Scattering matrix evaluation using spatial symmetry in electromagnetic modelling

In this paper we discuss the possibility of a drastic computational reduction in forming the scattering matrix for electromagnetic modelling of 3-D conductivity structure embedded in a stratified and vertically anisotropic earth using integral equations. This reduction is facilitated by using the lateral homogeneity of the space and the symmetry property of the Green's functions to reduce the redundancy of calculating the scattering matrix by identifying classes of cell pairs which give either identical entries in the scattering matrix or entries that differ only in the sign. It is required that a conductivity structure be discretized into equal-size or equal-sizebased cells. By the latter we mean that the structure is first divided into equal-sized basic cells, and some odd numbers of the basic cells may form secondary, bigger cells where the scattering currents and other field quantities may be assumed to be constant, in order to allow the symmetry reduction while keeping the dimension of the linear system as low as possible. This method of reduction is valid for arbitrary conductivity structure. The factor of reduction depends mostly on the number of cells in the lateral direction and can be up to several hundred.