Efficient reversible-jump Markov-chain Monte Carlo sampling in trans-dimensional Bayesian geoacoustic inversion

Abstract

This paper considers efficient computational approaches to estimate the posterior probability density (PPD) of seabed geoacoustic profiles in the Bayesian inversion of ocean acoustic data, a numerically intensive problem. Trans-dimensional (trans-D) inversion is applied, which samples probabilistically over an unknown number of seabed layers as well as the layer geoacoustic properties and parameters of the error model (variances and autoregressive coefficients). Sampling is based on the reversible-jump Markov-chain Monte Carlo algorithm, the efficiency of which depends strongly on the formulation of the proposal density by which new candidate models are generated for probabilistic acceptance/rejection. A highly efficient proposal density is presented which combines principal-component (PC) reparameterization with parallel tempering. PC reparameterization applies an adaptive linearized approximation to the PPD as the proposal density, which provides effective directions and length scales for model perturbations in high-dimensional parameter spaces. Parallel tempering considers a series of interacting Markov chains with successively relaxed likelihood functions, which greatly improves the sampling of multi-modal parameter spaces and trans-D transitions. These approaches are combined by computing different PC reparameterizations for each Markov chain in the parallel tempering formulation. Inversion results are presented as marginal probability profiles for geoacoustic properties, marginalized over the number of layers.