A 2-SCALE MODEL FROM THE POINT-OF-VIEW OF THE SMALL-SLOPE APPROXIMATION

General results for the scattering cross section following from the sm all-slope approximation (SSA) are applied to the case of two-scale sur face roughness which can be represented as a superposition of small-sc ale and large-scale components. The purpose of the paper is to obtain analytically tractable results with obvious physical meaning which can be used for estimates prior to undertaking extensive numerical calcul ations according to exact unambiguous expressions of the SSA. The gene ral case of vector (electromagnetic) or scalar (sound) waves is consid ered. The statistics of small-scale roughness is not assumed to be Gau ssian (in any sense) or space-homogeneous, and the possible dependence of the statistics of small-scale roughness on a large-scale undulatin g surface is taken into account. As a result, a modified local spectru m of small-scale components of roughness enters into corresponding exp ressions for the scattering cross section. It is demonstrated that und er appropriate conditions, the resulting formulae for the scattering c ross section reduce to the conventional two-scale model.