A robust integral equation solution for electromagnetic scattering by a thin plate in conductive media

Abstract

An integral equation solution for electromagnetic (EM) scattering by a thin plate robustly models scattering in either perfectly resistive, very resistive, or conducting host media. Because the solution is not restricted to modeling certain ranges of host conductivity, it can be used to model scattering over the large ranges in conductivity encountered in geophysics. The solution is developed around a pair of coupled integral equations for the scattering distributions on the plate. In one equation, the scattering distribution is the scalar potential set up by the scattered charge distribution. In the other, it is the component of the scattered magnetic field perpendicular to the plate. The equations are solved numerically using the Galerkin method with simple polynomial basis functions. To find the fields scattered by the conductor, the scattered current density is first calculated from the scalar potential and the magnetic field. The scattered fields can then be found by integrating over the scattered current density. To test the solution, we model horizontal loop EM responses with our solution and compare the results with those from two established integral equation solutions. One of these solutions models pure induction and is used to test our solution when the host is perfectly resistive. Agreement with this solution is very good. Comparisons with the other solution, an electric field integral equation, tests our solution when the host medium is conductive. Agreement with the latter solution is good where induction is not too strong: i.e., where the electric‐field solution is known to work well. Our solution therefore can accurately model EM scattering by a plate in a host medium with any conductivity.