A finite-difference, time-domain solution for three-dimensional electromagnetic modeling

W. Hohmannt ABSTRACT An inhomogeneous Dirichlet boundary condition is imposed at the surface of the earth, while a homoge We have developed a finite-difference solution for neous Dirichlet condition is employed along the subsur three-dimensional (3-D) transient electromagnetic face boundaries. Numerical dispersion is alleviated by problems. The solution steps Maxwell's equations in using an adaptive algorithm that uses a fourth-order dif time using a staggered-grid technique. The time-step ference method at early times and a second-order meth ping uses a modified version of the Du Fort-Frankel od at other times. Numerical checks against analytical, method which is explicit and always stable. Both integral-equation, and spectral differential-difference so conductivity and magnetic permeability can be func lutions show that the solution provides accurate results. tions of space, and the model geometry can be arbi Execution time for a typical model is about 3.5 trarily complicated. The solution provides both elec hours on an IBM 3090/600S computer for computing tric and magnetic field responses throughout the earth. the field to 10 ms. That model contains 100 x 100 x 50 Because it solves the coupled, first-order Maxwell's grid points representing about three million unknowns equations, the solution avoids approximating spatial and possesses one vertical plane of symmetry, wit