750 NAVAL RESEARCH LAB WASHINGTON DC F/ 20/1 SOLVING … · DISTRIOUTIGN STATE1IMNT (of be SwIftI...

AD-Al19 750 NAVAL RESEARCH LAB WASHINGTON DC F/ 20/1SOLVING THE PARABOLIC EQUATION FOR UNDERWATER ACOUSTIC PROPAGAT-ETC(U)

AUG 82 L F ROCHE

UNCLASSIFIED R-80NL

SECUORTY CLISIFICATION OF ?to$l PAO% 1 110 De Eae..

REPORT DOCUMENTATOW PAGE1. OMIOR M.0119 GOVT ACCESSION 11 3 19I1"T AAO umg

NRL Repoft 8607 , ___ _______

4. TITLE foe LbIftle) 5. TYPE OF REPORT 4 PECO GOVERE

SOLVING THE PARABOLIC EQUATION FOR IIutechn tepot on a conduftnUNDERWATER ACOUSTIC PROPAGATION BY NRL problemTHE SPLIT-STEP ALGORITHM S. PCIOM ONG . 11EPORT "UK="W

7. AUTHOR(m) It. CONTRACT Oil GRAT N&UMUERI.)

JSA Perkins, R.N. Baer, E.B. Wright, and LF. Roche

1. PERFORMINIG ORGANIZATION4 NAME AND ADDRESS I.PgGA .E3PRdl.TK

Naval Research Laboratory 611 S3Washingon, DC 20375 RR110243

It. CONTROLLING OFFICE N6AUE AND ADDRESS Mi. REIPORT DATE

Office of Naval Research Anp" 30, 1982Arlingon, VA 22217 is. NUMOeR OF PAGES

14. MONITORING A46NCY NME a AGOREItsro EDleftme =7=00 C Oma es) IS.SEURTY CIL.A8&I ams tme.UNCLAMIFID

IM. ~C~6PCATI~WlGUDRA

to. meIIIINTION STATEMNT (of Me~ RaIamI)

Approved for public release; distribution ulmited.

tIt. DISTRIOUTIGN STATE1IMNT (of be SwIftI mlmd in 111100 15. it dobem 60 alp"

10. WIUPLtEMENTARY NOTES

it. KEY weli05 (cawhow evn AM mo" f 1" ya IdM* I* S

Acoustic propagatio

* Praboli si Ic

11A05TRACT (GaMIM. 40 eeYm SM 0 016061 MWeein 111110f ~I* 'SeS

.)Mathwms ic mode of underwateracousti proption awe uso in desinLg depoybng andusfn underwaer acoustic =mllaace systems. This repor documents a package of computerpropams which aclt we parabolit eqution for underwater wacout praoption oftm a s0pla

at NRLB-~ s un of it plpenh sad boowhkapblls Te a de tnhepwart correct for Soe etror Iduce by tde pasbolle mu pdloms. All of Me p ofma. thMs

00~ un 1473 " E~OF I, "V sho a f.i

SECURITV CLASSI CATION Of THIS P*0I (Men Date Rna....

20. AISYNACT rConlfu w

packag can plot their outputs. Thene plots include sound-speed contmws sound-speed profies, theinitial presure field, transmission lass a a function of range, transmission low as a function of depth,transansson-lou histograms In specified range-and-depth regions, and intensity contours al a functionof range and depth. The report smmarizes the theory, describes the Inpenetation, and tells howto run the progrms.

siCUm?, CLASSIMiASOU 0 OP AOMTM~ am"*

CONTENTS

INTRODUCTION ....................................................... I

OUTLINE OF THE THEORY AND ITS IMPLEMENTATION............................ 2

PROFIL: PROGRAM TO GENERATE SOUND-SPEEDPROFILES............................................................................ 5

START: PROGRAM TO GENERATE THE INITIALPRESSURE FIELD .................................................................. 7

CSPLIT: PROGRAM TO MARCH THE PARABOLICSOLUTION OUT IN RANGE...................................................... 10IREFERENCES .................................................................................. 13

APPENDIX A - VCUT: Program to Plot Transmission Loss Versus Depth ............ 15'IAPPENDIX B, - INTCON: Program to Plot Intensity Contours.......................... 17

APPENDIX C - TLWIST, Program to Plot Transmission-Loss Histograms ............. 19

APPENDIX D - Sample Outputs............................................................. 21

Sccession For7I1,ITS GRA&I.r,:r TAB

Avail.ability &des

Ic a IDit Specil1

SOLVING THE PARABOLIC EQUATIONFOR UNDERWATER ACOUSTIC PROPAGATION

BY THE SPLIT-STEP ALGORITHM

INTMODUCTION

Computer implementations of mathematical models of underwater acoustic propegatio_ can beused to analyze the performance of underwater acoustic surveillance systems. Such models enable Imore efficient use of existing systems and assist in optimal design and placement of proposed systems.They can also be used in the development of deployment strategies.

The propagation of sound in the ocean is influenced by many factors. These include processesthat are deterministic and processes that can be best described statistically. Deterministic processesinclude refraction and diffraction; an example of processes best described statistically is scattering byeither volume inhomogeneities or bathymetric irregularities. There are many theoretical formulationsand computer-based algorithms for deterministic solutions of the equations governing sound-propaFation in the ocean. An excellent survey of these models is contained in Ref. 1.

When the environment can be assumed to be cylindrically symmetric about the sound source, asis often the case, a i wo-dimensional (range-and-depth) treatment is sufficient. When the source fre-quency is low, say be~ow 200 Hz, and diffraction effects should be included with the gross refractioneffects, a wave-theoretic approach is better than one based on geometric optics. The parabolic-equationapproximbtion to the Helmholtz equation for wave propagation, developed by Fock [21 and first opplied

* to underwater acoustics by Tappert and Hardin (3,41, has proven itself applicable to a wide range ofproblems (4-131. Much has been written concerning the advantages and limitations of the parabolic-equation approximation (6,14-191, the techniques which are used to solve the equation [6,20-221, andways to improve the approximation (18,23,241.

We have developed a sequence of FORTRAN programs to model underwater acoustic propagationby solving the parabolic equation using the split-step (3,4,61 technique. The speed of this range-stepping algorithm is due to the use of a sine transform which is essentially the fast Fourier transform(FFT). Also, this approach makes it possible to take advantage of the vectorizing and pipelining capa-bilities of the Texas Instruments Advanced Scientific Computer (ASC) at NRL.

In our implementation we have included the option to partially correct for the errors inherent inthe parabolic approximation by a technique discussed in Ref. 24. We have also provided the user withthree alternatives for generating the initial pressure field required by the range-stepping alorithm: anormal-mode calculation, a functional form which Is Gaussian in depth, or a ussr-supplied complexFORTRAN function. All of the programs in this package can produce plots of their outputs. Theseinclude sound-speed contours, sound-speed profiles, the Initial pressure field, transwison los versusrange, transmission loss versus depth, intensity contours versus range and depth, and lop*ms oftransmission los in specified range-and-depth regions.

II2

PERKINS, BAER, WRIGHT, AND ROCHE

If the solution file is transferred (via magnetic tape) to a computer with a matrix plotter, thengray-scale plots of intensity versus range and depth can be generated. Also, if cylindrical symmetry isassumed, the effect of tilt on the performance of an array of hydrophones in the calculated pressurefield can be simulated. This is done in an auxiliary program which provides either gray-scale orisometric plots of intensity as a function of arrival angle and range from the source and which providesestimates of array signal gains and 3-dB widths.

The next section briefly describes the parabolic-equation approximation, the split-step technique,and the implementation on the ASC. The three sections after the next section describe how to accessand use the three main programs of the model. The inputs for each program are explained and theirformats are given. The various outputs are described. Three auxiliary programs are described inAppendices A, B, and C. Appendix D contains output plots from a sample case.

All of the programs described in this report are available for use by the Navy scientific communitythrough the Navy Laboratory Computer Network (NALCON).

OUTLINE OF THE THEORY AND ITS IMPLEMENTATION

The Helmholtz equation for two-dimensional acoustic wave propagation in the ocean isV2 #(r,z) + ki n2 (r,z) (r,z) - 0, (1)

where

/o - reference wave number- 2irF/co,

n (rz) - refraction index - co/c(rz),ane

(rz) - time independent acoustic pressure,

in which

F - source frequency,

ca - reference sound speed,

c(rz) - sound speed,

and

z - depth coordinate.

Usually the reference sound speed co is taken to be the average sound speed over the water column at-the source.

The solution of Eq. (1) is written as

(r,a) - ,-(Z), (2)

where satisfies

+ 2ko, + , + k In2 (rz) - I + 01 0.

4(kr)2(3

2.

-- ---- -

?JRL REPORT 360

It is assumned that ,/2is negligible in the far &iel and that [2)

1#,, I « 12ko,I.The physical assumptions of this approximation have been discussed in the literature (14-191. Thus~is approximated by a function p which satisfies the parabolic equation

*2ikop, +p+ ki [n 2(r~z) I]p -O. (4)

The solution of Eq. (4) is approximated by using the "split-step' algorithm [3,41,61, which marchesin range:

S(r + 4,,z) -~ eouIA/2..(iAa/(2ko) F ((zl.()

in Eq. (5), Fj(,,z)) is the Fourier transform of P(raz), s is the transorm variable, and J p. Tomeet the boundary condition at the ocean surfaice (p - 0), we add an imag source (SM as indicated inFig. 1. In the shaded region, n2 is given an exponentially increasing imaginar part which has theeffect of causing the pressure to die off as the boundaries at D + d and - (D + d) are approaced.L (Dis the maximum water depth and usually d - (113MD) This prevents energ from the periodicallyrepeated regions containing image sources from entering the transform region. In practice, we use adiscrete sine transform over the smaller region indicated in Flig. 1.

The speed of this algorithm is due to the use of a sine transform which is essentially an MrT. The

subroutine 125) which performs this transform makes full use of the vectorizing and pipelining capabili-

0 7 wI0vWKWCD+ d

4

- >. . - "

PERKINS. BAEIR. WRIGHT, AND ROCHE

The error which occurs from solving Eq. (4) by the split-step algorithm can be mh by t*:small range steps [6]. In our implementation we have included the option to partially correct for theparabolicw approximations preceding Eq. (4) 1241. Analytically, we can express these corrections by

rZ (rz) + rr 2k0 I2

where the second-derivative term represents the corrections (a second-derivative term having beenneglected in the parabolic equation), ana dropping this teim yields the usual parabolic-equation approxi-mation.

To implement the algorithm of Eq. (5), the sound-speed field c(rz) must be known (in order tocalculate n(r,z)), and an initial pressure field must be given (which will be marched out in range). Wehave separated these tasks from the range-stepping program, called CSPLIT, by writing two preliminaryprograms called PROFIL and START. PROFIL reads the environmental data, interpolates sound-speedprofiles; writes the bathymetry and a list of sound-speed profiles on a file for use by START andCSPLIT, and draws a plot of these profiles and the ocean bottom. START creates a file containing theinitial pressure field corresponding to # in Eq. (2). The user can choose an initial field from threealternatives. a normal-mode'calculation 126,271, a functional form which Is Gaussian in depth f28], ota user-supplied complex FORTRAN function which wEI override the Gaussian. A flow chart indicatingthe relationships between the basic programs is shown in Fig. 2.

. r2- sun yI ---

inleegmmPA, 6AT ~~

............................. ..".......... ..........mi sm:I Ii l'lrm no. . '

n u a . . • . ; , -: ..'!

NOW


The error which occurs from solving Eq. (4) by the split-step algorithm can be reduced by takingsmall range steps (6]. In our implementation we have included the option to partially correct for the"parabolic" approximations preceding Eq. (4) [241. Analytizaliy, we can express these corrections by

(rZ) "=-z e k (rz) + 'r0"P + 2k0 8r2 J

where the second-derivative term represents the corrections (a second-derivative term having beenneglected in the parabolic equation), and dropping this term yields the usual parabolic-equation approxi-mation.

To implement the algorithm of Eq. (5), the sound-speed field c(rz) must be known (in order tocalculate n (rz)), and an initial pressure field must be given (which will be marched out in range). Wehave separated these tasks from the range-stepping program, called CSPLIT, by writing two preliminaryprograms called PROFIL and START. PROFIL reads the environmental data, interpolates sound-speedprofiles, writes the bathymetry and a list of sound-speed profiles on a file for use by START andCSPLIT, and draws a plot of these profiles and the ocean bottom. START creates a file containing theinitial pressure field corresponding to # in Eq. (2). The user can choose an initial field from threealternatives: a normal-mode calculation 126,271, a functional form which is Gaussian in depth 1281, ora user-supplied complex FORTRAN function which will override the Gaussian. A flow chart indicatingthe relationships between the basic programs is shown in Fig. 2.

.1

. 2 - Flow € tt IndicWang te relaionul bteen t

main prop'ams: PROFIL, START, and CSPLIT

4

NRL REPORT 8607

The direct outputs from CSPLIT are a listing and/or plot of transmission loss versus range foreach input depth. If the user wishes, CSPLIT will produce a file containing the parabolic solution atevery depth grid point for evenly spaced range steps. This file can be used as input to three auxiliaryprograms: VCUT, INTCON, and TLHIST. VCUT creates a transmission-loss-versus-depth listingand/or plot for each input range, INTCON draws intensity contours, and TLHIST draws histograms oftransmission loss.

The three sections that follow describe how to access and use PROFIL, START, and CSPLITrespectively. The inputs for each program are explained and their formats are given. The various out-puts are described in more detail. The auxiliary programs VCUT, INTCON, and TLHIST are describedin Appendixes A, B, and C respectively. Appendix D contains output plots from a sample case.

*PROFIL: PROGRAM TO GENERATE SOUND-SPEED PROFILES

The purpose of PROFIL is to read the environment, interpolate sound-speed profiles, create a listof profiles on file FT02F001 for later use, and plot these profiles. Careful consideration should begiven to the interpolation, since each profile is in effect until the range of the following profile isreached.

The following sample job deck indicates how to access and use the program:

/ JOB EXAMPLESPROFIL,account number,user code,LOC-RTE7,OPT-(R),CAT-9/ LIMIT BAND-35,SEC-400/ LIMIT BAND-35,SEC-200/ PD P,USERCAT/D8I/L60/PARA/ PD YOURPATH,USERCAT/.../ ASG SYS.OMOD,P/PROFIL/OBJ,USE-SHR/ ASG LIBSUBS,P/LIBSUBS/OBJ,USE-SHRI ASG CONLIB,USERCAT/D81/L60/CONLIB/OLIB,USE-SHR/ DISSPLA VERS-8.2/ LNK LSPACE-15000LIBRARY CONLIBLIBRARY DISSPOBJLIBRARY LIBSUBS/ FXQT OPT- (I),CPTIME-20000... DATA...I CAT YOURPATH/FT02F001,ACNM-FT02F00I/ FOSYS Fr59F001,TYPE-PLOT,FORM-00IEOJ

Job category 9 (CAT - 9) will not suffe if more than 50 bands or more than 600 pseudo-seconds arei required.

I The inputs are as follows:

NBOT Number of bottom points: I < NBOT < 101.

NP Value such that ABS(NP) is the number of input profilem NP < 0 turns offthe spherical-earth correcton.

i 1 --

RMAX ~ ~ ~ ~ b ftxmw which (1m) whc a e vrhe b SL

4R), ~(l)Rang. mad dept =ac that RD(l) is &C depth (W7'kWW at R-ge 510". 1) INS1, MWO, Iand, BR1(1) mwust howe*.

NSPFYD NaMbr-o osoeicten speeld by peire a-oftmM74% lO .edM() *blIafedescribed below: NSPFYD < 50.

MRON. Number of prvem to be gemerae betwen the -urn o lopet in* Now, the onext. input: prot.. UnIs 12 > 0, themeprofAe OII bew *Ow- sumed.between the two Input profile.

Ri Starting rung (1cm) for the current input pofie.

R2 Ending rowg (kim) for the curren iput -prfie. If R2, >.O and lO >0,then the interpolated profiles will hoeqalapd betWeen rage R2 OWdtrange, of thle next input pofile.*1DOl), CO) Depth and sound speeds such that Cl) isbe sond.5eed (1014)at dbpD(O) (in); 1 1 , NC and DOl) must baxero-

NOl),M(I) Pair of indices which indicates timt the, tist pionte uatto

Rang. profinleh plt

MSlScale, ((i/s)/l.) for plotl*n pwk& *

Starting r ffp (c)for t CobtMu $tK reQuie .* IfILT 2 ort

11libs raws (kO ibr fti eafttu Oki it, lit - 1,

. ... .....

W1 All

CF....l"

NRL REPORT 8607

KMPI Horizontal (range) scale (km/in.), if IPLOT -2 or 3.

NCL Total number of contour levels (evenly spaced between CLMIN and CLMAX),if IPLOT - 2 or 3.

The formats of these inputs are as follows:

Card Inputs FormatI NBOT, NP, [PLOT, RMAX (315, F10.3)2 BR(I), 1113[), 1 - 1, NOOT 01OF8.2)3* NC, NSPFYD, IRON, RI, R2 (315, 21710.3)V DOI), C(I), 1 -1, NC (1OF8.2)

SO (NW, M(0), 1 1, NSPFYD (1615)6' KMPERI, MPSPI (215)7# RANi*.lN, RANMAX, DEPMIN, DEPMAX,

CLMIN, CLMAX, VERTIN, KMPI, NCL (7F10.3, 215)

ranse.t Card 5 is omitted if 0 is inputted for NSPFYD.

*Card 6 is omitted if IPLOT - 0 or 3.'Card 7 is omitted if IPLOT - 0 or 1.

The outputs are the following:

* Input profiles on print file FTO6FOOI.

" A plot of profies on FT59FlOI1, if [PLOT -I or 2. A delta or a nabla will mark the range foreach profile. A nabla indicates that the profile was an input profile, and a delta indicates that theprofile is an interpolated profile. Each profile is positioned with respect to its symbol so that thesymbol marks a 1 500-in/s reference point for plotting the profile. If a contour plot is requested, itwill also be on FTS9FOOI.

* Profiles and the bottom on FTO2FOOI. The user should catalog 17112F0O1.

START: PROGRAM TO GENERATE THE INITIAL PRESSURE FIELD

The purpose of START is to create the initial pressure field on FTI1FOOI. A sample job deckindicatinS bow to access and use the program is as follows:

/ JOB EXAMPLESSTART,account number,user codeLOC-RTE7,OPTU (R),CAT-9/ LIMIT BAND-..I-./ PD P,USERCAT/DS1/L60/PARA/ ASO FT2F0OI ,YOURPATH/FTO2FOI,USE-SflR/ ASO SYS.OMOD,P/STARTIO3J,USB-SHRI ASO LIUSUDS, P/LI3SLJ3S/OB,USE-SHR/ DISSPLA VERS-S.2/ LNK LSPACE- IS00LIBRARY LIUSUBSLIBRARY DISSPOBJ/ PD I'TOEF0,BAND-l/IS/l/ FXQT CPTIME-. ..,ADDMEM-. . .,OPT-(I)

.... AT...

7


/ CAT YOURPATH/FTI8F001,ACNM-FTI8F00I/ FOSYS FT59F001,TYPE-PLOTI EOJ

Again CAT - 9 will not suffice if more than 50 bands or more than 600 pseudo-seconds arerequired. If ISTART - 1 or ITAPE - 0, 20 bands should suffice; otherwise the number of bands touse is ((guess for the number of modes)*NN + 5"NN)/16384 + 20, where NN is the number ofpoints in depth (NN - 2**NPOW).

On the ASC, CPTIME must be specified in hundredths of seconds. If the normal-mode calcula-tion is used, the time needed may exceed the default. To do a problem with NPOW - 9, NINT - 4,and 164 modes, 45 seconds were needed. Another problem with NPOW - 11, NINT - 4, and 325modes required 430 seconds.

The ADDMEM value to use is MAX(8*NN + 4000, 8000).

The file containing the profile(s) created by PROFIL must be assigned with the access nameFT02F001. Other inputs are as follows:

ISTART An integer 0 or I indicating how the initial field will be calculated. If ISTART- 0, the initial field will be created by a normal-mode calculation [26,271. IfISTART - 1, a real Gaussian 128] will be used, or the user may supply an ini-tial field by writing a complex FORTRAN function with the name STFTN,which will return for a given depth the complex pressure at that depth. Thefollowing FORTRAN statements may be used:

COMPLEX FUNCTION STFTN(Z)DOUBLE PRECISION RO,C,FBSS,SOURDCOMMON /OUT/ RO, CO, F,BSS,SOURD

STFTN-...RETURNEND

The normal-mode start should be more accurate bui can be very expensive athigher frequencies. The source must be several wavelengths away from thesurface and bottom in order. to'use the Gaussian start.

NPOW Integer < 13 specifying that the number of points in depth on the initial fieldwill be 2**NPOW. NPOW should be large enough so that the depth grid spac-inS Az, which equals (4./3.)**(maximum depth along thck)/2" WPOW, is lessthan 1/2 wavelength.

[PLOT Plot choice, 0 or 1. If IPLOT -1, a plot fil for the initial field is produced.

F Source frequency (Hz).

RO Range (kin) where the initial field is desired. For a norriin-mode start, ROmust be at least several times the wavelength. For the Gausdan start, :R0should be set to 0.001 kin.

BSS Speed of sound (mis) in the botton.

8

NRL REPORT 3607

SOURD Depth of the source (i).

CO Reference sound speed (m/s). If CO - 0.0, a water-column average is used.

The remaining inputs, which are not needed if ISTART - 1, are as follows:

ITAPE File choice 0 or 1. If ISTART - 0 and ITAPE - 1, the eigenvalues andeigenfunctions are written on FTI7FOO1 (a QDAM file), and some unformattedinformation is on FT03FOOl which could be used to open FTI7F00I. Unlessthere is some use for the eigenvalues and eigenfunctions, ITAPE - 0 shouldbe used.

NINT Factor giving the number of points in depth used by the program in calculatingthe modes, which is NINT*(2**NPOW) points in depth. HINT must be apower of two, and NINT*(2**NPOW) must be no greater than 16364. NINT

4 is good in most cases.

MAXMOD The maximum number of modes that will be used. if all modes are to beincluded, MAXMOD must be at letst as large as the actual number of modes.If MAXMOD is less than the actual number of modes, then only the lowestmodes (those with 0 to MAXMOD - I turning points) are included. A goodapproximation to the actual number of modes is 2*F*H*SQRT./C0**2 -I./BSS**2), where H is the water depth at the source and CO is the averagesound speed in the water column.

RHOI Water density (i/cm3).

RH02 Density (g/cm3) in the bottom.

EPSILN Convergence parameter, with a suggested value being EPSILN - 0.001.

The formats of the inputs are as follows:

Card -n iwts FoatI AR, [POF, , m

2* ITAPE, NINT, MAXMOD, RHOI, RHO2, EPSILN (315, 3P10.3)*Cad 2 is not nee if ISTART - 1.


0 The eilgenvalues and the initial pressure field on file FTO6F00I.

* The initial preuwre field on file FMlU1M01. This file should be cataloged.

* Plot of the initial field on file FTS9F00 (only if IPLOT - 1).

Files FT03F101 and FTI7F00I (only if ITAPE - I). (The description of the inputITAPE explains of these files.)


CSPLIT: PROGRAM TO MARCH THE PARABOLIC SOLUTION OUT IN RANGE

The purpose of CSPLIT is to use the split-step algorithm in calculating the'solution to theparabolic-equation approximation to the Helmholtz equation. A sample job deck indicating how toaccess and use the program is as follows:

/ JOB EXAMPLE$CSPLIT,account number,used code,LOC-'RTE7,OPT-(R),CAT-9/ LIMIT BAND..,MN./ PD P,USERCAT/D81/L60/PARA/ PD YOURPATH,USERCAT/.../ ASO FrF22PO1,YOURPATH/FTr02FOO,USE-SHR/ ASO FrlgFOOl,YOURPATHIFrl8FOO,USE-SHR/ ASG SYS.OMOD,P/CSPLIT/OB,USE-SHR/ ASO LIDSUDS,P/LIDSUBSIOB,USE-SHR/ DISSPLA VERS-8.2/ LNK LSPACE -15000LIBRARY LIBSUBSLIBRARY DISSPOBJ/ PD FT06PO1,BAND-1I50/1/ PD FTO9FOO,BAND- 1/15/1 ,RCFM -PBA,BKSZ-3944,LREC- 136/ FXQT CPTIME-. .. ,ADDMEN -. .. ,OPT-(Q)

... AT...ICAT YOURPATH/Fr66F001 ,ACNM-Fr66FOOI,DTYP-TAPE/ OSYS Fr59POO1,TYPE-PLOT,FORM -00F OSYS FTO8FOOI

/EOJ

Again CAT - 9 will not suffice if more than 50 bands or more than 600 pseudo-seconds are required.If ISKPR - 0, 30 bands should suffice. Otherwise the number of bands to use is 2*NN* (number ofrange steps)/l(ISKPR*16384) + 30, where NN - 2**NPOW and ISKPR is described below.

CPTIME is approximately proportional to the number of points in depth and the number of rangesteps. To do a problem with 1024 points in depth and 1000 range steps, 16 seconds were needed.Also, this problem required 64 pseudo-seconds. If ICORR - 1, the run time will approximately dou-ble. The ADDMEM value is 6*NN + 8000.

The file containing the profile(s) created by PROFIL must be assigned with the access nameFrO2170O1. The file containing the initial pressure field created by START must be assigned with theaccess name FTiSFOOI. Other inputs are as follows-.

j IBFLAG Bottom flag, 0 or 1, with 0 implying that the bottom is flat

IPFLAG Profile fleg, 0 or 1 with 1 being used if the sound-speed profile is to changewith range. If IPFLAG - 0, the first profile on Fr02F00I will be used overthe entire range of the rue.

IPLOT Plot choice, 0Oor 1. If IPLOT i- 0, no plot files will be..creted.

NPOW Integer living the number of points in depth, which will be 20*NPOW. NPOWmust be the same as it was for START.

NRD Number of receiver depths: 0 < NRD < 6.

10 3

NRL REPORT 8607

ISKPR Number of range-step increments in creating file FM66F001, containing thesolution. As the parabolic solution is marched out in range, the complex-valued parabolic pressure at each depth grid point is written to file FT66F001every ISKPR range steps. If ISKPR - 0, no file is created.

ICORR Number of steps to take between corrections. If ICORR - 0, then no correc-tions will be made.

NBSS Number of ranges where the bottom sound speed is to be changed: 0 < NBSS4 10. The ranges and corresponding sound speeds are the inputs RBSS(I) andXBSS(I) (1 < I < NBSS) described below. If NBSS - 0 and CRTANG -0.0, (as described below) then the bottom sound speed used in START will beused throughout. If NBSS > 0 is used, then probably CRTANG - 0.0 shouldbe used.

RBSS(I), XBSS() Range (kin) and sound-speed (m/s) values to be inputted only if NBSS > 0.XBSS(I) is the bottom sound speed to be used from range RBSS (I) to rangeRBSS (I + 1) for 1 < I < NBSS - 1. The bottom sound speed used inSTART will be used from the initial range to range RBSS(I). XBSS (NBSS)will be used from range ROSS (NBSS) to the end of the run.

DELR Range step (km). In many cases with typical ocean sound-speed profiles andwater-borne propagation, range steps as large as 5 or 10 wavelengths are per-missible. 'When rapid sound-speed changes (such as those often seen at thewater-bottom interface) are important, range steps as small as I or 2wavelengths may be required [191.

RMAXX Final range (kin) for the run. If RMAXX is not positive, then the maximumrange which was inputted to PROFIL will be used.

STARTR Restart range (km). If STARTR > 0.0, then the pressure field at the rangestep nearest STARTR km is written on file FTl9F001. This file can be used to"restart" CSPLIT by releasing FTISF001 and then renaming FT19FOO1 asFTISF00I. If STARTR - 0.0, no restart file is created. If STARTR < 0.0. arestart file is created at the final range of the run.

CRTANG Critical angle (O). If CRTANG > 0.0, then each time the sound-speed profileis changed, the bottom sound speed Cb will be changed so that Cb -C,/cos(CRTANG), where C, is the water sound speed at the depth grid pointimmediately above the water-bottom interface at the current range. IfCRTANG > 0.0 is used, then probably NBSS - 0 should be used. (If NBSS-0, no values for RBSS(1) and XBSS(1) should be inputted.)

RECD(I) Receiver depth (in): 1 (1 NRD.

ACOEF Parameter effecting the attenuation in the deep bottom. This is an artificialattenuation, designed to prevent false reflections from the boundary below thebottom and is not Intended to effect a realistic bottom attenuation. (Thetransform region is shown In Fig. 1, and the attenuation inputs DIPKM andDBPWL are described below. A value of 0.01 is recommeded for ABCOEF.

I I i I I "I i . . . ..


DBPKM Attenuation (dR/kin) in the water. If DDPKM > 0.0, then the attenuation winlbe DBPKM dB per km. If DBPKM < 0.0, then the attenuation will be calcu-

lated as a function of the frequency.

DBPWL Attenuation (dB/wavelength) in the bottom, where the wavelength depeds onthe bottom sound speed.

SMKM Smoothing window (kin) for the transmission-loss printout and plots. Gaussianweights are used with 6o, - SMKM km. SMKM - 0.0 causes no smoothing.The window will be reduced, if necessary, so that it does not extend over morethan 101 range steps.

AKMPI Scale (km/in.) for the transmission-loss plots.

DBI, DB2 Minimum and maximum transmission-loss values for the plots. DBI -DB2- 0.0 gives default values of DB1 - 40 dB and DB2 - 130 dB. If DB2 -DB1 > 90.0, then DRI wini be set equal to DB2 - 90.0.

The formats for the inputs are as follows:

Card Inguts FormatI IBFLAGIPFLAG,IPLOTNPOW,NRD,ISKPR,ICOR,NBSS (8MI)2* RBSSI,XBDS(I),I - 1,NDSS (10F8.2)3 DELR,RMAXX,STARTR,CRTANG (4178.2)4 REDC(I),J - 1,NRD (1OF3.2)5 ABCOEF,DOPKM,DBPWL,SMKM (4178.2)6 AKMPI,DB1,DB2 (3F8.!U

*Card 2 is omitted iV NUISS - 0.


* Transmission loss at all ranges for each receiver depth on FlO6FO0l.

* A table summarizing profile changes and bottom-sound-speed changes on 1717817001.

* Plots of transmission loss versus range at each receiver depth on FTS9FOO1 (only if IPLOT -1).

* The pressure field at evenly spaced ranges on FT66FOOI (If ISKPR > L.,. This file can be used(by VCUT, described in Appendix A) to draw transmission loue-versus-depth plots at-severalranges, can be used (by INTCON, described in Appendix I) to draw intensity contours, or can beused (by TLHIST described in Appendix C) to draw histograms of transmission loss.

*A restart field on F1719170O1 (if STARTR if 0).

Milk- -1

NRL REPORT 3607

REFERENCES

1. P.C. Etter and R.S. Flum, Sr., 'A Survey of Underwater Acoustics Models and Environmental-Acoustic Data Banks," Anti-Submarine Warfare Systems Project Office Report ASWR-80-115,Sept. 1980.

2. V.A. Fock, Electromagneti D1raction and Propagation Problems, Pergamon, 1965.

3. F.D. Tappert and R.H. Hardin, "Computer Simulation of Long-Range Ocean Acoustic PropagationUsing the Parabolic Equation Method,* p. 452, in Proceedings qf the Eighth International Congresson Acoutics, Vol. II, Goldcrest, London, 1974.

4. C.W. Spofford, "A Synopsis of the AESD Workshop on Acoustic-Propagation Modeling byNonray-Techniques, 22-25 May 1973," Acoustic Environmental Support Detachment, Office ofNaval Research, Technical Note TN-73-05, p. 14, Nov. 1973.

5. S.M. Flatti and F.D. Tappert, 'Calculation of the effect of internal waves on oceanic soundtransmission,' J. Acoust. Soc. Am. 58, 1151-1159 (1975).

6. F. Jensen and H. Kro, 'The Use of the Parabolic Equation Method in Sound Propagation Model-ing,' SACLANT ASW Research Centre La Spezia Memorandum SM-72, Aug. 1975.

7. J.S. Hanna, 'Example of acoustic model evaluation and data interpretation,' J. Acoust. Soc. Am.66, 1024-1031 (1976).

8. K.M. Outhrie and D.F. Gordon, "Parabolic Equation Predictions Compared with Acoustic Propa-ption Measurements from Project TASMAN TWO," Naval Ocean Systems Center TeclinicalReport 133, 1977.

9. R.W. Bannister, R.N. Denham, K.M. Guthrie, and D.G. Browning, 'Project TASMAN TWO:Lowfrequency propagation measurements In the South Tasman Sea,' J. Acoust. Soc. Am. 62,847-859 (1977).

10. B.A. Gold, V. Vigliotti, and J. Clark, "Comparison Between Measured and Theoretical Transmis-S~sion Loss Across the Gulf Stream,' U.S. Naval Oceanographic Office Technical Note TN 9000-

91-79, Nov. 1979.

11. R.N. Baer, 'Calculations of sound propagation through an eddy,' J. Acoust. Soc. Am. 67, 1180-1185, 1980.

12. G.V. Frisk, J.A. Doutt, and E.E. Hays, 'Bottom interaction of low-frequency acoustic signals atsmall grazing angles In the deep ocean,' J. Acoust. Soc. Am. 69, 84-94 (1931).

13. J.S. Hanna and P.V. Rost, "Parabolic equation calculations versus North Pacific umurementdata,' J. Acout. Soc. Am. 70, 504-515 (1981).

14. S.T. McDaniel, 'Propagation of normal mode in the paraboc approximation," J. Acoust. Soc. Am.57, 307-311 (1975).

15. R. Fltzrad, 'Helmholtz equation as an initial value problem with appllmlent to acoutic pro-pagtlon,' J. Acoust. Soc. Am. 57, 839-842 (1975).

Ii - D


16. S.T. McDaniel, 'Parabolic approximation for underwater sound propagation,' J. Acoust. Soc. An.58, 1178-1185 (1975).

17. D.R. Palmer, 'Bikonal approximation and the parabolic: equation," J. Acoust. Soc. Am. 6, 343-354 (1976).

18. F.D. Tappert, 'The Parabolic Approximation Method," p. 224 in Were Ptuqaa amd UndenveterAcowuse J.D. Keller and J.S. Papadakis, editors, Lecture Notes in Physics, Vol. 70, Springer-Verlag, Heidelberg, 1977.

19. R.L. Dicus, 'Boundary'reflection/diffraction effects and the parabolic equation algorithm, submit-ted to J. Acoust. Soc. Am.

20. H.P. Bucker, 'Equivalent bottom for use with the split-step parabolic equation sound propagationmodel,' J. Acoust. Soc. Am. U8 (SI), S78 (A) (1980).

21. D). Lee and i.S. Papadakis, 'Numerical solutions of the parabolic wave equation: An ordinary-differential-equation approach,3 J1. Acoust. Soc. Am. 65, 1482-1488 (1980).

22. D. Lee, G. Dotmess and J.S. Papadakis,' Finite-difference solution to the parabolic wave equation,'J. Acoust. Soc. Am. 76, 79S-800 (1981).

23. H.K. Brock, R.N. Buchal, and C.W. Spofford, 'Modifying the sound-speed profile to improve theaccuracy of the parabolic-equation technique," JI Acoust. Smc. Am. 62, 543-552 (1977).

24. LA. DeSanto, J.S. Perkins, and R.N. bar, 'A correction to the parabolic approximation,' J.Acoust. Soc. Am. 64, 1664-1666 (1978).

25. H.K. Brock, Naval Research Laboratory, unpublished subroutine.

26. A.V. Newman and F. Ingenito, 'A Normal Mode Computer Program for Calculating Sound Propagation in Shallow Water with an Arbitrary Velocity Profile,' NRL Memnorandum Report 2381, Jan.1972.

27. J.F. Miller and S.N. Wolf, 'Modal Acoustic Transmission Loss (MOATL): A Trauunlssion-LousComputer Program Using a ?4ornul-Mode Model of the Acoustic Field in the bcean, NRLj

Report 8429, Aug. 1980.28. liK. Brock, 'The AESD Parabolic Equation Model,' Naval Ocea Research and Development

Activity Teccal Not 12, Jan. 1978.

14

AppemlzAVCUT: PROGRAM TO PLO)T TRANSMSSION LOSS VERSUS DEPTH

The purpose of VCUT is to draw plots of transmission loss versus depth at several ranges usingthe data file created by CSPLIT. A sample job desk indicating how to access and use the program is asfollows:

/ JOB EXAMPLESVCUT,account number, user code,LOC"RTE7,OPT-'(R),CAT-9/ LIMIT BAND -.. .,MIN -I/I'PD P,USERCAT/1)8l/L6O/PARA/I'PD YOURPATH,USERCAT.../ ASOP PT66F001,YOURPATHIFTr66FOO,USE-SHR/ ASG SYS.OMOD,P/VCUTIOB,USE-SHRI / ASO LIDSUBS,PILIBSUDSIORJ,USE-SHR/ DISSPLA VERS-8.2/ LNK LSPACE -15000LIBRARY DISSPOBJ

LIBRARY LIDSUBSIWAIT

!FXQT... T...

/ FOSYS FrS 9FOO1,TYPE-PLOTFORM -00/ EOJ

Space for the data file F176617001 which was created by CSPLIT must be provided. The defaultCPTIME is normally sufficient for less than ten ranges. The ADDMEM value is MAX(6NN +4000,8000).

The data file created by CSPLIT must be assigned with the access name FT66FOOI. Odher inputsare as follows:

NPOW [nteger which must be the same as for START and CSPLIT.

NRAN Number of ranges on file F1760F01. NRAN - WFIX((total number of stepstaken by CSPLIT)/ISKPR ) + 1.

NR Number of ranges tobe inputed: 0 <NR <51. A mranm slo-b veruus-depth plot will be generated for each range.

RANOE(I), DEL(I) Range (kin) and range-Interval (kin) values. For tbm plot ousadlag torange RANGE(I), I - 1,NR, the tfansulson-lou value at a given depth wIN

* I be calculated from the average intensity from rage RANGE(I - DELG)/2.Oto range RANGE(I) + DEL(I)/2O at that depth. IN DEL(I) - &,0, then Oheplot for RANOE(I will not lncorporate a rnge average. RANOI) endDELVI) my be modified by VCUT to that the natnaeIoved Inathe aiwla-ilon ame on range grid Koem


DI Starting depth (in) for the plots.

D2 Final depth (in) for the plots.

DMAX Maximum depth (in) of the water.

AMPI Depth scale (rn/in.) for the plots.

SMM Smoothing window (in). Gaussian weights are used with 6. SMM in, andSMM-O.O is used for no smoothing. Smoothing takves Place after rangeaveraging.


Card !nPuts Format-NPO0W,NRAN,NK (15

2 RANGE(I)DEL(J,- l,NR I (SF10.3) I*3 D1,D2,DMAX,AMPI,SMM I(SF10.3)

* The outputs are the following:

* Depths and transmission losses for each input range on FTO6FOOl.

0 T.'anission-loss-versus-depth plots for each input range on F1759F001.

INTCON: PROGRAM TO PLOT INTENSITY CONTURS

The purpose of INTCON is to draw intensity contours using te data Ale created by CSPLT. Asample job dock indicating how to access and use the program is as follows:

/ JOB EXAMPLESINTCON,account number,user code,LOC".RTE7,OPT-.(R),CAT.13/ LIMIT BAND-.. .MIN-10/I'PD PUSERCATID8lIL6OIPARA/I'PD YOURPATH,USRRCAT/.../ AsOP Fr02F001 ,YOURPATH/inFro2oO,usE.sHR/ ASOP Fr66r001,YOURPATHFr66FOIlUSE-SHRt/ ASG SYS.OMOD,PIINTCONIOB,USE-SHR/ ASG CONLIB,USERCATIDIL60ICONLIBIOLIB,USE-SHR/ ASO LIBSUDS,PILIBSUBSIOB,USE-SHR/ DISSPLA VERS-8.2/ LNK LSPACE- 15000LIBRARY CONLIBLIBRARY DISSPORJLIBRARY LIBSUBS/ FXTTCflIME-...ADDMEM-wscete..S.~uterole.o

required. Space for the data file FT66FOOI wihwscetdb SLTmmb rvdd oCPTIME, 30 second. for each 100 range steps should sufie. The ADDMEN value is MAX(6*NN +4000,8000)

The file containing the profile(s) c-reated b R ILmust b sindwt h cesnmFIO2FOOI1. The data fie created by CS3PLIT must be assigned with the access name FT66FOWl. Otherinputs are a follows:

NPOW Integer which must be the same as-for START and CSPLIT.

NRAN Number of ranges on file Fr66FO0l: NRAN - IFI((tota number of stepstaken by CSPLIT)IISKPR ) + 1.

NCI. Number of contour levels to be plotted: 0 < NCI. < 21.

LMIN inimum contu level (mls) to be drawn. Vf LMIN - 0, the the Iki,.

contour level will be calculated.

IDBLCL Diffesrence (W/O) between two consecutive contour levels.

ICMIN Starting rang. (kin) for the plot

PERKINS, BAE, WRIGHT, AND ROCH

XMAX Ending range (km) for the plot. If XMAX is more than 1000 range stepsbeyond XMIN, XMAX will be reduced by the program.

YMIN Starting depth (m) for the plot.

YMAX Ending depth (m) for the plot. If YMAX is more than 400 depth points deeper

than YMIN, YMAX will be reduced by the program.

AKMPI Range scale (km/in.) for the plot.

AMPI Depth scale (rn/in.) for the plot.


Card I ts FomatI NPOW,NRLNN [LLIN,IDELCL I -1

2. XMIN,XMAX,YMINYMAX,AKMPI,AMPI 0 .4


* Some information about the length and number of contour levels on 0O 1.

0 The contour plot on FrS9FO01.

.i

1S .

4 NIL RSPORT WM

Awift CTUE 1ST: PROGRAM TO PLOTr 7tRANSMdISON-LOSS HISTOGRAIS

The purpose of TWHIST is to draw histogroms of eatnhuiea loe using the date fife created byCSPLIT. A sample job dock indicating how to access and use the program is to follows:

I JOB EXAMPLEVSLHISTaccount number,usarcodeLOCRT.7,OPT- (R),CAT-9/ LIMT BAND-.. ..SEC-600/ PD P.USERCAT/DlI/L60/PARA/ III YOURFATHIUSERCATI.../ ASGP Fr66FOOIYOURPATIHFT66FOO1,USE-SHRI ASO SYS.OMODIP/TLHIST/OJU2-Swh

* I~ ASO LIUSUBSUBISUDS/OUSE-SHRI DISPLA VERS-9.2/LNK LSPACE-20000

LIBRARY LI3SUISLIBRARY DISSPOB/ WAITf~ FXQT OPT- Q),CPTME-.. .,ADDbM~f4-...

DATA../FOSYS FFS9FOO,TYPE-PLOT

The data Mie created by CSPLIT must be ssgnd with the amcm name FT166POI1. Other inamtwe foftw

NPOW Intoer which dust bw the $a*- to for CffIwM 2'NPOW be% tdo<I number of points in depth on fibe lT66POOL.

NRam Number of MUMge on fl PFOOI: NRAN WI(ttlatbe fUea ~taken by COPUA/IK) + I.

NHIS Number of bletgra to be olotted(14.

.1NUN Nmbe of " oft toern ahstefd willi am W Cm a thlam to

ths 4 ad + . ble e p NW is 4dm. dma it hM e

ow4 go .,1 164,lo"a

Th-~otswpo vwinmw wes wts te f'e NM >h 9 mMnpi bgTA okG fdexak(*o"k*x ~ Tw "m10 w ~wo 6 oot f,**v INII


XMAX Transmission-loss (dB) value at the center of the last histogram bin.

BINW The width of a histogram bin (dB).

YAXIS Length (in.) of the y axis (number of occurrences).

YMAX Maximum value desired on the y axis (number of occurrences). This value isautomatically increased if it is not large enough.

YSTP Tick-mark spacing on the y axis (number of occurrences).

DMAX Maximum water depth (m).

The following four variables are required for each histogram:

D Depth (m) at which the transmission-loss histogram is to be centered.

ND Number of depths to be used in the calculation of transmission losses centeredon depth D.

R Range (km) at which the transmission-loss histogram is to be centered.

NR Number of ranges to be used in the calculation of transmission losses centeredon range R.


Card Inputs Format1 NPOW,NRAN,NHIS,NBIN (415)2* XAXIS,XMIN,XMAX,BINW,YAXIS,YMAX,YSTP (7F10.3)3 DMAX (F10.3)4' D,ND,R,NR (2(F10.3,I5))

*Card 2 Is inputted when NBIN - 0.

tCard 4 is repeated for each histogram (NHIS times).


* Histogram statistics on FT06FOO1 including the mean, median, and one-sigma points.Any transmission tosses that are too large or too small for the plot will be outputted onFT06Foo1.

* Histogram of transmission loss on FTS9F001, including the mean and standard deviationin the heading of each plot.

20

i

Appendix DSAMPLE OUTPUTS

Figures DI through D7 are some plots from the program package for a sample problem. Thissample problem is test case IB from the AESD Workshop on Acoustic Propagation Modeling by Non-Ray-Tracing Techniques [41, except that the sound-speed field has been given a range dependencebeginning at 70 km. This range dependence can be seen in Figs. D1 and D2, a profile plot and sound-speed contour from PROFIL. Figure D3 is a plot of the initial pressure field from START, Fig. D4 is aplot of transmission loss versus range from CSPLIT, Fig. D5 is a plot of transmission loss versus depthfrom VCUT, Fig. D6 is a plot of intensity contours as a function of range and depth, and Fig. D7 is ahistogram of transmission-loss values.

By a transfer (via magnetic tape) of the solution file to a computer with a matrix plotter, gray-scale plots of intensity versus depth and range can be generated. Figure D8 is an example of such aplot.

0.0

500.0

10M.0

21000 4WSC

3000.0

4000.0

4500-0

-10.0 0.0 40 &0 36.0 40 W0 7000 .0 100.0 110.0 I 130.0RANGE (KIM

Fig. DI - A sound-speed profile plot from PROFIL

21

*1 ',.J .

PERKINS, BAER, WRIGHT. AND ROCHE

bOUND mapD

, 011101 WNWs

z a

40000 lb 1b SO 40 In U 0 )b o a t lie 10

RANGE 10010

Fig. D2 - A sound.'pes contour plot from PROMI

INITIAIL PROFILE INITI19L FIELD

X- X

14A A4 5 5 50 1610 Is 04

Sound Speed (We/) Ti'oneo~evLon Lose (dB re 1 m)

Fig. D3 - An Initial pueusr1Mi plot born START

22

NRL REPORT 8607

tf vi0

g. D S SWo~ b rmVU

0 2 4 40 U 40 2023

PERKINS, BAER. WRIGHT, AND ROCHE

INTENSTY CONTOURS

0

I-IL

0.5 10.5 20.5 30.5 40.5 50.5 6.5 7056 0.5 O .S f 00. I I0.5 1*5. 136ARANGEMICM

Fig. D6 - An intensity contour plt rm. INTCON

O&PTI - 71 TO IM4ll ANITHITIC MEAN -11,11RANGE - UAU 0TO Si., GEOMETRIC 57.0E. - LiE

12-

42

NRL REPORT 3607

RESD 180

1000

2000 - s

4000

5000

0 20 40 s0 s0 100 120 140RAN4GE 1KM)

Fig. D8 -~ An intensity pray-scale plot generated from thesolution (k. using a matrix Plowte

25

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