Toward a practical cross section for rough surface scattering

Abstract

The lowest-order small slope approximation (SSA) provides a practical means of obtaining the scattering strength for rough surfaces. While results are accurate over a wide range of scattering angles, as surface slopes increase and for forward scattering beyond the specular angle, even higher-order SSA results become inaccurate. This is due, in part, to the lack of nonlocal interactions in the SSA. Voronovich introduced the nonlocal small slope approximation (NLSSA) as a generalization of the SSA to explicitly include nonlocal interactions. It has been shown that the NLSSA is more accurate than the SSA both for larger surface slopes and at low forward grazing angles. However, the computational cost precludes use of the NLSSA in practice. The NLSSA expression for the scattering strength can be separated into two terms. The first term is identical to the lowest-order SSA and, hence, the second term of the NLSSA can be considered a correction to the lowest-order SSA. In this paper, we make an approximation to the second term at forward scattering angles that reduces it to a simple algebraic expression. We present numerical results and discuss the region of validity for the reduced form of the equation. [Work supported by ONR.]