# Scattering statistics of rock outcrops: Model-data comparisons and Bayesian inference using mixture distributions

## TL;DR

This study compares statistical models for acoustic scattering from rocky seafloor, finding that two-component mixture models, especially a mixture of two K distributions, best fit the measured data and can be effectively inferred using Bayesian methods.

## Contribution

It demonstrates that two-component mixture models outperform single models in representing seafloor scattering, with Bayesian inference applied to estimate model parameters.

## Key findings

- Two-component mixture models outperform single models.
- K-K mixture model best fits the data.
- Bayesian inference estimates model parameters effectively.

## Abstract

The probability density function of the acoustic field amplitude scattered by the seafloor was measured in a rocky environment off the coast of Norway using a synthetic aperture sonar system, and is reported here in terms of the probability of false alarm. Interpretation of the measurements focused on finding appropriate class of statistical models (single versus two-component mixture models), and on appropriate models within these two classes. It was found that two-component mixture models performed better than single models. The two mixture models that performed the best (and had a basis in the physics of scattering) were a mixture between two K distributions, and a mixture between a Rayleigh and generalized Pareto distribution. Bayes' theorem was used to estimate the probability density function of the mixture model parameters. It was found that the K-K mixture exhibits significant correlation between its parameters. The mixture between the Rayleigh and generalized Pareto distributions also had significant parameter correlation, but also contained multiple modes. We conclude that the mixture between two K distributions is the most applicable to this dataset.