Layer-stripping solutions of multidimensional inverse scattering problems

Abstract

A layer-stripping procedure for solving three-dimensional Schrödinger equation inverse scattering problems is developed. This method operates by recursively reconstructing the potential from the jump in the scattered field at the wave front, and then using the reconstructed potential to propagate the wave front and the scattered field further into the inhomogeneous region. It is thus a generalization of algorithms that have been developed for one-dimensional inverse scattering problems. Although the procedure has not yet been numerically tested, the corresponding one-dimensional algorithms have performed well on synthetic data. The procedure is applied to a two-dimensional inverse seismic problem. Connections between simplifications of this method and Born approximation inverse scattering methods are also noted.