The small slope approximation<th>+<th>(S S A+) for rough surface scattering

Abstract

To be practical, a rough surface scattering model must be easy to implement and easily incorporated into existing models. At the same time, it must be accurate enough to give useful results. Here ‘‘practical’’ is defined to mean (1) no more than N-D integration away from low grazing angles, where N represents the dimension of the surface, (2) no more than 2N-D integration at low grazing angles, and (3) accuracy to within a few dB. In previous work it was shown that at low forward grazing angles an approximation to the nonlocal small slope approximation (NLSSA) satisfies the first and third criteria but not the second. It was also shown that the NLSSA cross section can be written as the sum of the lowest-order SSA cross section and an additional term, the latter of which can be considered a correction term for the lowest-order SSA. In this paper the SSA+, which is based on the NLSSA but includes three approximations to the correction term, is presented. The SSA+ satisfies all three criteria for a ‘‘practical’’ scattering model at low forward grazing angles. Numerical results are presented. [Work supported by ONR.]