Matched-field Inversion Research Articles

Geoacoustic information content of bottom-moored horizontal line array data

This paper considers geoacoustic information content in matched-field inversion of acoustic data from bottom-moored horizontal line arrays. Bayesian geoacoustic inversion is applied to low-frequency multi-tone data in a synthetic shallow water environment under realistic signal-to-noise ratios and for frequency bands relevant to both controlled-source experiments and ship-noise inversion. The information content is quantified in terms of widths of marginal a posteriori probability densities of model parameters obtained by fast Gibbs sampling. The information content dependence on factors such as array length and sensor configuration, source range and bearing (from endfire to broadside), and frequency content is studied.

Geoacoustic Information Content of Horizontal Line Array Data

This paper examines the effectiveness of horizontal line arrays (HLAs) for matched-field inversion (MFI) by quantifying geoacoustic information content for a variety of experiment and array factors, including array length and number of sensors, source range and bearing, source-frequency content, and signal-to-noise ratio (SNR). Emphasis is on bottom-moored arrays, while towed arrays are also considered, and a comparison with vertical line array (VLA) performance is made. The geoacoustic information content is quantified in terms of marginal posterior probability distributions (PPDs) for model parameters estimated using a fast Gibbs sampler approach to Bayesian inversion. This produces an absolute, quantitative estimate of the geoacoustic parameter uncertainties which can be directly compared for various experiment and array factors.

Bayesian geoacoustic inversion in a range-dependent environment

In August 2006 a series of experiments was carried out on the New Jersey continental shelf to investigate geoacoustic inversion in a range-dependent shallow water environment. The experimental site was instrumented with multiple oceanographic sensing systems to provide spatial and temporal ground truth of the ocean environment throughout the experiments. The acoustic experiments used multiple receiving systems and sound sources operating over a large frequency band from 50 to 20 kHz. This paper presents results from inversion of low-frequency (<1000 Hz) data obtained along a radial track from one of the 16-element vertical line arrays. The track was surveyed with a chirp sonar to establish bathymetric and subbottom ground truth. Continuous wave tones were recorded at ranges of 1, 3, and 5 km where the source ship held station for several minutes. Bayesian matched field inversion was applied at each of the sites. The effects of unknown range dependence were taken into account by estimating the data error covariance from multiple data windows at each range station. The inversions indicate that the long-range experimental geometry provided reliable estimates for the sea floor sediment parameters in the range-dependent environment. [Work supported by ONR Ocean Acoustics Team.]

Estimating parameter uncertainties in matched field inversion by a neighborhood approximation algorithm

In Bayesian inversion, the solution is characterized by its posterior probability density (PPD). A fast Gibbs sampler (FGS) has been developed to estimate the multi-dimensional integrals of the PPD, which requires solving the forward models many times and leads to intensive computation for multi-frequency or range-dependent inversion cases. This paper presents an alternative approach based on a neighborhood approximation Bayes (NAB) algorithm. For lower dimension geoacoustic inversion, the NAB can approximate the PPD very well. For higher dimensional problems and sensitive parameters, however, the NAB algorithm has difficulty estimating the PPD accurately with limited model samples. According to the preliminary PPD estimation from the NAB, this paper developed a multi-step inversion scheme, which adjusts the parameter search intervals flexibly, in order to improve the approximation accuracy of the NAB and obtain more complete parameter uncertainties. The prominent feature of the NAB is to approximate the PPD by incorporating all models for which the forward problem has been solved into the appraisal stage. Comparison of the FGS and NAB for noisy synthetic benchmark test cases and Mediterranean real data indicates that the NAB provides reasonable estimates of the PPD moments while requiring significantly less computation time.

Inversion of Lloyd Mirror Field for Determining a Source's Track

This paper describes a simple approach for inferring the depth and track of a sound source at short ranges by inversion of acoustic field data at a set of sea bottom hydrophones. At short ranges, the acoustic field consists of a dominant Lloyd mirror (LM) signal from the direct and surface-reflected ray paths and a series of bottom-reflected paths that modulate the LM signal. A computationally efficient propagation model based on the method of images is developed to calculate replica fields for the inversion. The matched field inversion method for inferring the source depth and track is demonstrated using data from an experiment carried out in shallow water off the east coast of Canada. The estimated values were in very good agreement with independent measurements taken during the experiment.

Geoacoustic inversion of short range source data using a plane wave reflection coefficient approach

Acoustic time series data were collected in a shallow, hard bottom lake environment located in central Texas using both short range (2 m) implosive data, obtained with the source and a single hydrophone located near mid-depth in the waveguide, along with longer range implosive and explosive data from a near surface source to a bottom mounted hydrophone. Matched field inversions using simulated annealing were performed with a ray trace plus complex plane wave reflection coefficient forward propagation model that was validated in previous work. Isolating bottom interacting paths to perform the inversions is shown to be essential to reduce parameter uncertainties in the hard bottom environment and enables a systematic approach to the inversions which establishes the number of layers needed to represent the lake environment. Measured transmission loss data from a towed source were compared through a RMS error analysis to modeled transmission loss, constructed with the parameters from inversions of data from several source types, to further establish the validity of the inversion approach for this environment. Geoacoustic parameters obtained by inversions of short range, low frequency impulsive data are used to predict transmission loss at longer ranges and higher frequencies. The range dependence of the global minimum is discussed.

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 analytic multiple frequency adjoint-based inversion algorithm for parabolic-type approximations in ocean acoustics

Inverse problems in ocean acoustics are generally solved by means of matched-field inversion in combination with meta-heuristic global search algorithms. Recently adjoint-based optimal nonlocal boundary control has been proposed as a possible complement or alternative to the traditional geoacoustic inversion methods. Especially for the assessment of a shallow water environment where field data are recorded on non-fully populated hydrophone arrays there is an inherent need for observation over a broad range of frequencies, as has been widely experimentally demonstrated. This article presents an analytic multiple frequency adjoint formulation for estimating an acoustically equivalent model of the seabed based on local impedance boundary conditions. It is intended as a benchmark solution for an extension of the approach to more sophisticated boundary conditions by means of automatic differentiation. The approach, coming from control theory, aims at inverting the impedance boundary condition along the water–sediment interface via measurements of the acoustic propagation in the water column. The impedance boundary condition thus plays the role of the control parameter of the complex pressure field in the waveguide. The developed multiple frequency adjoint method of optimal control provides an explicit representation of the gradient of the matched-field oriented cost function, and the article further proposes an analytical second-order adjoint formulation which permits the computation of the product of the Hessian matrix by a vector. By means of example inversion results the feasibility of the multi-frequency approach is discussed and the effect of a limited set of receiving locations is illustrated.

Electromagnetic source localization in shallow waters using Bayesian matched-field inversion

The propagation of an electromagnetic signal in a marine environment cannot be modelled as a plane wave due to the high attenuation in seawater and the interactions with the ocean boundaries. Consequently, conventional beamforming techniques are not applicable for electromagnetic source localization. In this work, the Bayesian approach to matched-field processing is used to localize an electromagnetic source and estimate the environmental parameters. In this formulation, the solution to the inverse problem is given by the a posteriori probability distribution calculated here using the Gibbs sampling method. Bayesian inversion theory provides the formalism for estimating parameters, their uncertainties and verification of the estimates convergence. Two situations were investigated for the case where the single frequency measurements represent the magnitudes of two orthogonal horizontal electric field components: (1) all environmental parameters known and (2) unknown seabed conductivity. The objective function that relates the array data to the propagation model and environment parameters was chosen for the practical situation considered.

Estimating geoacoustic properties of marine sediments by matched field inversion using ship noise as a sound source

The first stage of a seafloor observatory to monitor marine gas hydrates will be deployed in the Gulf of Mexico in the fall of 2005. One component of the monitoring station is a vertical line hydrophone array moored on the seafloor. This paper reports research to investigate using matched field inversion of sound generated by passing ships to detect changes in the geoacoustic parameters of the seabed that may indicate the occurrence of a gas hydrate dissociation event. First, synthetic multifrequency data were used to investigate the performance of the inversion method for estimating sediment sound speeds near the seafloor. The synthetic data were generated using the parabolic equation method for a geoacoustic environment that simulated the seabed at the site in Mississippi Canyon. The geoacoustic model consisted of a multilayered structure with relatively slow sound speeds to significant depths below the seafloor. The inversion based on normal mode replica fields indicated that performance strongly depends on using a realistic parametrization of the geoacoustic model. Experimental ship noise data were recorded along radial tracks in a preliminary deployment of the vertical array. Results are reported for estimating a geoacoustic model from the noise data.

A Sound Approach to Soft Sediment Resolution

The last few years has seen a surge in research activities directed towards investigating properties and dynamics of young marine, limnic and fluvial sediments. It is by now a well established fact that the sequence of sediments ranging from concentrated benthic suspension over fluid mud to un-consolidated material summarized as liquid sediments (LS), act as carriers for a wide range of pollutants discharged or migrated into waterways. Knowledge of the transport and fate of LS allows determining the transport and fate of adsorbed constituents (e.g., heavy metals, pesticides, PCBs, PAHs). To assess the environmental impact of LS, efforts have to be made to better understand the processes in relation to hydrodynamics and the chemical and physical properties of the layers. Since physical laws limit the resolution and detection power of conventional seismo-acoustic systems in respect of LS, alternative measurement, data analysis and processing approaches have to be found. Adapted acoustic procedures initially developed for shallow water marine environments to extreme shallow water regimes using matched field inversion techniques can reveal geoacoustic parameters including density, compressional wave speed and attenuation as a function of depth and time. The paper outlines the effects of sediment mobility upon the environment followed by a short overview of techniques commonly used to investigate sediments and other freshwater/marine events. The problems faced and limitations of existing systems are briefly outlined. Results obtained with recently developed and refined geoacoustic inversion methods are presented highlighting their potential for long-term study of physical properties and dynamics of LS.

The effects of ignored seabed variability in geoacoustic inversion

Geoacoustic inversion using a matched-field inversion algorithm is a well-established technique for estimating the geoacoustic parameters of the seabed. This paper demonstrates how parameter estimation can be affected by unknown or wishfully ignored random range dependence of the true environment when the inversion model is--for practicality--assumed to be range independent. Simulations with controlled statistics were carried out using a simple shallow water model: an isospeed water column over a homogeneous elastic halfspace. The inversion parameters included water depth, compressional speed in the seabed, seabed density, and compressional wave attenuation. On average the environment is range independent: some parameters are constant while other parameters are random with range-independent means and variances. A Parabolic Equation underwater acoustic propagation model is used to calculate the simulated data fields for the range-dependent environment as well as to calculate the model fields for the range-independent inversion model. The Adaptive Simplex Simulated Annealing inversion algorithm is used to estimate the best-fit solution. It is found that ignoring the variability of even a single geoacoustic parameter leads to significant and correlated uncertainty (bias and variance) in the estimation of all inverted parameters. Results are presented for range variation of compressional sound speed and water depth.

Multistep Matched-Field Inversion for Broad-Band Data From ASIAEX2001

This paper discusses the results of geoacoustic inversion carried out using explosive charge data from the Asian Seas International Acoustic Experiment (ASIAEX) East China Sea (ECS) Experiment. A multifrequency incoherent matched-field inversion processor and a genetic algorithm (GA) are used for the inversion. A multistep matched field inversion approach is presented, which makes use of the varying sensitivities of wave fields at various frequencies to reduce the inversion problem into a sequence of smaller inversions with fewer unknowns to estimate at each stage. Different parameters are estimated using data at different frequencies according to their sensitivities. Inversion results for different areas in the ECS region are summarized and compared with core data.

Estimation of seabed reflection loss properties from direct blast pulse shape (L)

The decay rate of a smeared multipath arrival received many water depths from a broadband source has been shown to be closely related to bottom reflection loss properties [Smith, J. Acoust. Soc. Am. 50, 332–336 (1971)]; [Harrison, J. Acoust. Soc. Am. 114, 2744–2756 (2003)]. This suggests a simple way of measuring bottom properties with active sonars. The method is demonstrated with experimental data measured in a shallow water region of the Mediterranean Sea. Seabed properties are deduced directly by the method in the form of the rate of change of reflection loss with respect to angle close to grazing. Agreement is shown between the results of the method and the results of matched field inversions carried out in the same area. Good agreement is also shown between measurements and predictions of propagation loss made using seabed properties deduced via the method.

Geoacoustic inversion of M-sequence data from experiments in the South Florida Straits

Matched field inversion is applied to low frequency data from experiments in the South Florida Straits to estimate a sediment velocity profile. The acoustic data consist of signal envelopes derived from M-sequences that were transmitted to a vertical hydrophone array over a range of 10 km. The sound speed profile supported a strong waveguide in the deeper parts of the water column. Signal propagation for a source in the waveguide was dominated by waveguide refracted paths, and surface-reflected bottom-reflected paths that interacted eight to ten times with the bottom. The very long range, shallow water geometry presents a significant challenge for an inversion based on matched field processing. However, examination of the spatial coherence of the received signal indicated useful spatial phase information for spectral components with high signal-to-noise ratios. A Gibbs sampling approach was used to test two different geoacoustic models for the site: (a) a constant gradient sediment and (b) a constant velocity sediment over a half space. The inversion showed a preference for slower speeds of around 1550 m/s at the sea floor, increasing to higher values up to 1700 m/s within about 100 m deeper. These values are consistent with ground truth at the site.

Data error estimation for matched-field geoacoustic inversion

Nonlinear Bayesian methods have been applied to geoacoustic inversion to estimate uncertainties for seabed parameters by sampling the posterior probability density. This procedure requires quantifying the errors on the acoustic data, including both measurement and theory errors, which are generally not well known. To date, point estimates for data errors have been derived using a global maximum likelihood approach. However, this is not consistent with the Bayesian formulation, and ignores the effects of uncertainty in the error estimates and interdependencies between the data errors and geoacoustic parameters. The Bayesian approach treats the data errors as random variables and includes them as additional parameters within the inversion. However, this increases significantly the number of unknowns and the computational effort. A third approach is to use a local maximum likelihood error estimate evaluated independently for each geoacoustic model considered in the sampling procedure. This has the benefit of not increasing the number of unknowns or computational effort, but includes some of the effects of the error uncertainties and interdependencies. The three approaches are compared for Bayesian matched-field geoacoustic inversion of both synthetic and experimental data.

Optimal passive source localization in a fluctuating ocean waveguide based on an analytic model for the mean field and covariance

The ocean acts as an enormously complex channel for signal transmission. It is characterized by temporal fluctuations and spatial variabilities that often lead to significant randomization of the measured field. Signal processing techniques must be derived from fundamental physical models to attain statistical optimality in such an environment. Here we present such an analysis with a new analytic model [Ratilal and Makris, J. Acoust. Soc. Am. 114, 2428 (2003)] for the mean field and its covariance after propagation through a fluctuating ocean waveguide based on the first principles of waveguide scattering theory. The model is advantageous because it includes the primary physical effects of attenuation, dispersion, and coupling of modal energy due to multiple forward scattering in a convenient and intuitive form that is well suited to analytic manipulations. An example will be presented for passive source localization in range and depth in a fluctuating ocean waveguide by nonlinear matched field inversion. The necessary conditions on sample size and signal-to-noise ratio (SNR) for unbiased and minimum variance (optimal) estimates of source postion are then derived using asymptotic statistical inference theory [Naftali and Makris, J. Acoust. Soc. Am. 110, 1917–1930 (2001)]. Degradation in performance by environmental uncertainties are quantified within this statistical framework.

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.

Geoacoustic inversion of broadband data in the Florida Straits

Acoustic propagation experiments have been carried out in the Florida Straits with a multi-frequency broadband source that transmitted m-sequence pulses over a range of 10 km to a sparse-filled vertical line array. This paper presents results of matched field inversions of the acoustic field data at low frequencies to estimate geoacoustic model parameters for the experimental site. Two approaches were taken for the inversions. The first was a conventional matched field inversion using multi-frequency data centered at 200 and at 400 Hz from the vertical array. The second approach was designed to model the low frequency waveform at a single hydrophone. For the very long range experimental geometry, the waveform was modeled in terms of modes. Each inversion was cast as an optimization problem using the adaptive simplex simulated annealing algorithm. The inversions provide a comparison between approaches that take advantage of the spatial coherence in one case, and the time coherence in the received signal in the other case. Both inversions give similar results for the parameters of a simple geoacoustic bottom model, and the sensitivities and relative uncertainties of the model parameters are consistent for the two approaches. Notably, the inversions are sensitive to compressional wave attenuation.

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.