A Generalized Material Averaging Formulation for Modelling of the Electromagnetic Fields

Abstract

In this paper, we derive a general electromagnetic material averaging formula for anisotropic inhomogeneous media. In deriving the homogenization formula for the effective medium, we employed the extended Born approximation applied to the Lipmann-Schwinger integral equation for multiple scattering. It is shown that even if the inhomogeneous medium to be averaged is isotropic, the resulting averaged medium can be anisotropic. We further show that, for some special cases, the homogenization formula reduces to well-known material averaging formulas such as the effective medium approximation for spherical inclusions and the Backus averaging formula for finely layered media. The derived averaging formula can be used as a tool to study rock heterogeneities, multiphase structures, as well as an upscaling scheme to assign proper material properties to finite-difference modeling grids when the model under consideration has features that are smaller than the grid size. The latter allows us to use nonconformal grids that will significantly reduce the simulation time of the forward modeling code.