Three-dimensional Topographic Responses In Magnetotelluric Modeling Using Vector Finite Element Method

Magnetotelluric sounding is a frequency domain electromagnetic sounding method which use the spread of natural variation of the alternating electromagnetic field for deep geological studying. So the field construction is convenient and low-cost, besides, It shields from high resistivity layer, high resolution for low-resistivity layer, so it has been widely applied in the geophysical exploration. Magnetotelluric forward modeling can make us have a better understanding of various electrical structure field of the laws, to provide a basis and guarantees for the final inversion. The content of this article based on the three-dimensional magnetotelluric forward modeling studies including surface topography is achieved by using vector finite element method.First of all, starts from the maxwell equations, According to the boundary conditions satisfied by 3D MT. Using the weighted residual method to derive the equivalent variational equations with electromagnetic field boundary value problem. Using regular hexahedral element to divide computational region and vector interpolation function to analysis, the interpolation function is sample and have a high calculation accuracy. Moreover, the discontinuity of vertical component of electric field is satisfied, it can avoid spurious solutions in node finite element method, so we do not need to do divergence correction. Finally, the element stiffness matrix is very large and very sparse, considering the computation speed and memory problems, put the overall coefficient matrix into one-dimensional non-zero element storage. Combining incomplete cholesky decomposition with complex conjugate gradient algorithm to solve the equations, ensure the accuracy of calculation, high efficiency, stable convergence.Secondly, building homogeneous half space and layers model, comparing with analytical solution, the resistivity and phase accuracy are very high, verifying the correction of the algorithm and the program. When checking the forward modeling results, by using the past three dimensional electromagnetic boundary conditions, low accuracy, slow calculation speed and so on. For this condition, the boundary conditions of the four sides of the calculation area need to be given. In addition we realize mesh generation has a great influence on the calculation results, and getting some meaningful conclusions about the subdivision. On this basis, building 3-D anomalous bodies model(including high resistance and low resistance body), the abnormal response of apparent resistivity and impedance phase in XY mode and YX model are calculated respectively, and their response characteristics are analyzed.Finally, three-dimensional topographic responses in magnetotelluric modeling using vector finite element method is achieved. In order to verify the results, a 3D common used topography was simulated for a positive trapezoidal-hill model and a negative trapezoidal-hill model respectively. The frequency of f=2Hz for apparent resistivity and impedance phase diagram was calculated in XY mode and YX mode, and a positive trapezoidal-hill model response curves of different lines, analyzing the result. In order to study the influence of topography on the electromagnetic response under different frequencies, the numerical simulation Three frequency points of 2Hz, 50 Hz and 2000 Hz in two different modes was calculated, and the influence law is discussed. In order to determine whether the 2D topographic simulation results can be used to approximate the 3D topography, we compared theresults of 2D and 3D simulation along the X section(Y=0), their cross section is the same. The simulation results are compared, and the following conclusions are obtained: the 2D TM mode response is similar to the 3D XY mode. And the difference between 2D TE model and 3D YX model response is great.