| With the development of geophysical prospecting in 1000 meters below surface, the High-Frequency Magnetotelluric (HMT) method is applied more and more extensively in our country, represented by EH-4 conductivity imaging system which is made in USA. HMT method belongs to the passive source electromagnetic method which collects natural electromagnetic signals. And the required frequency range is from 10Hz to 100 KHz, correspondingly, the prospecting depth varies from a few meters to one kilometer. The paper not only has academic value but also has some effect in guiding the practice of the engineering. Aiming at the target of HMT filed, this paper successfully implements the HMT forward numerical modeling with scalar/node and vector/edge finite element method respectively. This paper focuses on four important aspects as follows. The first one is the establishment of variational quations which provides the mathematics theories for the finite element method of HMT; the second one is for the study of scalar/node and vector/edge finite element method; the third one is about how to solve faster for the large-sacled matrix system of scalar/node and vector/edge finite element; and the last one is achieving the forward modeling with high precision of HMT method. The author hopes that this work can provide a reference for further research and could do well for reducing the multiplicities of geophysical interpretation for the exploration and practice.The following is the main contents and results of the paper:1. Based on the work of predecessors, this paper derives the variational equations of HMT field by generalized variational principle and the weighted residual method from the Maxwell's equations which guarantees the mathematical accuracy and the stability of the finite element method.2. When solving the HMT field boundary value problems by traditional scalar/node or vector/edge finite element, we should transform unknowns into the scalar field problems, and then solve it. But such scalar basis function is far away from efficiency when dealing with vector electromagnetic field problems. This is because it can result in fake solution or some solution which can not be interpreted by using physical conceptions. And also it is difficult to impose the essential boundary conditions on the interface of abnormal body. Lastly, it is inconvenient to deal with the angle and margin of the conductive bodies. In this paper, a new vector basis function is used to describe the unknowns, and then the degree of freedoms will be assigned to the edges rather than the nodes of the element by which the problems of the traditional scalar/node finite element are solved. The work has proved that the vector finite element method is remarkably efficient in the HMT forward modeling.3. In this paper, we study an efficient method for solving the large sparse linear equations—the ameliorating Wilkinson method. It has been proved not only for accelerating the convergence rate of the finite element linear equations, but also for remarkably reducing the time to solve the matrix equation, especially in electromagnetic field with very ill-conditional matrix. The conventional numerical methods generally can not convergence to the cut-off error, but the ameliorating Wilkinson method is able to achieve good results.4. This paper simulates the 3D response characteristics of HMT with scalar/node and vector/edge finite element method, analyzing the numerical precision and speed. By analyzing the characteristics of the valley and ridge terrains and other complex conditions, we sum up the law of the HMT field.In the last part of this paper, the author give the main conclusions and proposals which point out the deficiency in the paper and some things which are needed to be perfected in the future.
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