Gradient Representations in Seabed Geoacoustic Inversion by Bernstein Polynomials

Abstract

Geoacoustic properties of the upper-most transition layer of mud seabed sediments often change rapidly with depth as continuous gradients, rather than discontinuous layers. However, most geoacoustic inversion approaches are based on layered sediment models. This paper presents a seabed parameterization approach that represents continuous geoacoustic gradients as a sum of Bernstein polynomial basis functions weighted by unknown coefficients which are estimated by Bayesian inversion of seabed acoustic reflectivity data. The Bernstein representation is efficient/effective in representing a wide variety of gradients with a small number of coefficients, and has optimal numerical stability to perturbation of the coefficients in the nonlinear inversion scheme. The Bernstein parametrization in geoacoustic inversion is illustrated with simulated data and with experimental data from four mud sites on the Malta Plateau in the Strait of Sicily. The inversion results are in good agreement with sound speed and density estimates from co-located sediment cores, and serve to illustrate the ability of the Bernstein polynomial parameterization to represent steep and strongly-variable gradients.