Matched-field Inversion Research Articles

Estimation of Geoacoustic Parameters from Narrowband Data Using a Search-Optimization Technique

Geoacoustic parameters were estimated for vertical array data from the matched-field inversion benchmark data sets. Separate inversions were performed for narrowband data at 25 Hz, 50 Hz and 75 Hz, using a matching function consisting of the incoherent sum of the Bartlett outputs for the five vertical arrays at ranges of 1, 2, 3, 4 and 5 km. Parameter estimation was performed using a parabolic equation sound propagation algorithm to generate the replica fields, and a search-optimization technique to obtain estimates of the optimized parameter values. This technique involved an initial search stage in which the parameter space was sampled, and a second optimization stage in which each of a specified number of the best matches found in the search stage was used as the starting point for optimization. This approach provided multiple independent estimates of the geoacoustic parameters, and allowed assessment of the non-uniqueness of the problem and the sensitivity of the matching function to the individual parameters. A method was developed to combine the results for several frequencies to estimate the parameters. It used a weighted average with weights computed on the basis of the relative sensitivities at those frequencies; these sensitivities were estimated by the root-mean-square (RMS) gradient observed during the optimizations. Strong interdependencies among the parameters were found in the analysis, particularly between the sediment thickness and the sound speed at the bottom of the sediment. For the single-frequency matching function used here, it was observed that the inversion problems were ill-posed in that sets of parameter values from a wide region of the parameter space gave essentially perfect matches. The consistency of the parameter estimates was greatly improved by including a regularization term in the matching function. Regularized search-optimization provided an efficient method for estimating an effective geoacoustic model for acoustic field prediction.

Geoacoustic Inversion for the Workshop '97 Benchmark Test Cases Using Simulated Annealing

This paper applies simulated annealing matched-field inversion to the Workshop '97 geoacoustic inversion benchmark test cases. The unknown parameters in these test cases include various combinations of sediment and basement geoacoustic properties (layer thickness, compressional and shear speeds, attenuations, and densities) and geometric parameters (water depth, and source range and depth). The sensitivity of the acoustic field data to the different parameters varies substantially. The simulated annealing inversion developed here minimizes a measure of mismatch based on the average Bartlett processor for acoustic data at a number of ranges. The replica pressure fields are computed by summing the modal components provided by an elastic normal mode model, which allows replica fields at multiple ranges to be calculated efficiently. A total of 15 different geoacoustic inversions are considered (three realizations each for five test cases). Excellent results are obtained in a reasonable amount of computation time for all cases. In particular, the final mismatch values are exceedingly small and relatively sensitive parameters (geometric parameters and sediment properties) are generally estimated to high precision. Relatively insensitive parameters (shear speeds and, in some cases, basement properties) are somewhat less well determined, but generally good estimates are obtained.

Broadband Geoacoustic Deduction

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

Multi-Frequency Inversion of Synthetic Transmission Loss Data Using a Genetic Algorithm

The organizers of the Benchmark Workshop for Geoacoustic Inversion Methods (Vancouver, June 1997) produced in advance several sound propagation scenarios, simulated using the wavenumber integration model SAFARI. The simulated pressure fields were made available to all interested, while several key geoacoustic properties of their environments were kept secret. For a number of these test cases we have applied Matched-Field Inversion to determine the unknown geometric and geoacoustic parameters. A Genetic Algorithm has been used together with the normal-mode model MODELOSS as a forward model. The parameters from the benchmark tests, which the forward model was most sensitive to, were well determined in this way (water depth, source depth and range, the attenuation in the sediment layer and the velocity in the upper part of the layer). The less influential parameters were not found with the same accuracy and were often not reliable. The density in the basement may have been just a random choice.

The variation of modal wave numbers with geoacoustic parameters in layered media

Analytic expressions are derived for the variation of modal wave numbers due to variations in five basic properties of a layered environment: the compressional wave speed, shear wave speed, density, and thickness of any layer, and the depth of an interface between layers. Both fluid and solid layers are permitted. The layers may absorb energy, and the modal wave numbers and their variations are generally complex valued. The analytic expressions provide an efficient way to linearize the relation between the modal wave numbers and many geoacoustic parameters, for use in field sensitivity studies, range-dependent propagation models, partially linearized matched-field inversion schemes, and in the study of modes generally.

On the use of matched-field processing and hybrid algorithms for vertical slice tomography

Matched-field processing and a hybrid scheme for vertical slice tomography are studied in characteristic cases of range-independent and range-dependent ocean environments using simulated data obtained at discrete points in the sound field along a vertical line, representing a vertical array of hydrophones. The matched-field processing is associated with a Genetic Algorithm, while the basic characteristic of the hybrid scheme is the application of matched-field processing for the definition of a reference environment to be subsequently used in connection with a modal-phase inversion scheme. In all cases studied, the sound-speed profiles are reconstructed with the use of empirical orthogonal functions. It is shown that the reconstruction of either the single sound-speed profile characterizing the range-independent environment, or the set of profiles characterizing an eddy in the range-dependent environment is achieved with good accuracy, despite the fact that a very wide search space has been considered. The apparent nonuniqueness in the solution of the inverse problem for the range-dependent case is remedied by applying physical constraints in the structure of the sea eddy and averaging over the admissible solutions obtained by the matched-field inversion scheme.

Algorithms for matched-field inversion: Comparison and performance

Successful MFP requires a knowledge of the bathymetry and the existence of a suitable geoacoustic model for the sound-speed profile and the bottom characteristics. In practice, these parameters are known only approximately, and it is desirable to obtain more accurate estimates to improve the effectiveness of MFP. This aim may be achieved through matched-field inversion (MFI) of data obtained using a source at a series of known locations in the environment. Development of effective inversion procedures requires the use of appropriate numerical optimization techniques suited to the nature of the multimodal multidimensional matching functional to be optimized. This study examines several approaches to global optimization, including simulated annealing, a genetic algorithm, and a combined random search/local optimization approach. Results comparing these approaches were obtained using a model multimodal function with provision for correlated parameters; the performance of several local optimization algorithms was also compared using this model function. For the case of a realistic range-independent waveguide, the functional interactions between several sensitive model parameters were examined by generating 2-D plots of the matching function as a function of selected parameter pairs, using the normal mode program ORCA to generate the fields for matching. Results of inversion for range-dependent environments using this system will be presented and discussed.

Acoustic inversion of bottom reflectivity and bottom sound-speed profile

This paper applies a full-field technique to invert bottom sound profile and bottom reflectivity from simulated acoustic data in a shallow water environment. Bottom sound-speed profile and bottom reflectivity have been traditionally estimated using seismic reflection/refraction techniques when acoustic ray paths and travel time can be identified and measured from the data. However, in shallow water, the many multipaths due to bottom reflection/refraction make such identification and measurement rather difficult. A full-field inversion technique is presented here that uses a broad-band source and a vertical array for bottom sound-speed and reflectivity inversion. The technique is a modified matched field inversion technique referred to as matched beam processing. Matched beam processing uses conventional beamforming processing to transform the field data into the beam domain and correlate that with the replica field also in the beam domain. This allows the analysis to track the acoustic field as a function of incident/reflected angle and minimize contamination or mismatch due to sidelobe leakage.

Direct measurement and matched-field inversion approaches to array shape estimation

Accurate knowledge of array shape is essential for carrying out full wavefield (matched-field) processing. Direct approaches to array element localization (AEL) include both nonacoustic (tilt-heading sensors) and acoustic (high-frequency, transponder-based navigation) methods. The low-frequency signature emitted from a distant source also can be used in an inversion approach to determine array shape. The focus of this paper is on a comparison of the array shape results from these three different methods using data from a 120-m aperture vertical array deployed during SWellEx-3 (Shallow Water evaluation cell Experiment 3). Located 2 m above the shallowest array element was a self-recording package equipped with depth, tilt, and direction-of-tilt sensors, thereby permitting AEL to be performed non-acoustically. Direct AEL also was performed acoustically by making use of transponder pings (in the vicinity of 12 kHz) received by high-frequency hydrophones spaced every 7.5 m along the vertical array. In addition to these direct approaches, AEL was carried out using an inversion technique where matched-field processing was performed on a multitone (50-200 Hz), acoustic source at various ranges and azimuths from the array. As shown, the time-evolving array shape estimates generated by all three AEL methods provide a consistent picture of array motion throughout the 6-h period analyzed.

Matched-field inversion for geoacoustic model parameters in shallow water

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 /spl sim/1700 m/s and shear speed /spl sim/400 m/s, overlying a layer with compressional speed /spl sim/1900 m/s. This model is consistent with the results from conventional seismic experiments carried out in the same region.

Characterizing parameter landscapes for poroelastic media

There is presently a great deal of interest in modeling ocean sediments as poroelastic media. One of the topics of particular interest is matched-field inversion for sediment parameters. This paper will investigate the resolvability of poroelastic parameters in ocean sediments using acoustic sources and receivers located in the water column. The eigenvectors and eigenvalues of the covariance matrix of the gradient of the cost function indicate the most important underlying parameters as well as the degree of coupling between parameters [M. D. Collins and L. Fishman, ‘‘Efficient navigation of parameter landscapes,’’ J. Acoust. Soc. Am. 98, 1637–1644 (1995)]. This information is useful for designing effective experiments for resolving the desired parameters. The information in the covariance matrix can be used to determine the most effective frequencies and array configuration and to optimize the performance of the inversion at each frequency. Wave-number integration and parabolic equation models are available for solving the forward problem [M. D. Collins, W. A. Kuperman, and W. L. Siegmann, ‘‘A parabolic equation for poro-elastic media,’’ J. Acoust. Soc. Am. 98, 1645–1656 (1995)].

Adaptation of genetic-algorithm search for matched-field inversion of ocean bottom compressional wave speed profiles

Matched-field inversion for ocean bottom compressional wave speeds using a synthetic horizontal aperture has been demonstrated previously in simulations and data analyses employing optimization by simulated annealing [M. Collins, W. Kuperman, and H. Schmidt, J. Acoust. Soc. Am. 92, 2770 (1992)] and genetic-algorithm search [P. Gerstoft, J. Acoust. Soc. Am. 95, 770 (1994)]. The first reference noted a lack of sensitivity of the matched-field ambiguity function to zero-mean functional variations of the sound-speed profile. This lack of sensitivity sometimes results in slow convergence of the search algorithm when applied to profiles with several unknown parameters. This problem is observed in simulations using genetic algorithm search. Improved convergence of the genetic algorithm is then achieved by using some nonstandard procedures, including autologous gene exchanges, to generate new solutions. The simulations indicate the practical feasibility of inversion for deep-bottom (up to 500 m) compressional wave speeds at a shallow-water site using a single receiver and coherent synthetic horizontal aperture processing of a towed-source signal.

Matched-field inversion of multifrequency data

Geoacoustic inversion using single-frequency data measured on a vertical array has become a popular method for estimating sub-bottom parameters. Inclusion of multiple frequencies in the inversions allows exploitation of both the waveguide dispersion and the different penetration into the sub-bottom at different frequencies. This is achieved, however, at the expense of greater required computing time, and more complicated processing schemes. Several approaches exist for defining a broadband object function, i.e., coherent or incoherent addition across frequencies and hydrophones. Each approach has specific requirements with regard to the recording geometry and the source spectrum. For coherent addition across frequencies not only the source spectrum but also the absolute propagation time must be estimated. When a useful object function has been defined it is optimized using genetic algorithms [P. Gerstoft, J. Acoust. Soc. Am. 95, 770–782 (1994)] for both the sediment and the geometric parameters. Different approaches are illustrated on broadband data from the Mediterranean North Elba site with center frequencies of 170 and 330 Hz. The water depth was 130 m and the source range was 5.5 km. The normal-mode code snap was used as the forward model.

Matched-field inversion for source localization with uncertain bathymetry

A good knowledge of the bathymetry is required for reliable matched-field source localization in shallow-water environments. However, bathymetry can be difficult to measure in ice-covered Arctic waters. This letter describes a method for determining source location using simulated annealing to perform matched-field inversion with poor or little knowledge of the bathymetry. The inversion is carried out for source range and depth and a (range-dependent) model for bathymetry. Although the bathymetry cannot be determined uniquely in this manner, an effective model can be computed which allows accurate source localization. This method essentially applies the concepts of ‘‘focalization’’ [M. D. Collins and W. A. Kuperman, J. Acoust. Soc. Am. 90, 1410–1422 (1992)] to ocean bottom parameters.

Estimation of ocean-bottom properties by matched-field inversion of acoustic 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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Estimation of seismoacoustic properties of the ocean bottom by matched-field inversion

Matched-field processing of acoustic field data provides a straightforward but powerful method for estimating the elastic properties of the ocean bottom. The success of the inversion depends in part on having an efficient algorithm for searching the multidimensional parameter space of ocean bottom models. This paper considers the use of simulated annealing as a search algorithm for matched-field inversion (MFI), and presents results of inversions for data obtained from the PACIFIC ECHO experiments. A method is described for adaptively guiding the annealing process by adding a feedback loop that assesses the significance of the matched-field correlations for each parameter. The search is guided to regions of the parameter space associated with above-average correlations. Simulations for a vertical line array (VLA) are presented to demonstrate the limits on performance of MFI with respect to uncertainties in experimental geometry, and low signal-to-noise ratio. The method is applied to VLA data from thin-sediment PACIFIC ECHO environments where the age of the upper oceanic crust varied from 0.1 to 66 million years. The MFI results indicate an age dependence of the compressional and shear wave speeds of the basalt, and the values are significantly lower than those obtained for thickly sedimented crust.

A review of initial matched-field inversion experiments

The first successful demonstration of the feasibility of localizing a source in the ocean with matched-field processing was in the Arctic Ocean (Fizell and Wales). This environment/site was chosen because of the essential range independence of its sound-speed structure and minimal bottom reflectivity. Replica fields were generated with Kutschale’s well-tested, precise but computationally exhaustive FFP code. Soon thereafter Porter demonstrated that the precision of his much faster normal mode code equaled FFP, permitting computations of large numbers of replica fields and rapid ‘‘testing’’ of numerous environmental hypotheses,’’ i.e., matched-field inversion. The first inversions were of under-ice reflectivity and phase versus grazing angle (Livingston and Diachok). Other inversions through matched-field processing soon followed: ocean sound-speed profile (Kerengeleu and Diachok; and Goncharov and Voronovich), and bottom geoacoustic parameters (Fizell and Diachok; Chapman and McKirdy; and Collins, Kristensen etal.).

Matched-field inversion for range-dependent bottom properties and source location

Ocean-bottom properties such as bathymetry and bottom sound speed can be difficult to measure directly in ice-covered Arctic waters, particularly if they vary with range. However, inversion procedures hold much promise for determining range-dependent bottom properties from acoustic measurements. The inversion is 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 and modeled acoustic fields. Two practical problems are considered. The first problem involves determining range-dependent bathymetry and bottom sound speed using a number of sources at known ranges. The second problem involves source localization when available knowledge of the bathymetry is inadequate. In this case, the inversion is carried out for source range and depth as well as bathymetry. Although the bathymetry cannot be determined uniquely in this manner, an effective bathymetry model can be computed which allows accurate source localization. This latter case is essentially an extension of the method of ‘‘focalization’’ [M. D. Collins and W. A. Kuperman, J. Acoust. Soc. Am. 90, 1410–1422 (1991)] to bottom parameters.

Matched-field inversion of geoacoustic parameters of elastic bottoms.

The potential of matched-field inversion of ocean bottom parameters is demonstrated through simulation of signals transmitted by one ship and received on a 1.5-km-long horizontal ship-towed array in end-fire mode. The simulations use an ocean model that is representative of a thinly sedimented (36-m) basalt bottom. The output of a matched-field processor (Capon correlator) at a known source position is maximized by searching through bottom parameter differences from a geoacoustic profile. In particular, the shear velocities, Cs, in a model of the upper crust and an overlying thin sediment layer are varied about the true values. Relatively small differences (15% of true) in basement shear velocity produce a 4-dB degradation in processor output. Shear speed mismatch in the sediment produces thin film effects that appear in the processor output function as resonance peaks at several values of ΔCs. The values of ΔCs for most peaks vary strongly with source frequency except the peak at ΔCs=0. The results illustrate the potential of broadband matched-field processing to invert elastic bottom parameters, particularly shear speeds in thin sediments and upper crust, which to date have generally proven inaccessible with existing methods.