Fast and stable method for 3-D modelling of electromagnetic field

Abstract

The paper discusses constrains imposed by the energy conservation law on a set of possible solutions to Maxwell's equations. An integral equation having a contraction kernel is derived for the electromagnetic field induced by an external source in a dissipative medium. The equation can always be solved using simple iterations. The Iterative-Dissipative Method (IDM) based on this integral equation has been successfully applied to a wide range of practical 3-D problems encountered in surface and borehole electromagnetic exploration. The approach imposes no restrictions on the frequency of the field variations, gradients of the electric conductivity or dielectric permittivity. It can also be applied to an anisotropic medium. The IDM integral equation keeps its contraction properties on a numerical grid. This makes the convergence of the iterative process practically independent of the grid parameters. The paper presents a brief theory of the method and an example of the electromagnetic field calculation for a geoelectric model of the Australian continent and the surrounding oceanic area.