A scattering-chamber approach for solving finite rough surface scattering problems

Abstract

In this paper a new method is derived for the computation of scattering from a finite, rough free surface. The free surface is infinite in extent but only a portion of it is rough. In order to reduce the amount of numerical computation for such a problem, it is desirable to restrict the computations to the interval of roughness, even for remote sources and receivers. This can be easily done in the case that the rough portion of the surface is only directed into the surrounding fluid medium. In this case, the use of the appropriate half-space Green’s function will restrict the integral equation to the interval of roughness only. However, for general deformations this Green’s function cannot be used. The use of truncated integral equations utilizing the free space Green’s function is discussed. An alternate approach is then described. A system of boundary conditions is derived for a finite curve containing the interval of roughness and a surrounding contour in the fluid half-space. The resulting equations are solved using the method of wave-field superposition. The derived method is also easily generalized to the case that the rough surface under consideration is the upper boundary of a waveguide.