Finite-Difference–Integral Method for Computing Low-Frequency Electromagnetic Fields in a Nonhomogeneous Medium

Abstract

We derive integral relationships for electromagnetic fields, integral recalculation formulas for anomalous electric and magnetic fields, and integral boundary conditions. The efficiency of the finite-difference–integral method is checked by computing the apparent resistance curves for the graben model. Apparent resistance curves computed from finite-difference formulas and from formulas with integral smoothing are compared. Finite-difference graphs are polygonal curves that for small wavelengths lie below the smoothed curves, because the finite-difference computation of the derivative as if reduces the impact of the surface skin effect on the apparent resistance. As the wavelength increases, the surface skin effect diminishes and the finite-difference curves approach the integral curves.