Modeling and inversion of 1‐D profiles in time‐domain

Abstract

PurposeThe purpose of this paper is to present a time‐domain technique to compute the electromagnetic wave field and to reconstruct the permittivity and electric conductivity profile of a one‐dimensional slab of finite length.Design/methodology/approachThe forward scattering problem is solved by a Green's function formulation to generate synthetic data that are used as a testbed for the inversion scheme. The inverse scattering problem is solved by reconstructing the unknown permittivity and electric conductivity profile of the medium with the help of an invariant embedding method.FindingsThe Green's operator maps the incident field on either side of the medium to the field at an arbitrary observation point inside the slab and hence, the internal fields can be computed directly without computing the wave field throughout the entire medium. The invariant embedding method requires a finite time trace of reflection data and therefore it is suitable for reconstructing the material parameters in real‐time.Practical implicationsThe implemented methods have been validated against synthetic and measured time domain reflectometry data.Originality/valueThis paper fulfils an identified need to determine unknown one‐dimensional profiles and thus plays an important role in electromagnetics, non‐destructive testing, and geophysics.