Space-time integral equation solution for hard or soft targets in the presence of a hard or soft half space

Abstract

The responses of a hard or soft target in the presence of a hard or soft half space are computed using space-time integral equations formulated in the time domain. The incident pressure wave is a ‘smoothed impulse“ with a Gaussian-shaped time dependence, whose width is of the order of a target dimension. A space-time integral equation for the pressure field and the gradient pressure field on the outside of the target surface is solved for the pressure and the pressure gradient by stepping on in time. The scattered field is then computed from these source fields. The technique is applicable to targets of arbitrary contour and is demonstrated for a sphere and right-circular cylinder at various locations relative to the half space.