Modular finite volume approach for 3D magnetotelluric modeling of the Earth medium with general anisotropy

Abstract

Electrical property of the Earth should be best depicted by anisotropic 3D models, while many numerical issues remain to be solved before it becomes practical, such as implementation complexity and computational efficiency. Magnetotellurics (MT) is the primary method to explore electrical property of the deep Earth, and MT forward modeling with 3D anisotropy has been investigated primarily by finite element methods (FEM) and finite difference methods (FDM). Here, we present a new implementation of finite volume method (FVM) accounting for general anisotropy. Theoretically, FVM can combine the advantages of FEM in mesh flexibility and superior accuracy, and the advantages of FDM in straightforward implementation and economic computation load. For demonstration, a modular framework to approximate Maxwell's equations on a structured staggered-grid (mesh flexibility ignored), which solves electric fields tangential to cell edges, is implemented in an object-oriented paradigm. Synthetic examples are presented to verify its accuracy and feasibility, which includes (quasi-) analytic solution of simplified models and numerical solution of a dyke model. A variant of COMMEMI 3D-2 model with general anisotropy is simulated to probe the characteristic behaviors of EM fields under such circumstance. This approach makes the dependence of model operators on anisotropic conductivity parameters explicit and can simplify further sensitivity derivation, and takes a step forward for the feasible development of MT inversion algorithms concerning 3D anisotropy.