Ea. Badea et al., Finite-element analysis of controlled-source electromagnetic induction using Coulomb-gauged potentials, GEOPHYSICS, 66(3), 2001, pp. 786-799
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.