WAVE SPLITTING IN THE TIME DOMAIN FOR A RADIALLY SYMMETRIC GEOMETRY

A decomposition of the field of the wave equation in three dimensions is suggested. This wave splitting decomposes the field into two components such that in free space simple propagation properties are obtained. The inhomogeneous region is assumed to have a phase velocity variation that varies only in the radial coordinate r from the origin. The suggested wave splitting is a generalization of the wave splitting concept in one spatial dimension. Specifically, the propagation properties in free space in the three-dimensional wave splitting are very analogous to the corresponding properties in free space in one dimension. The three-dimensional decomposition is illustrated in an example of scattering by a sound-soft sphere of radius a. © 1990.