Journal of Computational Acoustics

This paper discusses the motivation, preparation of data, and analysis of presented results for the Geoacoustic Inversion Workshop held in Vancouver, BC, on June 24–26, 1997.

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.

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.

An analysis of the 1997 Geoacoustic Inversion Workshop test case data was carried out to benchmark the performance of a Genetic Algorithm (GA) inversion code called SAGA_INV.¹ The inversion program made use of Westwood's ORCA propagation model,² FORTRAN subroutines, and Interactive Data Language (Research Systems Inc. IDL). SAGA_INV is capable of performing inversions with either Simulated Annealing (SA) or GA optimization schemes; however, only the GA portion of the code has been benchmarked with the workshop test cases at the present time. Not all of the workshop test cases were processed: this study was concerned only with the CAL, SD, SO, AT, and WA data sets. The CAL data was processed using three different cost functions: (i) standard Bartlett processor, (ii) a broadband coherent processor, and (iii) a transmission loss mismatch function. These processors were applied to three frequency bands: (i) 76 frequencies between 25 Hz and 100 Hz, (ii) nine frequencies between 28 Hz and 36 Hz, and (iii) 13 frequencies between 44 Hz and 56 Hz. The latter two frequency regimes were intended to simulate 1/3-octave bands centered at 32 Hz and 50 Hz, respectively. Four different receiving arrays were simulated: (i) a 1550 m aperture horizontal, bottom mounted array at approximately 1-km range, (ii) a similar array at approximately 4.2-km range, (iii) a 55-m aperture 12-element vertical array located at 1-km range, and (iv) a similar vertical array at 5-km range. In addition to processing the CAL data set, all three subcases of the SD, SO, AT, and WA data sets were also processed; however, only the transmission loss cost function and the two simulated 1/3-octave bands were considered for these test cases.

The principles for estimating sea floor parameters via matched-field processing (MFP)-based techniques are now well known. In pure MFP, source localization is often seen as a range-depth estimation problem while the use of MFP on geoacoustic estimation generally involves a computationally intensive optimization procedure. In the last few years, much effort has been devoted to developing new or improving upon existing search procedures to solve the optimization problem Little, or no, attention has been given to the ensemble MFP-optimization treating it as a single technique. The question addressed in this paper is centered on the relation between the MFP parameter estimator technique, defining the objective function and the search procedure used to optimize it. In particular, we are interested in questions like: Can a faster search or more accurate estimate be achieved with a "peaky" surface instead of a flat and ambiguous surface? Is the inversion process affected by cross-frequency estimators and model mismatch? Does the search procedure need to be modified, and if yes how to account for this "peaky" surface navigation? This paper attempts to answer these and other related questions in the context of the June '97 geoacoustic inversion workshop data set.

An optimization approach is used to estimate waveguide parameters for selected test cases of the Geoacoustic Benchmark Inversion Workshop held in Vancouver, June 1997. The approach uses multiple acoustic data samples to decouple the original N–dimensional problem into several smaller-dimensional problems. A nonlinear least squares approach is used to estimate parameters in each subset. The estimation of parameters in each subset proceeds until convergence is reached. Predicted values are in good agreement with the true values, which suggests that the decoupling of waveguide parameters allows a nonlinear least squares approach to be an effective tool in the inversion of ocean waveguide parameters.

Based on waveguide physics, a subspace inversion approach is proposed. It is observed that the ability to estimate a given parameter depends on its sensitivity to the acoustic wavefield, and this sensitivity depends on frequency. At low frequencies it is mainly the bottom parameters that are most sensitive and at high frequencies the geometric parameters are the most sensitive. Thus, the parameter vector to be determined is split into two subspaces, and only part of the data that is most influenced by the parameters in each subspace is used. The data sets from the Geoacoustic Inversion Workshop (June 1997) are inverted to demonstrate the approach. In each subspace Genetic Algorithms are used for the optimization — it provides flexibility to search over a wide range of parameters and also helps in selecting data sets to be used in the inversion. During optimization, the responses from many environmental parameter sets are computed in order to estimate the a posteriori probabilities of the model parameters. Thus the uniqueness and uncertainty of the model parameters are assessed. Using data from several frequencies to estimate a smaller subspace of parameters iteratively provides stability and greater accuracy in the estimated parameters.

Matched-field acoustic inversion techniques were investigated using data from sparsely populated vertical receiving arrays and a single receiver element. The purpose of considering sparse data sets is to investigate, under simulation, the feasibility of reducing the number and complexity of acoustic measurements needed for geoacoustic inversion. The entire bandwidth of the 1997 Geoacoustic Inversion Workshop provided data (25–500 Hz) was used which compensates for the lack of spatial information when a limited number of receivers is considered. The forward model PROSIM and inversion code SAGA were applied to benchmark cases: sd, wa, and n. The inversion results generally showed good agreement with the ground truth for full arrays, sparse arrays and single receiver elements. With a simple two-layer model, an effective sound speed profile in the bottom was determined which produced a good fit between the model and observed pressure fields for the multi-layer case n.

For a selected number of shallow water test cases of the 1997 Geoacoustic Inversion Workshop we have applied Matched-Field Inversion to determine the geoacoustic and geometric (source location, water depth) parameters. A genetic algorithm has been applied for performing the optimization, whereas the replica fields have been calculated using a standard normal-mode model. The energy function to be optimized is based on the incoherent multi-frequency Bartlett processor. We have used the data sets provided at a few frequencies in the band 25–500 Hz for a vertical line array positioned at 5 km from the source. A comparison between the inverted and true parameter values is made.

This paper presents different neural network approaches for geoacoustic inversion. The basic idea of neural inversion is to approximate the inverse function from a set of behaviors, i.e. relations between acoustic fields and geoacoustic parameters. In this work, such methods have been applied in two different forms: a global approach which aims to estimate all parameters from all data, and a hierarchical approach in which the most sensitive parameters are estimated before the least sensitive. The methods are tested using synthetic data. Statistical results, as well as benchmark results show that such approaches are efficient and have similar performances.

Matched-Field Processing with a Genetic Algorithm is applied to the problem of bottom recognition with synthetic noise-free acoustic data. The data correspond to three classes of benchmark problems. Four alternative objective functions have been tested, all of them defined to be used with broadband data with either coherent or incoherent processing in the frequency domain. It has been concluded that the parameters corresponding to the sediment layer and especially the sound speed, are more accurately recovered by all means. Source localization and water depth estimation are made with good accuracy in all cases. It has also been shown that incoherent processing in the frequency domain has led to better results for the cases studied.

This paper discusses the geoacoustic inversion results obtained on the Workshop '97 benchmark data via the Refined Iterated Grid Search (RIGS) method. We find that the method can be highly accurate in estimating geoacoustic and source localization unknowns for the ten test scenarios attempted. The original method formulation using KRAKEN as the embedded propagation code produced the results presented at the workshop where we found that some parameters are extremely well determined, i.e. sediment attenuationα_sed (within 1% in all 3 cases: ATa, ATb, ATc), sediment densityρ_sed (within 5% in all ten subcases: SD, AT, SO, WAa), source ranger_sou to within 40 m and source depthz_sou to within 2 m (in all four subcases SO and WAa). Moreover, sediment sound-speed gradients γ were also well determined (within 8%) except for very thin sediments/subcase ATb where sediment thickness h_sed ≈ 13 m). However, more recent, post-workshop results using ORCA embedded in the RIGS inversion software has resulted in even better results. Five of the original ten subcases have been re-done, and those results are also shown in this paper. In particular, we find that for the new results: r_sou is now accurate to within 11 m, z_sou to within 0.2 m, and all geoacoustic properties (except for half-space density ρ_hsp) are accurate to within 5%.

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.

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.

In this paper, geoacoustic inversion based on simulated annealing and the BDRM propagation model is applied to the test cases from the 1997 Geoacoustic Inversion Workshop. The effects of the bottom parameters on the sound field are discussed theoretically and two characteristic angles dependent upon geoacoustic parameters are defined. Based on the theoretical analysis of the characteristic angles, a multi-frequency inversion scheme is given as follows: High frequency and farfield data are used to invert the upper bottom parameters first, and then low frequency and nearfield data are used to invert the lower bottom parameters. Simulated tests show that the results of multi-frequency inversion are more accurate and reliable than single frequency inversion.

In this paper we present a simple approach for estimating the compressional wave speed and density profiles of sediments in a shallow water environments from modal eigenvalues. Methods published earlier in the literature called for data at two frequencies and had to make the assumption that the density profile is a continuous function. Further, the processing scheme was difficult to implement. The method presented here requires data from only one frequency and allows for discontinuities in the density profile. The performance of the proposed method is studied using synthetic data.

Estimation of the integral geoacoustic properties of the sea floor based on real data drawn from a shallow water site is presented. Two independent inversion schemes are used to deduce these properties. The first is matched-field processing of the pressure field on a vertical line array due to a projected source. The second approach is the inversion of ambient noise on a vertical array. Matched-field processing has shown to be successful in the inversion of high quality field data. Here, we show that it is also feasible with a more practical and less expensive data collection scheme. It will also be shown that low frequency inversion is more robust to variation and fluctuation in the propagating medium, whereas high frequencies are more sensitive to mismatches in a varying medium. A comparison is made of the estimates obtained from the two techniques and also with available historical data of the trial site.