Bayesian Inversion of Interface-Wave Dispersion for Seabed Shear-Wave Speed Profiles

Abstract

This paper applies Bayesian inversion to estimate seabed shear-wave speed profiles and their uncertainties from interface-wave dispersion data. A nonlinear formulation is developed to estimate the most probable profile together with marginal probability distributions and credibility intervals from the posterior probability density (PPD) using adaptive hybrid optimization and Metropolis-Hastings sampling (MHS). To address correlated data errors, a full error covariance matrix is estimated from residual analysis, and rigorous a posteriori statistical tests are applied to validate the covariance estimate and the assumption of a multivariate Gaussian error distribution. The most appropriate parameterization for the shear-wave speed profile is determined using the Bayesian information criterion (BIC), which provides the simplest model consistent with the resolving power of the data. Parameterizations considered vary in the number and type of layers, and include layers with uniform speed, and with linear and power-law shear-speed gradients. For the data considered here, a power-law parameterization is indicated, which is consistent with theoretical expectations for uniform, unconsolidated sediments under overburden pressure. The maximum depth to which the dispersion data constrain the shear-speed profile is investigated using an approximate analytic formula for power-law profiles and repeated inversions in which the maximum depth to an underlying half-space is systematically increased.