Bayesian inversion methods in ocean geoacoustics

Abstract

This paper describes a complete approach to the inversion of ocean acoustic data for environmental model parameters, which is also applicable to other inverse problems. Within a Bayesian formulation, the general solution is given by the posterior probability density (PPD) of the model parameters, which includes both data and prior information. Properties of the PPD, such as optimal parameter estimates, variance/covariance, inter-parameter correlations, and marginal probability distributions, are computed numerically for nonlinear inverse problems using Markov-chain Monte Carlo (MCMC) importance sampling methods. Since the data uncertainty distribution (including measurement and theory errors) is generally not known a priori, a simple, physically-reasonable form, such as a Gaussian or double-exponential distribution, is assumed, with statistical properties estimated from data residual analysis. In many cases, the full error covariance matrix (including off-diagonal terms) is required, and in some cases effects of nonstationary errors must be included. If biased data errors are suspected, additional unknown parameters representing the biases are included explicitly in the inversion. The validity/applicability of the above assumptions and estimates is examined a posteriori by applying both qualitative and quantitative statistical tests. New advances in efficient and adaptive MCMC sampling for nonlinear inversion will be presented.