Nonlinear two-dimensional velocity profile inversion using time domain data

Abstract

An iterative algorithm is developed to solve the nonlinear inverse scattering problem for two-dimensional lossless dielectric inhomogeneities using time-domain scattering data. The method is based on performing Born-type iterations on a volume integral equation and, hence, successively calculating higher-order approximations to the unknown object profile. Both the full-angle and the limited-angle problems are considered. Solutions are obtained for cases where the first-order Born approximation is severely violated. Wideband time-domain scattered field measurements make it possible to use sparse data sets and thus reduce experimental complexity and computation time. Several examples are given to show the ability of this method to invert arbitrarily shaped permittivity profiles using few transmitters and receivers. The high-resolution capability of the algorithm is also demonstrated.