Statistical Non-Gaussian Model of Sea Surface With Anisotropic Spectrum for Wave Scattering Theory. Part I - Abstract

Abstract

In part I of this paper we analyze which statistical properties of a random surface are necessary to describe a wave scattering cross section from this surface. We develop such a mathematical model of sea surface that allows us to find scattering cross section. This model corresponds to statistically homogeneous rough surface that satisfies the following conditions: (1) It has the given two-dimensional (anisotropic) spectrum. (2) It has the given (non-Gaussian) joint probability distribution function (PDF) of two principal slopes at any fixed point. (3) It allows us to obtain in an explicit form the joint probability distribution (characteristic function) for an arbitrary number (N) of differences in of the surface. (4) It allows us to find in an explicit analytical form any mean scattering cross sections appearing in any theory of wave scattering from rough surface. (5) In describing the non-Gaussian PDF we use, instead of the cumulant expansion, another approach: decomposition of the multivariate non-Gaussian PDF in the sum of multivariate Gaussian PDF having different positions and different variances and correlation coefficients. In part II of this paper, we calculated in the Kirchhoff approximation the scattering from a perfectly reflecting rough surface, having non-Gaussian PDF of slopes and anisotropic spectrum.