A variational approximation for scattering of scalar waves by stochastic surfaces

A variational method is developed for the scattering of scalar waves by statistically rough surfaces. It provides a procedure for recasting other approximations so that errors cancel to first order, and also yields a quantity that is indicative of the quality of the approximation. The method is tested by application to a corrugated surface for which some exact solutions are known. Scattering from stochastically rough surfaces continues to be of importance in many areas, but analytical difficulties generally preclude obtaining an exact solution to significant problems. Accordingly, various approximation methods are used. Since no quantitative index of approximation quality is generally available, there is often doubt not only as to which method is best but even whether any available one is adequate.