Three-Dimension Magnetotellurics Adaptive Edge Finite-Element Numerical Simulation Based On Unstructured Meshes

The three- dimensional(3-D) magnetotelluric(MT) forward modeling which can be fast solved with high accuracy has become the basis of making the 3-D inversion case practical. Its wide application in geophysical surveying has led it to being mostly focused. The finite element method which has an excellent theory basis and flexibility of modeling complicated problems has been a much popular tool among the numerical techniques. Aiming at the problems which appeared in conventional finite element method, such as the existence of fake solution, the large discretization error encountered when structured mesh was adopted to simulate the complex models and the accuracy being determined by just one time mesh generation and so on, an 3-D h-adaptive MT finite element method which employed the fully unstructured mesh for 3-D MT modeling was introduced. Some standard models were tested which has remarkably validated our algorithm. The work is supported by grants from the National High Technology Research and Development Program of China (863 Program) (2006AA06Z105) and National Natural Science Foundation of China (40874072). The whole framework of our work can be divided into:1. A systematical study of fully unstructured mesh generation and the corresponding optimal strategy was made. Base on this, a mesh refinement strategy which was controlled by quadrilateral was presented. By using this technique, not only the geometrical discretization errors derived from modeling complicated electromagnetic models were dramatically reduced but also the local refinement could be executed in the area of interest by which both the accuracy and efficiency were mostly improved.2. Starting from the 3-D MT boundary value problem under the quasi-static limitation, the finite element equation which was derived based on the Galerkin-residual approach was presented. The coordinate transformation and numerical integration was executed on the discretized tetrahedral elements based on which the 3-D MT vector-finite element method was implemented. A whole computation framework for 3-D vector-finite element method with unstructured mesh was given. Based on this some typical models were tested which has demonstrated that our algorithm could distinctively avoid problems caused by the fake solution and both the accuracy and efficiency were enhanced which made our algorithm has a bright future for further application.3. According to theory of Sobolev vector space and the discretization of Helmholtz space, the error estimate which was suitable for 3-D MT vector-finite element modeling was deduced by which the procedure of adaptive technique was guaranteed.4. Based on the fully unstructured tetrahedralization and optical strategy, the 3-D magnetotelluric h-adaptive vector-finite element method was presented through combining the error estimate. With this work, the accuracy and creditableness for 3-D MT complicatedly modeling was guaranteed.5. The 3-D magnetotelluric h-adaptive vector-finite element algorithm with unstructured mesh was implemented. The numerical results have shown that the complicity of electromagnetic models generally will not effect the convergence with satisfactory accuracy being obtained. Thus, 3-D h-adaptive vector-finite element has remarkably guaranteed the accuracy and efficiency by which a broad application in the future can be predicated.