Geoacoustic Inverse Problems Research Articles

Geoacoustic inversion performed from two source‐receive arrays in shallow‐water waveguide.

Raylike propagation of acoustic waves in a shallow‐water waveguide between two vertical line arrays is investigated by applying a double beamforming algorithm, which performs time‐delay beamforming on both emitting and receiving arrays and allows identification of eigenrays by their emission and reception angles and arrival times. From the intensity of each eigenray, it is possible to determine reflection coefficient from the bottom of the waveguide as a function of an angle of incidence. The procedure was initially tested in a small‐scale tank experiment for an acoustic waveguide with either steel or Plexiglas bottom. By fitting an experimentally found reflection coefficient with a corresponding theoretical expression, an estimate for the speed of shear waves in the bottom material was obtained. Similar analysis was subsequently applied to the data obtained during an at‐sea experiment, which was performed between two vertical transducer arrays in shallow‐coastal waters of the Mediterranean. An angle‐dependent bottom reflection coefficient was extracted and geoacoustic inversion was performed by fitting the data with theoretical calculations, in which bottom sediments were modeled as a multilayered system. Good agreement between experiment and theory was observed. Our results indicate possible application of eigenray intensity analysis based on double beamforming algorithm for geoacoustic inversion problems.

Tracking of geoacoustic parameters using Kalman and particle filters

This paper incorporates tracking techniques such as the extended Kalman, unscented Kalman, and particle (PF) filters into geoacoustic inversion problems. This enables spatial and temporal tracking of environmental parameters and their underlying probability densities, making geoacoustic tracking a natural extension to geoacoustic inversion techniques. Water column and seabed properties are tracked in simulation for both vertical (VLA) and horizontal (HLA) line arrays using the three tracking filters. Filter performances are compared in terms of filter efficiencies using the posterior Cramer-Rao lower bound. Tracking capabilities of the geoacoustic filters under slowly and quickly changing environments are studied in terms of divergence statistics. Geoacoustic tracking can provide continuously environmental estimates and their uncertainties using only a fraction of the computational power of classical geoacoustic inversion schemes. Interfilter comparison show that while a high-particle-number PF outperforms the Kalman filters, there are many cases where all three filters perform equally well depending on the inversion configuration (such as the HLA versus VLA and frequency) and the tracked parameters.

AN ASSESSMENT OF THE PERFORMANCE OF GLOBAL OPTIMIZATION METHODS FOR GEO-ACOUSTIC INVERSION

Having available efficient global optimization methods is of high importance when going to a practical application of geo-acoustic inversion, where fast processing of the data is an essential requirement. A series of global optimization techniques are available and have been described in literature. In this paper three optimization techniques are considered, being a genetic algorithm (GA), differential evolution (DE), and the downhill simplex algorithm (DHS). The performance of these three methods is assessed using a test function, demonstrating superior performance of DE. Additionally, the DE optimal setting is determined. As a next step DE is applied for determining the geo-acoustic properties of the upper seabed sediments from simulated seabed reflection loss, indicating good DE performance also for real geo-acoustic inversion problems.

Adapting results in filtering theory to inverse theory, to address the statistics of nonlinear geoacoustic inverse problems

The intrinsically non-Gaussian statistics of nonlinear inverse problems, including ocean geoacoustic problems, is explored via analytic rather than numerical means. While Monte Carlo Bayesian methods do address the non-Gaussian statistics in nonlinear inverse problems, they can be very slow, and intuitive interpretation of the results are at times problematic. There is great theoretical overlap between recursive filters/smoothers, such as the extended Kalman filter, and methods of linear and nonlinear geophysical inversion. The use of recursive filters in inversion is not in itself new, but our interest is in adapting statistical developments from one to the other. Classic analytic methods in both filtering theory and inverse theory assume Gaussian probability distributions, but newer nonlinear filters do not all make this assumption and are explored for their potential application to nonlinear inverse problems. The similarities and differences between the frameworks of filtering theory and inverse theory are laid out in a series of geoacoustic inverse problem examples. Recent work in nonlinear filters handles non-Gaussian probability densities that are constrained to a particular form, and also derives analytic expressions for higher order moments of these density functions. The application of these developments to geoacoustic inverse problems is addressed. [Work supported by ONR.]

Robust matched-field processor in the presence of geoacoustic inversion uncertainty

This presentation examines the performance of a matched-field processor incorporating geoacoustic inversion uncertainty. Uncertainty of geoacoustic parameters is described via a joint posterior probability distribution (PPD) of the estimated environmental parameters, which is found by formulating and solving the geoacoustic inversion problem in a Bayesian framework. The geoacoustic inversion uncertainty is mapped into uncertainty in the acoustic pressure field. The resulting acoustic field uncertainty is incorporated in the matched-field processor using the minimum variance beamformer with environmental perturbation constraints (MV-EPC). The constraints are estimated using the ensemble of acoustic pressure fields derived from the PPD of the estimated environmental parameters. Using a data set from the ASIAEX 2001 East China Sea experiment, tracking performance of the MV-EPC beamformer is compared with the Bartlett beamformer using the best-fit model.

Anomalous sound propagation due to the horizontal variation of� seabed acoustic properties

The sound propagation in shallow water is greatly influenced by the acoustic properties of seabed. An anomalous transmission loss was observed in an experiment, and a range dependent bottom model with horizontal variation of seabed acoustic property is proposed and could be well used to explain the anomalous phenomena. It is shown that the horizontal variation of bottom properties has a great effect on underwater sound propagation, and it should be given much attention in sound propagation and geoacoustic inversion problems.

Bayesian geoacoustic inversion for the inversion techniques 2001 workshop

This paper applies a Bayesian formulation to range-dependent geoacoustic inverse problems. Two inversion methods, a hybrid optimization algorithm and a Bayesian sampling algorithm, are applied to some of the 2001 Inversion Techniques Workshop benchmark data. The hybrid inversion combines the local (gradient-based) method of downhill simplex with the global search method of simulated annealing in an adaptive algorithm. The Bayesian inversion algorithm uses a Gibbs sampler to estimate properties of the posterior probability density, such as mean and maximum a posteriori parameter estimates, marginal probability distributions, highest-probability density intervals, and the model covariance matrix. The methods are applied to noise-free and noisy benchmark data from shallow ocean environments with range-dependent geophysical and geometric properties. An under-parameterized approach is applied to determine the optimal model parameterization consistent with the resolving power of the acoustic data. The Bayesian inversion method provides a complete solution including quantitative uncertainty estimates and correlations, while the hybrid inversion method provides parameter estimates in a fraction of the computation time.

Ray-based geoacoustic inversion for high frequency broad band data

One of the difficulties in making reliable acoustic propagation predictions in shallow water is the lack of good information about the seabed type. In recent years, matched field processing- (MFP-) based geoacoustic inversion has been shown as a practical technique for estimating properties of the seabed. The MFP inversion method compares measured acoustic fields to those generated using an acoustic propagation model. Often, thousands of forward model calculations are required to find a set of seabed parameters that correlate well with the measured data. The large number of forward model calculations is computationally demanding and this is made worse when matching at higher frequencies or over broad band data. Ray-based propagation modeling relieves some of the computational burden since the calculation time is fairly insensitive to frequency and is inherently broad band. Further, the ray arrival amplitudes and delays are well suited for interpolation and this allows the seabed parameter search space to be explored using just a few ray trace calculations. The broad band nature of the modeled data provides flexibility in choosing correlation functions and this allows for more robust inversions. In this presentation, techniques using ray-based propagation modeling will be applied to the geoacoustic inversion problem.

Measures of uncertainty in geoacoustic inversion

Inversion methods for estimating geoacoustic model parameters from acoustic field data have been applied with considerable success over the past decade. The most effective methods that have been developed generally fall into two categories, nonlinear methods that are posed as optimization problems, and linearized methods that invert quantities such as horizontal wave numbers that are derived from the acoustic field data. For either case, the complete solution of the geoacoustic inverse problem requires a measure of the error for the estimated parameter, as well as the estimate itself. This paper describes an approach for specifying an error measure in nonlinear inversion processes based on matched field processing. The inversion uses an optimization algorithm that combines global and local search processes to sample the model parameter space. An effective error measure is obtained from information in scatter plots of the cost function versus parameter values for models that were tested in the search process. Examples are presented to demonstrate the application of the method to test cases from the recent Geoacoustic Inversion Benchmark Workshop, and from experimental data from vertical line arrays and seafloor horizontal arrays. [Work supported by ONR.]

Wigner–Ville representations for acoustic source localization

Signal dispersion in a waveguide can be linked to source and receiver location as well as physical properties of the propagation medium. Traditionally, the main methods used for source localization in the ocean and in geoacoustic inversion problems have been based on the use of the spectrogram for the extraction of the dispersion information. In this work we explore the possibility of using other time-frequency transforms because other transforms, such as the Wigner–Ville representation, reflect the dispersion properties of the waveguide more accurately than conventional spectrograms. We apply the Wigner–Ville distribution, in conjunction with sound propagation models, for inversion with underwater sound. Results with synthetic data calculated for simplified ocean media indicate the potential of the approach for successful parameter estimation. [Work supported by ONR.]

Quantifying data information content in geoacoustic inversion

This paper examines the information content in matched-field geoacoustic inverse problems as a function of a variety of experiment factors, with the aim of guiding data collection and processing to achieve the best possible inversion results. The information content of the unknown geoacoustic parameters is quantified in terms of their marginal posterior probability distributions, which define the accuracy expected in inversion. Marginal distributions are estimated using a fast Gibbs sampler approach to Bayesian inversion, which provides an efficient, unbiased sampling of the multi-dimensional posterior probability density. When sampled to convergence, the marginal distributions are found to have simple, smooth shapes that facilitate straightforward comparisons. The approach is general; the specific examples considered here include factors such as the number of sensors in the receiving array, array length, source-receiver range, source frequency, number of frequencies, source bandwidth, and signal-to-noise ratio.

Quantifying uncertainty in geoacoustic inversion. II. Application to broadband, shallow-water data

This paper applies the new method of fast Gibbs sampling (FGS) to estimate the uncertainties of seabed geoacoustic parameters in a broadband, shallow-water acoustic survey, with the goal of interpreting the survey results and validating the method for experimental data. FGS applies a Bayesian approach to geoacoustic inversion based on sampling the posterior probability density to estimate marginal probability distributions and parameter covariances. This requires knowledge of the statistical distribution of the data errors, including both measurement and theory errors, which is generally not available. Invoking the simplifying assumption of independent, identically distributed Gaussian errors allows a maximum-likelihood estimate of the data variance and leads to a practical inversion algorithm. However, it is necessary to validate these assumptions, i.e., to verify that the parameter uncertainties obtained represent meaningful estimates. To this end, FGS is applied to a geoacoustic experiment carried out at a site off the west coast of Italy where previous acoustic and geophysical studies have been performed. The parameter uncertainties estimated via FGS are validated by comparison with: (i) the variability in the results of inverting multiple independent data sets collected during the experiment; (ii) the results of FGS inversion of synthetic test cases designed to simulate the experiment and data errors; and (iii) the available geophysical ground truth. Comparisons are carried out for a number of different source bandwidths, ranges, and levels of prior information, and indicate that FGS provides reliable and stable uncertainty estimates for the geoacoustic inverse problem.

Parameter coupling in broadband geoacoustic inversion

For many geoacoustic inverse problems involving a single frequency data set, the search parameters are often strongly coupled to one another. This may mean that individual parameters are difficult to determine, but combinations of parameters can be resolved. In terms of the optimization process, the parameter landscape that is being searched has multidimensional valleys that hinder location of a global minimum. A coordinate rotation technique has been developed [J. Acoust. Soc. Am. 98, 1637–1644 (1995)] to speed the search for optimal parameters. This technique also gives valuable information about the parameter hierarchy and parameter couplings. One approach to decoupling the parameters and obtaining realistic physical parameter values is to process broadband data or multifrequency data. A new fast forward modeling technique [J. Acoust. Soc. Am. 106, 1727–1731 (1999)] makes it possible to consider broadband data for geoacoustic inversion. The coordinate rotation technique is combined with fast forward modeling to study parameter couplings for broadband and multifrequency problems. [Work supported by ONR.]

Estimating elastic sediment properties with the self-starter

The self-starter is implemented by the method of undetermined coefficients for ocean acoustics problems involving elastic sediment layers. This approach is efficient when the ocean bottom can be approximated by a relatively small number of homogeneous layers. For many problems, the self-starter only requires on the order of 10 wave number samples to provide accurate solutions at ranges on the order of 10 wavelengths. The geoacoustic inverse problem can be solved in nearly real time with this approach, which can generate on the order of a thousand forward solutions per second on the current generation of desk-top computers.

An efficient parabolic equation solution based on the method of undetermined coefficients

An implementation of the self-starter based on the method of undetermined coefficients is described and tested. For many problems, this parabolic equation technique for solving short range propagation problems provides an efficiency gain of an order of magnitude or more over the finite difference solution. With this forward model, it is possible to solve geoacoustic inverse problems in seconds on the current generation of desktop computers. The approach can be implemented for the inverse problem so that efficiency is essentially independent of the depth of the water column.

Geoacoustic inversion techniques applied to field data

Reliable and efficient techniques for solving geoacoustic inverse problems have been developed. A coordinate rotation technique can be used to identify the best resolved combinations of parameters for a given frequency and configuration of hardware [M. D. Collins and L. Fishman, J. Acoust. Soc. Am. 98, 1637–1644 (1995)]. Problems involving a vertical array of receivers at short range can be solved in a few seconds with an implementation of the self starter that is based on the method of undetermined coefficients [D. K. Dacol and M. D. Collins, J. Acoust. Soc. Am. (accepted for publication)]. These techniques are applied to data that were obtained in the Straits of Florida during the KWIX ’98 experiment. [Work supported by ONR.]

Wave number sampling at short range

The self-starter is an efficient approach for solving geoacoustic inverse problems involving a vertical array of receivers located on the order of ten wavelengths from a source [R. J. Cederberg and M. D. Collins, J. Acoust. Soc. Am. 22, 102–109 (1997)]. With this approach, accurate solutions can be obtained by sampling the wave number spectrum at approximately ten points. There have been unsubstantiated claims that the spectral solution provides similar efficiency when implemented with an approach that involves perturbing the integration contour off the real line [F. B. Jensen et al., Computational Ocean Acoustics (American Institute of Physics, New York, 1994), pp. 231–240]. It is demonstrated that this quadrature scheme breaks down at short ranges and that the self-starter solution is about an order of magnitude faster. These conclusions are based on comparisons of the rational approximations associated with the self-starter and the quadrature scheme, comparisons of acoustic fields for particular problems, and a simple analysis of the spectral integral. These conclusions are not surprising since the rational approximation associated with the self-starter is based on the analytic evaluation of the spectral integral while the other rational approximation is based on numerical integration. [Work supported by ONR.]

Estimation of anisotropic sediment parameters

Parabolic equation techniques have recently been developed for solving geoacoustic inverse problems [R. J. Cederberg and M. D. Collins, IEEE J. Ocean Eng. 22, 102–109 (1997)] and for handling propagating problems involving anisotropic elastic layers [A. J. Fredricks, J. Acoust. Soc. Am. 101, 3182 (1997)]. These techniques are used to investigate inverse problems involving anisotropic elastic layers. Complications arise from the direction dependence of the two sediment sound speeds. For the particular case of transverse isotropy, both sound speeds need to be estimated in two different directions. A coordinate rotation technique [M. D. Collins and L. Fishman, J. Acoust. Soc. Am. 98, 1637–1644 (1995)] will be employed to estimate the resolvability of the direction-dependent wave speeds for different experimental configurations. [Work supported by ONR.]

Broadband Geoacoustic Deduction

A two-stage approach to the geoacoustic inversion problems of selected Workshop '97 test cases is described. Initial parameters are deduced by inspection of transmission losses versus range, depth and frequency, and comparison with the calibration case. These provide a starting point for a conventional matched-field inversion applied to individual frequency data sets for a vertical array at 5-km range using the normal mode model SUPERSNAP and the standard Bartlett processor. Grid searches are carried out over pairs of parameters using: 500-Hz data to establish the sediment density and top sediment sound speed, 100-Hz data to estimate the sound speed gradient in the sediment layer and 25-Hz data for the remaining parameters. Results and error bounds are presented for two realizations of the SD workshop case. Partial results are presented for the SO case. Issues regarding SUPERSNAP/SAFARI mismatches are also discussed.

Analytic implementation of a parabolic equation solution

There are two basic approaches for discretizing the differential equations that are solved in propagation models: (1) Approximate the differential operator with a finite-difference formula; and (2) approximate the medium in terms of layers that may be treated analytically and solve for a set of coefficients. The analytic approach is more efficient for problems involving a small number of layers. Both approaches have been implemented for normal mode and wave-number integration models. The finite-difference approach has been implemented for parabolic equation models. This paper describes an analytic implementation of a parabolic equation model that is efficient for geoacoustic inversion problems [R. J. Cederberg and M. D. Collins, ‘‘Application of an improved self-starter to geoacoustic inversion,’’ IEEE J. Ocean. Eng. (in press)]. Using the finite-difference implementation, the self-starter can solve nonlinear inversion problems in minutes on a workstation (techniques that were developed previously require hours of run time). The analytic implementation reduces run times to seconds. [Work supported by ONR.]