| Electrical prospecting is one of traditional geophysical exploration methods. It has been widely applied in the fields of geological examination, ground water development, mining exploration, et al. From 1980s, having higher horizontal resolution of electrical profiling and higher vertical resolution of electrical sounding, resistivity tomography has become an important approach of geoscience CT that have had seismic wave tomography and electromagnetic wave tomography. In the disposal of practical materials such as hydrology, archaeology, architectonics, et al, we are still carrying out 2-D and 2.5-D numerical calculation and inversion for the speed and validity. So we must penetrate into the inversion research. The dissertation was divided into 5 chapters totally, including the sectors of the basic principle of resistivity modeling, finite element method, the object function of the least structure resistivity inversion and the calculation of partial derivatives matrix, which are discussed respectively.Firstly, in the chapter of 2.5 dimensional resistivity modeling, The boundary value, variation equation of total potential on point source electrical field of two dimensional geoelectric section and some problem of program (including the storage of matrix, the solution method of big sparse equation and the speedup method of modeling), were introduced beginning with the differential equation of potential. We calculated some simple model by using FEM method, get the profile fig of some kind configuration and improve the reliability of the program. Secondly, in the chapter of the processing of resistivity inversion, one hand, the traditional calculation of partial derivatives matrix (including the FEM standard method, difference method, compensating circuit method and Green function method in 2-D and 3-D inversion), the object function of resistivity inversion (including the least structure inversion, the broad sense converse method, and the introduce of damp and roughness factor), the calculation of partial derivatives matrix in the optimization progressing of nonlinear problem, the solution of big morbidity equation (including the conjugate grad method and singularity value decomposition)which are discussed respectively. Aiming at the restriction of inversion based on FEM, getting the logarithm of actual resistivity and theoretic resistivity, can improve the stability of inversion. Using exponential form to correct value of the model can fetch up the bug which get minus resistivity and reduce iterations in inversion. Hanging full inversion into target inversion can reduce the time of calculation. So in this paper, we advise to calculate the partial derivatives by using the spheriform element, which has theoretical partial derivatives, to replace the grid element. The way using in this paper is get from conjugate gradient method, which speed and precision is appropriate, fits to complex structural inversion. |
