Three-Dimensional Numerical Modeling Considering The Topography Of TEM

Recently, the transient electromagnetic method (TEM) has been widely used for allkinds of exploration. Because these explorations are often carried out inmountainous regions, the topographic effect and complicated three-dimensional (3-D)situations of target can't be negligible. Therefore, the modeling technique has to beable to represent arbitrary 3-D subsurface and topography with high accuracy toincrease reliability of the exploration method. Also, the research for 3-D forwardproblem of TEM can offer necessary theoretic base and instruction to reverseinterpretation, and the research for transient electromagnetic response is the key ofimproving degree of applying TEM and precision of data interpretation.According to the algorithm of Wang T. and Hohmann G.W. in 1993, afinite-difference, time-domain solution to Maxwell's equation has been developedfor a 3-D subsurface and topography . In this algorithm, we use the staggered-gridscheme combining with a modified version of the DuFort-Frankel scheme todiscretize the quasi-static Maxwell's equations. The algorithm allows not onlyarbitrary electrical conductivity variations but also arbitrary topography within amodel. We use the boundary-fitted coordinate method to calculate the response ofthe topographic model. In this method, calculation is accomplished in thecomputational domain, which is transformed from the physical domain by usingcoordinate-transformation coefficients.In this paper, we offer finite-difference equations for electromagnetic components,and gain the magnetic values in the air using upward-continuation boundarycondition. We can obtain the solution to electromagnetic problem step by step anddescribe the field configuration with boundary and initial conditions.We have implemented the program using Fortran and visualized the results usingMatlab. Numerical solution for a homogeneous half-space, some 3-D models andrelief models showed that the solution provides accurate results. It is indicated thatthe three-dimensional modeling considering the topography is required to interpretthe data obtained in mountainous areas, and improve the degree of exploration.