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

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.