Numerical integral equation solution for scattering from a one-dimensional penetrable fluid interface and a buried rigid cylinder

Abstract

Ocean bottom scattering problems involve contributions from both the roughness of the seafloor and inhomogeneities within the sediment or buried objects. Here, a numerical procedure has been developed to find an exact solution for scattering from an infinitely long rigid cylinder buried beneath a one-dimensional rough interface. In this model, the water–sediment interface is a penetrable fluid boundary with the conditions that pressure and vertical particle velocity are continuous. The cylinder surface is rigid, i.e., the vertical particle velocity on the boundary is zero. A boundary integral approach is used: the pressure field and its normal derivative on the rough surface, and the pressure field on the cylinder surface, are determined, then used to find the far-field scattered field. This method was previously used for a pressure-release boundary condition [E. I. Thorsos, J. Acoust. Soc. Am. 83, 78–92 (1988)] and the penetrable boundary [E. I. Thorsos, J. Acoust. Soc. Am. 90, 2232(A) (1991)]. It is now developed for the combination of a penetrable boundary and a rigid cylinder to validate possible approximation methods. As a benefit of this formalism, the shape of the buried object may be readily varied to model elliptical and perhaps other cylinder cross sections.