Sequential Bayesian strategies in geoacoustic inverse problems.

Abstract

This paper considers sequential Bayesian strategies for geoacoustic inverse problems which are difficult to solve simultaneously due to computational constraints. Bayesian inference provides a powerful approach to learning problems such as this since sequential inversions of multiple data sets [with the posterior probability density (PPD) of one inversion applied as prior information in the subsequent inversion] are equivalent to simultaneous inversion of all data. However, passing PPDs forward as priors has its own challenges when the PPD is sampled numerically for nonlinear inverse problems, particularly when the model parameter space is of high dimensionality and the data information content is high. In such cases, approximations are required to efficiently carry PPD information forward to subsequent inversions. The approach developed here represents numerically sampled PPDs in terms of discretized marginal probability distributions for principal components of the parameters, which minimizes the loss of information in representing inter‐parameter correlations. The sequential Bayesian approach is applied to seabed reflectivity inversion with multiple data sets representing travel‐time data and frequency‐domain reflection coefficient data for a series of increasing penetration depths. Data information content is quantified by accounting for potential error biases as well as data error covariances. [Work supported by the Office of Naval Research.]