Model selection for profile structure in Bayesian geoacoustic inversion

Abstract

This paper considers model selection in Bayesian geoacoustic inversion, specifically, the role of seabed parameterization in resolving geoacoustic profile structure. Bayesian inversion is formulated in terms of the posterior probability density (PPD) over the model parameters which are sampled numerically: Metropolis-Hastings sampling in principal-component space enhanced by parallel tempering is employed here. A key aspect of quantitative geoacoustic inversion is that of parameterizing the seabed model. Trans-dimensional (trans-D) inversion methods model the seabed as a sequence of discontinuous uniform layers and sample probabilistically over the number of layers. However, in some cases it may be expected for seabed properties to vary as smooth, continuous gradients which are not well represented by uniform layers. Most gradient-based inversions assume a representative functional form, such as a power law. A recent alternative is based on a linear combination of Bernstein-polynomial basis functions. This approach is more general and allows the form of the profile to be determined by the data, rather than by a subjective model choice. This paper compares trans-D, power-law, and Bernstein-polynomial inversions for the problem of estimating seabed shear-wave speed profiles from the dispersion of interface waves. Simulations and data from Oslofjorden and/or the North Sea will be considered.