Research On Complex Resistivity 3D Modeling And Inversing Problem

Electromagnetic method exploration is one of effective geophysical methods. High resolution exploring technology was developed in recent year, which asked for more efficient forward modeling and inversion method. Complex Resistivity(CR) method could be used for analyzing abnormally from different way with several parameters, and the method was suitable for small scale inversion. CR modeling and inversion technology could not meet the needs from application; Three Dimension(3D) modeling and inversion were still in the stage of researching. We carry out 3D CR modeling and inversion in the thesis, and made some progress in artificial data inversion.We choose 3D staggered grid finite difference method to solve modeling problem. Finite length electric dipole source was used to calculate electromagnetic field. Total field was divided into primary field and secondary field. Primary field was calculated by solving layer earth with finite length electric dipole source, Hankel transform was also used in the calculation. We set up CR with Cole-Cole model and mesh grid with staggered grid. After discretizing continual integral equation, linear equation was formed. Direchlet boundary was used as boundary condition. Secondary field could be obtained by solving linear equation. Cross check was made with integral equation code to testify accuracy of 3D staggered simulation method.The goal of CR 3D inversion is to get distribution of Cole-Cole model parameters, 3D Conjugate Gradient(CG) Least Square sequence inverse method was used as inversing method. In order to get the CR model parameter in each cell that changes with frequency, pseudo-modeling was used in 3D CG inversion to avoid computing Jacobin matrix. One time modeling and two time pseudo-modeling were computed in each time inversion. Updating direction was obtained by computing transformed Jacobin matrix multiply with a vector, updating step could be obtained by Jacobin matrix multiply with another vector. Updating vector was the only vector need be stored in each inversion, demands for storage space was decreased.CR model could be got by 3D CG inversion. Least square method was used to obtain Cole-Cole model parameter in each cell. Artificial data by theoretical model was used to check the stabilization and validation of the code.