Finite element resistivity modelling for three-dimensional structures with arbitrary anisotropy

Abstract

We present a three-dimensional finite element algorithm for direct current resistivity modelling. The standard Fortran code allows for nearly arbitrary conductivity structures including general anisotropy. The problem is formulated in terms of secondary potentials where mixed boundary conditions are incorporated. Also in case of anisotropy, this type of boundary condition is superior to the Dirichlet type. We have verified the finite element method using an anisotropic two-layered earth, whose analytical solutions are available. For this simple model, the algorithm achieves high accuracy. The relative deviation between numerical and analytical solution is less than 1.2%. Due to the lack of further analytical references, the responses of three representative model types serve as a cross-check for plausibility and prove the operativeness of the code.