A finite-difference, time-domain solution to Maxwell's equation has been developed for a three-dimensional subsurface and topography. We use the staggered-grid scheme combined with a modified version of the DuFort-Frankel scheme to discretize the quasi-static Maxwell's equations. The algorithm allows not only arbitrary electrical conductivity variations but also arbitrary topography within a model. We use the boundary-fitted coordinate method to calculate the response of the topographic model. This method is used popularly in the field of fluid dynamics, and also in the field of electromagnetic propagation. In this method, calculation is accomplished in the computational domain, which is transformed from the physical domain by using coordinate-transformation coefficients. Numerical checks against the analytical solution for a homogeneous half-space, the numerical solution for a 3-D model, and an inclined-surface model showed that the solution provides accurate results. The TDEM responses of topographic models are shown as numerical examples, and it is indicated that the three-dimensional modeling considering the topography is required to interpret the data obtained in mountainous areas.
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