Numerical aspects of a dissipative inverse problem

Abstract

Two numerical aspects of the solution of a one-dimensional electromagnetic inverse problem are considered: the numerical solution of delay integral equations and the sensitivity of the solution of the inverse problem to small changes in the data. In addition a numerical technique is developed for the solution of the direct problem in the time domain. The problem considered is one in which the conductivity and permittivity of the scatterer are continuous functions of depth. The incident field is a transverse electric (TE) plane wave of arbitrary shape, and the inverse problem uses the resulting reflected and transmitted transients to reconstruct the scatterer. For the sake of simplicity, a known scatterer is used to numerically generate the data required for the inverse problem. This is done by using the scattering operators for the problem. The scattering data thus obtained is used to formulate a generalized Gelfand-Levitan integral equation whose solution yields the conductivity and permittivity profiles of the scatterer. The sensitivity of this inversion process is investigated by altering the scattering data.