Contributions to the theory of scattering by randomly irregular surfaces

Abstract
This paper discusses the scattering of waves by an irregular boundary. Classical single scattering theory and Kirchoff diffraction theory cannot handle waves at near-grazing angles of incidence nor account satisfactorily for the intensity of the field scattered into near-grazing directions. Problems of this type are of increasing scientific and technological importance in such fields as radio astronomy, terrestrial radio communication, the design of radar and sonar devices, as well as in many geophysical situations involving large-scale wave motions. In this paper a theory of multiple surface scattering is proposed, and described, in terms of a simple model problem of the scattering of sound from a randomly irregular, hard surface. Multiple scattering becomes significant at grazing directions of incidence and scattering, and the theory is expected to give an accurate description of the scattering processes in such circumstances. The analysis is strictly valid only in the case of small surface roughness, and in this limit numerical results are presented which illustrate the considerable divergence between predictions based on the multiple scattering theory and those of single scattering and Kirchoff diffraction theory.

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