Quantifying uncertainty in geoacoustic inversion. II. Application to broadband, shallow-water data

Abstract

This paper applies the new method of fast Gibbs sampling (FGS) to estimate the uncertainties of seabed geoacoustic parameters in a broadband, shallow-water acoustic survey, with the goal of interpreting the survey results and validating the method for experimental data. FGS applies a Bayesian approach to geoacoustic inversion based on sampling the posterior probability density to estimate marginal probability distributions and parameter covariances. This requires knowledge of the statistical distribution of the data errors, including both measurement and theory errors, which is generally not available. Invoking the simplifying assumption of independent, identically distributed Gaussian errors allows a maximum-likelihood estimate of the data variance and leads to a practical inversion algorithm. However, it is necessary to validate these assumptions, i.e., to verify that the parameter uncertainties obtained represent meaningful estimates. To this end, FGS is applied to a geoacoustic experiment carried out at a site off the west coast of Italy where previous acoustic and geophysical studies have been performed. The parameter uncertainties estimated via FGS are validated by comparison with: (i) the variability in the results of inverting multiple independent data sets collected during the experiment; (ii) the results of FGS inversion of synthetic test cases designed to simulate the experiment and data errors; and (iii) the available geophysical ground truth. Comparisons are carried out for a number of different source bandwidths, ranges, and levels of prior information, and indicate that FGS provides reliable and stable uncertainty estimates for the geoacoustic inverse problem.

Data error estimation for matched-field geoacoustic inversion

“…This section considers a synthetic study o f inversion performance for the various objective functions based on a shallow-water geoacoustic experiment carried out in the Mediterranean Sea southeast of Elba Island [2]. The seabed model consists of a sediment layer over a semi infinite basement.…”

“…In addition, small corrections to the water depth, D, and source range and depth, r and z, are also included in the inversion as these geometric parameters are generally not know to sufficient accuracy. Synthetic acoustic fields were generated at 50-Hz intervals from 300-500 Hz, with Gaussian noise added so that the signal-to-noise ratio decreased uniformly from 12 to 0 dB across the band, reflecting the observed increase in theory error with frequency [2].…”

“…However, this is often a poor assumption in practice [2]. A straightforward approach for unknown uncertainties is to explicitly estimate the standard deviations as part o f the inversion by minimizing the objective function…”

“…Theory errors in particular are generally not well known, and tend to increase w ith frequency due to the effects o f scattering, 3-D environmental variability, sensor location errors, etc. [2]. This paper derives several likelihood-based objective functions and examines their performance in MFI o f acoustic data w ith unknown, frequency-dependent uncertainties.…”

“…However, as m entioned above, data uncertainties are rarely w ell know n due to theory errors. The standard approach is to assume that the uncertainty weighting factor |df |2 /off is uniform over frequency, and minimize an objective functionHowever, this is often a poor assumption in practice [2]. A straightforward approach for unknown uncertainties is to explicitly estimate the standard deviations as part o f the inversion by minimizing the objective function…”