A finite-element algorithm for electromagnetic induction in two-dimensional anisotropic conductivity structures

Abstract

Electromagnetic fields are computed for a 2-D electrically anisotropic earth using a finite-element technique. The models consist of a background layered structure, containing anisotropic blocks. Each block and layer may be anisotropic by assigning to them 3x3 conductivity tensors. The forward modelling problem leads to a coupled system of two partial differential equations for the strike-parallel field components E-x and H-x. They are solved numerically using the finite-element (FE) method. The resulting system of linear FE equations is solved using a preconditioned conjugate gradient method. Subsequently, strike-perpendicular field components E-y and H-y at the surface are found by numerical differentiation of E-x and H-x, using spline interpolation. The 2-D FE algorithm has been validated by comparison with a 2-D finite-difference solution. Three model types are used to demonstrate the effect of anisotropy upon the magnetotelluric responses: horizontal, vertical and dipping anisotropy. A fourth model simulates the effect of anisotropy in the context of shear and subduction zones. The model responses simulate the splitting of apparent resistivity curves at long periods, as well as the existence of tensor impedances with significant diagonal elements, as has been observed previously.