Asymptotic models for wave scattering from very rough surfaces

Asymptotic methods are developed that can be used in wave scattering from very rough surfaces. The very rough surface is modeled by either a periodic function or a random process. An asymptotic method for periodic surfaces is illustrated for scalar wave incidence. A second method starts by viewing the scattering problem as one involving wave propagation in a layered random medium. A wave equation for the average scattered field is obtained by an application of the method of smoothing perturbation, and by expanding the average field in powers of epsilon. The solution of the wave equation shows that the scattering from the very rough surface can be characterized by reflection coefficients on the mean plane. Methods of computing the reflection coefficients are derived. The incidence of electromagnetic waves of arbitrary polarization is also considered. The expression for a first order correction to the average field is derived in the case of scalar wave incidence.