3D Numerical Simulation Of Transient Electromagnetic Field Based On Finite-Difference Time-Domain Method

Transient electromagnetic method (TEM) has been widely used in metal, oil and geothermal exploration of mineral resources, but also widely used in engineering, find bedrock and groundwater and the prevention of disasters, are increasingly shown its important position. Because relatively backward of explain technology, the inversion and forward of complex algorithm require a large amount of time and computer memory, and other factors, severely restrict the development of TEM. Therefore, it is theoretical and practical to study the transient electromagnetic response of three-dimensional models. In addition, the three-dimensional (3-D) TEM forward provided the necessary theoretical foundation and guidance for the inversion and explain of the 3-D electromagnetic method.In this dissertation, the discretization of the quasi-static Maxwell's equations were obtained by using the staggered-grid scheme combining with a modified version of the Dufort-Frankel scheme. We consider the Maxwell equations in source and source free media and introduce and excitation source current density into Maxwell equation according to the Ampere circuital theorem. In fact, the modification makes the models arbitrarily complex in resistivity distribution though the computation time cost increases.In order to demonstrate the algorithm, a homogeneous half space model is first used to compare with its analytical solution, the result shows less than 4% relative error in both decay emf and the late time resistivity. Then, four types of three layered earth models (A, H, K and Q) are used to compare with their linear digital filter solutions. The method is demonstrated with homogeneous half space model and four types of layered models. The correctness of this FDTD algorithm has been further verified by the more complex three-dimensional model.According to the geophysical characteristics in gob areas, the apparent resistivity section are analyzed to detect the position of the gobs. In this paper, taking the ShuoZhou obs in Shanxi as an example, the application of the transient electromagnetic technology to mining gobs is described and the results turn out to be accurate.