WAVE SCATTERING BY A 2-DIMENSIONAL PRESSURE-RELEASE SURFACE-BASED ON A PERTURBATION OF THE GREENS-FUNCTION

An approximate method is described, to calculate the two-dimensional a coustic scattering, from a slightly rough, time-independent, pressure- release surface. The formulation is based on a perturbation of the Gre en's function allowing an approximation of the propagator in the kerne l of the Helmholtz integral equation which reduces the integral equati on to a convolution equation. The complexity of the problem is reduced from O(MN(2)) (for an iterative method where M is the number of itera tions) to O(N 1n N), where N is the number of discretizations used to describe the surface numerically. The specific surface examined has a sinusoidal profile, although the method may be applied to any slightly rough surface (hK much less than 1). We use this solution to generate plane-wave reflection coefficients from the Fourier transform of the pressure gradient on the surface. These may be used to calculate the s cattered pressure. The existence of the exact solution for periodic su rfaces, due to Holford [J. Acoust. Sec. Am. 70, 1116-1128 (1981)1, all ows comparison of the convolution approximation with the exact solutio n. The reflection coefficients and scattered energy are then compared with the approximate solutions of Rayleigh and Kirchhoff. (C) 1995 Aco ustical Society of America.