The Forward And Inversion Of MT Field In Anisotropic Conductivity Structures

This thesis deals with the forward and inversion problem of the magnetotelluric (MT) in a two-dimensional (2-D) medium with anisotropic conductivity structure. The goal of this thesis is to obtain quasi-analytic solution of2-D MT fields on an an axially anisotropic infinite fault, and to develop a code by finite element method which can be used to model the magnetotelluric fields and calculate the MT responses in anisotropic conductivity structures, and to carry out the inversion of MT field data in1-D medium.From the magnetotelluric theory in the simplest case, i.e. isotropic half space model, the MT theory of the one-dimensional (1-D) isotropic layered media, the2-D isotropic midia and the three-dimensional (3-D) case are introduced in sequence. And then the MT theory of the1-D anisotropic layered media and the2-D model with anisotropic conductivity structure are considered.For the general2-D earth, the magnetotelluric fields must be calculated by numerical modeling methods. And the numerical modeling method can indeed be used to various calculation of2D model, however, sometimes the numerical results given by different methods differ from each other, then it is difficult to tell which of the methods is giving the correct solution and even if two methods do yield the same numerical solution, this does not prove conclusively that it is, in fact, an accurate one. In this case, it is desirable to assess the correctness and precision of the methods by a simple2D model which can also be solved analytically. Hence, the quasi-analytical solutions of the2-D magnetotelluric fields on the finite fault with special anisotropic condutivity structure (i.e. diagonal anisotropy, horizontal anisotropy and azimuthal anisotropy) are given based on that of the isotropic caseThe difference between the Maxwell equations corresponding to the2-D isotropic media and anisotropic ones, respectively, is analysed carefully. Base on this, the numerical modeling equations are derived using the galerkin weighted residual finite element method (FEM). The element stiffness matrix is optimized based on the transformation properties of the matrix equation when the FEM numerical modeling equations are derived, which makes the data storage required in the calculation of the overall stiffness matrix equations reduce to the least level so as to reduce the cost of the memory of the computer effectively.When the overall stiffness matrix equations for the2-D symmetric anisotropic conductivity media are obtained, the corresponding finite element numerical simulation code is developed in Matlab language. The code applys the sparse matrix storage technology provided by the Matlab platform to store the coefficient matrix, which reduces the strorage and memory at the maximum level and improves the computational efficiency significantly. The programming of the code is simple when the method for solving finite element stiffness matrix equation within the Matlab platform is applied, and the results of the calculation are stable and reliable.In order to examine the correctness of the FEM code, the quasi-analytical solution are used to check the FEM code in this thesis. After the correctness of the FEM code is confirmed, the magnetotelluric fields and the MT responses over several well-known2-D anisotropic media (Reddy&Rankin model, Pek&Li model) are calcalated, and the effects of the anisotropy on the MT fields are discussed.When the numerical modeling of MT fields in2-D anisotropic conductivity structures is finished, a inversion method of the whole tensor impedance response to one-dimensional anisotropic structure is considered. And then the inversion method is applied to MT field data.Finally, the work of this thesis is summarized and some directions of the future research are given.