Bayesian geoacoustic inversion.

Abstract

This paper describes a general Bayesian approach to estimating seabed geoacoustic parameters from ocean acoustic data, which is also applicable to other inverse problems. Within a Bayesian formulation, the complete solution is given by the posterior probability density (PPD), which includes both data and prior information. Properties of the PPD, such as optimal parameter estimates, variances/covariances, correlations, and marginal probability distributions, are computed numerically for nonlinear problems using Markov-chain Monte Carlo methods. However, in many practical cases, both an appropriate model parametrization and the data error distribution are unknown and must be estimated as part of the inversion. These problems are linked, since the resolving power of the data is affected by the data uncertainties. Model selection is carried out by evaluating Bayesian evidence (parametrization likelihood given the data), or a point estimate thereof such as the Bayesian information criterion, which provides the simplest parametrization consistent with the data. The error covariance matrix (including off-diagonal terms, as needed) is estimated from residual analysis under the assumption of a simple, physically reasonable distribution form, such as a Gaussian or Laplace distribution. The validity of the above assumptions and estimates is examined a posteriori using both qualitative and quantitative statistical tests.