Three Dimensional Controlled-source Electromagnetic Edge-based Finite Element Modeling of Conductive and Permeable Heterogeneities

Abstract

Presence of cultural refuse has long posed a serious challenge to meaningful geological interpretation of near surface controlled–source electromagnetic data (CSEM). Cultural refuse, such as buried pipes, underground storage tanks, unexploded ordnance, is often highly conductive and magnetically permeable. Interpretation of the CSEM response in the presence of cultural noise requires an understanding of electromagnetic field diffusion and the effects of anomalous highly conductive and permeable structures embedded in geologic media. While many numerical techniques have been used to evaluate the response of three dimensional subsurface conductivity distributions, there is a lack of approaches for modeling the EM response incorporating variations in both subsurface conductivity σ and relative permeability μr. In this dissertation, I present a new three dimensional edge–based finite element (FE) algorithm capable of modeling the CSEM response of buried conductive and permeable targets. A coupled potential formulation for variable μ using the vector magnetic potential A and scalar electric potential V gives rise to an ungauged curl–curl equation. Using reluctivity (v=1/mu ), a new term in geophysical applications instead of traditional magnetic susceptibility, facilitates a separation of primary and secondary potentials. The resulting differential equation is solved using the finite element method (FEM) on a tetrahedral mesh with local refinement capabilities. The secondary A and V potentials are expressed in terms of the vector edge basis vectors and the scalar nodal basis functions respectively. The finite element matrix is solved using a Jacobi preconditioned QMR solver. Post processing steps to interpolate the vector potentials on the nodes of the mesh are described. The algorithm is validated against a number of analytic and multi dimensional numeric solutions. The code has been deployed to estimate the influence of magnetic permeability on the mutual coupling between multiple geological and cultural targets. Some limitations of the code with regards to speed and performance at high frequency, conductivity and permeability values have been noted. Directions for further improvement and expanding the range of applicability have been proposed.