Gaussian beam summation formulation for rough surface scattering in complex configurations

Abstract

A Gaussian beam summation (GBS) representation for wave propagation problems in the presence of rough surfaces is introduced. In this formulation, the coherent and incoherent scattered fields are decomposed into a discrete phase space summation of Gaussian beams (GBs) that emanate from a discrete set of points and directions on the rough surface. The formulation therefore involves stochastic GB-to-GB scattering matrices for the coherent and incoherent fields, and deterministic GB propagators. It benefits from the simplicity and accuracy of the latter, and can be used in applications involving propagation in complex environments and in inverse imaging. The coherent and noncoherent GB2GB scattering matrices are calculated from the statistical moments of the rough surface scattering amplitude, which is given either analytically or empirically. As an example, closed form expressions are calculated within the small perturbation regime. The GB2GB matrices are then used to analyze the propagation along rough-surface waveguides and to estimate the bi-static reverberations. The results clearly demonstrate and explain the phase-space footprints of the stochastic multiple scattering events and of the deterministic propagation between the surfaces.