An adaptive-hybrid algorithm for geoacoustic inversion

This paper presents an adaptive hybrid algorithm to invert ocean acoustic field measurements for seabed geoacoustic parameters. The inversion combines a global search (simulated annealing) and a local method (downhill simplex), employing an adaptive approach to control the trade off between random variation and gradient-based information in the inversion. The result is an efficient and effective algorithm that successfully navigates challenging parameter spaces including large numbers of local minima, strongly correlated parameters, and a wide range of parameter sensitivities. The algorithm is applied to a set of benchmark test cases, which includes inversion of simulated measurements with and without noise, and cases where the model parameterization is known and where the parameterization most be determined as part of the inversion. For accurate data, the adaptive inversion often produces a model with a Bartlett mismatch lower than the numerical error of the propagation model used to compute the replica fields. For noisy synthetic data, the inversion produces a model with a mismatch that is lower than that for the true parameters. Comparison with previous inversions indicates that the adaptive hybrid method provides the best results to date for the benchmark cases     

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     

Estimating geoacoustic parameters using matched-field inversion methods

In this paper, we use matched-field inversion methods to estimate the geoacoustic parameters for three synthetic test cases from the Geoacoustic Inversion Techniques Workshop held in May 2001 in Gulfport, MS. The objective of this work is to use a sparse acoustic data set to obtain estimates of the parameters as well as an indication of their uncertainties. The unknown parameters include the geoacoustic properties of the sea bed (i.e., number of layers, layer thickness, density, compressional speed, and attenuation) and the bathymetry for simplified range-dependent acoustic environments. The acoustic data used to solve the problems are restricted to five frequencies for a single vertical line array of receivers located at one range from the source. Matched-field inversion using simplex simulated annealing optimization is initially used to find a maximum-likelihood (ML) estimate. However, the ML estimate provides no information on the uncertainties or covariance associated with the model parameters. To estimate uncertainties, a Bayesian formulation of matched-field inversion is used to generate posterior probability density distributions for the parameters. The mean, covariance, and marginal distributions are determined using a Gibbs importance sampler based on the cascaded Metropolis algorithm. In most cases, excellent results were obtained for relatively sensitive parameters such as wave speed, layer thickness, and water depth. The variance of the estimates increase for relatively insensitive parameters such as density and wave attenuation, especially when noise is added to the data.     

Benchmarking geoacoustic inversion methods for range-dependent waveguides

Inversion methods have been developed over the past decade to extract information about unknown ocean-bottom environments from acoustic field data. This paper summarizes results from the Office of Naval Research/Space and Naval Warfare Systems Command (SPAWAR) Geoacoustic Inversion Techniques Workshop, which was designed to benchmark present-day inversion methods. 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 a high-angle parabolic approximation and verified using coupled normal modes for three range-dependent shallow-water 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 in these environments. Several different approaches for inverting the acoustic field data were presented at the workshop: model-based matched-field methods; perturbation methods; methods using transmission loss data; and methods using horizontal array information. An effective inversion must provide both an estimate of the bottom parameters and a measure of the uncertainty of the estimated values. New methods were presented at the workshop 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 range-dependent waveguides.     

An investigation of algorithm-induced variability in geoacoustic inversion

This paper investigates the inherent variability in the results of matched-field geoacoustic inversion algorithms. This algorithm-induced variability must be considered when interpreting inversion results in terms of environmental changes as a function of time or space. Fast simulated annealing (FSA), genetic algorithms (GA), and a hybrid algorithm (adaptive simplex simulated annealing; ASSA) are compared by performing multiple inversions of benchmark synthetic data (noise free and noisy) and acoustic data measured over both low- and high-speed sea-bed sediments in the MAPEX 2000 experiment. ASSA produced the lowest variability in inversion results for all cases, followed by GA and FSA. For the high-speed MAPEX 2000 case, the variability is essentially negligible, while for the low-speed case the variability is significant as compared with environmental variations reported in the literature.     

Matched-field inversion for geoacoustic model parameters in shallowwater

Matched-field inversion is used to, estimate geoacoustic properties from data obtained in an experiment with a vertical line array (VLA). The experiment was carried out using broad-band sources (shots) in water depths of about 200 m on the continental shelf off Vancouver Island. The data were processed to obtain spectral components of the field for frequencies near the bubble frequency for the shot. The ocean bottom in this region consists of a layer of mainly sandy sediments (about 100 m thick) overlying older consolidated material. Consequently, the inversion was designed to estimate the parameters of a two-layer elastic sediment model. In the inversion, an adaptive global search algorithm was used to investigate the multidimensional space of geoacoustic models in order to determine the set of values corresponding to the best replica field. Convergence is driven by adaptively guiding the search to regions of the parameter space associated with above-average values of the matched field correlation between the measured and replica fields. The geoacoustic profile estimated by the inversion consisted of a 125-m layer with compressional speed ~1700 m/s and shear speed ~400 m/s, overlying a layer with compressional speed ~1900 m/s. This model is consistent with the results from conventional seismic experiments carried out in the same region     

Benchmarking geoacoustic inversion methods using range-dependent field data

Over the past decade, inversion methods have been developed and applied to acoustic field data to provide information about unknown ocean-bottom environments. 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 Office of Naval Research (ONR)/Space and Naval Warfare Systems Command (SPAWAR) Geoacoustic Inversion Techniques Workshop, test cases 4 and 5. The workshop 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 measured acoustic transmission loss data in octave bands and reverberation envelopes. The data sets for test cases 4 and 5 were taken at two locations in shallow water, one in the East China Sea and the other along the southwest coast of Florida. The limitations of the data and the limits to the knowledge of the sites are discussed. In both cases, impulsive sources were used in conjunction with air-deployed sonobuoys. Since the measured data was incoherent, only methods consistent with total energy matching were applicable. Comparisons between the different inversion techniques presented at the workshop are discussed. For test cases 4 and 5, a precise metric was unavailable for comparison.     

Perturbative inversion of geoacoustic parameters in a shallow waterenvironment

In many strategic shallow water areas, the geoacoustic properties of the sub-bottom are largely unknown. This paper demonstrates that inverse theory and measured data from a single hydrophone can be used to accurately deduce the geoacoustic properties of the sub-bottom, even when the initial background geoacoustic model is a highly inaccurate estimate. Since propagation in shallow water is very sensitive to the geoacoustic properties of the sub-bottom the inverse technique is a vitally important, practical, and inexpensive means to improve sonar performance prediction in a potentially hostile environment. To provide ground truth for the inverse technique, measured data collected during Project GEMINI were compared to the inverse solutions. Detailed, site-specific geoacoustic models were developed for two array locations and the finite-element parabolic equation (FEPE) model was used to estimate transmission loss (TL). The model estimates from FEPE compared well with the measured data and the detailed geoacoustic models were considered as “ground truth.” To test the efficacy of the technique, initial background geoacoustic models were constructed assuming no a priori information of the bottom. The resultant inverse solution was used to predict the geoacoustic properties at each of the sites. The final results were in excellent agreement with the measured data and the resulting TL estimates derived from the inverse technique were as good or better than the TL estimates obtained from the detailed, site-specific geoacoustic models     

Performance comparison between vertical and horizontal arrays for geoacoustic inversion

Most of the research on model-based geoacoustic inversion techniques has concentrated on data collected using moored vertical receiver arrays. However, there are many advantages to considering geoacoustic inversion using a towed horizontal array. Towed arrays are easily deployed from a moving platform; this mobility makes them well suited for surveying large areas for sea-bed properties. Further, if a model-based geoacoustic inversion scheme uses both a towed source and array, the separation between the two can be kept short, which reduces the requirement for range-dependent modeling. Range-independent modeling is used for inverting all the horizontal array data considered in this paper. Using the Inversion Techniques Workshop Benchmark Test Cases, the performance of a horizontal (simulated towed) and vertical arrays are compared and found to be very similar. However, it will be shown that, for Benchmark Test Case 3, where the bathymetry is flat and a hidden bottom intrusion exists, a towed horizontal array is ideal for determining the range-dependent sea-bed properties. The practical advantages of using a towed array are clear and the purpose of this paper is to show that the performance is similar (and in some cases better) than using moored vertical arrays.     

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.     

Effective parameters for matched field geoacoustic inversion in range-dependent environments

Using the well-established technique of geoacoustic inversion, one can estimate a set of acoustic sea-bed parameters from sonar array data. Simultaneously, one can search for geometric parameters such as range, water depth, and hydrophone depth. When the technique is applied in a range-dependent environment, there is a potentially much larger set of parameters to match, unless one has perfect knowledge of the bathymetry. From the point of view of optimization, one needs to handle uncertainties in bathymetry without hugely increasing the amount of computation. A simple time-domain view (which is shown to be equivalent to the adiabatic approximation) suggests that it is sufficient to use a range-independent model with an empirical "effective" depth even when the bottom is not flat. In fact, there is a set of effective environments that will suffice; one can choose whichever is the most convenient. The success of this concept is demonstrated with some test cases from a recent Geoacoustic Inversion Techniques Workshop.     

Matched field inversion for geoacoustic model parameters usingadaptive simulated annealing

A method is described for the estimation of geoacoustic model parameters by the inversion of acoustic field data using a nonlinear optimization procedure based on simulated annealing. The cost function used by the algorithm is the Bartlett matched-field processor (MFP), which related the measured acoustic field with replica fields calculated by the SAFARI fast field program. Model parameters are perturbed randomly, and the algorithm searches the multidimensional parameter space of geoacoustic models to determine the parameter set that optimizes the output of the MFP. Convergence is driven by adaptively guiding the search to regions of the parameter space associated with above-average values of the MFP. The performance of the algorithm is demonstrated for a vertical line array in a shallow water enviornment where the bottom consists of homogeneous elastic solid layers. Simulated data are used to determine the limits on estimation performance due to error in experimental geometry and to noise contamination. The results indicate that reasonable estimates are obtained for moderate conditions of noise and uncertainty in experimental geometry     

Reverberation vertical coherence and sea-bottom geoacoustic inversion in shallow water

Optimal array-processing techniques in the ocean often require knowledge of the spatial coherence of the reverberation. A mathematical model is derived for the reverberation vertical coherence (RVC) in shallow water (SW). A method for analysis of RVC data is introduced. Measured reverberation cross-correlation coefficients as a function of time and frequency, obtained during the Asian Seas International Acoustic Experiment (ASIAEX) in the East China Sea, are reported. SW reverberation from a single shot provides a continuous spatial sampling of the surrounding sound field up to several tens of kilometers and holds valuable information on the geoacoustic properties of the sea floor over this distance. SW reverberation data can, therefore, be used as the basis for a quick and inexpensive method for geoacoustic inversion and has the obvious advantage that acquiring the data in situ requires only a single platform. This paper considers the use of the vertical coherence of the reverberation as the starting point for such an inversion. Sound speed and attenuation in the sea bottom at the ASIAEX site are obtained over a frequency range of 100-1500 Hz by finding values that provide the best match between the measured and predicted RVC.     

Range-dependent geoacoustic inversion: results from the Inversion Techniques Workshop

Model-based geoacoustic inversion in range-dependent underwater environments is a challenging task constrained by data quality (synthetic or measured) and propagation-model efficiency and accuracy. The Inversion Techniques Workshop (ITW), held in Gulfport, MS, May 15-18, 2001, was organized for the acoustics community to present state-of-the-art numerical geoacoustic inversion capabilities in range-dependent shallow-water environments. The organizers defined five range-dependent test cases (three synthetic and two experimental cases). Two of the synthetic cases were adopted for geoacoustic inversion in this paper. The first test case (TC1) is a monotonic down-slope bathymetry problem and the adiabatic normal-mode model PROSIM was applied for the inversion in this case. The second test case (TC3) is a flat-bottom case with an intrusion. The forward model used in this case was RAMGEO. The global optimization package SAGA was used for geoacoustic inversion of the synthetically generated reference solutions for TC1 and TC3. In general, the geoacoustic inversion results are in good agreement with the true solutions provided by the organizers. The results obtained demonstrate the feasibility of performing geoacoustic inversion in synthetic range-dependent shallow-water environments. However, results show that the propagation model choice in the inversion is strongly dependent on the specific range-dependent environment.     

Time-domain geoacoustic inversion of high-frequency chirp signal from a simple towed system

An inversion method using a towed system consisting of a source and two receivers is presented. High-frequency chirp signals that have been emitted from the source are received after multiple penetrations and reflections from the shallow water sub-bottom structure and are processed for geoacoustical parameter estimation. The data are processed such that a good resolution and robustness is achieved via matched filtering, which requires information about the source signal. The inversion is formulated as an optimization problem, which maximizes the cost function defined as a normalized correlation between the measured and modeled signals directly in the time domain. The very fast simulated reannealing optimization method is applied to the global search problem. The modeled time signal is obtained using a ray approach. An experiment was carried out in the Mediterranean Sea using a towed source and receiver system. The inversion method is applied to the experimental data and results are found to be consistent with previous frequency-domain analyses using measurements from a towed horizontal array of receivers and measurements on a vertical array.     

Modal evolution and inversion for seabed geoacoustic properties inweakly range-dependent shallow-water waveguides

In a shallow-water ocean environment, the range dependent variation of the geoacoustic properties of the seabed is one of the crucial factors affecting sound propagation. Since the local modes of propagation depend on the spatial changes in the bottom sediments, the local eigenvalues of these modes are useful as tools for examining the range dependence of the sediment properties. In order to extract the local eigenvalues from measurements of the pressure field in a laterally inhomogeneous waveguide, the zeroth-order asymptotic Hankel transform with a short sliding window is utilized. The local peak positions in the output spectra differ from the local eigenvalues due to both the range variation of the local modes and the interference of adjacent modes. The departure due to the former factor is evaluated analytically by using the stationary phase method. In order to reduce the error induced by the latter factor, mode filtering is utilized by incorporating data from a fixed vertical array of receivers. The methods developed are applied to simulated pressure field data as well as experimental field data, and it is shown that the range evolution of the local modes can be successfully estimated. In addition, field measurements are used to demonstrate that the modal trajectories in range can be used to infer the range-dependent geoacoustic properties of the seabed     

Matched-field geoacoustic inversion of low-frequency source tow data from the ASIAEX East China Sea experiment

Geoacoustic inversion results based on data obtained during the Asian Seas International Acoustics Experiment (ASIAEX) 2001 East China Sea experiment are reported. The inversion process uses a genetic-algorithm-based matched-field-processing approach to optimize the search procedure for the unknown parameters. Inversion results include both geometric and geoacoustic variables. To gauge the quality of the inversion, two different analyses are employed. First, the inversion results based upon discrete source-receiver ranges are confirmed by continuous source localization over an interval of time. Second, separate inversions at many different ranges are carried out and the uncertainties of the parameter estimation are analyzed. The analysis shows that both methods yield consistent results, ensuring the reliability of inversion in this study.     

Rapid geoacoustic characterization: applied to range-dependent environments

The problem of rapid environmental assessment in a range-dependent environment is addressed. For rapid assessment, the exact geoacoustic parameters are not required, nor is it a requirement that the exact structure of the acoustic field (location of peaks and s) be matched by an acoustic prediction model. The parameters that are relevant are the overall transmission loss (incoherent TL), the time spread (/spl tau/), and the slopes of the range/frequency interference patterns (/spl beta/, the waveguide invariant). The rapid geoacoustic characterization algorithm uses a homogeneous single-sediment layer overlying a hard acoustic basement model to optimally match the predicted acoustic observables with those estimated from data. The approach is presented here and is applied to the range-dependent benchmark cases TC1 and TC2 from the Inversion Techniques Workshop held in Gulfport, MS, in May 2001. The technique successfully reproduces the acoustic observables and estimates the sediment sound-speed, density, and attenuation profiles, as well as the sediment thickness.