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An Improved Nodal Finite-Element Method for Magnetotelluric Modeling

Numerical modeling is an efficient tool for theoretical study and interpretation of electromagnetic geophysical phenomena. The magnetotelluric method (MT) is a frequency-domain electromagnetic tool that utilizes natural variation in the Earth's magnetic field as a source. Numerical modeling of MT requires solving low-frequency time-harmonic plane-wave electromagnetic induction problem and computing electromagnetic responses of inhomogeneous medium in which electrical conductivity generally varies drastically. Conventional node-based finite-element method (FEM) is not suitable for computing electromagnetic field in inhomogeneous conductivity structure. In this article, an improved nodal FEM is proposed. The method contains the current continuity condition in the governing equations, where the electrical field is decomposed into two parts: one is divergence-free and another is curl-free, and a penalty stabilizing term is introduced into the double-curl equation. Furthermore, the right-hand side of the linear system is replaced by an equivalent source vector, which can be analytically calculated with a background model, to improve the accuracy of the solution. Numerical examples show that the proposed method is accurate and stable for the quasi-static magnetotelluric modeling of structures with highly discontinuous conductivity.