2-D CSAMT OCCAM Inversion Research

As the artificial signal source of the controlled source audio-frequency magnetotellurics , the artificial signal source is three-dimensional characteristics, at the far-field is plane wave ,but at the transition field and the near-field is complex wave field with distance,the complex feature make a difficult of the data inversion,thus limits the development of data processing methods . Magnetotelluric data is currently widely used two-dimensional or three-dimensional inversion method, CSAMT rule the majority remain in the one-dimensional inversion , and two-dimensional,three-dimensional inversion methods in the research or in the application of stage-specific manner.The method of CSAMT inversion is currently mostly linear inversion, least squares method is one of the most traditional method,also an effective way. one-dimensional CSAMT inversion method can accurately simulate the electromagnetic field, but it is only confined to simple horizontal layered model, however, in two-dimensional or three-dimensional case, this method will appear wrong solution. If give the least square method with a smooth limit function can be model regularization solution, OCCAM inversion, the minimum structure inversion, RRI rapidly relaxation method belong to this type of algorithm, these methods in two-dimensional data inversion achieved good results. This paper research the theory of CSAMT forward and two-dimensional inversion method, then set the initial model, and two-dimensional finite element method of forward calculation, analysis of calculated results, data processing use OCCAM inversion method . Analyzed and summarized the laws of OCCAM inversion method, set up a set of ideas can be highly efficient method. Papers the main contents include the following five parts.The first part reviews the study status of the CSAMT forward and inversion , introduced three mainly CSAMT forward numerical simulation method : finite difference method, integral equation method and the finite element method. In this parper forward calculation using the finite element method, it was first set up electromagnetic equations and boundary conditions to the Variational principle for the foundation, require solution of differential equations put into the corresponding extremal problem functionals, and the computational domain is divided into a finite number of non-overlapping unit, in each unit, select some suitable nodes as interpolation points for function, differential equations in the variables will be read by the variable or its derivative of the node value and the selected interpolation function composed of linear expressions, solving the differential equations. Research inversion the most widely used has: Constable etc. OCCAM smooth inversion method,Smith and Booker RRI rapidly relaxation method and conjugate gradient method (ICCG).The second part gives the CSAMT two-dimensional finite element method basic theory formula, assumed that the underground medium parameters not change along the y-axis coordinates, through the electromagnetic field components in the y direction for the fourier transform, converted into a parameter with the wave numbers u and v, on the wave numbers u, v set up two-dimensional problem functional equation, and through seeking functional extremum Variational set up finite element linear equations, obtain wave numbers nodes of u, v numerical solution. And compare the calculation of two one-dimensional model, verify the method of correctness and feasibility.The third part gives the CSAMT OCCAM inversion of the basic theory formula, OCCAM inversion with smoothness constraint is nonlinear least squares inversion, fitting the data requested smooth resistivity model. In this section set up a one-dimensional layered model, and one-dimensional layered model OCCAM inversion, the results of the inversion agree well with theoretical model, and the results of the initial model inversion is independent, model resistivity is gradual change style, resistivity of the model has smooth effect. And give an example a one-dimensional application of OCCAM inversion.The four part discuss the sensitivities calculation, in this paper, the sensitivities matrix calculated using reciprocity theorem, put forward value at the receiving point for the location of the source, the electromagnetic field values of each unit cell through the finite element method,then could get the sensitivities matrix, compared and analyzed at a single point sensitivities characteristics at different frequency and model resistivity ;And analyzed lagrange multipliers of the search path, lagrange multiplier path find a concave area to complete an iteration in a certain range., Lagrange multiplier value with the number of iterations chang smaller, inversion of the fitting error gradually reduced.compared the Wu Xiaoping's the lagrange multiplier improving method to the search path, analysis the advantages and disadvantages of different methods, one-dimensional search method require much forward calculated, the Wu Xiaoping's method need the initial value with experiences;The five part set up several theoretical models for OCCAM inversion, theoretical models have layered model,a low-resistivity body in the geoelectric modeh two low-resistivity bodies in the geoelectric model,a combination of low-resistivity body model in the geoelectric model. The results show that the inversion of geoelectric model can better fit with the theoretical model, and the results inversion model are Smooth ,the result has shortages , at the border on the finite element model calculation error caused inversion distortion,inversion results of resistivity larger than the theoretical value.