3D MT Data Modelling using Multi-order Hexahedral Vector Finite Element Method, including Anisotropy and Complex Geometry

Abstract

We will present the progress made on the development of a computational algorithm to model 3D Magnetotelluric data using Vector Finite Element Method (VFEM). The differential equations to be solved are the decoupled Helmholtz equations for the secondary electric field, or the secondary magnetic field, with a symmetric conductivity tensor. These equations are modified to include anisotropic earth and complex geometry (such as surface topography, and subsurface interfaces). The primary field is the solution of an air domain, homogeneous half-space or layered earth. This study will compare the application of two boundary conditions, the Generalize Perfect Matched Layers method (GPML) versus Dirichlet boundaries. Dirichlet boundary conditions are applied on the tangential fields, assuming that the boundaries lie far away from the inhomogeneous model. The GPML scheme defines an artificial boundary zone that absorbs the propagating and evanescent electromagnetic fields, to remove boundary effects (Fang, 1996). In this algorithm, high order edge elements are defined based on covariant projections for hexahedral elements (Crowley, et al., 1988). The vector basis functions are defined for the 12 edges (linear) element, 24 edges (quadratic) element, and 48 edges (cubic) element. By this definition, the vector basis will have zero divergence in the case of rectangular elements and relatively small divergence in the case of distorted elements. They are defined to study their numerical accuracy and speed, and to see if the divergence correction is automatically satisfied.