Trans-dimensional Bayesian inference for large sequential data sets

Abstract:

This work develops a sequential Monte Carlo method to infer seismic parameters of layered seabeds from large sequential reflection-coefficient data sets. The approach provides parameter estimates and uncertainties along survey tracks with the goal to aid in the detection of unexploded ordnance in shallow water. The sequential data are acquired by a moving platform with source and receiver array towed close to the seabed. This geometry requires consideration of spherical reflection coefficients, computed efficiently by massively parallel implementation of the Sommerfeld integral via Levin integration on a graphics processing unit. The seabed is parametrized with a trans-dimensional model to account for changes in the environment (i.e. changes in layering) along the track. The method combines advanced Markov chain Monte Carlo methods (annealing) with particle filtering (resampling). Since data from closely-spaced source transmissions (pings) often sample similar environments, the solution from one ping can be utilized to efficiently estimate the posterior for data from subsequent pings. Since reflection-coefficient data are highly informative, the likelihood function can be extremely peaked, resulting in little overlap between posteriors of adjacent pings. This is addressed by adding bridging distributions (via annealed importance sampling) between pings for more efficient transitions. The approach assumes the environment to be changing slowly enough to justify the local 1D parametrization. However, bridging allows rapid changes between pings to be addressed and we demonstrate the method to be stable in such situations. Results are in terms of trans-D parameter estimates and uncertainties along the track. The algorithm is examined for realistic simulated data along a track and applied to a dataset collected by an autonomous underwater vehicle on the Malta Plateau, Mediterranean Sea. [Work supported by the SERDP, DoD.]