Scattering statistics of glacially quarried rock outcrops: Bayesian inversions for mixture model parameters

Abstract

Knowledge of the probability distribution of the scattered amplitude return from the seafloor in reverberation measurements and seafloor sonar images is a prerequisite to designing effective target detection systems and predicting their performance. Previous measurements have revealed that the distribution is often heavier tailed than the Rayleigh distribution, and may be modeled by the K, Weibull, and log-normal distributions, among others. Recent measurements of the scattering statistics from rock seafloors resulted in a bimodal distribution, which is poorly modeled by many commonly used distributions. The rock surfaces were formed from glacial quarrying and exhibit a stepped structure. The observed distribution is hypothesized to result from a mixture, where the scattered field from vertically oriented facets is modeled as a K distribution, and the scattered field due to the horizontally oriented facets is modeled as a Rayleigh distribution. If this hypothesis is true, then roughness parameters may be estimated from scattering data. A Bayesian technique for estimating the distribution of mixture parameters from the probability distribution of the scattered field is presented. This technique, while computationally expensive, reveals the relationship between the mixture model parameters, and can reveal any degeneracies that could lead to problems during inversions.