Finite‐element analysis of controlled‐source electromagnetic induction using Coulomb‐gauged potentials

Abstract

A 3-D finite‐element solution has been used to solve controlled‐source electromagnetic (EM) induction problems in heterogeneous electrically conducting media. The solution is based on a weak formulation of the governing Maxwell equations using Coulomb‐gauged EM potentials. The resulting sparse system of linear algebraic equations is solved efficiently using the quasi‐minimal residual method with simple Jacobi scaling as a preconditioner. The main aspects of this work include the implementation of a 3-D cylindrical mesh generator with high‐quality local mesh refinement and a formulation in terms of secondary EM potentials that eliminates singularities introduced by the source. These new aspects provide quantitative induction‐log interpretation for petroleum exploration applications. Examples are given for 1-D, 2-D, and 3-D problems, and favorable comparisons are presented against other, previously published multidimensional EM induction codes. The method is general and can also be adapted for controlled‐source EM modeling in mining, groundwater, and environmental geophysics in addition to fundamental studies of EM induction in heterogeneous media.