Efficient trans-dimensional Bayesian inversion for geoacoustic profile estimation

Abstract

This paper considers sampling efficiency of trans-dimensional (trans-D) Bayesian inversion based on the reversible-jump Markov-chain Monte Carlo (rjMCMC) algorithm, with application to seabed acoustic reflectivity inversion. Trans-D inversion is applied to sample the posterior probability density over geoacoustic parameters for an unknown number of seabed layers, providing profile estimates with uncertainties that include the uncertainty in the model parameterization. However, the approach is computationally intensive. The efficiency of rjMCMC sampling is largely determined by the proposal schemes applied to perturb existing parameters and to assign values for parameters added to the model. Several proposal schemes are examined, some of which appear new for trans-D geoacoustic inversion. 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 successive models along the Markov chain, a diminishing adaptation). The relative efficiency of proposing new parameters from the prior versus a Gaussian distribution focused near existing values is considered. Parallel tempering, which employs a sequence of interacting Markov chains with successively relaxed likelihoods, is also considered 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.