Bayesian matched-field geoacoustic inversion

Abstract

This paper describes a Bayesian approach to matched-field inversion (MFI) of ocean acoustic data for seabed geoacoustic properties. In a Bayesian formulation, the unknown environmental and experimental parameters are considered random variables constrained by noisy data and prior information, and the goal is to interpret the multi-dimensional posterior probability density (PPD). The PPD is typically characterized in terms of point estimates, marginal distributions, and posterior correlations (or joint statistics). Computing these requires numerical optimization and integration of the PPD, which are carried out efficiently here using adaptive hybrid optimization and Metropolis–Hastings sampling in principal-component space, respectively. Likelihood and misfit functions for multi-frequency MFI with incomplete source spectral information are derived based on the assumption of complex Gaussian-distributed data errors with covariance matrices estimated from residual analysis; posterior statistical tests are applied to validate these estimates and assumptions. Model selection is carried out by applying the Bayesian information criterion to determine the simplest seabed parameterization consistent with the resolving power of the data. Bayesian MFI is illustrated for shallow-water acoustic data measured in the Mediterranean Sea.