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

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.