SCATTERING MATRIX EVALUATION USING SPATIAL SYMMETRY IN ELECTROMAGNETIC MODELING

In this paper we discuss the possibility of a drastic computational re duction 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 facilit ated by using the lateral homogeneity of the space and the symmetry pr operty of the Green's functions to reduce the redundancy of calculatin g the scattering matrix by identifying classes of cell pairs which giv e either identical entries in the scattering matrix or entries that di ffer only in the sign. It is required that a conductivity structure be discretized into equal-size or equal-size-based cells. By the latter we mean that the structure is first divided into equal-sized basic cel ls, 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 whil e 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 late ral direction and can be up to several hundred.