Nonlinear two-dimensional velocity profile inversion in the time domain

Abstract

The authors develop a time-domain method to solve the nonlinear inverse scattering problem for two-dimensional dielectric objects. The problem is formulated in terms of a time dependent volume integral equation using line sources with pulse excitations as transmitters. The unknown object is expressed as a finite summation of known functions, giving rise to an approximate representation of the original problem. The solution is obtained by performing Born-type iterations on the resulting integral. A variety of permittivity profile reconstructions is presented. The superresolution capability of this algorithm is demonstrated. It is concluded that the high-resolution feature, along with the feasible experimental setup, efficient computer run times, and rapid data acquisition, renders the present method an attractive candidate for practical applications.