Comparison of scattering from Gaussian and non-Gaussian rough surfaces having the same spectrum

Abstract

Presents theoretical calculations relevant to the scattering of ground penetrating radar signals. The authors construct a statistical model that satisfies three conditions. to describe the non-Gaussian multivariate probability distribution function (PDF) they use decomposition of an arbitrary PDF in the sum of auxiliary multivariate Gaussian PDF (for a single random variable this method is sometimes used in the Monte-Carlo simulation of a non-Gaussian PDF). This approach replaces the conventional cumulant expansion. The method suggested in this paper does not lead to negative probabilities and because of its simplicity it successfully replaces the cumulant expansion. The solution obtained is simple enough to perform the necessary calculations and obtain the analytical formulae for joint characteristics functions of differences of elevations and for the scattering cross section in the Kirchhoff and other approximations for a non-Gaussian surface with the realistic anisotropic spectrum and PDF of the principal slopes.