Coherent scattering indicatrix for arbitrary medium inhomogeneities the general mathematical solution and feasibility of a fast computer code

Abstract

A general solution of Equation (1) in a three-dimensional inhomogeneous medium is found. Use is made of the available ray-optical approximate solution of (1) and the Riemann geometry of wave rays. This allows an exact solution in series form, where the first term coincides with the approximate solution. The second term of the exact solution contains the major part of the scattered wave and its computation gives the right value of the coherent scattering. The second term and its transformation leading to easier computation are analysed. The main result of this work is that the mathematical approach used is convenient for a description of the coherent scattering in inhomogeneous media when solving direct and inverse problems of wave propagation. The description is of a very general character and contains Bragg scattering as a particular case. The application of this approach to the development of the computer codes can provide a powerful tool for studying inhomogeneous media. Developing these codes would be time consuming but provide a fast solution of many difficult problems.