Invariant imbedding and wave splitting in R ³ : II. The Green function approach to inverse scattering

Abstract

For pt.I see ibid., vol.6, p.1075 (1990). The results of a previous work on invariant imbedding and wave-splitting applied to the wave equation, are extended to the wave-splitting of the Green function. The system of equations for the up- and down-going wave components G+ and G- of green function (associated with a fixed point impulsive source, exterior to the scattering medium) are obtained. The (short-time) asymptotic behaviour of the wave components G+, G- are derived. The application of the system of equations for G+, G- to the layer stripping process is examined, and the consequent utilization of this process to the inverse problem is treated. Some of the problems in the numerical implementation of such a procedure are examined, and remaining additional analysis along these lines, that remains to be investigated, is given.

“The source problem” — Transient waves propagating from internal sources in non-stationary media

“…The same technique applies for the solution of three-dimensional inverse scattering problems, and several interesting results have been reported, see e.g. Refs 13,[30][31][32][33]. In the present paper, the scattering analysis for non-stationary media is extended to include internal sources in the scattering media.…”

Transient waves from internal sources in non-stationary media — Numerical implementation

“…A challenge of great interest today, is to solve transient wave propagation problems in three dimensions. Some interesting results have been reported [25,26].…”

Transient waves in nonstationary media

“…This method is an extension of the wellestablished methods of wave splitting, invariant imbedding and Green functions techniques, see Refs. [3,5,6,12,16,17] and [7]. Wave propagation in non-stationary media has also been investigated with other methods, see, e.g.…”