The validity of the operator expansion method, a new formalism for wave scattering from rough surfaces.

Abstract

A new method for computing wave scattering from rough surfaces has been proposed [D. M. Milder, J. Acoust. Soc. Am. 89, 529–541 (1991)]. The solution is obtained using a nonlocal operator that directly relates the surface values of the scattered field to the surface values of its normal derivative. This operator is expressed as a series of terms containing powers of an integral operator, which for a field incident on a flat surface provides the vertical derivative of the scattered field through Fourier transforms. The method has been applied to Dirichlet surfaces whose height varies randomly in only one direction (1-D surfaces) with either Gaussian or power law (Pierson–Moskowitz) spectra. Through comparison with an exact numerical method, the tapered plane-wave integral equation method [E. I. Thorsos, J. Acoust. Soc. Am. 83, 78–92 (1988)], the operator expansion (OE) solution is seen to have a remarkably broad region of validity, while its computational cost is orders of magnitude lower than that of the integral equation. Indeed, when computed to first order, the OE method is accurate when the Kirchhoff approximation is valid, and also when first-order small perturbation theory is valid, a result expected from the asymptotic properties of the analytical solution. Several numerical examples illustrating the wide accuracy of the rapid convergence of the OE solution will be presented. [Work supported by ONR.]