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NAVAL POSTGRADUATE SGRQOL
Monterey, California
iii oT
A COMPARISON OF TWO ACOUSTIC PARABOLIC EQUATION
TRANSMISSION LOSS MODELS FOR COMPATIBILITY
WITH THE WAVENUMBER TECHNIQUE IN THE
DETERMINATION OF SOURCE DEPTH
by
Joe Lane Blanchard II
March 1984
Thesis Advisor: A. B. Coppens
Approved for public release; distribution unlimited
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4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED
A Comparison of two Acoustic Parabolic Master's Thesis
Transmission Loss Models for Compatibilit March 1984
Determination of Source Depth
7. AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(s)
Joe Lane Blanchard II PE 63785N, NORDA
9. PERFORMING ORGANIZATION NAME ANO AOORESS 10. PROGRAM ELEMENT, PROJECT, TASK
AREA & WORK UNIT NUMBERS
Naval Postgraduate School N6846283WR30089
Monterey, California 93943 on 29 APRIL £983
11. CONTROLLING OFFICE NAME ANO ADDRESS 12. REPORT DATE
Naval Postgraduate School March 1984
Monterey, California 93943 [oe NUMBERICr GAGES
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18. SUPPLEMENTARY NOTES
19. KEY WORDS (Continue on reverae aide if neceseary and identify by block number)
Parabolic Wave Equation, Underwater Acoustics, Implicit
Finite-Difference, Split-Step Fast Fourier Transform,
Wavenumber Technique, Source Depth Determination, Acoustic
Propagation, ASW, Lloyd Mirror
20. ABSTRACT (Continue on reverse side if necessary and identify by block number)
mae Brock version Of the Split-Step Fast Fourier
meensform (SSFET) and the Jeager version of the Implicit
Finite Difference (IFD) acoustic parabolic equation models
are compared with a Lloyd mirror interference pattern in the
Gange domain. The SSFFT displays the inability to place the
Peansmassion loss nulls at the correct ranges. It is also
Baap le to utilize bottom loss information correctly. . The
Oe ene.
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a
SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)
IFD produced nulls at the correct ranges; however, it
inserted an unaccepable amount of noise except when small
(1 m) vertical grid steps were used and the pressure release
bottom was placed at extended depths. In shallow water
cases, the IFD is able to properly represent the pressure
information. Each model is explored in the wavenumber
domain by use of a "Wavenumber Technique" (WT) model with
emphasis on source depth determination. The source depth
may be determined by measuring the distance between the
equally spaced nulls in the wavenumber representation.
Neither acoustic model was able to provide accurate source
depth information when the null spacings were compared to a
known source-depth determination curve. Since the null
Spacings were not uniformly spaced, this was to be expected.
Some specific problem areas in the models were identified by
the use of the WT.
S/N 0102- LF- 014-6601
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2 SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered)
<n ne
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Approved for public release; distribution unlimited.
A Comparison of two Acoustic Parabolic Equation
Transmission Loss Nodels for Compatibility with the
Wavenumber Technique in the Determination of Source Depth
by
Joe L. Blanchard II
Lieutenant, United States Navy
Berce, University of North Carolina at Charlotte, 1974
Subarzteceds an partial fulfalinent of the
requirements for the degree of
MASTER OF SCIENCE IN METEOROLOGY AND OCEANOGRAPHY
fron the
NAVAL POSTGRADUATE SCHCOL
March 1984
ABSTRACT
The BEocK version of the Splze=Step Fast Fourier
Peanstocm (SSFFT) and the Jeager version of the Implicit
Finite Difference (IFD) acoustic parabolic eguation models
ace compared with a Lloyd mirror interference pattern in the
mange domains, The SSFFT displays the inability to place the
transmission loss nulis at the correct ranges. & 2S also
unable to utilize bottom loss information correctly. The
IFD produced nulls at the correct canges; however, IE
inserted an unacceptable amount of noise except when small
(1 m) vertical grid steps were used and the pressure release
bottom was placed at extended depths. In shallow water
cases, the IFD is able to properly represent the pressure
information. Each model is explored in the wavenunmter
domain cy use of a "Wavenumber Techniyue" (NT) model with
emphasis on source depth determination. The source depth
May be deternined by measuring the distance between the
equally spaced nulls in the wavenumber representation.
Neither acoustic model was able to provide accurate source
depth information when the null spacings were compared toa
knowh source-depth determination curve. Since the null
spacings were not uniformly spaced, this was tc be expected.
Some specific proplem areas in the modeis were identified by
the use of the WT.
pcg ta
: (tt. |
tid «
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i. INTRCDUCTION . .. «
If. WAVENUMBER TECHNIQUE (WT)
Ae BACKGROUND
Bat) PHYS PCAL PROGE'SS
rei ACOUSTIC MODEL ANALYSIS
A. PARABOLIC EQUATION
Dist gt ht oe 6, 6 ye) ys
1. Transmission
Bloyd Mirror
Zep pe Anda ly Sas
Ca Le oo noose Gc
to. 2 bans Sssion
PAV Mirror
Zee in Ala Ly SiS
IV. CONCLUSIONS ete Se
APPENDIX As:
APPENDIX Bs;
APPENDIX C3
APPENDIX Ds
fest OF REFER
BIBLIOGRAPHY
ENDZELAL DIS
Sort SCURCE CODE {AT
TABLE OF CONTENTS
WT SOURCE CODE
aT
1e3)
(LLOYD MIRROR)
®
Loss Comparison
GRAPHICS SOURCE CODE
e es s e e s
TREE LEON LiS® ..
U1
NPS)
“a what area or
on
wy
p 1
anee Athi
LIST OF FIGURES
PiovdewIrEoOrecconetrylGsilad. Us. 55308 «© = «
Theoretical Lloyd Mirror Transmission Loss
QladraburerDemodulationtof aySignal)). « «
Example of WIE Output at 50 Hz {From Lauer,
WIV) ceed a6 4 6% gS 5S 4 6 6h Ses See
Source Depth Deter minatzon Curve < .« « « «
Testor Sstit Model for Nall Spacangs . <
Test Of SSPrT Model tor Bottom Interaction
Ssrpe Wi Plot with Source at 500 meters .
SSFFI WT Plot with Receiver at 1000 meters
SSFRIAWTLP Let wathasource at S800 meters «<
SD Me VeIOMMeCMt miss 5s) =) sis. so 6 «6 « «
Pee anos SSLOn LOSS uss = Ww 6) 6 je =: «| “3
Peo Weta Leds rans mLssLOn LOSS < . < « « <
EMD NOwSelrreeertransmiSsion LosSS S62 a2 <<
ios Shatiitiow Waternatransmission Loss .« « «
IFD: 500 meter Source, 15 meter Vertical
Case Sep iPmart aio! ofc =) “at ‘o) fe) 6 «)) is) es
IDs 500 meter Source, 3.75 meter Vertical
Erde oe ete con ieies io!) eel 96 ie) ea!) 6 @ -, a
IFD: 500 meter Source, 0.8 meter Vertical
Grid step s es es ad es ad ad s se ad 4 es e . e s
ce0:) Shaltow Watecr WI, 1 meter Vertical Grid
step e e = es e s se e e es se e es Ld . se e e. bad
40
41
42
44
Acronyms
AESD Acoustic Environmental Support Detachment
of the Office of Naval Research, now
the Numerical Modeling Division
(Code 320) of the Naval Ocean Research
and Development Activity (NODA).
ASTREX Acoustic Storm Transfer and Response
Experiment, conducted by the Naval
Postgraduate School (NPS) in the
northeastern Pacific during November and
December of 1980.
NORDA Naval Ccean Research and Development
Rcovity at Bay St. Lours, Mississippi
NPS Naval Postgraduate School at Monterey,
€aia Porpiia
NUSC Naval Underwater Systems Center at New
Londen, Connecticut
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3 3,/) SOF
Receiver Depth
Frequeacy
Source Depth
Square, Roct_of.=-1
index.of Resraction,(C.7C)
Index in Calculations or Null
Number in the Range Domain
Time Independent Factor of Complex Pressure
Distance of the Direct Path Wave
Distance to the Image (Reflected Path)
Source Depth
Amplitude
Sound Speed (C(c,Z))
Reference Sound Speed (@ininaum sound speed
in water mass profile)
Pressure Field in the Wavenumber Space
Fast Fourier Transform
Inverse Fast Fourier Transform
Hankel function
Wavenunber
Reference Wavenumber ((G)/C )
Horizontal Wavenumber
NPT
Number of Points in the Wavenumber
Spectrum
Complex Pressure
Range between Source and Receiver
Range Increment
Envelope function
Envelope function (Imaginary part)
Envelope function (Real part)
Receiver Depth
Source Depth
Scaled Wavenumper
Scaled Wavenumber Increment
Angular Frequency
Partial Derivative Operator
2 ed sees
Laplacian Operator
Square Root Operator
1eagrseg
/LIcau> ego
> sgolews
Sct © wae.
ACKNOKLEDGEMZNT
Pewoubd Like: “to express my deepest appreciation to Dr.
Ne Bs Coppens for his guidance in analytical processes and
fundamentals of acousitcs. His understanding and encourage-
Ment provided the sound basis for this research effort. Dr.
Coppens' knowledge of the subject matter combined with the
ability to communicate this knowledge from many different
perspectives is a unique talent recognized his students.
menpn Go R. Dumlap, ~ USN (Ret) was very supportive and
Sreouraging during my entire thesis research effort. ag
appreciate his assistance with this project and his contin-
uing work with the Environmental Acouctics Research Group.
mewouldy irke to” thank the personnel of the Wek. Church
Bomputcer Center and especially Ur. D. Nac and: Mr <a
Norton.
10
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I. INTRODUCTION
Conventional methods used to represent underwater sound
transmission have deficted transmission loss (d3) as a func-
eton of range in either tabular or graphical forn. Since
the interest was in determining quantities such as range of
bottom kounce, convergence zones, and “probabidaty of
detection, these methods proved very satisfactory. However
when it became necessary tc compare various underwater
Beoustic propagation loss models with each other or actual
in-situ experiments, they provided the analyst with less
than adeguate insight into the causes for the observed
errors in the various models outputs. Furthermore, interest
has been generated in analyzing the received signal for
information from the sound source which cannot easily be
madauced from transmission loss as a function of range.
One method, the Wavenumber Technigue (WT), described by
Pens DiNapoli of NUSC [Ref. 1] and applied by Richard Lauer
of NORDA [Eef. 2], provides more information for model
comparisons and may have the capability of determining sound
Source depth and range from the receiver in certain cases.
DiNapoii used an analysis of acoustic propagation in the
Wavenumber domain as an intermediate step in getting the
EcanSmission loss curve in the Fast Field Program (FFP).
Lauer studied the wavenumber domain information from the FFP
and concluded that source localization might be vossible.
Ee BS. Stamey [Ref. 3] investigated the potential for deter-
Mining the source depth by using the Brock Split-Step Fast
Fourier Transform (SSFFT) [Ref 4] parabolic eguation model
with the "Wavenumber Technique" (WI) model. His preliminary
investigation involved the use of isospeed and ASTREX sound
fweed profiles with a fully absorbing botton, varied
source/receiver combinations, and multiple freguencies.
11
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The present investigation uses two acoustic parabolic
eguation models for comparison with theoretical Lloyd mirror
depictions, and the effects of observed inconsistencies in
predicted transmission loss curves on the calcuiated results
feom application of the WI model. An analysis of the sensi-
tivity in determining source depth based on model output is
attempted to ascertain possible use in naval operations.
To facilitate a straight-forward analysis of the results
and evaluation of the WT technigue for the cases studied,
only a selected aumber of the various computer runs are
included. Jnly those curves which best illustrate the
effects revealed py this research are presented.
12
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II, WAVENUMBER TECHNIQUE (WT)
eee ae SS eee ee
A. BACKGROUND (LLOYD MIRROR)
The WI can be elucidated with the help of the classical
Lloyd mirror effect [Ref. 5] which describes the interaction
between direct path and surface reflected sound signals fron
the same continuous wave (CW) source. Figure 2.1 illus-
trates the geometry involved in the Lloyd mirror effect.
ees
Figure: 2.1 Lloyd Mirror Geometry.
405 pee
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(ft tea] foexae
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The ccmplex pressure (P) can be expressed by
1 -j z -j u
psa| re ae eel ha
: (eqn 2.1)
when ©, and rz are related by
R= ieee aees r= R= «(d+h)* (eqn 2.2)
with the assumption r,~1r, the pressure amplitude (p) can be
approximated by
Ry = ain SUS ae (eqn 2.3)
The interaction between the direct path and surface
reflected waves produces constructive and destructive inter-
ference which is manifested as peaks and nulls for the in
phase and out of phase conditions respectively. Figure 2.2
waS produced by using equation 2.3. The null locations can
be obtained by the relationship.
2) ee (ns | :
pes ———— (egn 2.4)
9) R sin R Yy
When equation 2.3 is expressed in the horizontal wavenumber
domain (k,), the details of the resultant functional depen-
dency on horizontal wavenumber yield useful information.
14
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B. PHYSICAL PROCESS
The WI is a process by which the complex pressure wave
(with range dependent amplitude and phase) is transformed
mmeo the spectral density as a function of the horizontal
wavenumber. The use of the WT in the operational environ-
ment would require a quadrature demodulation of the source
signal to attain the complex pressure. The quadrature
demodulation process can best be defined by the illustration
meetigure 2.3 [Ref. 6].
2cos (ut)
Acos|(w -W)t+ x]
LP
filter
Asin[(w ~G)t+ x|
-2sin (axt)
Figure 2.3 Quadrature Demodulation of a Signal.
When acoustic models are used to simuiate the environment,
the requirement to perform a quadrature demodulation is
eliminated since the complex pressure is directly
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accessible. Eo waGtidLae yy “aGoustwe parabolic, equation
models provide the complex envelope function (U) which must
be multiplied by the Hankel function in order to obtain the
complex pressure. The acoustic wave iS written in the forn
P=UHS(k rye ut (eqn 2.5)
where the reference wavenumrer is defined by
Ko= - (eqn 2.6)
and
BeUGs, Zz) (eqn 2.7)
is the solution to the appropriate parabolic equation. The
complex pressure is corrected for volume attenuation and
Fourier transformed to attain the spectral density. A plot
displaying the results graphically with the horizontal wave-
Humber on the x-axis and the normalized spectral density on
the yr-axis is constructed and the spacings between the nulls
measured. Figure 2.4 {from Ref. 2] is an example of the NT
for a source and receiver in the same type of water mass.
Since the Lloyd mirror field in the wavenumber domain is
given by [Ref. 2]
E(k) = ae elie Ze) (eqn 2.8)
A)
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an alternative formulation [Ref. 2], which produces evenly
spaced nulls, is obtained by converting the horizontal wave-
number to beta
BsAke = ke ails
By using beta instead of tne horizontal wavenumber, the
distance, delta beta, between any two nulls can be used to
ascertain the source depth by
maze (egn 2.10)
as illustrated in figure 2.5.
The application for implying tne method of images, in
isospeed cases, to describe the erfects of a perfectly flat
pressure release boundary can be justified by inspection.
Therefore the parabolic equation can be used to produce the
DPoyd's mirror effect and surface decoupling 1S not an
issue, cf. Chapter 4 of Brekhovskikh [Ref. 7].
When the WT is implemented, care must be exercised to
ensure that the complex pressure contains an adequate number
Seepoints to describe the shortest periodicity in the pres-
Sure ficid. Phas will preclude the possibility of aliasing
in the wavenumber domain. The ceal and imaginary elements
of the pressure signal must be modified so that the signal
begins and ends with zero values. Piss WOdLeLeation 2's
hecessary because the pressure signal must represent a
repetitive oscillaticn for the transform. The complex pres-
Pime array is zero-filled beyond the data in order to
gemerate an array which has the length of a power of 2 for
eae Fast Fourier Transform (FFT). The horizontal wavenumber
increment is generated within the computer code by
18
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III. ACOUSTIC MODEL ANALYSIS
A. PARABOLIC EQUATICN
The elliptical wave eguation can be approximated bya
parabolic equation (PE) when it is assumed that the envelope
function varies slowly with range. A detailed nathematical
@escription of the PE from an acoustic point of view is
presented by DeSanto [Ref. 8 and 9] and a simpler but less
general description can be found in Coppens [Ref. 10}. The
parabolic equation has the forn
2
= + 2)k (LY) + (k?-KE)U =O (ean 3-1
Z
where it is assumed that the pressure has the form of equa-
elon 3.2,
Pree 2) Sp) (eqn 3.2)
S(t) represents the primary radial dependence of the field
in terms of an outward propagating cylindrical wave of the
form [Ref. 4]
(act
Se ao ules) (eqn 3.3)
If it is assumed that the range of interest is many wave-
lengths from the source; then the asymptotic form of the
Hankel function (equation 3.4) can be used [Ref. 11].
22
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Two PE models, the Brock version of the Split-Sterp Fast
Fourier Transform (SSFFT) and the Jeager version of the
Implicit Finite Difference (IFD) were investigated for
compatibility with the WT in determination of source depth.
Be SSFFT
1. Cansmission Loss Comparison with Lloyd
LEEOL
— ==
To analyze sound waves in the wavenumber domain, we
needed a model to fprovide the pressure as a function of
range. Initially the SSFFT model [Ref. 4] was selected .
This model generates successive values for U as a function
of range with the helr of the algoritha
U(rear, 2) = e@Jarke(n?-1)/2
(eqn 3.5)
FRalech ojark?
e JAPK2Ke FE T(U(r 7)
This model was a natural choice since it was the model used
in the preliminary study dealing with the determination of
tae source depth by the WT [Ref. 3]. However, Zt Soon
became apparent that this model's inherent weaknesses would
require the consideration of another nodel if ocean botton
interactions were to be studied. These weaknesses, and
their impact upon the WT, will be discussed shortly.
The SSFFT is a range dependent acoustic wave model
which, for this analysis, will be operated in a range inde-
pendent manner. in othe xs words, only one sound speed
profile will be used, the water mass will be assumed homoge-
neous, and the bottom flat. TO) facriitate Che study of the
SSFFT model, the source code of the nodel was modified to
generate the variables required for follow-on programs to
23
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Seeamstorm the pressure information and then display the
results graphically. LA copy Or tae, source code Listing for
Gach program is provided in appendices A, B, and C. These
programs were then linked by Job Control Language (JCL) so
that the WT graphics were an automatically executed.
A ieese rina t tne SSEPL was made tor 100 (nz, 500 mn
source and receiver depths, 0.019 km range step, fully
absorbing botton, 2000 m water depth, and an isospeed
profile at 1500 n/sec. These values were chosen so that a
comparison could be made with the theoretical Lioyd mirroc
Beansmission loss (figure 2.2). Tre output was displayed as
a@etransmission loss curve (figure 3.1). From equation 2.4,
meemerccation o£ null number 1 (R1)’ should be 33.33 km and
Hib: number 2 (R2) should be at 16.67 xn. The’ SshriLr placed
fieadt approximately 38.3 km and R2 at 17.1 kno. Since the
model kept the frequency, source depth, and receiver depth
constant, then this equates to a reference sound speed of
1305 and 1462 m/sec respectively. ft 2S “apparent fhatwa’s
the range decreases the error is reduced which indicates the
Bossibility of a problem in the range step section of the
model which leads te the introduction of a systematic and
increasing deviation of the calculated sound field from that
Meedicted by the classical Lloyd's mirror interference
pattern. Th2 “washing out" of the interference pattern for
Bamges less tian about 2 km is a cesult of the particular
appeoximation of a point source used to initiate the
program, which is tc be expected. Ratner regular fluctua-
tions develop beyond about 30 ka; from the geometry of the
Sase, it is plausible that this arises from interference
with bottom reflected signals.
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({tigure 3.2). Since the half beamwidth is 2) degrees and
fme bottom is £ully absorbing, the shortest range at which a
Peace reflection cculd occur is’ approximately 8.2 kn;
beyond this range, surrace reflections should be spaced in
accordance with equation 2.4. The nulls beyond 8.2 km do
occur at the correct ranges; however, there are slow nodula-
tions of the overall transmission loss signal. These siow
modulations are another indication that the bottom is not
mally aksorbing as had been specified as input to the
progran.
26
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2. kT Analysis
ine wi. Cutpue trom the SSFFT model 1s in Eng
units, which is a probiem when comparing different nodels.
However, for this investigation the problem was minimal. As
expressed by equation 2.6, the reference wavenumber for 100
hz with a reference sound speed of 4921.26 ft/sec (1500
msec) is 0.1277 1/ft. After correction of the reference
wavenumber for arrange increment of 62.3 it and the 2048
points used to represent the wavenumber spectrun, ene
Maximum beta value should be 0.1243 1/ft which agrees
reasonably well with the maximum beta vaiues in figures 3.3,
3.4, and 3.5. Contrary to theory the nuils are not equaily
Seaced and the expected delta beta vaiue of 0.00192 1yit
(Equation 2.10) is net represented by any of the null spac-
ings. Stamey [Ref. 3], observed tne same non-uniforn
Spacing of beta nulls. The reason why the source depth is
not represented by any of the nuli spacings may be traced to
the improper null placement in the raage domaiz. The Lack
@£ egual spacing between the nuils must be attributed to
something else, possibly the pressure wave was improperly
represented as a continuous Signal or numerical errors exis
W2Zthin the source ccde. Whatever the reason for this
difference, it must Le resolved before the SSFFI can be used
ie
e
epth.
with the WI to determine the source dep
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IFD
the IFD nodel [Rref. Az 4 which was jnstalles and
ssted inf September 4983 at NPS [ kef- 13] was the next nodel
hosen as a sound source for the Wide This decision “ids made
ecause the IFD was capable of properly handling the oceab
orton qnteractions and was the only othet Acoust Te Vee nodel
in cresidence at NPS- a copy of the source eoae Lasting cs
provided rel appendix De
The IFD also presented probiens which will be
discussed further. The same initial test ran useé with the
SSFFT was ysed with the IFD- Since the IFD requires more
pottom jnfornation,s addit ional pesting we- nerformed in
order to obtain 4 fui Ly apsorbing potton. Figure 3216 LS =
trates the environment as seen DY the IFD model.
The densities in the water maSS,y sediments and a6 ti-
ficial attenuatiob layer were set to 4 constant of 1.0 and
the attenuation in the sediment was adjusted until the elim
qnation of bottom jnterfrerence was observed. Figure 324 2S
an example of the IFD ¢transmissioa loss output for a 500
source/receiver depth, #@4 water depth or 2000 He an uprer
surface of the artificial attenuation layer at 3000 , and a
lower pressure release surface at 1G00 Gs 22° bottom atten
fieron used to produce figure 3.7 was 0.00 16 sa/wavelengt he
17)
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water
sediment
“~upper surface of
artificial attenuation layer
b= ange = ee
pressure release surfaces
Figure 3.6 IFD Environment.
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Mmmerocation of the nulls in figure 3.7 coincide with those
predicted by equaticn 2.4 if the higa frequency noise is
fapereda Out by either a running average process or low pass
d@mgatal filter. A careful examination of the transmission
Weegee curve (figure 3.8) reveals the real problem, which is
the long wavelength noise near tae wavelength of interest.
fme Long wavelength noise will cause erroneous spikes on the
Meeplots after being Fourier transiormed. Continued anal—
Mumemeecevealcd that -the noise could be eliminated if the
thicknesses of the artificial attenuation layer and the
bottom pressure release suriace are chosen so that they are
at least twice the water depth. Phe, choice of a ‘small
Memtical grid step will reduce the thickness reguired for
Hee pressure release surface, but this version of the IFD
Meegram 75 limited to 5000 vertical grid points due to soft-
ware restrictions. FLgGUre 3.9 iS ,a transmission loss curve
Obtained from a 500 m Source/receiver depth, a 2000 m water
Bepth, a400) wm upper level artificial attenuation layer,
and an 8000 m bottom pressure release surface. Comparison
mmergures 3.1 and 3.9 with the classical Lioyd's mirror
Peansmission loss (figure 2.2) shows that the shape of the
curve beyond 30 km is greatly improved with the IFD. The
Mumber of vertical grid steps was 5000. When the IFD is
used in a sShallcw water situation and at 25 Z, the noise
Mees not appear to be present. Figure 3.10 is a plot of the
Beagsmission loss for a signal at 25 hz, with the sou
Beceiver depth at 50 m, the bottom sloping up from 350 t
M, and an artificial attenuation layer and pottom pressure
Bebease surface located at 750 and 1000 om, respectively.
Miesnoise which was so evident in tigure 3.7 is absent fron
the shallow w«sater case. Producing tne noise free curves
Tequires excessive computer time except for shallow water
Cases.
38
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To reduce the amount of the pressure information and
Wee preserve the detaiis, the IFD tests were conducted
between 10 and 40 km in range. The reference wavenumber for
eae test input with the [FD was 0.4189 1/m which, after
Correcting for a range increment of 7.5 m with 4096 pocints,
produced a beta maximum of 0.4188 1/n. Pagures. S46 11, Ss. 12,
and 3.13 indicate agreement with the beta maximum and a
Metta beta of 0.00628 1/m can be found among the null spac-
ings. When the vertical grid step is reduced in size, the
Saeout Signal contains more information of finer detail.
The finer detailed information will, if noise is present,
Beagduce more clutter on the WT depiction (figure 3.13). in
Numerous WI depictions a peak was observed at the nininun
and maximum waveaumbers. Stamey believed that the right and
left intensity maxima corresponded to beam elevation angles
of 0 and 30 degrees, respectively. He further stated that
the left maxima also may be reiated to algorithmic inaccura-
eves [Ref. 3]. The "U-shaped phenomenon" observed during
Seamey's investigaticn of the SSFFI, is present with the IFD
and the nulls are not equally spaced.
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fhe reason for the "U-shaped phenomenon" appears to be
related to noise in the envelope function field which is
further amplified when the Hankel function is inserted to
obtain the conplex pressure. Using a low pass filter and
increasing the vertical grid step size appear to reduce the
'problen. tier giTe Seo, che mulls occur at 33.30 and 33.39
| km men a Single null should exist at 33.33 km. This condi-
tion or noise produces the most devastating erfects by
| masking the desired density spectrun. A narrow band pass
| filter would probably solve this problem in the short tern
but eventually the IFD will require further study to elini-
Mate the noise. When the shallow case is used in the WT
(igure 3.14), the "U-shaped phenomenon" is absent and the
mull locations are more distinct. However, in the shallow
Water case, the bottom interaction produces high frequency
anterference but the null Spacings occur near the expected
Value for the source depth (0.0628 1/m).
43
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: are _
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ALISN3INI WeLI3dS J3Z1 WRYON
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0?
ot
0°0
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-0.5 -0.4 “0.3 -0.2 -0.1 0.90
-0.6
=027
-0.8
HORIZONTAL WAVENUMBER
1 meter Vertical Grid Step.
Shallow Water WT,
ERD
Figure 3.14
I¥. CONCLUSIONS
iwo EalLabolic equation models, the SSFFT and IFD, were
used to predict sound fields for comparison with the Llo
Mirror interference fattern in the range domain and then in
the wavenumber domain. In the range domain, th SSFFT
mapEoperily handled the location of pressure nulls and
displayed bottom interference. While these weaknesses in
the SSFFI were absent in the IFD, the inadvertent and dele-
terious insertion of noise was extensive. In tae wavenumber
domain, the noise in the IFD was prohibitive in ail but the
deep sediment and shallow water cases. The IFD produced
results which were ccmparable with the SSFFI when the noise
Was not a factor. The range step and the bottom attenuation
aegorithms of the SSFFI should be reviewed in order to
correct those problems described above. in the 25D, . the
noise problem will require further investigation. ii tie
problem in the iFD is not corrected, this model will be
severely limited. With the guidance provided by Lauer
[Ref. 2], the wavenumber domain can provide tne detailed
information needed tO gusackiy correct inconsistencies
observed between acoustic models. Therefore, the WT should
be investigated further to ensure that any soitware weak-
messes are eliminated and a thorough understazding of the
process is assured.
Experiments in the operational environment should be
Planned to test the WT with actual sound sources. The ship-
board experiment could be easily accomplished since the WT
Can be iaplemented on micro-computers if the pressure infor-
maewen 1S provided from an outside source. fhe WI, if it is
going to be considered as a method to determine source
depth, appears to have three major shortcomings:
45
|
‘sc wi* alae
Celle 2269) 763
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LBS eae
~
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ty
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2 20s
I
1. A clean CW Signal with phase information is essen-
tial, which will require quadrature demodulation and
extensive filtering.
2. Prediction models are required which will provide
equally spaced beta nulis so that software can be
developed to automate the process.
3. High resolution processing equipment is necessary
because the change in beta spacing for shallow sound
sources is small (figure 2.5).
46
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APPENDIX A: SSFFT SOURCE CODE (AT NPS)
ZH
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Fj Aur Ay [o<] re E> a2} & OURAN M
<s f Yas e Ay 4 Et ey by
Aawa ~~ Oo S) am Ww YQ ica) OnavuU a
ANZ yY=Z N YH Oo «ss HY H (=) HOR hy
oN aD fy VU H bs » BOR ON
= Oo Pola ° O HW H fq tH 09 Oh Ole fe (S)
HOH s by A Q YH HH YO hy ot 4 D= A HQ mm
(ei feo} > 4 4 ND} (4 G4 AD Ao wa NH
foe t-—-] Up] et) e fea] Nau = & = Ae HH -OmMN ©
onHoe oz ~ 4 [7 <2 (oS) . =) Hao Awe <x
Fey OG HY OG fo a=——AaASe = fo] H OS eH RONO >
NO ag 4 HAHN Ne WN Zz OW AQWnetee .
Nop) NO = ez) SSS Wany = ee mA ck, BA So
NW He co fy AQVO 4 eof) oe = ou OHHAOHN »& nN VO
PHS i=) Cy Ge Meqg4jyaAngeg 2zaaza De WH Om aUROZTH .
BAHN aH A 2 Haeatg gy VU SD HS = SBM GMOHOZDWH =
yZz=zO BH HW A aa MAHHOBAHSHGO OF He FD HAW DYHSO =
APaAg ln el sn I ia] nN HOHOHSE UO YO BAN MHAZMQGEAGQHH=
io] ZDHRPRHO Ga Fey eye N AH SAH EHet eee 2
HaHMN > 2 HoD< =) T=\olo}=) BNeEDRA Om moO DHmMDAGOUNA »
Sa HDeX<UH ARTZ 20 NE OH He BSH eZNOSNEQ &
[atye-t—-1@) BD PMH S~NDPTAZHORO Hae <= _ =
He PAAWHD Se BDOsO~QVaHYmDN = Ae [eo] Yn
Soar QA AeE OF NACKMase Ww RON Ae aX Ao HH Oo N
OORYU ZPmWD OW A QMO Dceyay Fy WO s <—28Hn00 H2
NG FORO RA kao BwROWmk=s Ah rye=) AGAaH OF
oH es AORHWOHUU Hon WRO H OC ARAANHy <az
Swan ZS2Z2ZzH OF AZBZTBVZBHAzMmBA oO a oy BAA BQ
mor aero GC WWOD HRD Pee
ze ay meg WHO GSS Ye SQDY N ~*~
Hy Oc BHHH DHS QDOWHHOUGHHHAma
Ned pafanfe-fe-t-—p >t 1b ahat csi eee Li -2 lpi 9s] hon Q Q
ae COCO PH SP SRM ae tH atHHEe Se A [oa] ion]
aaa tyke ry Sy SOAS HOszr & < <a
HHHO < 1S) O
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RQ MN Ye aac Ps aaa! mam
OQ Set eH ag MeNSHA el
AHA UNH RBHOhRAMN OFS GBAQQHnVU Gz tw
UH AAA HAR SHRSNHOURMAULUULAAZAZ UO
x ic
= UO | i=)
ae 4
Ge & &
ORICe = =
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VUVVOVYV VS VVVPOVVVVVSV YVVVVVYVVVV VV VVUVVVVUVVVVVVUVVUVUU
47
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DATA INPUT FILE FROM THE PEMODEL
LO IS THE LATA INPUT FILE OF WAVENUMBER DATA FRCM THE FFT
LT1 IS THE KANGE CATA INPUT FILE FROM THE PEMCDEL
LE 2D, THE EIAGNOSTIC OUTPUT FILE
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(C, U,N,CR, CTWO)
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= Chl). * C (= 1 4}
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M,4)-C (4,3) *U (M+1)
(1,4)
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*** NOW
RETURN
U (N)
END
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146
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END
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Vas
12.
LIST OF REFERENCES
Naval Underwater Systems Center Technical Report 4103,
Fast Fieid Program for the Multilayered M2dia, by F.k.
DiNapotzi, 26 June 197 7T.
Naval Underwater Systems Center Technical Memorandua,
Signal I[ransmission in tae davenumpber Domain, by Re
Tauer, 5 June W793.
Stamey, 3.B., P2reliminary Investigation of the
Environmental Sensitivity or Acoustic Signal
TransGisSion in the Favenumoer Domain with Respect TS
ones Bees Determination, Naval Postgraduate School,
Decemrer T3982-
Naval Ocean Research and Development Activity
Teconical Note 12, The AESD Parabolic Equation Model,
Hoke SEOCK, January, 1973
Orficer, C.B.-, | introduction to the Theory of Sound
Transmission | with “Application to “the ~ ocean,
MGGEaAW-hLIL; S58.
Buckner, "§se of calculated sound fields and
He P.
matched-field “detection to locate sound sources in
Shallow water, " J. AGCOUSTE. » 90C. “Ame, V- 295. Dis
366-373, February 19706.
Brekhovskikh L.M., Fundamentals of Ocean Acoustics,
Springer-Verlag, New York, 139362.
Desanto, J-A., “Relation between the Solutions of the
Helmholtz and Parabolic Ejuations £or. sound
pepe dees on,” Wet AGOMNSte SOC. Alc, Vs O25 Pe 295-297,
Auguse 1977.
DeSanto, JeAs, Zap ics in Current Physics: Ocean
Acoustics, Springer-Verlag, 19795.
Coppens, . A.B., AR VERtEoducGtion to the Paraboiic
Ejuation for Acoustic Propagation, Naval Postgraduate
School Technical Report, NPSOT=335-002Z, November 1982.
Kinsler, L-E&., Frey, A.R., Coppens, A.B., and Sanders,
:V-, Fundamentals of Acoustics fTaird Edition, John
Wiley and Sons, 19982.
Padet acy paravortc BgQuatLon, by wen sceerand TG.
eas, 27 May 1982.
147
a
; > : : -
‘SDasartss PO te
|
|
ee hs ee i. Isa tndoe? 36 3feD"; ces ted Bi
LADS YRIST Sei UF eid Epos
° reek Gt >
saa5 i 77a8. cme aye
mone Ses 2
oh ai te os, a
‘e
vn ”
eesti BAZ «AE
2 £8 et mie
r i ae . eee
ss 4 . -
= io
U LIB GLE PAS
© &
c £ f
~ ‘ oJ
t re
* r '
a * . )
A
it eos sazE
iy Jeo a 14
- * bo uo? SeteG
: af Agi a
Sie
JacgeL,. E. Cc er 2 a 2
Parabolic ua S 2B It te 2ECEe
solution “detno Phcorporatias Exact —- {nts S
Conditions, Naval Postgraduate School, September 983.
148
eas 79"" 4 loc
BIBLIOGRAPHY
Pammssten, RoA., “Low-frequency surtace interference effects
in long-range sound PEO eds et Obs Jc) AGCouUStT. Soc. Al., V-
peepee 76-683, January 1 31.
Brigham ES0.4., Lhe? fast OUrZer Transform, Prentice-Hall
ine., 1974. ae
PuGekeetak., SuUcChaL;GRSNs, cand Spoftford, C.W., "Modifying
Piece sounde Speed) Profile to improve the Gcuracy of the
Parabolic- Equation aecuasguels UeeAsOlace OOC. Alley Ve 62,
Be 2439-552, September, 1977.
Clay, sG-s. and H- Medwan, Acoustic Oceanography: Principles
and Applicatiogns, John Wiley andmsons, 0977 =
DiNapoli RokaeaendsnkeLe . Deavenport, "Theoretical and
Numerical Grean'situncet#on) field solution in a plane multi-
we ncamedaum!, Ss S9ghcousts Soc. Ams, ve 67, pe 92-105,
January 1980.
Hamming ReWe, Digital Filters Second Zdition, Prentice-Hall
tne, 1977.
Naval Undersea Center Technical Report TP 488, Low-Frequency
Propagation Efrects for Sources or Reclievers Near the Ocean
ce y.S.AlS "Pedersen, D.F. CObGOn. © and De. Whawe,
mlm
ULL reo ae:
eptember 1975.
: : Donald, Mechanics of Underwater Noise, Pergamon Press,
ELC Water Sound, Second Edition,
Gere k, Rade;
4 lon in the Sea, Derense Advanced
Research Proj
149
a od
(98 ial rt |
10.
11.
12.
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