Bistatic reverberation calculations using a three-dimensional scattering function

Abstract

The ocean bottom scattering function depends, in general, on the grazing angles and the azimuthal angles of the incident and scattered energy. However, most measurements are for backscatter only. The few general measurements that are available indicate strong forward scattering near the angle of the specularly reflected ray and weaker, azimuthally isotropic, diffuse scattering away from the specular angle. By combining Lambert’s law scattering with a surface scattering function based on the Kirchhoff approximation, Ellis and Haller [J. Acoust. Soc. Am. Suppl. 1 82, S124 (1987)] proposed a function that incorporated these features. The function is quite simple, and depends on three parameters that can be fitted to backscatter measurements. The functional form thus allows a reasonable extension from backscatter to the general three-dimensional scattering function, which can then be used in bistatic reverberation calculations. It is an improvement over two commonly used methods (which do not include azimuthal dependence) for extrapolating backscattering to general scattering: the separable approximation, and the half-angle approximation. This paper discusses the three-dimensional function in more detail, and presents some comparisons between model predictions and measured bistatic reverberation.