Extension of the region of convergence of an iterative method for solving the inverse refraction problem

The paper considers the problem of determining the inhomogeneity of wave propagation velocity in a medium on the basis of data regarding the field scattered by this inhomogeneity. A multistep iterative method is proposed for solving this problem; this method is free of limitations on the region of convergence and retains its effectiveness even in the case of strong inhomogeneities for which the scattered field is larger than the incident one. This extension of the region of convergence is achieved by solving at each step only for a small fraction of the scattered field, while the intermediate determinations of inhomogeneity are used to calculate Green functions for the following step of the iteration. Computer simulation results are presented.