Two models for the spatially covariant field scattered by randomly rough pressure-release surfaces with Gaussian spectra

Two models for the spatial covariance of scalar waves scattered by randomly rough pressure-release surfaces are presented. The first model is based on partial integration of the Helmholtz-KirchhofF integral. The second employs potential theory to solve the radiation problem from a surface that is thought of as a dipole source distribution. In-plane and out-of-plane intensity and coherence from both models are compared using flat surfaces and surfaces with a Gaussian spectrum. Comparisons of intensity show good agreement if the surface is very rough and/or the direction is specular, and that for directions far from the specular one the second model is more accurate. Comparisons of coherence, on the other hand, show good agreement under all circumstances.