Scattering of acoustic waves by randomly rough surfaces

Abstract

The scattering of acoustic waves by randomly rough surfaces has been investigated using an integral equation approach similar to the Helmholtz integral formula. For the calculation of the mean scattered intensity to remain analytically tractable, numerous approximations must be introduced. The five important quantities most often approximated in the scattering integrals are (1) the surface slopes, (2) the phase function, (3) the source directivity function, (4) the probability density function of surface heights, and (5) the surface autocorrelation function. The results to be discussed in this paper are based on an exact representation of the surface slopes, a Fresnel phase approximation valid for specular, forward, and backward scattering, a Gaussian source directivity approximation, both Gaussian and non-Gaussian surface statistics, and a general representation of the autocorrelation function. Several new results have been obtained and these provide considerable insight into the significance and consequences of the various approximations used in scattering calculations.