SIMULATION OF FIRST AND SECOND ORDER SCATTERING BY ROUGH SURFACES WITH A SOUND RAY FORMALISM

The sound ray technique is developed to simulate rough surfaces scattering processes which are consistent with the Kirchhoff approximation (KA) theory. It is first proved that both approaches (KA and sound rays) lead to the same theoretical expression of the first-order scattered intensity. An algorithm based on the random generation of surfacesʹ slopes is proposed, together with some results computed for Gaussian rough surfaces. This algorithm could be used in room acoustics more as a physical substitute for the cosine Lambert law of diffusion. The method is then extended to the analysis of second-order scattering effects, which are not taken into account by KA. This new approach does not require the generation of several profiles of rough surface. However, some assumptions must be made in order to derive a useful mathematical expression of the second-order scattered intensity. The first results obtained are fairly consistent with the present knowledge of multiple scattering effects (e.g., enhanced backscattering for very rough surfaces), but further work is needed to test the assumptions and to improve the method.