Scalar and vector potentials provide a convenient formulation for finite-difference modeling of harmonic electromagnetic (EM) fields in 3-D media. Because the EM potentials are continuous everywhere, the finite-difference method can handle large contrasts in conductivity or dielectric constant. In the Coulomb gauge, the method is stable at low frequencies because the potentials approach those for a static (dc) formulation. The linear system of finite-difference equations can be solved iteratively with a biconjugate-gradient method that is diagonally preconditioned. An impedance boundary condition terminates the grid.
Modeling of a crosswell EM survey with this method shows that 2-m electric dipoles radiating at 5 MHz can detect a small zone of dense nonaqueous-phase liquid (DNAPL) with high resistivity and low dielectric constant between wells 10 m apart. Because the responses to contrasts in dielectric constant and resistivity are distinctly different, both quantities could be estimated. The response changes significantly with the position of the DNAPL zone, the weakest response occurring when the zone is just below the water table.