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.     

Using the adaptive simulated annealing algorithm to estimate ocean-bottom geoacoustic properties from measured and synthetic transmission loss data

This paper presents the results obtained using the adaptive simulated annealing (ASA) algorithm to invert the test cases from the Geoacoustic Inversion Techniques Workshop held in May 2001. The ASA algorithm was chosen for use in our inversion software for its speed and robustness when searching the geoacoustic parameter solution space to minimize the difference between the observed and the modeled transmission loss (TL). Earlier work has shown that the ASA algorithm is approximately 15 times faster than a modified Boltzmann annealing algorithm, used in prior versions of our TL inversion software, with comparable fits to the measured data. Results are shown for the synthetic test cases, 0 through 3, and for the measured data cases, 4 and 5. The inversion results from the synthetic test cases showed that subtle differences between range-dependent acoustic model version 1.5, used to generate the test cases, and parabolic equation (PE) 5.0, used as the propagation loss model for the inversion, were significant enough to result in the inversion algorithm finding a geoacoustic environment that produced a better match to the synthetic data than the true environment. The measured data cases resulted in better fits using ASTRAL automated signal excess prediction system TL 5.0 than using the more sophisticated PE 5.0 as a result of the inherent range averaging present in the ASTRAL 5.0 predictions.     

A hybrid simplex genetic algorithm for estimating geoacousticparameters using matched-field inversion

Matched-fieId inversion (MFI) undertakes to estimate the geometric and geoacoustic parameters in an ocean acoustic scenario by matching acoustic field data recorded at hydrophone array with numerical calculations of the field. The model which provides the best fit to the data is the estimate of the actual experimental scenario. MFI provides a comparatively inexpensive method for estimating ocean bottom parameters over an extensive area. The basic components of the inversion process are a sound propagation model and matching (minimization) algorithm. Since a typical MFI problem requires a large number of computationally intensive sound propagation calculations, both of these components have to be efficient. In this study, a hybrid inversion algorithm which uses a parabolic equation propagation model and combines the downhill simplex algorithm with genetic algorithms is introduced. The algorithm is demonstrated on synthetic range-dependent shallow-water data generated using the parabolic equation propagation model. The performance for estimating the model parameters is compared for realistic signal-to-noise ratios in the synthetic data     

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.     

Estimation of ocean-bottom properties by matched-field inversion ofacoustic field data

A method for estimating properties of the ocean bottom such as bathymetry and geoacoustic parameters such as sound speed, density and attenuation, using matched-field inversion is considered. The inversion can be formulated as an optimization problem by assuming a discrete model of unknown parameters and a bounded search space for each parameter. The optimization then involves finding the set of parameter values which minimizes the mismatch between the measured acoustic field and modeled replica fields. Since the number of possible models can be extremely large, the method of simulated annealing, which provides an efficient optimization that avoids becoming trapped in suboptimal solutions, has been used. The matching fields are computed using a normal mode model. In inversions for range-dependent parameters, the adiabatic approximation is employed. This allows mode values to be precomputed for a grid of parameter values and stored in look-up tables for fast reference, which greatly improves computational efficiency. Synthetic inversion examples are presented for realistic range-independent and range-dependent environments     

Preliminary analysis of the applicability of adiabatic modes to inverting synthetic acoustic data in shallow water over a sloping sea floor

The May 2001 Geoacoustic Inversion Techniques Workshop provided synthetic transmission loss (TL) data for four cases with range-dependent shallow-water all-liquid environments. In two of these cases ("0" and "1"), the sea floor has constant slope and the geoacoustic model (GAM) is range independent. Cost functions have been computed using a new adiabatic-mode TL algorithm (which uses an exact velocity boundary condition at the sloping sea floor), as one parameter in the GAM is varied. Two frequencies (80 and 220 Hz) were selected. In case 0, the sea-floor slope is 0.0183 and the GAM comprises an inhomogeneous layer over a basement. The sea-floor sound-speed was selected as the variable parameter. The resulting cost minima at 80 and 220 Hz are displaced from the actual sound speed by 2.3 and 3.4 m/s, respectively. In case 1, the sea-floor slope is 0.012 and the GAM comprises one homogenous layer, five inhomogeneous layers, and a basement. The selected parameter was the sound-speed in the homogeneous layer. The corresponding cost minima are displaced by -1.2 and +1.1 m/s. The relative values of these four errors indicate that mode coupling increases with sea-floor slope and that there may be a dependence on frequency at the greater slope.     

Geoacoustic characterization of a range-dependent ocean environment using towed array data

This paper examines geoacoustic inversion over a range-dependent multiple-layer seabed using a towed acoustic source and towed horizontal array. The approach is based on combining the results of a series of short-range, range-independent inversions to form a range-dependent representation of the environment. The data were collected in the Strait of Sicily during the MAPEX 2000 experiment. Issues such as the resolvability of multilayer structure and the sensitivity of various geoacoustic parameters are investigated by inversion of simulated data and by comparison of the MAPEX 2000 inversion results to a high-resolution seismic profile and to sediment core measurements. It appears that two, and in some cases possibly three, sediment layers can be resolved.     

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.     

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.     

Geoacoustic inversion using a rotated coordinate system and simulated annealing

An efficient method for geoacoustic inversions in a range-dependent ocean waveguide is implemented and tested with synthetic data. This method combines a simulated annealing search with an optimal coordinate rotation that increases the efficiency of navigating parameter landscapes for which parameter coupling is important. The coordinate rotation associated with the parameter couplings also provides information about which parameters are resolvable for a particular inversion frequency and array geometry. Using this information, results from several single-frequency inversions can be combined to obtain an estimate for the sediment parameters.     

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.     

Inversion for Time-Evolving Sound-Speed Field in a Shallow Ocean by Ensemble Kalman Filtering

In the context of the recent Maritime Rapid Environmental Assessment/Blue Planet 2007 sea trial (MREA/BP07), this paper presents a range-resolving tomography method based on ensemble Kalman filtering of full-field acoustic measurements, dedicated to the monitoring of environmental parameters in coastal waters. The inverse problem is formulated in a state–space form wherein the time-varying sound-speed field (SSF) is assumed to follow a random walk with known statistics and the acoustic measurements are a nonlinear function of the SSF and the bottom properties. The state–space form enables a straightforward implementation of a nonlinear Kalman filter, leading to a data assimilation problem. Surface measurements augment the measurement vector to constrain the range-dependent structure of the SSF. Realistic scenarios of vertical slice shallow-water tomography experiments are simulated with an oceanic model, based on the MREA/BP07 experiment. Prior geoacoustic inversion on the same location gives the bottom acoustic properties that are input to the propagation model. Simulation results show that the proposed scheme enables the continuous tracking of the range-dependent SSF parameters and their associated uncertainties assimilating new measurements each hour. It is shown that ensemble methods are required to properly manage the nonlinearity of the model. The problem of the sensitivity to the vertical array (VA) configuration is also addressed.      

Inversion for Range-Dependent Sediment Compressional-Wave-Speed Profiles From Modal Dispersion Data

A perturbative inversion method for estimating sediment compressional-wave-speed profiles from modal travel-time data is extended to include range-dependent environments. The procedure entails dividing a region into range-independent sections and obtaining estimates of the sediment properties for each region. Inversion results obtained using synthetic data show that range-dependent properties can be obtained if an experiment is designed to include multiple source/receiver combinations. This approach is applied to field data collected during the 2006 Shallow Water Experiment (SW06). The sediment compressional-wave-speed profiles resulting from analysis of the field data are evaluated by comparing acoustic fields predicted based on the inversion to acoustic fields measured during a different experiment conducted in the same region. The model is also compared to seismic reflection survey data collected during SW06. Resolution and variance estimated for the inversion results are also presented.      

Active rapid geoacoustic characterization using a seismic survey source

A survey of received acoustic energy levels from a seismic profiler were performed in Long Beach Harbor, CA, for compliance with the Marine Mammal Protection Act (MMPA). In addition to direct acoustic measurements, a rapid geoacoustic inversion algorithm was applied to the data to estimate the sediment properties acoustically. This inversion algorithm has matching criteria based on time spread, range-frequency interference patterns, and the range dependence of transmission loss. Self-consistency was checked by comparing acoustic measurements with predictions based on the inversion. With an estimated geoacoustic profile, predictions of received levels as a function of position in the range-dependent environment of Long Beach Harbor were then performed.     

Phenomenological and global optimization inversion

This paper discusses geoacoustic inversion results based on benchmark range-dependent data using SAGA, a global inversion package, and using phenomenological inversions. In phenomenological inversions, physical and signal-processing approaches are used to enhance the data to extract specific features. The global optimization approach is carried out on complex-valued vertical array data, transmission loss data, and reverberation data. The importance of checking the solution is emphasized by inspecting the match with the data and the error estimates and by checking the solution using data that has not been used in constructing the solution. The results show that we are able to estimate the geoacoustic parameters and that these parameters could be used to predict the field for different frequencies and/or source-receiver geometry than used in the inversion.     

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.     

An Equivalent Transform Method for Evaluating the Effect of Water-Column Mismatch on Geoacoustic Inversion

An "equivalent transform method" for quantitatively evaluating the effect of water-column mismatch on geoacoustic inversions is presented. This method is based on the concept of error transferral from one medium to another and is derived from linear perturbative inverse theory. To illustrate the method, geoacoustic inversions using adiabatic mode data, including wave numbers, group velocities, and travel times, are considered. In the test cases, both linear and nonlinear internal waves are considered as the causes of the water-column mismatch, and the inversion errors due to the water-column mismatch in each case are discussed. In the case of linear internal waves, range-averaged inversion errors are largely eliminated at the full cycle distance of the internal wave; however, in the case of nonlinear internal waves, the range-averaged inversion errors are accumulated but scaled down with increasing range. Furthermore, the inversion errors produced by water-column mismatch will be large if the modes used for inversion are sensitive to the mismatch; for instance, using higher order modes might lead to increased error even though it would normally improve inversion results. Using lower frequency signal, which penetrates deeper into the bottom, extends the effective depth of the inversion solutions, but this also allows the water-column mismatch to transfer error into the deeper bottom     

Data Uncertainty Estimation in Matched-Field Geoacoustic Inversion

This paper examines a variety of approaches to treating unknown data uncertainties in matched-field geoacoustic inversion. Both optimal parameter estimation via misfit minimization and parameter uncertainty estimation via Gibbs sampling are considered. The misfit is based on the likelihood function for Gaussian-distributed errors, which requires specification of the data variance at each frequency. Unfortunately, independent knowledge of variance is rarely available due to unknown theory errors. Many applications of matched-field minimization implicitly assume that variance effects are uniform over frequency; however, this can be a poor assumption as theory errors generally vary with frequency. Parameter uncertainty estimation to date has used fixed maximum-likelihood (ML) variance estimates, which does not account for the variance uncertainty in estimating parameter uncertainties. This paper considers two new approaches to treating data uncertainty in matched-field inversion: Including variances explicitly as additional (nuisance) parameters in the inversion, and treating variances as implicit unknowns by constraining the misfit according to an ML variance formulation (this includes variance uncertainty without increasing the number of unknown parameters). All of the above approaches are compared for realistic synthetic test cases and for shallow-water acoustic data measured in the Mediterranean Sea as part of the PROpagation channel SIMulator experiment (PROSIM'97).     

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