Acoustic scattering from an arbitrarily rough surface

A method is described for dealing with acoustic scattering from a time-independent pressure-release surface. As in work by previous authors, the problem is formulated as an integral equation on the surface. This formulation takes account of arbitrarily large surface roughness and multiple scattering phenomena at the surface. The problem may be considered naturally in two stages. The first part of the problem is to invert the integral equation to find the pressure gradient on the surface. The eigenfunction expansion method used by Holford [J. Acoust. Soc. Am. 70, 1116–1128 (1981)] for periodic surfaces is extended to deal with more general aperiodic surfaces. It is then shown that this approach is almost exactly equivalent to a direct collocation method. The second part of the problem is to evaluate the scattered pressure away from the surface. The method used here is to calculate the reflection coefficients from the Fourier transform of the pressure gradient on the surface. The reflection coefficients give a convenient representation of the distribution of scattered wave energy with angle and can be used to find the scattered pressure directly. Results are presented showing the growth of fluctuations in the nearfield of the surface and demonstrating the qualitative as well as quantitative differences between a surface with a Gaussian correlation function and a more realistic surface with a modified Pierson–Moskowitz spectrum. From a study of the cases dealt with here, it appears that the Kirchhoff approximation is more successful with randomly modulated surfaces than it is with simple periodic surfaces.