kH2 for comparison to the predicted pres- sure field generated by the IFD. These comparisons cf the 1ID predictions with ether model estimates, theory, and laboratory measurements give an indication of the IFI's performance in a shallow water environment.

11

II. IHE IFE COMPUTER MO DEI

2. E1CKG£CQND

.fir iflrlicit finite-difference solution technique tc the pararciic equation has Deen studied and refined by many authors. The history of this development is explained in detail by Jaeger (1982), hut merits review in order tc gain a perspective on an aralysis of the IFD computer model. Ihe pararciic equation is an approximation to the elliptical wave eguaticn. The first means of solving the Pit used a

split-step fast Fourier transform method as developed fcy lappert and Hardin (1973). This metnod requires periodic boundary conditions ir depth because of the finite Fourier transform and handles this constraint ty introducing an artificial horizontal pressure release bottom below the actual physical bottom. This method of inplementing an

artificial bottom was incorporated into the earliest PE models developed by Jenson and Krol (1975) and Brock (1S76).

Errors in this split-step Fourier transform method were found tc be proportional tc the horizontal range step and the second derivative of the index of refraction. Ihe second derivative of the index of refraction tends to be large across tie ocean bottom interface. Another problem with the split-step method is that it does not consider density differences between two different media at an interface, which influences the reflection coefficient. For these reascns the split-step fourier transform method proved to be poorly suited for a shallow water environment.

Ihe HE solution method was introduced by lee and Papadakis (1979) as ai alternative to the split-step methcd. Ihe IID method employs a second order central difference

/

12

formula to solve the IE in the fcrm ox a tridiagonal matrix. Although the first version or the IPD did handle discortinu- ities in the sound speed profile/ it did not consider density discontinuities. In 1962 ttcDaniel and Lee introduced a meticd to handle a horizontal interface of different densities. In 1983/ they extended their treatment to include a sloping interface. It is this version of the IFD that is used in Jaeger's computer program.

£. HI CCflfUTEE MODIX

lie III computer program consists of a main program and twenty subroutines. Ihe prcgai utilizes a moduli r construc- tion so that each of the various subroutines are called fiom the main program to complete a specific calculation or func- tion when required. Ihe IPC is run interactively fron a user generated input file tnat contains values for frequency, one sound speed profile, a bottom prciile, source/receiver depths, attenuation coefficients for tcth the water and the bottom/ and several other input parameters that tell the the program where to obtain a solution within the field. The prociam initiates the calculations assuming an initial Gaussian pressure field and an artificial pres- sure release surface at a user specified deptn.

Atteruation in roth the water and the sediient is handled as complex indices cf refraction. An artificial attenuation layer is established beneath the sediirent to introduce attenuatior above the artificial pressure release surface. Ihe actual nagnitude of this enhanced attenuation is calculated using ai eguation derived by Brock (1978) for use in his IE computer model.

Ihe 1ID program steps along the specified bottom profile and cakes calculations down through the water/sediment column at each user specified horizonal range. The program

13

requires that tie bcttcm intersect exactly at a vertical grid jfcixt. As a result, for a sloping bottom the prcgram automatically calculates the range step to fulfill this requirement . This computer generated range step is always less than cr equal tc the user provided range step. As the slope ci the bottom increases, the range step must decrease and core calculations and computer time are reguirec" to solve tie entire pressure field. In seme situations an actual medification cf the user inputted bottom is required. Inis cccurs with a very gently sloping bottom when the required range step exceeds the user specified range step. Here, the program automatically models the bcttcm as a series cf level and sloping sections in order to ensure the user generated range step is net exceeded. This modification cf the bcttcm is always less than or equal to one-half the vertical grid spacing and the model issues a warning tc the user cf the modification.

Ecth printed and graphical output are provided fcv the IJD. Ihe printed cutout provides transmission loss and the real and imaginary components cf the pressure field at each depth for a specified horizontal range. The graphical output is a jlct cf transmission loss versus range at the user specified receiver de^th.

C. ICLE1 IBOBLEflS/MCIIFICAaiCNS

As this study of the IPD program progressed, it became necessary tc modify certain aspects of the model. West of these modifications were necessary to alter the program output irtc a mere desirable form, but a few were iirpie- mented tc correct programming deficiencies. Although this section cf the thesis discusses the earliest model runs, these results are ret presented in detail, but only discussed in general terms because they were obtained before

1U

the computer model \as fully modified- All modifications here jiade only after careful analysis of multiple model runs. It is important to realize that all results generated for comparison to otter models and laboratory measurenents came ficm a fully modified version of the IFD-

Since the ultimate objective of this study was to compare IfD model results with laboratory measurement 5 the program *as first rur with input parameters which exactly modeled conditions in tne tank. The experimental set up, explained later in great detail, consisted of a tank that is approximately two meters in length, one meter in depth, with a ten decree sloping sand bottom and a maximum water deptn cf 35 centimeters (cm} . Based on a test case run bv Jaeger (1983) cf a simple sloping bcttom, and by results shewn by Jenscr and Kuperman (1980) for propagation in a wedge-shaped ocean, it was expected that there would be certain recogniz- able patterns in the predicted propagation patterns. Specifically, since tie speed cf sound in the bottom exceeds that in the water (fast bottcm) , the simple sloping bcttom supports trapped ncrmal mede propagation (Coppens and Sanders, 1981). As the acoustic energy travels upslcpe toward the apex, successively lower modes are cut cfi and the energy contained in these modes is transmitted intc the bottcm. The range from the apex at which energy cf the lowest mede is transmitted intc the bottom is referred to as the dump distance and is a function of wavelength, wedge angle, and the ratic cf sound speed in the water tc the sound speed in the sediment- An empirical equation that defines this dump distance was derived by Coppens, Sanders, Ioanncu, and Kawamura (1978); and was used to identify the expected ranges of these dump distances for the given scenario described alcve.

lie initial unmodified IFD run used the parameters taken from the tank and showed ro recognizable patterns in the

15

acoustic field. Theie was no observable decrease in trans- nissicn less at the various dump distances as expected. Bather, results indicated widely fluctuating patterns in the acoustic rield that appeared inconsistent with both previcus studies and simple physical reasoning. Upon closer analysis, it was disccvered that although tne program was designed to he independent of scale there are several logic statements that are net implemented if the user provided range step is less thai cne meter. Because the logic statements aren't satisfied, the HEHSEG and NEiiMAT subroutines (Jaeger, 19S3) are net called correctly. The NEKSEG subroutine initializes the tcttcm slope and the NEWMA1 subroutine computes matrix elements foi the program. Obviously, errors in these two program functions seriously distort results. Because of this systenatic error in the program it became necessary tc scale up all tank parameters. All distances were scaled up by a factcr of 1C00, and ireguency was scaled down by a factcr of 1000. Careful analysis reveals that all input parameters are a furcticn ex either distance cr frequency, so this scaling produces results that model these expected in the tank.

The second modification of the IED was reguircd to provide a three dimensional graphics display. As discussed earlier, the IEE picvides a transmission loss plot versus range at a single depth. Hcwever, to study the model predictiens in greater detail it was felt that a twe dimen- sional analysis cf the model estimates would be mere mean- ingful. As a result a transmission loss contouring program was developed. The piogram (Appendix B) displays transmis- sion less contours for range versus depth. Use cf the contcur plct reguires that transmission loss values gener- ated ty the IFD be sent to a data disk used by the contour routine. 1c facilitate this transfer a dummy variable (LliD) was established in the PEIN12 subroutine to store the trans- mission loss values and then these values are written tc the data disk at the end cf the main program.

16

Anctier modification of tie IFD output was required to change tie real and imaginary components of the pressure to a single pressure amplitude magnitude. It was felt that dealing with the pressure magnitude was easier aid mere meaningful than with the real and imaginary components of the pressure field. This conversion was done in th€ PEINT2 subroutine and established a new variable (PEMAG) tc repre- sent tie pressure macritude.

A firal modification in tie computer program was made due tc a suspected error in tie computation of the attenua- tion in the artificial layer. Physical reasoning dictates that prcper implemertation of the artificial attentuation would result in a steady drcp off in acoustic pressure with depth throughout the artificial layer, with pressure drop- ping tc zeio at the pressure release surface. IPC model results en the other iand shewed wide fluctuations in pres- sure kith depth in tie layer and then only a minimal fall eff at tie pressure release surface. The equation in tne IFD tiat actually computes the magnitude of the attenuation in tie artificial layer was taken directly from Ercck's (1976; PI model (Jaecer, 1 S83) . However, Brock's equation was derived with feet as the unit of measurement while Jaeger's model is derived witi meters as the unit cf meas- urement, liith this in mind, Jaeger's equation stcula be approximately a factcr of three larger than Brock's eguation to correct for the difference in units. To correct for this error tie ecuaticn tc calculate attenuation (ATT (I)) in the NEWMAI subroutine was increased by a factcr of three. flien this ccrrection was implemented, the large fluctuations in pressure with depth were eliminated. The expected drop off in pressure with depti and the fall off of pressure tc zero at tie pressure release surface were noted.

A listing of the revised IFD computer program witi all modifications can be seen in Appendix A.

17

I. MCEI1 VERiriCATICli

1 • .Ccjij: arisen with Jaeger Model fiuc

In light of the so diii cations to the I FD computer program just discussed, it was necessary to ensure that the the chances themselves did not introduce errors irtc the model. So as a first step the modified IFD program was run for cne of the test cases used by Jaeger in his original work. This case analyzes propagation in an environment that moves fxcm deep to shallow water- This particular environ- ment is depicted in figure 2.1 and was chosen because it was very siflilai to the simple sloping bottom in the tank exper- iment. A solution is obtained for a bottom with an upsicpe cf 8.5 decrees. An isospeed water field is used with sound speed set at 1500 n/s. Source freguency is 25 Hz. Ihy scenario has a maximum depth of 350 meters and a range cf 40 kilometers. Both the source and the receiver are set at 25 meters.

The results using the modified IFE program were the same as Jaeger's for this test case above the artificial attenuation layer. As explained earlier, the prcgraa was modified tc reflect higher attenuation in the artificial layer, so as to properly reflect the effect of attenuation in this region. The modified program results did not show the large fluctuations in pressure with depth in the artifi- cial layer but rather the gradual decline in pressure towards a value of zero at the pressure release surface. Cut above the artificial layer the modified program results were identical with those achieved by Jaeger with the original program. Apparently, the ttincr changes in the prcgraa designed tc improve en the form of the program output dees not hinder the model's ability to achieve a soluticn m the upper sediment and water column.

16

FREQUENCY - 2.0 HZ. SOURCE DEPTH - 25 M.

250"

^§350

X

H

Q.

UJ

Q

1000

WATER

SEDIMENT

ARTIFICIAL LAYER

0.0

10.0

20.0 30.0

RANGE(km)

40.0

figure 2.1 Jaecer's Deep-to- Shallow Water Case.

2- Ccc f arisen with Jensec and Ku perman Model Run

Ihe second attempt at verifing the IFE ncdel involved a comparison of model results with those achieved fcith a El model designed by Jensen and Kuperman (1980). Ihe Jensen and Kuperman ficdel (JKfl) uses a split-step solution techrigue. Comparison with this particular model was chosen lecause it is one of the few that obtains a solution it two dimensions. Host acoustic models obtain a solution at only a single depth. In addition, Jensen and Kuperman made their nodel runs in a simple sloping ocean bottom environment very similai to the scenario of interest modeled in the tank. 3his envinenment is depicted in Figure 2.2 and featunes a gently sloping bcttcn of 2. 2 degrees. The water coluin has a

1S

unifcrn speed of 150C m/s. The source is placed just relow the midpoint in the channel at 112 meters and is driven at a frequency cf 25 Hz. The maximum depth in this scenario is 200 meters and has a naximun: range of 12.5 kilometers.

Ihe Jensen and Kuperman results were expressed as

FREQUENCY - 2.5 HZ. SOURCE DEPTH -112 M.

0

200

3 400 ■

II

|h-

,W 600 •

lj

800

0.0

WATER

SEDIMENT

2.5

5.0

2.2

7.5

10.0

12.5

RANGE(km)

figure 2^2 Jensen and Kuperman Sloping Bottom Case.

transcission loss ccrtours fcr range versus depth. Iheir study concentrated en transmission loss pattens in the sediment, rut results were obtained both in the sediment and in the water. These results are compared to the IFD results at ranges cf 2.5, 5.C, 7.5, 10.0, and 12.5 kilometers. Ihese ranges were chosen fcr analysis because the JKM results showed the greatest variation in transmission less with

20

depth and thus, makes for a more meaningful comparison with the III results.

lie IFD and JKU results can be seen in Figure 2.3 through figure 2.7. In all the figures, the IFD estimates are shewn as a solid curve while the Jensen and Kuperman results are depicted as circular points. Ihe first analysis is at a ranee of 2.5 kilometers. From Figure 2.2, it can be seen that the depth at this range is 200 meters and is ir a flat bottom region. From the results shown in Figure 2.3, it is ctvicus that both models obtained almost identical results frcm the sirface dewn to a depth of abcut 300 meters- Ihere are differences between the two sets of predictions from the ocean bottom to a depth of 100 meters below this ^oint. Eelow 300 aeters the Jensen and Kuperman results shcii a very slight increase in transmission less (II) fciti depth. The IFD also shows an overall increase in transmission loss with depth but with several fluctuations in trar snission loss and a marked peak at about 300 meters. So in general, the results from the two models have the same general tendencies although the IFD appears to shew greater detail in results near the water/sediment boundary.

Figure 2.4 shews results at 5.0 km in range. Here, the water depth is still 300 meters and marks the very beginrirg of the sloping bottom section. For this range ihe JKM predictions are crly available to a depth of 300 meters. Ihe results are nearly identical with those obtained by the IPD. Ecth models show a relative minimum in transmission loss at a depth of 1C0 meters and then a gentle increase in II with depth.

Ihe model results at a range of 7.5 km are seen in Figure 2-5. At this range the bottom depth is abcut 150 meters and the bottom is sloping. Ine models show the greatest difference at this range. Both models prcduce nearly identical results in the water column, but beneath

50.0

Iransmussuon loss ( d b ) 60.0 70.0 80.0 90.0

0.0

100.0-

^Jo.L1

; n -

_C 300.0-

— >

CD CD

*00.0-

500.0-

600.0

— IFD MODEL VRLUES o JKM VRLUES

^ni, i o 1

100.0

Figure 2.3 IFE and JKM Ccnfarison at a Bange of 2-5 Km

22

Transmission Loss ( d b 50.0 60.0 70.0

CO

100.0

JZ 300.0 o_

CD

a

400.0-

oOO.G -

600.0

0.0 90.0 10G.0 110.0 123.0

— IFD MODEL VRLUlS o JKM VRLUlS

n

?rnse: - 5.0 KM

Figure 2.4 IFD and JKfi Comparison at a Eange of 5.0 Km

i j

60.0

Trans mission Loss 70.0 80.0 90.0

ao J

I00.G

0.0

100.0

200.0-

-C 300.0 +->

D_

CD Q

400.0

500.0-

600.0

— IFD MODEL VRLUES o JKM VALUES

RANGE - 7.5 KM

110.0

Figuie 2.5 IFE and JKM Comparison at a Bange of 7-5 Km

24

60.0

Transmission Loss idb) 70.0 80.0 90.0 10G.0

0.Q

100.0-

-C 300.0 0_

o

400.0-

500.0-

600.0

— I ED MODEL VRLUES 0 JKM VALUES

RANGE - 10 „Q KM

11C.0

Figuie 2.6 IFE and JKM Comparison at a Range of 1C-0 Ka.

25

Transmission Loss (do

70. Q 50.0

3i U i

100.0 110.0 120.0

0.0

100.0

yr\c> r\

JZ 300.0

o_ o a

400.0-

500.0 -

— IPD MODEL VRLUlS 0 JKM VRLUES

500.0

RANGE - 12.5 KM

figure 2.7 IPC and JKH Comparison at a Eange of 12-5 Ki.

26

150 neters in depth the mcdel estimates iegi n tc slew cif f eiences . The Jersen and Kuperman results show a gradual increase ir TX with depth below the ocean bottom. The 1FD results en the other hand, shew a gradual decrease ic trans- mission less from 15C meters to 300 meters, with a relative minimum at 300 meters and then an increase in 11 rereath this depth. Althouct there are some differences in model estimates near the tcundary in the flat nottom sections previcus.lv discussed, the differences appear to he greater at tie tcurdary in this sloping bottom case. Ir these regions away from the tcundary in either the water column or in the sediment, hewever, both models produce similar results, lhe JKfl's difficulty in obtaining an accurate solu- tion at the sediment tcundary is not totally unexpected. Ine model uses a variation of the straight split-step solution technique similar tc Brock's computer model (Jersei and Kuperman, 1980), that has characteristically been ursuc- cessful in obtaining a reliable solution near a boundary.

Ihe results at a range of 10-0 km are seen in figure 2.6. ht this range the water depth is approximately 100 meters and the bottom is again in a sloping region. At this range Jensen and Kuperman results are only available to about 15C meters in depth. for the data availarle, the models predtee nearly identical results. Beth models predict a minimum at about 5C meters in depth and then ar almost linear increase in 11 with depth- The IfD results also reflect a transmissicn loss maximum at about 200 meters, and then a slight decrease of 11 beneath this depth. Data at these depths are not availarle from the Jensen and Kuperman run. Ir light of the results obtained at 7.5 km for a siopirg rcttom case cne might expect that the results fcr the two ucdels would show differences near the ocean tottcm. However, since there is enly one Jensen and Kuperman predicticn available rear the tottom for this range, it is

27

difficult tc make anj definite conclusions regarding differ- ences ir ncdei perfcriiarce at the boundary.

Jesuits at tie apex (range egual to 12.5 km) can be seen in figure 2.7. Since all estimates are made ii the sediment at this rarge, there is no boundary tc ccrtend Kith. At this range the two models snow the test agreemert. Eoth models show a gradual decrease in transmission less to a depth cf about 30C meters and then a gradual increase of II with depth.

In general, there appears to be good agreement between the IFD and the JKM model results in regicrs cot influenced by a boundary. In both the water and the deep sediment the twe models produce similar results. Although this is ret conclusive evidence, these similarities suggest that the III can successfully model acoustic propagation in these recicrs. Near tie water/sediment boundary however, the Jensen and Kuperman aid IFD predictions show marked differ- ences. Ihese differences appear to intensify as the tcttom beccmes mere sophisticated. In general, the Jensen and Kuperman results dc ret seem to show the detail the IFD results do. Considering the different solution techniques employed by the two medeis, these differences in results are expected.

3« Ccie pariscn with Cop pens ,, Humphries and Sanders Kg del Bun

Ihe third attempt at verifying the IFD perfcrmance was dcre by comparing results with an image theory node! derived by Coppens, Humphries, and Sanders (1984). This Coppers, Humphries, and Sanders Model (CHSM) uses a saddle point approximation to an image model tc solve fcr the acoustic field. Beth programs were run for the scaled scenario modeled in the tank experiment. This scenario is depicted in Figure 2.8 and features a ten degree sloping

26

rottca. Ihe maximum water depth for the run is 350 meters and the naximum range is two kilometers. The source gener- ates a 100 Ez signal and is set at a depth of 175 meters.

FREQUENCY -100 HZ. SOURCE DEPTH -175 M.

350 500

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Figure 2.8 10 legree Simple Sloping Bottom Case.

Ihe image model provides solutions onljy at the apex. Ihe cccpariscn of predictions at the apex (range egual to 2 .kiloiieters) , can be seen in Figure 2.9. In the Figure, the IfD values are plotted as the solid curve while the image itodel values are shown as circular points. The predictions are shcwr as values of noraalized pressure amplitude for a given depth. The different models produce pressure amplitude values in different urits, and thus, had to be normalized to jiake a ccmparison of values possible. This normalizaticr was

25

cone fcr each model ly dividing the presssure aiflituce by the naxiauii amplitude predicted by the model.

She results suggest that even though the ncdeis predict siniiar larce scale trends in pressurs aaplitude with depth, there are several differences in detail. The plot shews that toth the IFD and the iiiage mcdel predict an almost linear increase in anflitude with deptn down tc a specific naximum and then a slow decrease in anplitiide beneath this maximum. The IfD however, shows tne naximum at about 15.5 ireters in depth while the image model aaxiiui is deeper at 1S meters. Beneath this maximum the IFD shews a cuch sharper decrease in amplitude than the inage model. Ihe trend in the image mcdel data appears smooth, wnile the IfD curve reflects several small scale fluctuations.

It appears that both models predict siniiar large scale trends in pressure amplitude for this scenario. It is difficult, if not impossible, to account for the differences in detail. As a mininum, however, this comparison indicates that the two sets cf predictions are consistent with cne another and can be considered reasonable in this shallow water environment.

4 . ecu f arisen with Physical Beasoning

Ires model cenparisons it appears that the III at least makes a reasonable estimation of acoustic fields ir a shallcw water enviror nent. IfD results are also analyzed in comparison kith basic physical reasoning and theory as a fourth attempt at model verification. This analysis examines IFD trarsaission loss contours for the simple ten degree sloping ccean scenaric seen in Figure 2.8. The scenario is two kilcneters ir ranee with a maximum depth of 350 meters. The the source generates a signal at 100 Hz and is placed at 175 meters in depth.

30

NORMALIZED PRESSURE RMPLITUDE

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figcre 2-9 IFI and CESM Comparison at the Apex,

31

Trarsmissicn loss ccntour plots are displaced in Figure 2. 10 through Figure 2.13. All II contours are expressed ir decibels (db) and are shewn as a function of depth \ersus range. In all figures, the ten degree sloping rotten is shown as a solid unlabeled line- Ihe contcur plots are displayed over four range subsections due to computer graphics linitaticns and to emphasize different significant features in the field.

Ihe first figure shows transmission loss contours from the source to a range of 600 meters. The ccntcurs in the first 250 meters appear very symmetric, increasing outward from the source in a pattern that resembles spher- ical spreading. Since the 1IL program assumes a Gaussian starting field this early pattern is expected.

Frcir a range of about 300 meters to 600 meters the field in the water appears tc be dominated by a surface reflection pattern. From the spotty appearance cf the TI ccntcurs in this regicn there is an indication of ar irter- acticn cf surface reflection and bottom reflection en the contours. It is possitle to ccipare transmission less naxima with redes in the surface interference pattern. Eased on surface interference theory these nodes should occur fchere (Kinsler, Frey, Coppers, and Sanders, 1982) :

SIN (khd/r) = 0

or in ether words;

khd/r = nIV

where: n =0,1,2. . . r = fiange

k = Wave cumber (2*7,)) d = Source Lepth h = Depth cf Node * = Wavelength.

32

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Ey marip ula ting the above equation it is possible tc solve for the depth at which the ncdes should be observed. for this particular scenario at a range of 604 meters, nodes should cccur at integer multiples of 25 meters in depth (25n) . figure 2.1C shows that these transmissicn less maxima dc exist as expected, every 25 meters in depth at the stated range.

fased on simple physical reasoning one would expect refractive bending along the ocean bottom due to density differences between the water and the sediment. Ihe ccrtcur plot reflects a charge in basic pattern at the interface. Ihere is a bending of the Tl ccntours that suggest a refrac- tive influence.

figure 2.11 shows transmission loss contours from a range of 60C meters tc 1350 meters. Again in this recicn the water appears to be deminated by surface reflection. Sclving for the ncdes in this surface interference pattern at a range of 1350 meters, it is found that these nodes should appear ever^ 55 meters in depth, from the fiyure it is again seen that 11 maximums do occur every 55 meters in depth as anticipated. As in the first figure there is a change in the basic II pattern at the ocean bottom. The bending appears more accentuated thar in the previous figure, but still suggests the influence of refraction at the ccean lottcm.

figure 2.12 displays transmission loss frcm 1350 meters tc past the apex at a range of 2100 meters. In this figure, the dominance cf the surface reflection mechanism is less cbvious and the 11 patterns become more complicated. It is in this region that the influence of trapped normal mede propagation can be seen. As discussed earlier, as accustic energy travels up tie slope toward the apex, normal modes are cut off and energy is transmitted into the bcttcm. According tc adiabatic normal mode theory, medal separation

3 7

is rarce ascendent (C-iaves, Nagel, Uberall, and Zaur, 1S75 and Ccppers and Sanders, 1S80). The ranye from cue apex at wnich tie lewest mcde is transmitted into the bottom, can be calculated using the fcllowing equation (Coppens, Sanders, Icanncu, and Kawamura, 1978) :

1 = */4 SIN6»t TAN@

where:

1 = Dump Distance Of The Lowest Mcde i) = Wavelength &t~ Critical Angle (? = Wedge Angle.

According to adiabatic noraal mode theory (Kinsler, Prey, Coppers, and Sanders, 1982) , in deep water (near the source) the lewer normal modes are far above cutoff and the adia- ratic eigenfunctions consist cf an integer number cf half sine fcaves with zerc pressure at both the top and tcttom surfaces. At the cutcff of each mode, the pressure at the rotten must be naximi2ed, resulting in an adiabatic eigen- functicn that contains 1/4, 3/4, and 5/4 wavelengths at the respective cutoff distances cf 1X, 3X, and 5X for the three lowest iccdes. from figure 2.14 it can be seen that as the normal medes travel up the sloping bottom, succesive codes are fcrced into the tcttom at distances where a particular node reaches a depth at which it can not longer prcpacate. Also frcn the figure it is cbvious tnat a source set at nid-depth can net excite the second mode. Since this particular geometry is present in the tank scenario it is expected that the energy associated with this seccne mede snould ret be seer. Based on this line of physical reasoning, modes shculd be dumped into the sediment at the first dump distance, fifth dump distance, ninth dump distance and so en. If these modes are dumped as described

38

fl

RANGE FROM APEX

3X 1X

SOURCE MODES

figure 2.14 Normal Bode Prorogation in a Hedge Shaped Ocean.

then thej should he seen in the contour plot as reducticns cf transmission loss in the bottom at ranges cf 1952 meters, 1760 neters, 1568 meters, ard so on.

frcn Figure 2.12 it can be seen that there is an cfcvicus decrease in transmissicn loss at approximately 1S50 meters (dump distance #1) and 1760 meters (dump distaice #5) . 3tere is also a less clearly defined reducticn in 11 along tt€ rcttom at 1565 meters (dump distance #9).

The final cortcur plot (Figure 2.13) shows transmis- sion less contours from 1550 meters to 2300 meters. This figure is ar extensicr cf Figure 2.12, intended to emphasize how clearly the bean at the first dump distance is defined in the plots. The team at the fifth dump distance is also

3S

visits rut is not nearly as well defined, frca this figure, cue can also see an indication of a very narrow Lean ii the sediment at about 186C meters. Ihis distance corresponds to the tiird dump distance (second normal mode). Based cr. adia- iatic mode theory the secend mode is not expected tc te excited. Hcwever, adiabatic mede theory is only an approxi- mation cf rcrmal mode behavior. Ihis approximation cf nerval mode behavior teccnes less exact as the bottom slcpe increases and the clcser the source is to the apex. Ihe appearance cf a narrow beam at the third dump distance indi- cates that there is a strong possibility that the secend mode is present and that the adiabatic approximat icn is net exact Kith a ten degree bottom slope.

Ihe basic features of the IFE contour plcts are consistent with both physical reasoning and theory. Easic surface reflection and bottom refraction occur mere expected and behave as anticipated. In the far field, trapped noriral mede propagation is observed and can te veri- fied Kith simple dump distance calculations. The loeatien of teams dunped into the bottom appear consistent with basic mode theory. In short, the transmission loss contours indi- cate that the IFD is making reasonable predictions cf the acoustic field in a shallow water environment.

- • Verification Summary

It is difficult to say how exact the IFD predictions are fcr a shallow water environment based on these simple verification technigues. As a minimum it can be said that the model results are at least consistent witn other model predictions and expectations based on simple physical reasoning. Model estimates are virtually the same as the Jenser and Kuperman H model in regions not influenced ry a water/sediment boundary. Close to the boundary the IFD results appear to shew greater detail and variaticn than

40

this IE ncdel. The 1ID results also appear consistent with the general trends in pressure amplitude predictecd ty the Coppens, Humphries, and Sanders iaa-^e model. ftgain differ- ences were toted in the small scale structure. Finally, the IFD II contours verify well with tasic expectations fcased on physical reasoning and theory. Surface reflection and tottca refraction patterns are observed as anticipated. lar field ncrnal mode propagation can he verified in the zicts using sinple dump distance calculations. In short, all veri- fication methods attempted, fail to uncover any inconsis- tency in IFI performance in a shallow water environment.

41

III. liBOEAlCEI MEASUREMENTS

i. EaCKGECUND

The na-'cr attempt at appraising IFD performance involved ccmpaiirg model results with laboratory measurements, lie shallow water envirornent modeled in tne tank is very ideal- ized; a ten degree sloping sand bottom with an iscvelccity water ccluiin. Although this scenario appears eiterealy Simplistic, it is ore that car re reasonably modeled lr the iaboratcry and still approximate conditiors in an actual shallcw water ocean environment. The methods used tc node! and oeasure the accustic field are relatively untested. Indeed, this attempt at laboratory modeling was performed rot cnly tc verify HE predictions, but also to see if the environment could be successfully modeled in the labcratcry.

E. ESf EEIflEMTAL DESIGN

1 . She Tank

A fiberglass coated wocden tank was used. Ihe tank is 3C4 centimeters ir length, 117 centimeters wide ard 95 centineters deep. Sard filling the bottom of the tarX was shaped tc form th€ ten degree sloping botton:, and measurements were taken over a range of two meters. Maximum water depth in the tank was 35 centimeters. A 100 kHz source *as placed at mid-channel depth (17.5 centimeters; . The layout cf the tark is depicted in Figure 3.1.

42

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A slope of ten degrees was selected for several reasons. 1c begin with, even though a ten degree slept is greater than most ocean bottom slopes, it is still small enough tc be considered realistic. Pernaps most important, the ten degree slcpe was selected because given the frequency limitations (discussed later in this chapter) and range limitations, this wedge angle allowed the source tc be placed many (4 1.6) dump distances from the apex. A large number ci dump distances was necessary to simulate a distant source.

lhe bottcm material used in the experiment was #30 fine grade sand. The grain size ranged from 0.15 millimeters to 0.70 nilimeters. The sand was treated with a technique used ly Eaek (1984) tc remove air from the sediment. This technigue used a high speed jet to agitate the sand/water mixture tc remove the bubbles and then allowed the sand to settle fcr several da^s before the experiment was initiated.

Jresh(tap) water served as the medium in the tank, lo remove air bubbles, the water was allowed to settle in a settling tank before being transferred to the experimental tank icr use. The water in the tank was periodically treated with chlcrine bleach to prevent the growth of biclcgical material.

2 • Signal Gener a ting/Bee eiving Equipment

3he acoustic signal used for the measurements was produced by a function generator, sent through an amplifier and then transmitted into the water by a directional trans- ducer resonant at 100 kHz. The dimensions of the active race of the transducer were 7.0 cm in width and 2.0 cm in height. Ihese dimensions resulted in an approximate beamwidth (ancle from the acoustic axis to the first theoretical null) of 11.3 degrees in the horizontal and 46.3 degrees in the vertical- The narrow horizontal beam minimized reflections

44

from the sidewalls of the tark, while the wide vertical team allowed ccaplete ersonif icaticn of the chanr.el in the vertical diaensicn.

lie signal was received by an LC-5 omni-direct ior.al hydrcphcre, sent thicugn an aaplifier and filter, and then displayed en an oscilloscope and voltmeter. A schematic showing the electronic setup is shown in Figure 3.2.

A frequency cf 100 kHz was selected for tv»c prac- tical reasons. First, to avoid particle scatterir.c ty the sediment, the acoustic wavelength must be at least three times larger than the gram size of the sediment (Anderson and Iiehermann, 196€)- The largest grain size in the sand was C.C7 cm, so that a waveientn of 1-45 cm(100 khz) was sufficiently large enough to he immune to this effect. Second, the 100 kHz frequency and the properties of the sard provide a dump distance that is small enough to allow the source tc he positioned many dump distances from the apex.

Shaping the sand bottom into a ten degree wedge with a uniform and smooth interface proved to he a leng and tedious process. 1c facilitate this modeling, wcoden supports (two-by-fours) were mounted a^ong the length of roth sides cf the tark. These supports were elevated at cne end cf the tank to achieve the required ten degree slope. A scraping device was constructed with wooden supports and a metal scraping blade that extended across the width cf the tank. Ihis scraping device consisted of wooden supports along the top that reached across the tank and cculd be pulled along the elevated wooden supports on both side of the tank. Ihis scrapirg device was pulled along the supports repeatedly until a snooth slope of ten degrees was sculp- tured frcm the sand.

Ecles had tc be drilled into the metal scraping rlade because when a solid blade was used in the shallow portion cf the slope, water trapped behind the tlade was

45

1.) LC-5 HYDROPHONE. 2.) AMPLIFIER (HP 465A). 3.) ELECTRONIC FILTER (SK 302). 4.) OSCILLOSCOPE. 5.) VOLTMETER (HP 400D). 6.) FUNCTION GENERATOR WAVETEK 116. 7.) FREQUENCY OSCILLATOR (GR 1310). 8.) AMPLIFIER (HP 467A). 9.) FREQUENCY COUNTER (HP 5233L). 10.) 100 KHZ TRANSDUCER.

figure 3-2 Ilectronic Equipment Schematic,

46

forced beneath the sciaper gouging the smootn bottom. This hottcn modeling techrigue Mas slow because, once a pass was made ever the betteff, the water became turbid and it was then impossible to see the bottom. Wnen the bottom was not visible, it was impossible tc see wnere further smoothing was necessary until the water settled several hours later. In addition, as this smoothing process continued a silty residue became separated frcm the sand and settled cut on top of the sand. Ibis residue would he easily resuspended and eventually had tc he removed using a water syphon.

C- MIASCEEBENT PEOCIIORES

Measurement cf the pressure field within the water was done by lowering the receiver in depth at specific ranges of interest. The receiving hydrophone was attacned to a pair of nicrcmeters at right angles to one another, that was in turn bolted tc a board which spanned the width of the tank. Once the beard was placed close to a range of interest, cne nicrcmeter was used to give fine adjustments in range and the ether in depth.

The measurements were subject to both an accuracy and a precision error- On a given day, with the water level fried and the cross-tank support set at a particular place in the tank, it was possible to position the receiving hydrophone with an accuracy in depth and range or plus or mirus 0.06 centimeters (one turn of the micrometer) . To prevent the sand 'inland* of the apex frcm drying out when not taking measurements, enough water was added to the tank after each data run tc keep the sand completely submerged. The next time measurements were taken, water had to to he removed from the tank tc reestablish the beach. Because cf these small changes in the water level the horizontal position of the beach was subject tc a precison error estimated to be withir plus or minus cne centimeter.

47

e

Ifce final decision associated with the a easur events centered en whether tc use a triggered pulse cr a ccitiiucus wave (CF) signal. With a triggered pulse it -was possible to distirguish the received signal from interference caused by reflections off the side of the tank. On the other hand, by using a triggered pulse there was a possibility that the tulse length was not long enough for the acoustic energy associated v.ith paths reflecting off the top and bottom or the vater column to overlap the direct path from the scarce to receiver. A CW signal wculd avoid potential pulse length problems, but it would be impossible to distinguish between the actual signal arc interference. The use of a source with a narrow horizontal team reduced the effects of reflections from the side walls, but there was still the possibility of interference froa side lobes reflected from the sides.

It was necessary to determine the best means tc take ireasurements. This vas done by taking measurements at th same location with different pulse lengths to determine the required pulse length to give consistent results and then comparing these results to those obtained with a CW signal. The third dump distance (14.4 cm from the apex) and just past the tenth dump distance (50.0 cm from the apex) were chosen, and measurements were taken for pulsed signals of 64 and 256 cycles, and a CE signal. These measurements can be seen in figure 3.3 through Figure 3.5. In the figure depicting results at the third dump distance, the CW ireasurements are shown as the solid curve, the 64 trigger cycle results are displayed as circular points, and the 25fc trigger cycle results are depicted as triangular points. lor clarity, the measurements taken just past the tenth duip distance are shown ir two figures. Figure 3.4 compares CW results (solid curve) with the 64 trigger cycle signal (circular points). Figure 3.5 compares Civ a easureiients (solid curve) with the 256 cycle results (circular points) .

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51

The pressure amplitude values were normalized by dividing each pressure value ty the maximum pressure value ir. the field. lie depth values were also normalized by civrlin- each depth by the maximum depth.

The results in figure 2.3 show good agreement between the three curves. In particular, the results for the Cw signal ard the 256 cycle signal are very similar. Ihe 64 cycle signal shows the same .behavior as the CW signal, rut differs in nagnitude telow mid-depth.

Ihe results at 5C.0 cm frca the apex appear much more complicated tnan at the third dump distance. Figure 3.4 ccmpaies results acheived with the Cw signal ar.d the o4 cycle signal. From the figure it can be seen that the two sets cf results shew good agreement. Ihe measureirerts depicted in Figure 3.5, which compares the 256 cycle sigral and the C "R signal show poorer agreement, although the general shapes cf both curves remain similar.

These results indicate that interference from the side walls is sufficiently small so that it is possible tc make measurements with a CS signal to at least ten dump distances from the apex. Long pulses could also be used, but the difficulty cf maJcinc voltage measurements with an oscillo- scope cempared to reading a voltmeter, dictates that measurements should be made with a CW signal.

IV. tCdll EESU1I CCIJAEISONS 1IIH IABQBATOBY HElSOBfJlEKlS

A. IHIECLCCTION

IID model predictions and laboratory measurements were obtained fcr comparison in totJb a general and detailed anal- ysis. Ihe general analysis compared results every rive centimeters from the beach to a range or 50.0 ci. free the reach. Ihe measure iients were spaced to give results at approximately each cf the first ten dump distances. Ihe detailed analysis compared results every centimeter frcn 3.0 to 11.0 cm from the ajex. These measurements were taken to observe the sensitivity of the pressure field to small changes ir iange.

£• 1EE GENERAL ANAI5SIS

Ihe general anlysis compared IID results and latcratcry measurements at approximately eacn of the first ten dump distances (every five centimeters from the beach). These measurements were ortained by fixing the receiving hydro- phone kith respect tc the cress board and then moving the board out in increments of five centimeters to measure the desired field as a function of depth at each range. Ihe received Cw" signal was read on the voltmeter.

Ihe comparisons are shown in Figure 4.1 through Figure 4.10- In the figures, the IID predictions are displayed as a solid lire while the experimental measurements are snewn as circles connected by a dashed line. Each pressure value was normalized to unity ry dividing it by the maximum pressure value fcr the respective curve. The depth values were also normalized by dividing each depth by the maximum depth in the water eclumn.

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figure 4.1 CcmpariscE cf Results at 1.0X.

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55

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Pigcre 4.3 Comparison of Results at 3. 1 X.

56

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0.9-

JT \

/ \

/ S

/ >

/ \

1 & \ / \ /

1 n

\ / \ / \ /

i . u

— IFD MODEL

RRNGE = 4.2X

|-o-- EXPERIMENTAL

figure 4.4 Ccaparisou of Results at 4.2X.

57

I'lUni M IL1 LL-U nil: lJ iUuLli /I I ill A

N

1.0

1.0 1.2

— IFD riODEL o- EXPERIMENTAL

RRNGE - 5.2X

Pigure 4.5 Ccmparisoo of Eesults at 5-2X

58

N

NORMRL I ZED RMPL I TUDi ( P/PMflX )

0.0 0.2 0.4 0.5 0.8 1.0

0.0

0.1 -

0.2-

0.3

0.4

0.5

0.7-

0.8-

0.9

1.0

■IFD MODEL CXPERIKCNTaL

RRNGE = 6.2X

1.2

figure 4.6 Comparison of Results at 6.2X-

5S

N

NORMRLIZlD RMPLITUDl(d/PMRX

CO 0.2 0.4 0.6 0.8 1.0

0.1 -

0.3-

0.4

0.5

0.6

0.7

0.8

0.9-

1.0

- IFD MODEL

- EXPERIMENTAL

RANGE - 7.3X

1.2

figure 4.7 CcmparisoD of Eesults at 1.31.

60

NORMALIZED RMPLITUDE(P/PMRX

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.1-

0.2

0.3

0.4-

\ 0.5-

0.5

0.7-

0.8-

0.9-

1.0

IFD MODEL EXdlRIMlNTRL

1.2

DQKipr _ q 7v

figure 4.8 Comparison of Results at 8.3X.

61

NORMRlIZlD RMPLITUDE(P/PMFIX)

0.0 0.2 OA Q.5 0.8 1.0 1.2 n n -if—

"T:::^^-^^^ :

0.1 - 0.2-

^ — --^7_ Qr-'~

0.3- 0.4-

0.5-

0.6-

0.7-

_________ ' ~"~~-p

0.8-

<=:=^<--^^

0.9- 1 n

~JJ&

I . u

— IFD MODEL

RRNGE = 9.4X

o- EXPERIMENTAL

figure 4-9 Comparison of Besults at 9.4X.

o ^

NORMALIZED RMPLITUDE(P/PMRX)

0.0 C.2 0.4 0.6 O.S 1.0 1

.2

n n -t

■

u . u ^

^~~~^^-i^. 1 i i i 1

0.1 -

- o^\

0.2 - 0.3-

0.4-

^\ -'"e "

0.5- 0.6-

0.7-

0.8-

0.9-

1 n -

^- --__

1 . u

— IPC MODEL

RRNGE = 10. 4X

-c-- EXPERIMENTAL

Figure 4.10 Comparison of Besuits at 10. 4X.

63

Ir general, the pressure patterns predicted cj the IFD and those measured, roth become more complicated as the range frcm the teach increases. At all ranges, there is qualitative agreement in the scale of the predicted features and the scale of the neasured features. Quantitative agree- Eent is lacJeLng. This agreement in scale hut not detail, suggests that the phases amcng the normal modes predicted by the model do not accurately reflect the experimental situa tier.

C. Ill ZIl&ILEd ANAI3SIS

lie detailed analysis compared IFD values with experi- mental measurements every centimeter from 3. J ca to 11.0 cm from the teach (0. 7X tc 2.3X). The laboratory measurements were taken by fixing the hoard at one location and then using the micrometer to adjust the receiver to the desired range* The received Cfc signal was read from the voltmeter.

llese results are depicted in Figures 4.11 tnrough a. 19. In the figures, the IFD predictions are shown as a solid line and the experimental measurements are displayed as circles. Each pressure value was normalized to unity by dividing it by the maximum pressure for the respective curve. Ihe depth values were normalized by dividing each depth by the maximum depth at the particular range.

There is gualitative agreement in the scale of the tasic features fcr all ranees, but guantitative agreement is rot observed. Ihe IFD patterns change very little throughout the analysis, while the measured values change more rapidly (especially past 2. OX). The results at 2.1X and 2.31 (Figure ^.1£ and Figure 4. 1 S) show that the pressure field can change fairly significantly over a range as short as one centimeter. At those ranges where tnere is poor agreement between results, there is an indication of phase

64

NORMALIZED RMPL I TUDE C P/PMFIX

0.0 0.2 0.4 0.6 0.8 i.O

0.0^

0.1 -

0.2

0.3-

0.4-

\ 0.5- M

0.6-

0.7-

0.8

0.9

1.0

- IFD MODEL oEXPERIMENTRL

RRNGE

n 7y

U . / A

1.2

ligure 4.11 Comparison of Results at 0.71.

65

NORMRLIZlD flMPLITUDEtP/PMRX)

0.0 0.2 0.4 • 0.6 0.8 i.O 1 n n c- ■

.2

0.1 -

V 1 1 1 1 1

0.2-

o\

0.3-

\

0.4-

o \

\

M

0.5-

\

0.6-

0 \

0.7-

\

0.8-

0 \

— IFD MODEL

0.9-

1 n

o EXPERIMENTAL

1 . u

RANGE = 0.8X

Figure 4.12 Comparison of Results at 0. 8X.

66

NORMRLIZlD flf1PLITUDE(P/PMflX)

0.0 0.2. 0.4 0.5 0.8 1.0 1

.2

u . u ~<

'v 1 i 1 1 1

0.1 -

0 \^

0.2-

O Nv

0.3-

\

0.4-

0 \

IE \

INI

0.5-

o \

0.6-

o \

0.7-

0 \

0.8-

— IPD MODEL

o

0.9-

1 n

o EXPERIMENTAL

1 . u

RRNGl = 1 .OX

Figure 4.13 Comparison of Results at 1. OX.

67

NORMALIZED AMPLITUDE (P/PMAX)

0.0 0.2 0.4 0.6 0.8 1.0 1

n n r

.2

L.J ^

0.1 -

O ^v

0.2-

0 \

O \v

i

0.3-

0 \

0.4-

o \

N

.0.5- 0.6-

0.7-

0 \

o \

o \

0.8-

O l

\

— IFD MODEL

0.9-

o EXPERIMENTAL

o

1

/

1 . o

pq\inr = 1 7V

s.

figure 4.14 Comparison of Results at 1.3X.

68

NORMALIZED AMPLITUDE ( P/PMRX )

0.0 0.2 0.4 0.6 0.8 1.0 1

.2

u . u ~*

' i i i i

0.1 -

0 N.

0.2-

0 N.

0 N.

0.3-

O ' \.

0.4-

o \

N

0.5-

0 \

o \

0.6-

o \

0 \

0.7-

0 \

0.8-

0

— IFD MODEL

0 I

0.9-

o EXPERIMENTAL

o/

1 n

/

I . u

RANGE = 1.5X

figure 4.15 Comparison of Results at 1. 5X.

6S

NORMALIZED RMPLITUDC(P/PMRX

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.1

0.2-

n 4 _

\ 0.5 -\ M

0.6-

0.7-

0.8-

0.9-

FD MODEL o EXPERIMENTAL

RRN'GE = 1.7X

1 7

figure 4.16 Comparison of Results at 1. 7X.

70

NORMRLIZlD RMPLITUDl(P/PMRX)

0.0 0.2 0.4 0.5 0.8 1.0 1

.2

U. U "i

'n. 1 1 1 1 1

0.1 -

0 ^V 0 %.

0.2-

0 ^v

0 X.

0.3-

0 ^\

o \

0.4-

0 \ o \

0.5-

o \ Q \

0.6-

O \ O \

0.7-

O

O

0.8-

o /

— IFD MODEL

o /

0.9-

1 n

o EXPERIMENTAL

o /

r

1 . u =

RRNGE = 1.9X

figure U.17 Comparison of Results at 1. 9X

71

NORMALIZED AMPLITUDE (P/PMRX)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

M

u . u ->

1

i i i

0.1 -

0.2-

\i 0

\ °

0.3 -

■

\ ° \ °

0.4-

\ ° \ ° \ °

0.5-

\ °

0 \

0.6-

0 \

0 \

0.7-

o \ o \

0.8-

0 o / o /

IFD

MODEL

0.9-

O

EXPERIMENTAL

o /

° ./

1 n _

RRNGE - 2. IX

figure 4.18 Comparison of Results at 2- 1X

12

NORMRLIZED RMPLITUDliP/PMRX)

0.0 0.2 0.4 0.6 0.8 1.0 1

.2

u . u -*■

0.1 -

0 N. 0 N.

0.2-

0 ^v

0 >v

0.3 -

0 \.

0 \

0.4-

o \.

3Z N

0.5-

0 \

o \

0 \

0.6-

o \ o

0.7-

0 / 0 /

/o

0.8-

/ °

— IPD MODEL

/

/ o

0.9- 1 n

o EXPERIMENTAL

/ o

/

1 . u

RRNGE = 2.3X

figure 4-19 Comparison of Besults at 2. 3X

73

interference (Figure 4.18) . For distances less char. 5X, theory predicts that for a source at mid-depth, the lowest propagating mode should experience interference from only the evanescent tails of higher modes. Therefore, ir the region of the detailed analysis, one expects small interference effects. The experimental results in this regicn however, shew rather significant interference. Ihe interference suggests unsuspected propagating modes are present, or that the evanescent tails are larger than expected. from the trend in the carves it appears as if the phase interference is not a factor from 1.5X inward toward the teach (figures 4.11 through 4.15) .

74

V . COftCIDSIONS/EECOMMENDATIONS

4. CCNCI05ICNS

1 . leriormance cf the I ED Model

Ihis analysis of the II D acoustic aoiel did cot uncover any major failures cf model performance in a simpli- fied shallow water environment. But this is not to say that the mcdel consistently and accurately performs in such an ocean scenario. Although comparison of lid predictions Kith two cthei Bedels and with simple physica^. reasoning did not uncover any inconsistencies in performance, the agreement between IIL values and laboratory measurements is insuffi- cient tc give complete confidence in the performance cf either tie nodel or the experiment.

Ihere is reasonable agreement between trie scale of the features predicted by the II D model and the experiment. Eoth the model and the measurements show increasing complexity as range is increased from the beach. But despite the sinilarities , there is poor quantitative agreemert in results. Cre possible cause for the differences may he that the phases of the neural medes predicted by the mcdel are extremely sensitive tc minor irregularities in the shaje of the interface and the acoustic properties of the bcttcm. Ereliminary work (LeSesne, 1984) , suggests that the rhase relationships between modes is strongly dependent en the distarce of the source from the apex even at great ranges. Consequently, it appears that the collective influence cf the ncrnal modes is dependent upon careful geometric control cf the experiment.

3he detailed analysis around 2X, reveals that large phase interferences cccur where only one propagating mode is

75

expected. This indicates the existence of an extended evanescent taii withir cutoff ex tie higher modes. Kawsmura and IcauEcu (1978), noted that tne apparent phases cf the evanescent tails are extremely sensitive to the details of the erviicr. nent. The results indicate that tne tail dees not decay quickly, and its influence is pervasive (Figures 4.2 and 4.3). From the trend in the curves, it appears this phase interference is not a factor any closer to the teach than 1.5X (figures 4.11 through 4.15).

2 • Ecdelin g/Measuremen t jrocelures

Ihe laboratory measurements represent an initial attempt at modeling an idealized shallow water anvirenment. Ihe experimental techniques are not without problems. All sets cf measurements were repeated and snowed good agree- ment- The reproducibility cf the measurements suggest that randeir errors have teen minimized. However, systematic errors remain which also contribute to the discrepancies between predicted and measured values. Some of these errcrs derive from equipment, such as the fact that the size cf the hydrophone is of the same order of magnitude as the scale cf variations in the pressure field. In addition, the environ- ment in the tank may net be sufficiently close to the ideal environment assumed ty the model.

E. EICCfifilBCATICNS

Itrther study and verification of tne IFD computer model is recemmended. A cemparison cf IFD predictions with ether models net analyzed in this study, may uncover the cause of the inconsistency when compared to measured values. A detailed study of the pnase interaction of tne nornal meats, although extremely complex, may also offer insight intc the 1ID performance.

76

It arrears that the modeling of an idealized snaiicw hater environment in the laboratory is of value in acoustic model verification. respite the experimental difficulties, there *as qualitative agreement in the basic features between ircdel predictions and laboratory measure meats. Eat the experiment represents only an initial jrrDbe into the irodeling/measureaien t techniques of a shallow water ei-vircn- nent. further rerineiient of these techniques and the experi- iiental equipment nay result in better i'jantitacivH £_/r-_~ir£nt retweer. zigh^j. (iSuic. j.oi. s a I. .i _ , ^ v i 5 1 » .. _ iieasuremeDts.

77

APPENDIX A BEVISIE IFD PECGEAfl LISTING

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114

EONNING IHE CCNIOOB EICT ON THE NPS COMPETES

A- IKTECEDCTION

lhis Appencix describes a procedure £°r running the IX contcur plct on the HIS computer. Detailed instructions for runnirg the IFD program can £e found in Jaeger (1 983) .

E. CCEX1NG THE FILE ICE USE

Cnce the TI values have teen generated by the IFD program, ail that is needed to produce a 11 contour plot is the file EICTS FCETEAf.. This file is shewn in Appendix £ and can re copied Iron a computer account maintained by the Underkater Acoustics Curriculum. To linX with this account and cttain a copy of the file, the user should proceed as fcllchs:

(1) leg en terminal.

(2) Enter: CP LINK 0160P 1S1 195 ER .

(3) When prompted for the read password enter: OX .

(4) Enter: ACC 195 C .

(5) Enter: CCEY PICTS F0E1EAN C = = A -

At this pcint the PICTS FOEIEAN file should reside en the user's A disk.

C. BOOING THE EBOGEAfl

Eefcre runnirg the program the user must obtain the TL values from the IFD program. Ihese TL values must he sent to

115

a data disk in crder tor the HOIS program to be able tc use then:- Ibis can re dcre by placing a WRITE statement in the IJD program that sends the values to a data disk. Tie ncdi- fied IIC depicted in Appendix A uses this technique and can be used &s a guide.

Crce the data disk has teen created, the user mist assign temporary disk space (IDISK) to give the program sufficiert room to generate the II contcurs. For mere irfcr- maticr en how to assign temporary disk space, see ^PS Technical Note TN-VM-C1 which is availible in the computer consultant's office.

Kith these initial steps completed, all that remains is tc compile and run tie program. The program can te compiled ty:

Enter: FCEIGI PLOTS .

Ihe program must he run at the TEK618 graphics terminal under D1ZSIIA. This can be dene ty:

Enter: DISSPLA .

Ihe user will then te prompted for the compiled Fortran prograir rame and the file definitions for the data cisk, before tie program will run.

116

APPENDIX D SOUBCE IIPIH SENSITIVITY ANALYSIS

During the laboratory experiment two supplemental sets cf measurements were taken to obtain an indication of the sensitivity of the pressure amplitude to changes in the source depth. The first set of measurements was ottained by varying the source depth *ith the receiver fixed at 1.0X {4.8 cm frcii the beach) , and lowered in depth to the bcttcm. Eor tie second set of measurements, The receiver was fixed at the third dump distance (14.4 cm from the beach), and measurements were taken with the source fixed at 5, 7, 9, 11, 12, 15, 17, 19, 21, 23, 25, 27, 29, and and 31 cm from the surface.

The results of the first analysis are shown in Figure E.1. In the figure, pressure was normalized by dividing by the naximum pressure and depth was normalized by dividing by the depth cf the water column. Although theory predicts only cne propagating mode at this distance, the results show modal phase interf ererce.

The results cf tie second analysis are shown in Figure L.2 through Figure D.€. In the figures, each curve repre- sents a set of measurements taken with the source fixed at a specific depth. For convenience, more than one curve is shown en a given figure. All pressure values were normalized by dividing by the the maximui pressure in the field. The depth values were normalized by dividing by the maximum water depth.

Ir general, at i-OX there appears to be modal phase interference which is influenced by source depth. Giver the roughness of this analysis, the details of this interference are obscure. However, the modal interference does net appear

117

to he inconsistent vith either the placement oi the scuice ci with the previous experinental measurements.

116

NORMRLIZED RMPLITUDl

n n

0.0 0.2 0.4 0.6 0.8

1.0

u . u 0.1 - 0.2-

"^--■^ ' '

I

MEASURED VRLUES

0.3-

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0.4-

\

0.5- 0.6- 0.7- 0.8-

0.9- 1 n

\

i . u

DQM;T = 1 ny

i \ i 1 1 \ U i_. i . U A

figure D. 1 Socice Secsitivity Analysis at 1.0X.

11S

N

0.0

0.0

0.1

0.2-

0.3-

0.4

0.5

0.6

0.7

0.8-

0.9-

1.0

NORMRlIZEC RKPLITUDl

0.2 0.4 0.5 0.3

1.0

SOURCE DEPTH

5

CM

-e — SOURCE DEPTH

7

CI

— - — SOURCE DEPTH

Q

CM !

RANGE - 3. OX

figure D-2 Measurements with Source Depth of 5, 7, and S Cm

120

0.0

0.0

M

0.1 -

0.2

0.3-

0.4

0.5

0.5

0.7-

0.8-

0.9-

1.0

l\Ui\i li ll_ 1Z.I

0.2 0.4

rmplitude

0.5 C.3

1.0

SOURCE DEIPT^ 11 CM SOURCE CiPTH 12 Cr SOURCE DEPTH 15 CM

RRNGE - 3. OX

Jiguie D.3 aeasurei€iits with Source Depth of 11, 13, and 15 la,

121

NORMALIZED AMPLITUDE:

0.0 0.2 0.4 0.6 0.3 1

.0

0.0 -f

i i

i

; V

SOURCE DEPTH 17 CN

0.1 -

\ A

-Q- SOURCE 0EP7^ 19 CM

0.2-

-«- SOURCE DEPTH 21 CM

0.3-

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0.4-

0.5- 0.6- 0.7- 0.8-

<f/

0.9- 1 n

1 . U

RANGE - 3. OX

Bigux€ D.4 Measureaents with Source Depth of 17, 19, and 21 Cm,

122

0.0

0.0-*

0.1

0.2

0.3

0.4-

\ 0.5-

0.5-

0.7

0.8

0.9-

M

1.0

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0.2 0.4 0.6

AMPLITUDE

0.8 1.0

—

SOURCE DEPTH 23

C.I

-e-

source: depth zs

CM

-i—

source ::=:- 27

on

RRNGE - 3. OX

figure D.5 Measureaents with Source Depth of 23, 25, and 27 Cm,

123

0.0

M

0.1-

0.2

0.3

0.4-

0.5

0.6-

0.7

0.8-

0.9-

1.0

NORMRLIZED RMPlIIUDl

0.0 0.2

0.4

0.5

1.0

source: depth 29 en

SOURCE CEFTH 31 CI

RANGE - 3. OX

liguie D-6 Measureients with Source Depth of 29 and 3 1 Cm.

124

BIBIICGBAPHY

Andersen. C.I. , and Iiebermann, B.C., "Sound Velocities In Bocks And Minerals," Physical Acoustics, IV-B, Edited fy

5. P. Mason, Academic fress, "TT6B.

Eaek, C.K., The Accustic Pressure In A Bedge-S haped fcater i§y_er Cverlyin q I FasT Fluid" Fc^tTcm, Easterns Thesis, TIavaT Tost" g r a3 uaF. eSch 00 I, "Ear cE, ~Y9'&iZ

radstaw. J. A., laboratory Stu_d_y_ Of Sound Propagation lite A fast Ecttcm Medium, MasterTs THesis, Naval FcsTgr a cuate

Erads taw fast Ect "ScEcclT Uune^T'SFT.

Erock, H.K., The AESD Parabolic Equation Model, KCEDA

lechnical Note 1z, January, T5 /"8.

Coppers, A.E., Humphries, and Sanders, J.V.. "Propagation Of

Sound cut Or A Fluid Wedge Into An underlying Pluid

Substrate Cf Greater Sound Speed", Accepted for For

Eublicaticn by JASA, May 1984.

Coppers. A.E., and Sanders, J. v., "Propagation Of Sound From A Fluid Kedge Into A last Bottom," PLENUM, 1980.

Coppers, A.E.. Sanders, J.V., Icannou, G.I., and Kawamura, E-# 1}L£ Computer Programs For Ihe Evaluation Cf The Accustic £ less ur e InpTi t"ude Ind PEase It Tne ~ EoTtcm 0~r I "Siege "Shapea. Fluid layer flverTaying A Fast TTuTd Half S pace, "Raval- P cs^q I adua te 3clooI~Tec"Bni cal ^epoYT~WS 11- 7"5±T7c2 , Eecemier, 1S78.

Graves, E.E., Nagel, A., Uterall, H., and Zauer, G.I.,

"Eange Dependent Normal Modes In Underwater Sound

Propagation: Application lo A Wedge Shaped Ocean," JASA,

vol. 58, December 1975-

Eardin, E-H., and Tapiert, F.D., "Applications Of Ihe Split Step Fcirier Method lo The Numerical Solution On Nonlinear And Variable Coefficient Wave Equations, " SIAM Review, Vol. 15, 1S73.

Tke Paracolic _olu]:ior BeTncTd asterTs Tresis,

Jensen, F.E., and Kuperman W.A., Environmental Acoustical Modelinq At SACLANTCEN, SACIANTCEN FeporT~5U-377 "TTovelTerT

Jensen. I.E., and Kuperman, K.A., "Sound Propagation In A Jiedge-Shaped Ocean With A Penetrable Bottom," JASA, Vol. 67, May, 1S8C.

Jenser, E.E., and Krol, H., Ihe Use Of The Paratolic Equation Method In Sound Propagation Hoveling, STCLUTZ'ETI "Hemorandum F1F72 , lugust", T"97"5.

Kawamura, M., and Icannou, I- , Pressure On Tie Interface Eetween A Converging Fluid Wedjge And A Fa"s"E~ F1u"icT~Bc"ttcffl , "Mas:E€rTs Thesis, Naval Tost" graduate- School"^ Decern "Eer, lb /a.

125

Kinsier, I.E., Frey, Jl.fi., Coppens, A.B., AND Sanders, J.V., Fundamentals Of Acoustics, Third Edition, John Wiley and 3ons"T^"2-

lee, I., and Botseas, G. , IED: An Implicit F inite -Difference; Computer Model for Reiving The Faraxjouc- Equation, N LSC Technical "Eeport 5E5 S7~T3a77 15S2.

lee, I., Ecteas. G., and Papadakis, J. 5., "Finite -Difference Eciuticn Ic The Parabolic Equation," JASA, Vol. 70, Septenrer, 1981.

lee, E., and McDaniel, S.T. , "A Finite-Difference Treatment Cf Interface Ccnditcns For The Paracolic Equation: Ihe Irregular Interface," JASA, Vcl. 73, May, 1983.

lee, L., and Papacakis, J.S., Numerical Soluticns Of Underwater Acoustic Wave Erggagaf ion Problems, "NEST "Teclnical fieport" 5"92"5, Tesruary, "T9T9.

IeSesre, P., Personal Communication, 11 May 1984.

McDaniel, S.T., and lee, D. , "A Finite-Difference Treatment Cf Interface Conditions For The Paratoiic Equation: Ihe Eorizcntal Interface," JASA, Vcl. 71, April, 1982.

126

IHI3JA1 DIS1R1B0TION LIST

Nc. Copies

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127

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126

3 5 3 7 \

210309

Kosnik

The implicit finite- difference (IFD) acou- stic model in a shallow water environment.

01

?3 JUL 9?

36 1 U * 375U7

375*7

• r>

30

Thesis

K828

c.l

Kosnik

The implicit finite- difference (IFD) acou- stic model in a shallow water environment.