Geoacoustic Inverse Problems Research Articles

Solutions to muddy (geoacoustic inversion) problems

Waveguide propagation is a ubiquitous topic in ocean acoustics. This presentation focuses on low-frequency (f < 500 Hz) sound propagation in coastal oceans (water depth shallower than 500 m). These environments are highly dynamical and complex, and act as dispersive waveguides, bounded by the sea-surface and the seafloor. The underwater acoustic field can thus be described by a set of modes that propagate with frequency-dependent speeds. Propagation of transient acoustic signals to a distant receiver (range > 1 km) accrues multi-modal dispersion information about the propagation medium. To extract relevant information about the oceanic environment from the acoustic recording, physics-based processing methods must be used. In this presentation, I will briefly review modal propagation and time-frequency analysis. I will then show how these approaches can be combined into a non-linear signal processing method dedicated to extracting modal information from a single receiver: this information is the foundation of a transdimensional inversion method used to characterize the oceanic environment. This method will be used to perform geoacoustic inversion on the New England Mud Patch. Using several datasets collected under different oceanographic conditions, I will notably demonstrate a successful estimation of the seafloor properties, consistent with geophysical core measurements and other inversion studies, even when the water column is dynamical and mostly unknown.

Acoustic characterization of the seabed with a single-element time-reversal mirror

Motivated by the 2012 Florida Straits Noise Interferometry Experiment, this paper investigates a time-reversal-based approach to acoustic remote sensing of the ocean. The signal processing mimics operation of a physical time-reversal mirror. The input data for the simulated time-reversal mirror can be obtained using either a compact, broadband sound source or cross-correlation of the diffuse noise recorded by spatially separated receivers. Low-frequency sound propagation is considered over ranges that are large compared to the water depth. The approach exploits the notion that the “best” focusing of the backpropagated time-reversed signal occurs at the “right point,” when the backpropagation takes place in the same propagation medium as the one, where the data have been acquired. Various metrics of the focusing quality are considered. A combination of spatial and temporal characteristics of the focus is proposed that leads to a robust and unique solution of the geoacoustic inverse problems considered for a single-element passive time-reversal mirror. Inputs with rather low signal-to-noise ratio prove acceptable, which is particularly important in the passive remote sensing context.

Passive time-reversal mirror for acoustic characterization of the seabed

This paper investigates application of a signal processing technique, which is motivated by time reversal, to geoacoustic inversions in a shallow-water waveguide. The signal processing mimics operation of a physical time-reversal mirror. The input data for the simulated time-reversal mirror can be obtained using either a compact, broadband sound source or cross-correlation of the diffuse noise recorded by spatially separated receivers. Low-frequency sound propagation is considered over ranges that are large compared to the water depth. The approach exploits the notion that the “best” focusing of the backpropagated time-reversed signal occurs at the “right point,” when the backpropagation takes place in the same propagation medium as the one, where the data have been acquired. Various metrics of the focusing quality are considered. A combination of spatial and temporal characteristics of the focus is proposed that leads to a unique solution of the geoacoustic inverse problem for a single-element passive time-reversal mirror. [Work supported by NSF.]

Sequential Geoacoustic Inversion Using an Improved Kalman Particle Filter

Geoacoustic inversion is an efficient method to study the physical properties and structure of ocean bottom while sequential geoacoustic inversion is a challenging task due to the complexity and non-linearity of the underwater environment. In this paper, an ensemble Kalman Particle filter is described to address the sequential geoacoustic inversion problem of range-dependent environment in shallow water. This filter combines the advantages of Particle filter and ensemble Kalman filter so its ability of tracking dynamical geoacoustic parameters is improved. The proposed filtering method is demonstrated with simulated data in a changing oceanic environment and outperforms Particle filter and ensemble Kalman filter. This method is also tested in sea-trial data collected from a shallow-water experiment in the East China Sea. The inverted sound speed in sediment is consistent with in situ measurement and the error between transmission loss predicted by inverted parameters, and the experimental transmission loss is small.

Seabed classification using localized forward modeling and deep learning

We use full wave solutions to generate synthetic high-frequency data for training seafloor classifiers with acoustic signals in the ocean. We expect to recover high level details that cannot be achieved by standard forward models that do not include seafloor roughness. By creating acoustic templates using micro local analysis of full-wave simulations on smaller domains, we avoid the high cost of solving the equations on large domains, the main obstacle in full wave inversion. To demonstrate the usefulness of this modeling, we generate a training library of templates and show how well these can be used in classifying seafloor parameters. We consider two-layer seafloors with varying material types and thicknesses. We address the geoacoustic inversion problem with standard machine learning techniques and more sophisticated deep learning methods. The standard classifiers provide results with worse accuracy that do not generalize well to other test environments; the deep learning classifiers are more costly to train but have higher accuracy, generalizing better. We compare the performance with simulations performed at lower frequencies using a normal mode approach with no roughness effects, where the classification problem becomes simpler. [Work supported by NSF, EOARD, and ONR.]

Acoustic and geoacoustic inverse problems in randomly perturbed shallow-water environments.

The main goal of this paper is to estimate the regional acoustic and geoacoustic shallow-water environment from data collected by a vertical hydrophone array and transmitted by distant time-harmonic point sources. The aim is to estimate the statistical properties of the random fluctuations of the index of refraction in the water column and the characteristics of the sea bottom. It is explained from first principles how acoustic wave propagation can be expressed as Markovian dynamics for the complex mode amplitudes of the sound pressure. This makes it possible to express the cross moments of the sound pressure in terms of the parameters to be estimated. Then it is shown how the estimation problem can be formulated as a nonlinear inverse problem using this formulation, which can be solved by minimization of a misfit function. The method is applied to experimental data collected by the Acoustic Laboratory for Marine Applications system. A Bayesian analysis quantifies the uncertainty of the estimation.

Applications of a Motion Compensation Stabilized Vertical Array of Hydrophones

When a vertical array of hydrophones is used to determine the location of a submerged acoustic source in the ocean, performance is limited by the quality of the data, especially when there is interference from ambient noise and other sources or when there are uncertainties in the parameters of the environment. High-quality data may be obtained by anchoring a vertical array on the seafloor, but this time-consuming approach does not allow frequent deployments and mobility. By using motion compensation to eliminate the vertical motion of an array that is deployed from a surface platform, it may be possible to obtain high-quality data with a rapidly deployable system. Other applications that could benefit from this capability include the geoacoustic inverse problem of estimating the parameters of the sediment and studying the effects of horizontal diffraction and horizontal multi-paths for global-scale problems.

A Volunteer Computing Project for Solving Geoacoustic Inversion Problems

AbstractA volunteer computing project aimed at solving computationally hard inverse problems in underwater acoustics is described. This project was used to study the possibilities of the sound speed profile reconstruction in a shallow-water waveguide using a dispersion-based geoacoustic inversion scheme. The computational capabilities provided by the project allowed us to investigate the accuracy of the inversion for different mesh sizes of the sound speed profile discretization grid. This problem suits well for volunteer computing because it can be easily decomposed into independent simpler subproblems.

Resolution analysis of the inverse problem for geoacoustic experiment design

This work explores effects of experiment geometry and array configuration on the resolving power of a continuous ocean bottom geoacoustic inverse problem in a shallow water environment. The uncertainty and resolution of this problem, in which ocean bottom P-wave velocities as a function of depth are estimated from noisy acoustic pressure waveforms received on vertical and horizontal line arrays in the water, can be investigated before the experiment is conducted, allowing one to improve or optimize the problem parameters to best configure an experiment during its planning phase. In this work, the resolution results of complete synthetic geoacoustic inversions at varying geometries and array configurations are compared with resolution results at various candidate seabottom profiles, initially using standard techniques of linearized inverse theory. Singular value decomposition is used to interpret the tie between geometry and regularization in the inverse problem, which directly affects the resolution. Then, additional comparisons and analysis address the nonlinearity of the problem, which causes a dependence of the resolution results on the bottom profile being solved for—which is unknown, and Monte Carlo analysis is used to show where the linearity approximation breaks down in the resolution results. [Work partially funded by ONR.]

Geo-acoustic parameter estimation using a multistep inversion technique based on normal mode method

The geo-acoustic parameters are of great importance in determining how the sea bottom affects sound propagation in the ocean. Many inversion techniques have been developed to estimate geo-acoustic parameters. One-step inversion algorithms using a cost function defined only by energy loss may not result in a unique solution of geo-acoustic inversion problem because of the correlation between seabed sound speed and attenuation. This paper utilizes different characteristics of normal modes to define appropriate cost functions in a two-step inversion algorithm for inferring geo-acoustic parameters. This inversion scheme is applied to the combustive sound source data obtained by two L-shaped arrays. The inverted seabed sound speed and attenuation are comparable to the results derived from measured time series and transmission loss data at the same experimental site [Knobles, Wilson, Goff, and Cho, J. Acoust. Soc. Am., 124, 2008]. [Work supported by ONR321OA].

Parallel tempering for strongly nonlinear geoacoustic inversion

This paper applies parallel tempering within a Bayesian formulation for strongly nonlinear geoacoustic inverse problems. Bayesian geoacoustic inversion consists of sampling the posterior probability density (PPD) of seabed parameters to estimate integral properties, such as marginal probability distributions, based on ocean acoustic data and prior information. This sampling is usually carried out using the Markov-chain Monte Carlo method of Metropolis-Hastings sampling. However, standard sampling methods can be very inefficient for strongly nonlinear problems involving multi-modal PPDs with the potential to miss important regions of the parameter space and to significantly underestimate parameter uncertainties. Parallel tempering achieves efficient/effective sampling of challenging parameter spaces with the ability to transition freely between multiple PPD modes by running parallel Markov chains at a series of increasing sampling temperatures with probabilistic interchanges between chains. The approach is illustrated for inversion of (simulated) acoustic reverberation data for which the PPD is highly multi-modal. While Metropolis-Hastings sampling gives poor results even with very large sample sizes, parallel tempering provides efficient, convergent sampling of the PPD. Methods to enhance the efficiency of parallel tempering are also considered.

METAHEURISTIC OPTIMIZATION OF ACOUSTIC INVERSE PROBLEMS

Swift solving of geoacoustic inverse problems strongly depends on the application of a global optimization scheme. Given a particular inverse problem, this work aims to answer the questions how to select an appropriate metaheuristic search strategy, and how to configure it for optimal performance. Four state-of-the-art metaheuristics have been selected for this study; these are simulated annealing, genetic algorithms, ant colony optimization, and differential evolution. To make a careful comparison, each of these metaheuristic optimizers has been configured for two real-world geoacoustic inverse problems. The influence and sensitivity of specific performance parameters have been studied by analysis of repeated problem-solving. It is concluded that a proper configuration and tuning is just as important as selection of the best optimization scheme. The application in this work is geoacoustic inversion, but the argumentation on selecting and configuring an appropriate metaheuristic has potential for any indirect inverse problem.

Trans-dimensional strategies for geoacoustic posterior probability estimation

Choosing appropriate model parametrizations is a fundamental aspect of Bayesian parameter inference. Trans-dimensional inference is based on a hierarchical Bayesian model, where the number of unknowns in the problem is itself unknown. The methodology extends the state-space to the union of subspaces of a group of models of interest. This allows the data to estimate the support for the parametrizations under consideration while accounting for the limited knowledge about the parametrization in the posterior probability density estimate. Algorithms, such as reversible-jump Markov chain Monte Carlo, can be used to sample from the trans-dimensional posterior by proposing and accepting/rejecting dimensional transitions (jumps) according to a generalized Metropolis-Hastings criterion. Several challenges exist for the efficient application of trans-dimensional methods to geoacoustic inference including defining proposal distributions for efficient transitions between dimensions and within dimensions, and specifying (or quantifying) data errors distributions (or statistics). Example1109; of applying the trans-dimensional approach are demonstrated for several geoacoustic inverse problems, using trans-dimensional partition modeling and hierarchical data-error models.

Optimized constraints for the linearized geoacoustic inverse problem

A geoacoustic inversion scheme to estimate the depth-dependent sound speed characteristics of the shallow-water waveguide is presented. The approach is based on the linearized perturbative technique developed by Rajan et al. [J. Acoust. Soc. Am. 82, 998-1017 (1987)]. This method is applied by assuming a background starting model for the environment that includes both the water column and the seabed. Typically, the water column properties are assumed to be known and held fixed in the inversion. Successful application of the perturbative inverse technique lies in handling issues of stability and uniqueness associated with solving a discrete ill-posed problem. Conventionally, such problems are regularized, a procedure which results in a smooth solution. Past applications of this inverse technique have been restricted to cases for which the water column sound speed profile was known and sound speed in the seabed could be approximated by a smooth profile. In this work, constraints that are better suited to specific aspects of the geoacoustic inverse problem are applied. These techniques expand on the original application of the perturbative inverse technique by including the water column sound speed profile in the solution and by allowing for discontinuities in the seabed sound speed profile.

Geoacoustic inversion with two source-receiver arrays in shallow water

A geoacoustic inversion scheme based on a double beamforming algorithm in shallow water is proposed and tested. Double beamforming allows identification of multi-reverberated eigenrays propagating between two vertical transducer arrays according to their emission and reception angles and arrival times. Analysis of eigenray intensities yields the bottom reflection coefficient as a function of angle of incidence. By fitting the experimental reflection coefficient with a theoretical prediction, values of the acoustic parameters of the waveguide bottom can be extracted. The procedure was initially tested in a small-scale tank experiment for a waveguide with a Plexiglas bottom. Inversion results for the speed of shear waves in Plexiglas are in good agreement with the table values. A similar analysis was applied to data collected during an at-sea experiment in shallow coastal waters of the Mediterranean. Bottom reflection coefficient was fitted with the theory in which bottom sediments are modeled as a multi-layered system. Retrieved bottom parameters are in quantitative agreement with those determined from a prior inversion scheme performed in the same area. The present study confirms the interest in processing source-receiver array data through the double beamforming algorithm, and indicates the potential for application of eigenray intensity analysis to geoacoustic inversion problems.

Sequential Bayesian strategies in geoacoustic inverse problems.

This paper considers sequential Bayesian strategies for geoacoustic inverse problems which are difficult to solve simultaneously due to computational constraints. Bayesian inference provides a powerful approach to learning problems such as this since sequential inversions of multiple data sets [with the posterior probability density (PPD) of one inversion applied as prior information in the subsequent inversion] are equivalent to simultaneous inversion of all data. However, passing PPDs forward as priors has its own challenges when the PPD is sampled numerically for nonlinear inverse problems, particularly when the model parameter space is of high dimensionality and the data information content is high. In such cases, approximations are required to efficiently carry PPD information forward to subsequent inversions. The approach developed here represents numerically sampled PPDs in terms of discretized marginal probability distributions for principal components of the parameters, which minimizes the loss of information in representing inter‐parameter correlations. The sequential Bayesian approach is applied to seabed reflectivity inversion with multiple data sets representing travel‐time data and frequency‐domain reflection coefficient data for a series of increasing penetration depths. Data information content is quantified by accounting for potential error biases as well as data error covariances. [Work supported by the Office of Naval Research.]

Variation of uncertainty and resolution with problem formulation in continuous geoacoustic inversion.

In continuous geoacoustic inversion, the resolution and uncertainty of the estimated ocean bottom are inherently linked by a tradeoff with each other. They also depend on the experiment geometry and the choice of formulation for the data and for the bottom model. For example, the resolution and variance will differ if the data are represented by an intensity envelope timeseries or a tau-p timeseries, or if wave slowness or bottom impedance is estimated. Previous work by the authors investigated variations in resolution and uncertainty with geometry and problem formulation based on linearization of the geoacoustic problem at a given solution. However, the problem is further complicated by the fact that the solution point itself can also depend on the geometry and data and model formulation so that the resolution and uncertainty vary for that reason also. This aspect of the nonlinear geoacoustic inverse problem is explored here. [Work supported by ONR.]

Accounting for spatiotemporal variability of shallow water waveguides in the geoacoustic inverse problem.

Reliable acoustic field predictions are essential for sonar performance modeling and matched field processing, particularly related to the geoacoustic inverse problem. On continental shelves and slopes, properties of the water column can vary widely in both time and space, while the seabed can be heterogeneous over scales of only a few kilometers and sometimes less. This combined spatiotemporal variability of the acoustic waveguide was a hallmark of the Shallow Water Experiment 2006 (SW06). This is illustrated using data collected during SW06 for an acoustic field measured on a fixed receiver array for a source towed along a radial track and repeated several times. In these experiments, the large degree of variability in the observed acoustic fields was attributed to large-scale changes in the water column that occurred over the course of a day. Properly accounting for this variability proved to be essential for obtaining robust geoacoustic inversion results for the seabed. Specifically, the spatiotemporal properties of the water column had to be accounted for in the forward models from which objective functions were derived. Methods for capturing the observed water-column variability are discussed as used in the inverse problem as well as for the more general problem of model-data comparison.

Statistical signal characterization in ocean acoustic tomography and geoacoustic inversions.

A performance study of a statistical characterization of an underwater acoustic signal in relation to geoacoustic inversion or tomography problems is presented. The method of characterization has been presented by Taroudakis et al. [JASA 119, 1396–1405 (2006)] and is based on the use of an appropriate distribution law which describes the statistics of the sub‐band coefficients of the signal wavelet transform. The method has been applied with synthetic data simulating tomographic experiments with low‐frequency sources in shallow environments for the estimation of the water column and bottom properties. In this work the inversion procedure incorporating a genetic algorithm is applied in shallow water environments with simulated noisy data to assess the performance of the method and its limitations under realistic conditions.

Geoacoustic inversion using particle swarm optimization.

A novel optimization approach is applied to geoacoustic inversion with a towed horizontal array. Particle swarm optimization, a stochastic, population-based evolutionary algorithm, is applied to geoacoustic inversion problems in order to estimate unknown sediment and ocean parameters. Geoacoustic inversions with a towed array are applied to both synthetic data and experimental data from MAPEX 2000. Particle swarm optimization yields quick, consistent parameter estimates. These results will be compared with previously published results using an advanced rotated coordinate simulated annealing technique. [Work supported by ONR.]