On the Lynch variational method for scattering of waves by randomly rough surfaces

A modification of the physical optics surface source density based on the Lynch variational approach is proposed for the case of scattering by one-dimensional pressure-release Gaussian random rough surfaces. Rather than the local radius of curvature, it involves the surface correlation length and introduces new criteria validating the physical optics evaluation of the coherent and incoherent scattering intensities. Closed expressions for the coherent reflection coefficient and the incoherent scattering cross section are derived without resorting to high-frequency approximation techniques. Numerical data based on these expressions and conventional geometrical optics shadowing theory are presented and shown to be in very good agreement with recently published exact Monte Carlo simulation results.