Determining a Piecewise Conductive Medium Body by a Single Far-Field Measurement

Abstract

We are concerned with the inverse problem of recovering a conductive medium body. The conductive medium body arises in several applications of prac-tical importance, including the modelling of an electromagnetic object coated with a thin layer of a highly conducting material and the magnetotellurics in geophysics. We consider the determination of the material parameters inside the body as well as on the conductive interface by the associated electromagnetic far-field measurement. Under the transverse-magnetic polarisation, we derive two novel unique identifiabil-ity results in determining a 2D piecewise conductive medium body associated with a polygonal-nest or a polygonal-cell geometry by a single active or passive far-field measurement.

Keywords

Electromagnetic scattering / conductive transmission condition / inverse problem / single far-field measurement / polygonal / corner singularity