Comparison of semi-analytical and numerical methods for the scattering of acoustic waves by rough, sloped seabed geometries

Abstract

The seabed possesses variations in its material properties, layering structure, slope and roughness making prediction, and analysis of sound propagation in shallow water highly complex. For certain frequency ranges, the effect of roughness becomes significant. Numerous models have been adopted to account for the scattering of acoustic waves by rough surfaces, including Kirchhoff approximation (for relatively large scales of roughness), small perturbation theory (for relatively small scales of roughness), and small slope approximation, which bridges across the two regimes under certain conditions. Although grounded in analytical theory, these approaches invariably involve the computation of numerical integrals so additional approximation theories have been explored including stationary phase methods and Taylor series approximations. In this study, these semi-analytical methods are incorporated within a new sound propagation model and compared with a numerical graphics processing unit (GPU)-accelerated finite element model incorporating roughness parameters (root mean square height and correlation length) for rough, sloped seabed geometries (with gradients ranging from 0° to 45°) in shallow water environments. The effect of large- and small-scale roughness on sound propagation is investigated in two- and three-dimensional space. The finite element modelling is used to validate the optimal choice of semi-analytical method for the different environments considered.