Efficiency of Trans-dimensional Bayesian Inference for Geoacoustic Inversion

Abstract

This paper considers the efficiency of trans-dimensional (trans-D) Bayesian inference methods applied to seabed geoacoustic inversion. Trans-D inversion is applied to sample the posterior probability density over geoacoustic parameters for a variable number of layers, providing seabed-profile estimates with uncertainties that include the uncertainty in the model parameterization. However, the approach is computationally intensive. Sampling efficiency is largely determined by the proposal schemes which are applied to generate perturbed values for existing parameters and for new parameters assigned to layers added to the model. Perturbations of existing parameters are considered in a principal-component space based on an eigen-decomposition of the unit-lag parameter covariance matrix (computed from the history of sampled models, a diminishing adaptation). The relative efficiency of proposing new parameters from the prior versus a Gaussian distribution focused near existing values is examined. Parallel tempering, which employs a sequence of interacting samplers in which the likelihood function is successively relaxed, is also considered as a means to increase the acceptance rate of new layers.  The relative efficiency of various proposal schemes is compared through repeated inversions with a pragmatic convergence criterion.  Results are presented for inversions of simulated and measured seabed reflection data.