Estimating parameter uncertainties in geoacoustic inversion by a neighbourhood algorithm

In Bayesian inversion, the solution is characterized by its posterior probability density (PPD). A fast Gibbs sampler (FGS) has been developed to estimate the multi-dimensional integrals of the PPD, which requires solving the forward models many times and leads to intensive computation for multi-frequency or range dependent inversion cases. This paper presents an alternative approach in order to speed this estimation process based on a neighbourhood approximation Bayes (NAB) algorithm. For lower dimension geoacoustic inversion, the NAB can approximate the PPD very well. For higher dimensional problems and sensitive parameters, however, the NAB algorithm has difficulty to estimate the PPD accurately with limited model samples. According to the preliminary PPD estimation by NAB, this paper developed a multi-step inversion scheme, which adjusts the parameter search intervals flexibly, in order to improve the approximation accuracy of NAB and obtain more complete parameter uncertainties. The prominent feature of NAB is to approximate the PPD by incorporating all models for which the forward problem has been solved into the appraisal stage. Comparison of FGS and NAB for synthetic benchmark test cases indicates that NAB provides reasonable estimates of the PPD moments while requiring less computation time.