The Study Of Regularization Inversion Of Geophysics Based On The Framework Designing

In geophysics, we need to design the corresponding forward and inversion program in order to making the results close to the real geophysics model, but if develop the corresponding program for every practical problems, it will be spent a lot of time on the development of the program. For this, we design a program, it will improve the speed of the program development and the repetition of the computer code in the geophysics. For different geological unit adopt uniform subdivision method(mainly the triangle subdivision), it is much easier to have joint inversion program design.In this paper, we design a program named framework, the forward of the framework is based on the finite element method, the inversion of the framework is based on the regularization inversion. Generalized inversion includes forward. Discrete the calculation area, unit integral and the solution of the sparse linear systems are the core of the finite element method. The core of the regularization inversion are calculate the Fréchet matrix, the choice of regularization factor, the optimization method of the inverse problem(in this paper mainly use the conjugate gradient method) and the design for stabilizing factor. The study of the work focuses on the unity of the regularization inversion of stabilizing factor design, The calculation method of regularization factor, and completed the related program design.The choice of the regularization factor of the framework is the L curve method, this method is developed by Hansen. In this paper, we designed a modified L curve method for the practical geophysics problem, the actual application effect is very good. The main function of the stabilizing factor is to limit the model space, for this we can reduce the multiple solution and obtained the stabilizing solution. There are many kinds of stabilizing factor. In this paper, we introduced several kinds of stabilizing factor commonly used in geophysics. For example: the minimum norm stabilizing factor, the maximum smoothness stabilizing factor(first-order derivative and second-order derivative), the modified total variation stabilizing factor, the minimum support stabilizing factor and the minimum gradient support stabilizing factor. In order to laid a solid foundation of the framework of the regularization inversion.In the framework, it is taken 1D magnetotelluric method for instance, studying the auto-selecting method of the regularization parameter through modified L-curve criterion. Using different stabilizing factor, and through a lot of trial, summarized the impact of the inversion result under the stabilizing factor and its different parameters. In order to study the feasibility of the framework, developed 2.5D DC resistivity inversion program, the practice shows that the framework improves the reusability of the code and improves the efficiency of the program development. Also proved the unified representation of the stabilizing factor and the algorithm of the parameter selection in the stabilizing factor are correct and efficient.