Computer Simulation of Two-dimensional Random Wave Propagation

Abstract

A straightforward numerical algorithm for simulating the propagation of a wavefield in a two-dimensional randomly varying medium is described. Both a finite-difference and a fast Fourier transform method are described. These methods are well known, but there is a novel treatment of the random scattering term in the wave equation that allows accurate answers to be economically obtained. The methods are then tested by comparison with known approximate solutions for the fourth moment of a propagating wavefield. The two approaches show good agreement, thus confirming the usefulness of the analytic results and at the same time indicating that the simulation process should be a powerful tool for investigating the higher-order statistics of the field. The agreement should hold in situations encountered in optical and acoustic scattering experiments.