Two-dimensional Magnetotelluric Modeling Simulation With Continuous Electric Parameters In Each Block Using Finite Elements

Magnetotelluric sounding (MT) is one of the electromagnetic exploration methods which belong to frequency domain. The natural alternating field source is used to study electrical parameters of rocks in deep earth with this method. Currently, the two-dimensional forward problem in MT is basically solved. The use of finite element method, finite difference method and integral equation method and other numerical methods in solving the problem of MT two-dimensional forward has a widespread research. However there are still some improvements to study in the area of mesh generation method, electrical parameters set, the auxiliary field definition and topographic simulation, etc. In this dissertation, continuous electrical parameters with each block is involved in two-dimensional forward modeling, numerical simulation algorithms of magnetotelluric sounding in the condition of two-dimensional flat and topographic terrain are derived. All the studies above can help to improve the accuracy of forward simulation and make a good basis for work of the inversion interpretation.In the beginning of this dissertation, the two-dimensional variational equation of MT method is derived from frequency domain Maxwell equations and the combination with discussion on boundary conditions. The rectangular grid within the subdivision triangle mesh is introduced in the FEM mesh generation method, which facilitates to simulate the sloping abnormal body and terrain to adapt the flat or topographic conditions. Accounting to the actual situation, that the rocks, minerals and other bodies in the horizontal direction and vertical direction usually have continuous variation of electrical parameters, and in some inversion methods, the inversion results of the electrical parameters have continuous variation, so the electrical parameters in each element is set to linear. The auxiliary field is calculated based on the relationship between the main field of the nodes and linear shape function in each element. In the aspect of equations solving, the variable bandwidth storage is used to solve storage problems of the large sparse matrix with large number of zero elements, which can help to save memory usage and improve the computing speed. The definition of apparent resistivity and impedance phase formula in TE and TM mode is based on the characteristics of the measured electromagnetic field components of flat and topographic condition. A set of two-dimensional MT forward procedure is created, which has the function of auto grid generating and using elevation information of the model parameters. It's able to calculate apparent resistivity and impedance phase values with different specified frequency.Through the verification on different geoelectric section models in the condition of flat and topographic terrains, it is proved that forward results are consistent with model parameters. Combining with the different resolution on horizontal and vertical direction of the two polarization modes of the apparent resistivity and phase characteristics, it shows a good result in the determination of underground abnormal body depth, size and sloping direction. The forward response of peaks, valleys and slopes and other topographic terrain are also consistent with their models, which verifies the correctness and validity of the method in this dissertation.