BENCHMARKING GEOACOUSTIC INVERSION METHODS
FOR RANGE DEPENDENT WAVEGUIDES
N. ROSS CHAPMAN
School of Earth and Ocean Sciences, University of Victoria, Victoria, B.C., Canada
E-mail: [email protected]
S. CHIN-BING AND D. KING
Naval Research Laboratory, Stennis Space Centre, MS, USA
R.B. EVANS
Science Applications International, Corp.
23 Clara Drive, Suite 206, Mystic, CT 06355, USA
Over the past decade, inversion methods have been developed to provide information
about unknown bottom environments from acoustic field data. An effective inversion
must provide both an estimate of the bottom parameters, and a measure of the
uncertainty of the estimated values. This paper summarizes results from the ONR
Geoacoustic Inversion Techniques Workshop that was held to benchmark present day
inversion methods for estimating geoacoustic profiles in shallow water. The format of
the workshop was a blind test to estimate unknown geoacoustic profiles by inversion of
synthetic acoustic field data. The fields were calculated using coupled normal modes
for three range-dependent test cases: a monotonic slope; a shelf break; and a fault
intrusion in the sediment. Geoacoustic profiles were generated to simulate sand, silt and
mud sediments. Several different approaches were presented for inverting the acoustic
field data: model-based matched field methods; perturbative methods; methods using
transmission loss data; methods using horizontal array information. New methods were
also discussed to formalize the measure of uncertainty in the inversion. Comparisons
between the different inversions are discussed in terms of a metric based transmission
loss calculated using the inverted profiles. The results demonstrate the effectiveness of
present day inversion techniques, and indicate the limits of their capabilities for rangedependent waveguides.
1
Introduction
The variability in the geological structure and in the geophysical properties of the ocean
bottom are known to have a significant effect on sonar performance in shallow water.
Sonar performance prediction systems that make use of geoacoustic information are
limited by the lack of high-resolution geophysical databases to describe the spatial
variability of the bottom properties in shallow water, where variations over scales of the
order of 100 metres are known to exist. To address this deficiency, comprehensive
experimental survey programs have been initiated to acquire geoacoustic data, and
model based inversion methods have been developed for estimating geoacoustic model
441
N.G. Pace and F.B. Jensen (eds.), Impact of Littoral Environmental Variability on Acoustic Predictions and
Sonar Performance, 441-448.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
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parameters from acoustic field data or from quantities derived from the fields
themselves. Examples of different inversion techniques include nonlinear methods
based on matched field processing [1,2], and linearized perturbative approaches [3].
There is an extensive literature that describes applications of different inversion
methods to experimental data for estimating geoacoustic model parameters.
With few exceptions, the inversions were generally designed to provide only the
estimates of a set of model parameters that defined a specific geoacoustic model for the
experimental site. However, the complete solution of the inverse problem requires not
only the estimates of the model parameter values, but also a measure of the uncertainty
of the estimates. For model-based sonar performance predictions, the parameter
uncertainties provide essential information to set confidence limits for predictions of
transmission loss and other quantities that affect detection or localization performance.
In order to obtain a reasonable measure of the errors, it is necessary to recognize the
sources of error in geophysical inverse methods. For most cases, the uncertainties due
to errors in the theory and the model are far more significant than errors that arise due to
inaccurate data. Examples of the former type of error are: mismatch in the geoacoustic
model of the actual environment; mismatch in the experimental geometry; and errors in
the acoustic propagation model. Since many of the model parameters are correlated, the
presence of mismatch can have a serious impact on the accuracy of the estimates,
especially in nonlinear inversion methods that search the model parameter space. A
simple example is the acoustic mirage effect that occurs in matched field source
localization if there is mismatch in the water depth [4].
This paper presents the results of a Geoacoustic Inversion Techniques Workshop
that was sponsored by ONR and SPAWAR to benchmark the accuracy and determine
the efficiency of inversion techniques that had been developed for estimating
geoacoustic model parameters in range-dependent shallow water environments. The
approach in the benchmark process was to compare the inversion performance of the
different methods against a standard set of range-dependent test cases. The workshop
was the second formal exercise for benchmarking geoacoustic inversion techniques.
The first workshop, held in 1997, carried out the initial phase to compare inversion
performance of different methods against test cases that were range independent [5].
All the test cases were synthetic, based on a known form for the geoacoustic model. In
the second workshop, both synthetic test cases and real data were provided, but we
focus on only the synthetic cases in this paper.
2
Workshop format
The benchmarking process described here was carried out using synthetic acoustic
pressure fields that were calculated for known values of the geoacoustic model
parameters for three range-dependent test case environments. The workshop format was
a blind test: participants were provided with only the acoustic field data, and were not
given the input parameters for the geoacoustic models. The tasks for the participants
were to invert the information in the acoustic fields to obtain estimates of the
geoacoustic model parameters of the environment, and to determine a measure of the
uncertainty of the estimates. A calibration test case was provided so that the
participants could benchmark the propagation model that was used for calculating the
BENCHMARKING GEOACOUSTIC INVERSION METHODS
443
acoustic fields in their inversions. For this case, the input geoacoustic profile was also
provided to the users.
The acoustic data for the test cases were provided in the frequency domain as
spectral components of the acoustic pressure field. This approach eliminates a signal
processing step that is normally carried out with time series data from experiments, but
was adopted for convenience in generating the large quantity of test case data. The
acoustic fields were calculated initially by the coupled normal mode propagation model,
COUPLE [6], as a benchmark, and these results were then duplicated by the parabolic
equation code, RAM [7]. All subsequent calculations for the workshop test case
database were done using RAM, to take advantage for its computational efficiency
compared to that for COUPLE. This approach provided accurate solutions for the
range-dependent test case environments. However, the environments were restricted to
fluid media.
The synthetic pressure fields were generated over a wide frequency band for
vertical and horizontal array geometries in the water layer, so that participants could
design their own ‘experiment’ to invert the data, using a subset of the available
information that was appropriate for their particular inversion method. The frequency
band was from 25–199 Hz in 1-Hz steps, and from 200–500 Hz in 5-Hz steps. The
spatial samples were provided as horizontal arrays at depths of 25 m and 85 m in 5–m
range steps from 5 m to 5000 m, and as vertical arrays with sensors from 20 m to 80 m
in 1-m increments, at ranges from 500 m to 5000 m in 500-m steps. The test case
environments were defined in a 5-km shallow water waveguide. For each test case, the
source depth was 20 m, and the water layer sound speed profile was downward
refracting and range-independent, according to
c w (z) = 1495.0− 0.04z
(1)
where z is the depth in metres. This information was provided to the participants.
Bathymetry was also provided, but with an uncertainty of ± 1 m.
There was no attempt in this workshop to add either incoherent or coherent noise to
the calculated spectral component data. However, since there is certain to be some
degree of geoacoustic model mismatch, errors due to this type of noise are inherent in
any of the nonlinear inversion methods that are posed as optimization problems. Formal
approaches t determine uncertainties due to theory and model noise have been proposed
by Gerstoft and Mecklenbrauker [8] and Dosso et al. [9].
3
Geoacoustic model
The geoacoustic model consisted of three components: a water layer with known profile
parameters; a series of fluid sediment layers; and a fluid basement halfspace. The
geoacoustic profile in the bottom layers was specified by the density, ρ, and the sound
speed, c, and attenuation, α, of compressional waves in each layer. The sediment
profile was an N-layer model, for which the number of layers and the geoacoustic
profile within each layer were unknown. Because the actual form of the multiparameter geoacoustic model was not known beforehand, the challenges in inverting the
synthetic test cases were similar to those for real data inversions. It was expected that
the participants would at best invert an approximation to the actual geoacoustic model
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N.R. CHAPMAN ET AL.
that was consistent with the information used in the inversion. The estimated profiles
could then be tested to determine the range of validity for other scenarios of sound
frequency and source/receiver geometry.
The geoacoustic profiles in the sediment were designed for specific sediment types
such as sand, silt or mud, using the empirical relationships of Bachman [10]. The
sediment material is described by the grain size parameter phi, given by −log2d where d
is the average grain size of the sediment particles. For sands, phi < 3.25 and for silts,
phi > 5.75. Phi values between these limits were classed as mixtures, and the
geoacoustic properties were determined according to weighted proportions of sand and
silt. The weights were defined by a silt factor φs given by:
φs = ( phi − 3.25) (5.75 − 3.25) .
The sound speed and attenuation profiles were given by:
•
Sands:
c(z) = c(0) × (20z )
0.015
α (z) = (0.23+ 0.268× phi) × (20z) −1/ 6
•
Silts:
(2)
(3)
c(z) = c(0) + 0.712z
α (z) = 0.297 − 0.035 × phi
where c(0) is the sound speed in the sediment at the sea floor according to:
c(0) = SSR × c w ,
and SSR = 1.180− 0.034 phi + 0.0013phi
2
(4)
for both sand and silt [10].
The density at the sea floor is ρ = (22.85 − phi ) 10.25 , and is approximately constant
with depth for both sands and silts over the shallow depths in the test cases. The
number of layers in the N-layer sediment profile was selected randomly from a uniform
distribution between [1–8], and the thickness of each layer was selected from a uniform
distribution from 1 to 5 m.
4
Range-dependent test case environments
Three test cases were designed to simulate:
• a monotonic downslope environment with a shallow slope (Fig. 1);
The sediment profile for this case consisted of a thin mud/silt layer (phi = 6.6) over
five layers of faster coarse sand (phi = 3.2), overlying a mudstone basement. The
total sediment thickness was 26.1 m.
• a shelf break environment (Fig. 2)
The sediment model for this case consisted of five layers of silty sand (phi = 5.25,
80% silt), overlying a sandstone basement. The sediment layer was 17.9 m thick. In
these first two cases, the sediment layers were parallel to the bottom slope.
•
an intrusion of basement material in the sediment layer to simulate an uplifted
fault (Fig. 3).
The geoacoustic profile in the third case was range dependent The sediment
consisted of a thin, slow velocity mud layer (phi = 7.5) over a sand-silt mixture of
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BENCHMARKING GEOACOUSTIC INVERSION METHODS
six layers (phi = 4.2, 38% silt), overlying a mudstone basement that was uplifted to
replace the sand silt layers for a portion of the range. The sediment thickness was
22.8 m.
Sediment
Mud: phi=6.6
Sand: phi=3.2
90 m
*
150 m
Basement
V = 2060.0 m/s
ρ = 2.1 g/cc
α = 0.02 dB/λ
5000m
Figure 1. Geoacoustic model for Test Case 1: Monotonic downslope.
Sediment
Silt/sand:
phi =5.25
140 m
*
Basement
V = 1861.0 m/s
ρ = 1.98 g/cc
α = 0.02 dB/λ
105 m
2100
5000m
Figure 2. Geoacoustic model for Test Case 2: Shelf break.
5
Inversion results for Test Case 1
Participants presented inversions using full wave signal processing methods (MFP) with
either vertical or horizontal array data; methods that used transmission loss data; and
specialized techniques such as plane wave beamforming and waveguide invariants.
Several different forward propagation models were used that proved to be effective for
range-dependent environments: parabolic equation, ray theory and adiabatic normal
modes. Although none of the participants recovered the exact form of the profile, the
sound speed profile was very well approximated by the estimated profiles. Density and
attenuation profiles were generally not as well estimated. For the MF inversions, new
hybrid search algorithms and inversions in reparameterized model spaces were
introduced that significantly improved the efficiency of the search process.
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N.R. CHAPMAN ET AL.
Sediment:
Silt: phi = 7.5
Sand/silt: phi=4. 2
*
100 m
Basement:
V = 1827.0 m/s
ρ = 1.98 g/cc
α = 0.02 dB/λ
1100 m
2900 m
5000m
Figure 3. Geoacoustic model for Test Case 3: An intrusion of basement material in the sediment
to simulate an uplifted fault structure.
The metric used to quantify the performance of the different inversion methods was
a simple comparison between transmission loss calculated using the estimated profiles
and those for the actual profile, for a different scenario of source/receiver (80m/80m
depths) geometry. Figure 4 shows the average rms transmission loss difference from
0–5 km at frequencies from 25–800 Hz. The most accurate results were obtained using
MF inversions based on nonlinear optimization techniques, with either horizontal or
vertical array data (shown by the + symbols). For these inversions, the differences are
slightly smaller at the frequencies that were used in the inversions, generally from
50–300 Hz. However, the analysis indicates that the estimated profiles provide accurate
transmission loss predictions at higher and lower frequencies as well. The differences
for profiles that were estimated from transmission loss data inversions (triangles) were
generally much greater.
Figure 4. Mean rms differences between transmission loss (TL) calculated for the estimated
profiles and the actual profile, for a source and receiver depths of 80 m.
BENCHMARKING GEOACOUSTIC INVERSION METHODS
447
Although the density and attenuations were not as well estimated, the analysis
summarized in Fig. 4 suggests that information about these quantities may not be as
critical as the knowledge of the sound speed profile in predicting transmission loss for
this environment. A measure of the sensitivity of each parameter was determined in
some of the inversion methods that used global search processes. An example is shown
in the scatter plots in Fig. 5, where the cost function is plotted versus parameter value
for one of the inversions that used a genetic algorithm in the SAGA inversion package.
The distributions in each panel indicate the range of values of each model parameter that
provide good fits to the acoustic field data. For sensitive parameters such as the sound
speeds or the thickness of the first sediment layer, the distributions are peaked, whereas
for insensitive parameters such as the attenuations or the sediment density, the
distributions tend to be flat. Although these displays are not true representations of the
a posteriori marginal densities for the parameters, they do provide a means to determine
which parameters were well estimated in the inversion.
Figure 5. Scatter plots of the cost function versus parameter values for geoacoustic models that
were sampled in the global search process. The distributions in each panel are normalized
independently to the maximum value. (After Siderius et al.)
448
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N.R. CHAPMAN ET AL.
Summary
Performance of present day geoacoustic inversion techniques was assessed in a
benchmark workshop, using realistic test cases that were generated for range-dependent
shallow water environments. Analysis of the results for the first test case, a monotonic
slope environment, indicated:
•
Inversion methods were capable of estimating highly accurate approximations
to the sound speed profile in the bottom. The most accurate results were
obtained by matched field inversions that used global search processes. These
techniques were also capable of generating effective measures of the parameter
sensitivity and the uncertainty of the estimates.
•
The estimated geoacoustic profiles provided the basis for accurate predictions of
transmission loss for independent scenarios of source/receiver geometry and
sound frequency.
•
Estimates of density and attenuation profiles were not as accurate. However,
the accuracy of these parameters does not appear to be critical for making
accurate predictions of transmission loss for use in sonar performance analysis.
Acknowledgements
This work was supported by ONR (NRC) and SPAWAR.
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