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.

On the feasibility of impulse reflection response data for the two-dimensional inverse scattering problem

“…The first is the 2-D version of the Gel' fand-Levitan and Marchenko integral equation methods [3]. The other is the 2-D version of the layer stripping differential methods [4]. Here, "exact" means that all diffraction and multiple scattering effects are included in the mathematical solution; errors in the solution will arise solely Manuscript received February 16, 1995;revised February 27, 1996.…”

An Iterative Method for the Inversion of the Two-Dimensional Wave Equation with a Potential

“…We refer readers to the survey papers [1,10]. In [21], Yagle and Levy suggested a layer-stripping method for the inverse problem (1.1) and in [22] Yagle and Raadhakrishnan presented the results of some numerical experiments. Their main idea is to regularize the ill-posed problem by cutting the lateral wave numbers.…”

Linearization Ill-Posedness for 2.5-D Wave Equation Inversion Model

“…For example, layer-stripping technique, linearization approximation and the generalized Marchenko procedure [1,3,6,13] are those used widely in practice, which concentrate on the inversion schemes. However, the well-known instability of inversion results in numerics imply the ill-posedness for multidimensional inverse problems.…”