Research Of Forward Using Finite Element Method And Regularized Inversion Using Hybrid Genetic Algorithm In Magnetotelluric Sounding

Magnetotelluric sounding is an important geophysical method to study the earth electrical structure using the natural EM field as its source. Magnetotelluric sounding has obtained quite great progress in instrumental acquisition system, data processing , interpretation, and research on basic theory , since its naissance in 1950's. However, with the in-depth theory research and wide practical application, many new problems are needed to be solved or to be more studied and consummated, these problems come down to technique of numerical value modeling about the forward and the study of inversion algorithm. In this dissertation, it main talk about that finite element method is used for the forward modeling and real coded hybrid genetic algorithm is used for solving the regularize inverse problem.Based on the Maxwell's equations, the boundary value problem, variation problem, interpolation function and stiffness matrix in two-dimensional magnetotelluric are derived. Combined with divergence condition, the finite element equation of three-dimensional magnetotelluric forward modeling is derived. Finite element method is formed a linear equation Ax=b, in which A is a large sparse, banded, symmetric, complex matrix. Its condition number is far larger than 1, and it is a severe ill-conditioned matrix. So to solve this large scale ill-conditioned linear equation is very difficult. However, the BICGSTAB algorithm with incomplete LU decomposition for preconditioning could be used to solve this system linear equation, with advantages of high speed, high precision and stability. In order to prove correctness of the forward algorithm in two- and three-dimensional magnetotelluric, we make a comparison of results which from the forward modeling in two-and three-dimensional magnetotelluric and analytic results in one-dimensional geo-electrical model. In addition, we compute some models which are provided by COMMEMI project, and compare all the simulation results with it, which also give a further evaluation for the forward algorithm in two- and three-dimensional magnetotelluric. The forward modeling results show that our algorithm is very efficient, ant it has a lot of advantages: the rapid degress, the high precision, the canonical process of solving problem, meeting the internal boundary condition automatically and adapting to all kinds of distribution of multi-substances.The magnetotelluric inverse problem is ill-posed. Therefore the inverse results are unstable and non-unique. This means that different geo-electrical model could fit the observed data with the same accuracy. A stable solution of an ill-posed inverse problem can be obtained by utilizing the regularization methods in the objective function. Genetic algorithm for regularize inversion is designed, which can avoid linearization difficulty in the nonlinear problem and solve the ill-posed problem in magnetotelluric inversion. The effectiveness of the inverse algorithm was verified with the inverse results. On the other hand, the inverse problem of magnetotelluric sounding is highly nonlinear and ill-posed. Real coded genetic algorithm can not eliminate the non-unique solution of this inverse problem in itself. This is due to the lack of observation data and the physical problem itself. However, the inverse algorithm is very robust. Through the study of inversion simulation, we believe this new approach to solve the inversion problem of magnetotelluric sounding will bring new hope and it worth in-depth studying.