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DUDLEY KNOX LIBRARY
NAVAL POS' 0L
A 93943
NAVAL POSTGRADUATE SGH
Monterey, California
THESiSA COMPARISON OF TWO ACOUSTIC PARABOLIC EQUATION
TRANSMISSION LOSS MODELS FOR COMPATIBILITYWITH THE WAVENUMBER TECHNIQUE IN
'
THE
DETERMINATION OF SOURCE DEPTH
by
Joe Lane Blanchard II
March 1984
Th esis Advisor: A. B. Coppens
Approved for public release; distribution unlimited
UNCLASSIFIED
SECURITY CLASSIFICATION OF THIS PACE (When Dete Entered)
REPORT DOCUMENTATION PAGEt. REPORT NUMBER
READ INSTRUCTIONSBEFORE COMPLETING FORM
2. GOVT ACCESSION NO 3. RECIPIENT'S CATALOG NUMBER
4. TITLE 'md Subtitle)
A Comparison of two Acoustic ParabolicTransmission Loss Models for Compatibiliwith the Wavenumber Technique in theDetermination of Source Depth
5. TYPE OF REPORT a PERIOD COVEREDMaster's ThesisMarch 19 84
6. PERFORMING ORG. REPORT NUMBER
7. AUTHOR*"*,)
Joe Lane Blanchard II
8. CONTRACT OR GRANT NUMBERf*.)
PE 63785N, NORDA
9. PERFORMING ORGANIZATION NAME AND AOORESS
Naval Postgraduate SchoolMonterey, California 93943
10. PROGRAM ELEMENT. PROJECT, TASKAREA 4 WORK UNIT NUMBERS
N6846283WR30089of 29 APRIL 1983
It. CONTROLLING OFFICE NAME ANO AOORESS
Naval Postgraduate SchoolMonterey, California 93943
12. REPORT DATE
March 198413. NUMBER OF PAGES
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It. SUPPLEMENTARY NOTES
19. KEY WOROS (Continue on reverie elde If neceeemty end Identity by block number)
Parabolic Wave Equation, Underwater Acoustics, ImplicitFinite-Difference, Split-Step Fast Fourier Transform,Wavenumber Technique, Source Depth Determination, AcousticPropagation, ASW, Lloyd Mirror
20. ABSTRACT (Continue on reveree elde If neceeeary end Identify by block number)
The Brock version of the Split-Step Fast FourierTransform (SSFFT) and the Jeager version of the ImplicitFinite Difference (IFD) acoustic parabolic equation modelsare compared with a Lloyd mirror interference pattern in therange domain. The SSFFT displays the inability to place thetransmission loss nulls at the correct ranges. It is alsounable to utilize bottom loss information correctly. The
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IFD produced nulls at the correct ranges; however, itinserted an unaccepable amount of noise except when small(1 m) vertical grid steps were used and the pressure releasebottom was placed at extended depths. In shallow watercases, the IFD is able to properly represent the pressureinformation. Each model is explored in the wavenumberdomain by use of a "Wavenumber Technique" (WT) model withemphasis on source depth determination. The source depthmay be determined by measuring the distance between theequally spaced nulls in the wavenumber representation.Neither acoustic model was able to provide accurate sourcedepth information when the null spacings were compared to aknown source-depth determination curve. Since the nullspacings were not uniformly spaced, this was to be expected.Some specific problem areas in the models were identified bythe use of the WT.
S N 0102- LF- 014- 6601
SECURITY CLASSIFICATION OF THIS P»GEfWiM Data Entarad)
Approved for public release; distribution unlimited.
A Comparison of two Acoustic Parabolic EquationTransmission Loss Hodels for Compatibility with the
Wavenumber Technique in the Determination of Source Depth
by
Joe L. Blanchard IILieutenant, United States Navy
B.S. , University of North Carolina at Charlotte, 1974
Submitted in partial fulfillment of therequirements for the degree of
MASTER OF SCIENCE IN METEOROLOGY AND OCEANOGRAPHY
from the
NAVAL POSTGRADUATE SCHOOLMarch 1984
ABSTRACT
The Brock version of the Split-Step Fast Fourier
Transform (SSFFT) and the Jeager version of the Implicit
Finite Difference (IFD) acoustic parabolic equation models
are compared with a Lloyd mirror interference pattern in the
range domain. The SSFFT displays the inability to place the
transmission loss nulls at the correct ranges. It is also
unable to utilize bottom loss information correctly. The
IFD produced nulls at the correct ranges; however, it
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 wavenumter
domain by use of a "Waver.u mber Technique" (WT) model with
emphasis on source depth determination. The source depth
may be deterained 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 carve. Since the null
spacings were not uniformly spaced, this was tc be expected.
Some specific proDlem areas in the models were identified by
the use of the WT.
DUDLEY K'-
NA 1
TABLE OF CONTENTS
I. INTSCDJCTION 11
II. WAVE NUMBER TECHNIQUE (WT) 13
A. BACKGROUND (LLO£D MIRROR) 13
3. PHYSICAL PROCESS 1b
III. ACOUSTIC MODEL ANALYSIS 22
A. PA3ABOLIC EQUATION 22
B. SSFFT 23
1. Transmission Loss Comparison witn
Lloyd Mirror 23
2. WT Analysis 23
C. IFD 32
1. Transmission Loss Comparison with
Lloyd Mirror 32
2. WT Analysis 3 9
IV. CONCLUSIONS 45
APPENDIX A: SSFFT SOURCE COLE {AT NPS) 47
APPENDIX B: WT SOURCE CODE 102
APPENDIX C: WT GRAPHICS SOURCE CODE 107
APPENDIX D: IFD SOURCE CODE (AT NPS) 112
LIST OF REFERENCES 147
BIBLIOGRAPHY 149
INITIAL DISTRIBUTION LIST 150
LIST OF FIGURES
2-1 Lloyd Mirror Geometry 13
2.2 Theoretical Lloyd Mirror Transmission Loss ... 15
2.3 Quadrature Demodulation of a Signal 16
2.4 Exaaple of SI Output at 53 Hz (From Lauer,
1979) 20
2.5 Source Depth Determination Curve 21
3.1 Test of SSFFT Model for Null Spacings 25
3.2 Test of SSFFT Model for Bottom Interaction ... 27
3.3 SSFFT FT Plot with Source at 500 meters . . . . 2S
3.4 SSFFT WT Plot with Receiver at 1000 meters ... 30
3.5 SSFFT ST Plot with Source at 600 meters .... 31
3.6 IFD Environment 33
3.7 IFD Transmission Loss 34
3.8 IFD Detailed Transmission Loss 35
3.9 IFD Noise Free Transmission Loss 36
3.10 IFD: Shallow Hater Transmission Loss 37
3.11 IFD: 500 meter Source, 15 meter Vertical
Grid Step 4
3.12 IFD: 500 meter Source, 3.75 meter Vertical
Grid Step 41
3.13 IFD: 500 meter Source, 0.3 meter Vertical
Grid Step 42
3.14 IFD: Shallow Water WT, 1 meter Vertical Grid
Step 44
k cronyjns
A£SD Acoustic Environmental Support Detachment
of the Office of Naval Research, now
the Nunerical Modeling Division
(Code 320) of the Naval Ocean Research
and Development Activity (NOSDA)
.
ASTRZX Acoustic Storm Transfer ana Response
Experiment, conducted by the Naval
Postgraduate School (NPS) in the
northeastern Pacific during November and
December of 1 980.
NORDA Naval Ccean Researcn and Development
Activity at Bay St. Louis, Mississippi
NPS Naval Postgraduate School at Monterey,
Calif or r.ia
NUSC Naval Underwater Systems Center at New
London, Connecticut
S ymbols
d
f
h
J
n
P
r
r
z
A
C
Co
F (K)
FFT
FFT -1
H
K
K
Receiver Depth
Frequency
Source Depth
Square Roct of - 1
Index of Refraction (C /C)
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(r , z))
Reference Sound Speed (minimum sound speed
in water mass profile)
Pressure Field in the Wavenumber Space
Fast Fourier Transform
Inverse Fast Fourier Transform
Hankel function
Wavenumber
Reference Wavenumber [QJ/C )
Horizontal Wavenumber
NPT Number of Points in the Wave number
Spectrum
P Complex Pressure
R Range between Source and Receiver
Ar Range Increment
U(r # z) Envelope function
Uj Envelope function (Imaginary part)
U r Envelope function (Real part)
Z r Receiver Depth
Z £ Soarce Depth
Scaled WavenumnerPh> Scaled Wavenumber Increment
CO Angular Frequency
Partial Derivative Operator
T 3.1415...
V Laplacian Operator
y Square Root Operator
ACKNOWLEDGEMENT
I would like to express my deepest appreciation to Dr.
A. 3. Coppens for his guidance in analytical processes and
fundamentals of acousitcs. His understanding and encourage-
ment provided tne 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.
LCDR C. S. Dunlap, U SN (Ret) was very supportive and
encouraging during my entire thesis research effort. I
appreciate his assistance with this project and his contin-
uing work with the Environmental Acouctics Research Group.
I would like to thank the personnel of the tf.R. Church
Computer Center and especially dr. D. Marr and Mr. J.
Norton.
10
I. INTRODUCTION
Conventional methods usea to represent underwater sound
transmission have depicted transmission loss (d3) as a func-
tion of range in either tabular or grapnical form. Since
the interest was in determining quantities such as range of
bottom bounce, convergence zones, and probability of
detection, these methods proved very satisfactory. However
when it became necessary tc compare various underwater
acoustic 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
induced from transmission loss as a function of range.
One method, the Eavenumber Technique («T) , described by
F. R. DiNapoli of NUSC [Ref. 1] and applied by Richard Lauer
of NCRDA (Ref. 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.
DiNapoli used an analysis of acoustic propagation in the
wavenumber domain as an intermediate step in getting the
transmission loss curve in the Fast Field Program (FFP) .
Lauer studied the wavenumber domain information from the FFP
and concluded that source localization mignt ce possible.
B. 3. Stamey [Ref- 3] investigated the potential for deter-
mining the source depth by using che Brock Split-Step Fast
Fourier Transform (SSFFT) [Ref. 4] parabolic equation model
with the "PJavenumber Technique" (WT) model. His preliminary
investigation involved the use of isospeed and ASTREX sound
speed profiles with a fully absorbing bottom, varied
source/receiver combinations, and multiple frequencies.
11
The present investigation uses two acoustic parabolic
equation models for comparison with theoretical Lloyd airror
depictions, and the effects of observed inconsistencies in
predicted transmission loss curves on the calculated results
from application of the WT 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 ST technique for the cases studied,
only a selected number of the various computer runs are
included. Dnly those curves which best illustrate the
effects revealed oy this research are presented.
12
II. W AVEHPHBEB TECHNIQUE (WT)
A. BACKGROUND (LLOYD MIREOR)
The WT 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 from
the same continuous wave (CW) source. Figure 2. 1 illus-
trates the geometry involved in the Lloyd mirror effect.
R
Figure 2.1 Lloyd Mirror Geometry.
13
The complex pressure (P) can be expressed by
P= A1 -JkGre 1 -jkft
jcjt
when r. and r s are related by
(eqn 2.1)
VR**(d-h)1
'
ij = VR2*(d^h)
2 ' (eqn 2.2)
with the assumption r~ rs
the pressure amplitude (p) can be
approximated by
p 2fhdKm= mC
,m =1,2,3,.. (egn 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.
2A . /khdp=— *"VTT(eqn 2.4)
Hhen equation 2.3 is expressed in the horizontal wavenumber
domain (k r), the details of the resultant functional depen-
dency on horizontal wavenumber yield useful information.
14
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wo~i
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15
B. PHYSICAL PROCESS
The ST is a process by which the complex pressure wave
(with range dependent amplitude and phase) is transformed
into the spectral density as a function of the horizontal
wavenumber. The use of the ST in the operational environ-
ment would require a quadrature demodulation of the source
signal to attain the complex pressure. The quadrature
demodulation process can bast be defined by the illustration
in figure 2.3 [Ref. 6].
2cos(cat)
®
AC0S(<dt+x)
(*>
-2sin(<ut)
LPfilter
Acos[(cJ-<J.)t+x]
Asin[(oj-oj.)t + x]
Figure 2.3 Quadrature Demodulation of a Signal.
When acoustic models are used to simulate the environment,
the requirement to perform a quadrature demodulation is
eliminated since the complex pressure is directly
16
accessible. In actuality, acoustic 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 form
P = UhC(k r^e-J^ < e<3 n 2 - 5 )
where the reference wavenumber is defined by
and
U = U(r\z) (eqn 2.7)
is the solution to the appropriate parabolic equation. Ihe
complex pressure is corrected for volume attenuation and
Fourier transformed to attain tne spectral density. A plot
displaying the results graphically with the horizontal wave-
number on the x-axis and the normalized spectral density on
the y-axis is constructed and the spacings between the nulls
measured. Figure 2.4 [from Ref. 2] is an example of the WT
for a source and receiver in the same type of water mass.
Since the Lloyd mirror field in tne wavenumber domain is
given by [ Ref. 2
]
p(fc) - Sin(flZs) e KflZr) (eqn 2.8)
17
an alternative formulation [ Ref . 2], which produces evenly
spaced nulls, is obtained by converting the horizontal wave-
number to beta
/?=V^-k,2
'
(egn 2 - 9)
By using beta instead of the horizontal wavenumber, the
distance, delta beta, between any two nulls can be used to
ascertain the source depth by
-JL_A# =Z, (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 fiat
pressure release boundary can be justified by inspection.
Therefore the parabolic equation can be used to produce the
Lloyd's mirror effect and surface decoupling is not an
issue, cf . Chapter 4 of 3rekhovskikh [Ref- 7].
When the WT is implemented, care must be exercised to
ensure that the complex pressure contains an adequate number
of points to describe the shortest periodicity in the pres-
sure field. This will preclude tne possibility of aliasing
in the wavenumber domain. The real and imaginary elements
of the pressure signal must be modified so that the signal
begins and ends with zero values. This modification is
necessary because tne pressure signal must represent a
repetitive oscillation for the transform. The complex pres-
sure array is zero-filled beyond the data in order to
generate an array which has the length of a power of 2 for
the Fast Fourier Transform (FFT) . The Horizontal wavenumber
increment is generated within tne computer code by
18
k -k +22- mNPT
-1) (eqn 2. 11)
19
2SoNdoXLL
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III. ACOUSTIC MODEL ANALYSIS
A. PARABOLIC EQUATION
The elliptical wave equation can be approximated by a
parabolic equation (PE) when it is assumed that the envelope
function varies slowly with range. A detailed mathematical
description of the PE from an acoustic point of view is
presented by DeSanto [Eef. 8 and 9] and a simpler but less
general description can be found in Coppens [Ref. 10]. The
parabolic equation has the form
4-^- + 2jk (4^) (k2-kf)U = (
e <2* 3 - 1 >
oz o r
where it is assumed that the pressure has the form of equa-
tion 3.2,
P =U(r,z) S( r) ( e<3 n 3 - 2 )
S(r) represents the primary radial dependence of the field
in terms of an outward propagating cylindrical wave of the
form [Ref. 4]
S( r) = H o (kor) (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 [Eef. 11].
22
H (1) •V1- V TVkoTj(kor-rr/4) kor >=* 1
(eqn 3.4)
Two PE models, the Brock version of the Split-Step 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.
B- SSFFT
1 . Transmission loss Comparison with Lloyd Mirror
To analyze sound waves in the wavenumber domain, we
needed a model to provide the pressure as a function of
range. Initially the SSFFT model [Ref. 4] was selected .
This model generates successive values for (J as a function
of range with the help of the algorithm
U(r + Ar jZ ) = eJ Arko(n2 - 1 ) /2
(egn 3.5)
FFT-'j eJArV/2koFpT(u(r z))
'
This model was a natural choice since it was the model used
in the preliminary study dealing with the determination of
the source depth by the WT [Bef. 3]. However, it soon
became apparent that this model's inherent weaknesses would
require the consideration of another model if ocean bottom
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 other words, only one sound speed
profile will be used, the water mass will be assumed homoge-
neous, and the bottom flat. To facilitate the study of the
SSFFT model, the source code of the model was modified to
generate the variables required for follow-on programs to
23
transform the pressure information and then display the
results graphically. A copy of the source code listing for
each program is provided in appendices A, 3, and C. These
programs were then linked by Job Control Language (JCL) so
that the WT grapnics were an automatically executed.
A test run of the SSFFT was made for 103 hz , 500 m
source and receiver depths, 0.019 km range step, fully
absorbing bottom, 2000 m water depth, and an isospeed
profile at 1500 m/sec. These values were chosen so that a
comparison could be made with the tnaoretical Lloyd mirror
transmission loss (figure 2.2). Ine output * as displayed as
a transmission loss curve (figure 3.1). From equation 2.4,
the location of null number 1 (R1) snould be 33.33 km and
null number 2 (H2) should be at 1b. 67 Km. The SSFFT placed
E1 at approximately 38.3 km and H2 at 17.1 km. 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. It is apparent that as
the range decreases the error is reduced which indicates the
possibility of a problem in the range step section of the
model which leads tc the introduction of a systematic and
increasing deviation of the calculated sound field from that
predicted by the classical Lloyd's mirror interference
pattern. Tha "washing out" of the interference pattern for
ranges less than about 2km is a result of the particular
approximation of a point source used to initiate the
program, which is tc be expected. Ratner regular fluctua-
tions develop beyond about 30 km; from the geometry of the
case, it is plausible that this arises from interference
with bottom reflected signals.
24
CDa
M _
CD t\
3CJ) D
>— ID- Z. mz. : ;
LJ 1—
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25
Another test was made using the same inputs as above except
that the source and receiver were moved to a depth of 150 3 m
(figure 3-2). Since the half beamwidth is 23 degrees and
the bottom is fully absorbing, the snortest range at which a
surface reflection ccuid occur is approximately 8.2 km;
beyond this range, surface reflections should be spaced in
accordance with equation 2.4. Ihe nails beyond 8.2 km do
occur at the correct ranges; however, there are slow modula-
tions of the overall transmission loss signal. These slow
modulations ace another indication tnat the bottom is not
fully absorbing as had been specified as input to the
program.
26
CDaas
OM —X X
o t\o r-v
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a — m— t— mK LL *?-
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27
2- RT Analysis
The WI output from the S5FFT model is in English
units, wnich is a problem when comparing different models.
However, for this investigation the problem was minimal. As
expressed by aquation 2.6, the reference wavenumber for 100
hz with a reference sound speed of 4921-26 ft/sec (1500
m/sec) is 0-1277 1/ft. After correction of tne reference
wavenumber for a range increment of 62.3 it and the 2048
points used to represent the wavenumber spectrum, the
maximum beta value should be 0.1248 1/ft which agrees
reasonably well with the maximum beta values in figures 3.3,
3.4, ana 3.5. Contrary to theory tne nulls are not equally
spaced and the expected delta beta value of 0-001S2 1/ft
(equation 2.10) is net represented by any of tne null spac-
ir.gs. Stanley [Ref. 3], observed tne same non-uniform
spacing of beta nulls- The reason why the source depth is
not represented by any of the null spacings may be traced to
tne improper null placement in the raage domain. The lack
of egual spacing between the nulls must be attributed to
something else, possibly the pressure wave was improperly
represented as a continuous signal or numerical errors exist
within the source cede. Whatever tne reason for this
difference, it must be resolved before the SSFFT can De used
with tne KT to determine the source death.
28
33
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IFD ;v h Lloyd Birror
-rrarsaission Loss ^H^1. BM«> aas lnstalleu and
Ihe WD oodel [Eef. J ^s the next 2ode ,
sstsa lB Septet 19B3 at -
J» • ^ decision ,M .*.
|eause the IFD »« * otae , acoustic B*
^r-a-tions and was tii«= listing I s
)0t tominteraction tha source c0 .e
• 1once at NPS. A ~opim residence
_ .
Provided in appendix D.prob iea s which will be
'
The IFD also presented
P
^ ^ yitn the
The same ini^ --1-
fll. TPS nore
discussedfurther. TM
^^^ ^ „ D requires *
,,-pd with the I*. «- oerforiaea mSSFFT was u.ed
additionaltesting was pe
information,aaait
x
3<6 Lj.iu~bottom inform
dDSO rbing bottom. Fg
order to obtain a full* ^ I?D Bodei.
[ .t-a the environment as sesediment, and arti
trates the water aa;jS ,
^he densities xt to a constant o^ >•
the attenuation xi observeu. rJ-d
~«- - "";:;r,rr.:::r» «. -r;« .*. ::.:
an example or the Itfater depth of 2000 », **
./receiver depth, a waterq ^ ^ a
source/rective attenuation layer a-i+ ^n _
sar£ ace of the artificial t«» ^ ^ fcottos
10ver pressure release ««««•*, ^ a . 0016
uatioa used to produce rigure
22
r-»-
source
water
sediment
upper surface ofartificial attenuation layer
range
pressure release surfaces
Figure 3-6 IFD Environment.
33
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34
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37
The location of the nulls in figure 3.7 coincide with those
predicted by equaticn 2.4 if tne high frequency noise is
filtered out by either a running average process or low pass
digital filter. A careful examination of the transmission
loss curve (figure 3.8) reveals the real problem, which is
the long wavelength noise near tne wavelength of interest.
The long wavelength noise will cause erroneous spikes on tne
' WT plots after being Fourier transformed. Continued anal-
ysis revealed that the noise could be eliminated if the
thicknesses of the artificial attenuation layer and tne
bottom pressure release surface are chosen so that they are
at least twice the water depth, Tne choice of a small
vertical grid step will reduce the thickness required for
the pressure release surface, but this version of the IFD
program is United to 5000 vertical grid points due to soft-
ware restrictions. Figure 3.9 is a transmission loss curve
obtained from a 500 m source/receiver depth, a 2000 m water
depth, a HQOl m upper level artificial attenuation layer,
and an 3000 m bottom pressure release surface. Comparison
of figures 3.1 and 3.9 with the classical Lloyd's mirror
transmission loss (figure 2.2) snows that tne shape of the
curve beyond 30 i<m is greatly improved with the IFD. The
number of vertical grid steps was 5000. When the IFD is
used in a shallow water situation and at 25 hz, the noise
does not appear to be present. Figure 3.10 is a plot of the
transmission loss for a signal at 25 hz, witn the source/
receiver depth at 50 m, the bottom sloping up from 350 to 50
m, and an artificial attenuation layer and bottom pressure
release surface located at 750 and 1000 m, respectively.
The noise vhi^h was so evident in figure 3-7 is absent from
the shallow *ater case. Producing tne noise free curves
requires excessive computer time exoept for shallow water
cases.
33
2. WT Ana lysis
To reduce the amount of the pressure informatics and
yet preserve the details, the IFD tests were conducted
between 10 and 4 km in range. The reference wavenumber for
tne test input with the IFD was 0.4 189 1/ji which, after
correcting for a range increment of 7.5 m with 4096 points,
produced a beta maximum of 0.4188 1/m. Figures 3.11, 3.12,
and 3.13 indicate agreement with the beta maximum and a
delta beta of 0.00623 1/m can be found among the null spac-
ings. When the vertical grid step is reduced in size, the
output signal contains more information of finer detail.
The finer detailed information will, if noise is present,
produce more clutter on the WT depiction (figure 3.13). In
numerous WT depictions a peak was observed at the minimum
and maximum wavenumbers. Staney relieved that the right and
left intensity maxima corresponded to beam elevation angles
of and 30 degrees, respectively. He further stated that
the left maxima also may be related to algorithmic inaccura-
cies [Ref. 3]. The "U-shaped phenomenon" observed during
Stamey's investigation of the S3FFI, is present with the IFD
and the nulls are not equally spaced.
39
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42
The 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 coaplex pressure. Using a low pass filter and
increasing the vertical grid step size appear to reduce the
problem. In figure 3,8, the nulls occur at 33.30 and 33.39
km when a single null should exist at 33.33 km. This condi-
tion or noise produces the most devastating effects by
masking the desired density spectrum. A narrow band pass
filter would probably solve this problem in the short term
but eventually the IPD will require further study to elimi-
nate the noise. When the shallow case is used in the WT
(figure 3.14), the "U-shaped phenomenon" is absent and the
null locations are more distinct. However, in the shallow
water case, the bottom interaction produces high frequency
interference but the null spacings occur near tne expected
value for the source depth (0.0623 1/m) .
43
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44
IT. CONCLUSIONS
Two parabolic equation models, tae SSFFT and IFD, were
used to predict sound fields for comparison with the Lloyd's
mirror interference pattern in the ranga domain and then in
the wavenumber domain. In the range domain, the SSFFT
improperly handled the location of pressure nulls and
displayed bottom interference. While these weaknesses in
the SSFFT were absent in the IFD, the inadvertent and dele-
terious insertion of noise was extensive. In tne wavenumber
domain, the noise in the IFD was prohibitive in all but the
deep sediment and shallow water cases. The IFD produced
results which were comparable with the SSFFT when the noise
was not a factor. The range step and tne bottom attenuation
algorithms of the SSFFT should be reviewed in order to
correct those problems described acove. In the IFD, the
noise problem will require further investigation. If the
problem in tie 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 quickly correct inconsistencies
observed between acoustic models. Therefore, the «"T should
be investigated further to ensure tnat any software weak-
nesses are eliminated and a thorougn understanding of the
process is assured.
Experiments in the operational environment should be
planned to test the WT with actual soand sources. The ship-
board experiment could be easily accompli sned since the KT
can ce inpiemented on micro-computers if the pressure infor-
mation is provided from an outside source. The WT, if it is
going to be considered as a method to determine source
depth, appears to have three major snortcomin gs:
45
1. A clean CW signal with pnase information is essen-
tial, which will require quadrature demodulation and
extensive filtering.
2- Prediction models are required which will provide
equally spaced beta nulls so tnat 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
APPENDIX A: SSFFT SOURCE CODE (AT NPS)
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LIST OF REFERENCES
1. Naval Underwater Systems Center Technical Report 4103,Fast Fiaid Program for the Multila ye red Media, by F.R.UiHapoII, 26* June 1S7"T.
2. Naval Underwater Systems Center Technical Memorandum,Signal Transmission in the *
T av enu mber Dom ain, by R.lauer, 5 June T57U7
3. Stamey, 3. B. , Preliminary Investigation of theEnvironmental SensI tj.yj.ty or Acoustic S ignalTransmission in fne lavenumcer "Domain wifE R esp ect toSource"~Dep"EE Determination, Naval ?osTgraauate jcaooI,Decemref T^cJ2.
4. Naval Ocean Research and Development ActivityTechnical Note 12, The AESD Parabolic Equation M odel ,
H.K. Erock, January, T37B.
5. Officer, C.B., let reduction to the Theory of_ Soun i
Transmission wit l"
Tp ITcation tc tne Ocean,HcUra w^iTIIir 1 S537"
6. Buckner, H. P. , "Use of calculated sound fields andmatched-field detection to locate sound sources inshallow water," J. Acoust. 5oc. ia. , v. 59, d.368-373, February 197c.
7. Brekhovskikh , L. 8. , Fu ndamentals of Ocean Acoustics,Springer- Ver lag. New Yor*, 7732."
8. DeSanto, J.A-, "Relation between the Solutions of theHelmhoitz and Parabolic Equations for SoundPropagation," J- Acoust. Soc. la. , v. 62, p. 295-257,August 1977.
9. DeSanto, J. A., Topics in Current Pnysics: Ocea nAcoustics, Springer-v efTag, 1977.
10. Coppens, A. 3., An Introduction to the ParabolicEquation foe Acoustic P*rop
a
gafTon , TTaval 7ostgraauaTeScnool Technical Repor£,~i*?*SoT-3~3"-00 2, November 1982.
11. Kinsler, L.E. , Frey, A.R., Coppens, A. 3., and Sanders,J. V., Fundamentals of Acoustics Third Edition, JohnWiley ana" SonsT T5cJ2.~
12. Naval Underwater Systems Center Technical Report 6659,IFD: An Implicit Finite-Difference Com cuter Model forSolving" tne FaraboTic .c^uaTion , by L). "lee an "3 ~7J.DoTseas, "21 May T1T8Z.
~
147
+ h o13. Jaeger, I.E.. A Coa^uter Program for SolvingParatolic Equa tio n Us igg an Efflfilicrf Finite-I?ii:?reLC £ScTuTioa Zefnol racorporaTia-; Z^ a^t lLieri aceConaijETons # Uaval Pos tgraa aace~3caool, Septemoer T^cj.
143
BIBLIOGRAPHY
Bannister, R.EJ., "Low-frequency surface interference effectsin long-range sound propagation," j_. Acoust. Soc. Am., v.69, p. 76-8J, January 1981 -
Brigham, E.O. , The Fast Fourier Transform, 2 rent ice-HallInc., 197 4.
Brock, H.K., Buchal, R.N., and Spofford, C. H. , "Modifyingthe Sound Speed Profile to Improve tne Accuracy of theParafolic- Equation Iechnique", J. Acoust. Soc. km., v. 62,p. o43-552, September, 1977.
Clay, C.S. and H. Medwin, Acous tic Oceano gra phy : Prin c ip lesand Applications, John TJiley ana Hons,T^7T.
DiNapoli, F. R. and R.L. Deavenport, "Theoretical andNumerical Green' s function field solution in a plane multi-layered medium", J. Acoust . Soc. Am., v. 67, p. 92-105,January 1980.
Hamming, R. S. , Digital Filters Second Edition, Prentice-HallInc., 1977.
Naval Undersea Center Technical Report IP 488, Low-FrequencyPropagation Effects for Sources or Recievers Near Oe Uc^a ri
Suriace," Ly~I.A". Peaersen , "D.7. iJoraon, ana" D. ~ Unite,SepTemuer 1^75.
Ross Donald, Mechanics of. Underwater Noise, Pergamon Press,
Urick, R.J., Principles of Underwater Sound, Second Edition,McGraw-Hill, TS75T
Urick, R.J. , Sound Prqpagat ion in the Sea, Defense AdvancedResearch Project's Agency, T37U.
149
INITIAL DISTRIBUTION LIST
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1. Defense Technical Information Center 2Cameron StationAlexandria, 7 A 22314
2. Licrarv, Code 142 2Naval Postgraduate SchoolMonterey, CA 93S43
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Department of OceanographyNaval Postgraduate SchoolMonterey, CA 93 943
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Department of MeteorologyNaval Postgraduate SchoolMonterey, CA 93943
5- Prof. A.B. Cop pens (Code 61Cz) 4Department of PhysicsNaval Postgraduate ScnoolMonterey, CA 93943
6. Prof. C.R. Dunlap (Code 63Du) 3Department of OceanoaraphyNaval Postaraduate SchoolMonterey, CA 93943
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151
ThesishhQk3 Blanchard
205370
A comparison of twoacoustic parabolic eq-uation transmissionloss models for compa-tibility with the Wav-enumher Technique inthe determination ofsource depth.
205370
ThesisB5U8U3c. 1
BlanchardA comparison of two
acoustic parabolic eq-
uation transmissionloss models for compa-
tibility with the Wav-
enumber Technique in
the determination ofsource depth.
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