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 elec tromagnetic (EM) induction problems in heterogeneous electrically conductin g media. The solution is based on a weak formulation of the governing Maxwe ll equations using Coulomb-gauged EM potentials. The resulting sparse syste m of linear algebraic equations is solved efficiently using the quasi-minim al 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 term s of secondary EM potentials that eliminates singularities introduced by th e source. These new aspects provide quantitative induction-log interpretati on for petroleum exploration applications. Examples are given for 1-D, 2-D, and 3-D problems, and favorable comparisons are presented against other, p reviously published multidimensional EM induction codes. The method is gene ral and can also be adapted for controlled-source EM modeling in mining, gr oundwater, and environmental geophysics in addition to fundamental studies of EM induction in heterogeneous media.