Non‐Kirchhoff elastic wave scattering from rough interfaces

Abstract

An earlier developed solution technique for seismoacoustic scattering by stochastically rough interfaces [W. A. Kuperman and H. Schmidt, J. Acoust. Soc. Am. 79, 1767 (1986)] has been modified to treat the scattering without applying the Kirchoff approximation. This is accomplished by including the rotation of the boundary conditions in the perturbation formulation and by numerically evaluating the scattering integrals, allowing the roughness correlation lengths to be finite. It is demonstrated that the effect of the scattering on the mean (coherent) field can be accounted for in a self‐consistent manner by solving the unperturbed problem with modified boundary conditions. As was the case for the Kirchhoff approximation, the non‐Kirchhoff formulation has been implemented in the seismoacoustic SAFARI code [H. Schmidt and F. B. Jensen, J. Acoust. Soc. Am. 77, 813 (1985)], allowing for simultaneous treatment of multiple rough interfaces. The model is applied to analyze the effect of scattering from a rough shallow water sea bed as well as from an Artic ice canopy. By comparing these results to the Kirchhoff results for the same problems, it is demonstrated that the non‐Kirchhoff theory predicts significantly higher losses, in particular for acoustic wavelengths of the same order of magnitude as the roughness correlation length. [Work supported by NRL.]