Quantifying uncertainty in geoacoustic inversion. I. A fast Gibbs sampler approach

Abstract

This paper develops a new approach to estimating seabed geoacoustic properties and their uncertainties based on a Bayesian formulation of matched-field inversion. In Bayesian inversion, the solution is characterized by its posterior probability density (PPD), which combines prior information about the model with information from an observed data set. To interpret the multi-dimensional PPD requires calculation of its moments, such as the mean, covariance, and marginal distributions, which provide parameter estimates and uncertainties. Computation of these moments involves estimating multi-dimensional integrals of the PPD, which is typically carried out using a sampling procedure. Important goals for an effective Bayesian algorithm are to obtain efficient, unbiased sampling of these moments, and to verify convergence of the sample. This is accomplished here using a Gibbs sampler (GS) approach based on the Metropolis algorithm, which also forms the basis for simulated annealing (SA). Although GS can be computationally slow in its basic form, just as modifications to SA have produced much faster optimization algorithms, the GS is modified here to produce an efficient algorithm referred to as the fast Gibbs sampler (FGS). An automated convergence criterion is employed based on monitoring the difference between two independent FGS samples collected in parallel. Comparison of FGS, GS, and Monte Carlo integration for noisy synthetic benchmark test cases indicates that FGS provides rigorous estimates of PPD moments while requiring orders of magnitude less computation time.