Two-dimensional Magnetotelluric Forward And Inversion Research In Non-isotropic Medium

Vast observational data obtained by modern observation technology have indicated that the underground medium is anisotropic. It will lead to a great misinterpretation by applying the isotropic model to fit the data. To obtain more accurate interpretation results we must establish anisotropic models to do the numerical simulation. The magnetotelluric method has the advantages of lower costs and deeper prospecting depth over other electromagnetic methods. The response function is sensitive to the variation of conductivity in different direction of the earth medium. Special observation methods are not required in the study of non-isotropic medium. Therefore magnetotelluric method is an effective approach to study the electrical structure of the crust and upper mantle.In this paper, the two-dimensional isotropic magnetotelluric forward modeling equations are derived systematically and the forward modeling responses are compared with the published results to verify the algorithm. The non-isotropic medium is segmented into rectangular blocks to apply the linear-interpolated finite element method in the forward modeling. This scheme is different from that being used in the isotropic case as the electrical and magnetic components cannot be decoupled. The linear equations are completed by applying the one-dimensional anisotropic numerical simulation results to the vertical and bottom boundaries conditions. The upper boundary conditions are brought into the equation by adding two sets of electric and magnetic fields. The variable bandwidth method is applied in the storage of coefficient matrix and Cholesky column decomposition method is used as the equation solver. The forward modeling comparisons between our algorithm and Pek and Kerry Key’s in three anisotropic cases prove the correctness of our code. By introducing the layered medium theory into the second anisotropic case (existing dip angle) illustrates the effect of the anisotropic coefficient and dip angle. By simulating the near surface uneven abnormal body in the anisotropic medium shows the effect of the static effect.The NLCG and Quasi-Newton inversion algorithms are modified in this paper. The principles of the two methods are described by objective function, linear search method and the calculation of Jacobi matrix, and the inversion flowcharts of the two methods are also presented. The direct calculation of Jacobi matrix is not performed which reduce the time consumption. The two inversion examples validate the effectiveness of the inversion algorithm. It is found that the Quasi-Newton inversion is superior to the NLCG inversion with respect to computation efficiency due to a different linear search method. But the NLCG inversion is chosen to be the inversion scheme in this paper because of its better stability. As for the non-isotropic inversion, the third anisotropic case is well studied. It is also found that the conductivities in the electrical principal axis x’and y’can be inversed by the isotropic TE and TM inversion, by analyzing the forward equation itself and forward modeling results of the third anisotropic model.The inversion example also validates this conclusion.