Research Of The Three-Dimensional Magnetotelluric Inversion With Induced Polarization Effect

The MT method is a very effective geophysical exploration method.It is widely used in deep crustal structure research and oil and gas exploration.The three-dimensional inversion theory and technology are also mature,but most of them are carried out on the premise of neglecting the induced polarization effect,and only consider the electromagnetic effect of the underground medium.Due to the inevitable existence of the induced polarization effect in the actual medium,the model of MT inversion,which does not consider the induced polarization effect in theory,is incomplete and the result of the inversion is also biased.Therefore,the study of three-dimensional MT inversion with induced polarization effect can not only make the results of the inversion close to the actual conditions of the underground medium,but only from the update of the forward and inversion theory and method,it can obtain more abundant geoelectric information and further expand the application domain of the MT method.In this paper,the IP effect is introduced into the Maxwell equation with the Cole-Cole model,and the research content of the three-dimensional MT forward and inversion considering the IP effect and the electromagnetic effect is realized.The feasibility of extracting the four parameters of the Cole-Cole model from the observed data is discussed.A staggered grid finite difference method is adopted in the forward modeling.The electrical conductivity in the Maxwell equation is replaced by complex resistivity through the Cole-Cole model.The Maxwell equation is discretized and combined with the corresponding boundary conditions to obtain the large linear equations.Finally,the response values at the surface measurement points are obtained.In order to understand the relative size of Cole-Cole model parameters to the sensitivity of response,four sets of comparison models of single parameter change were designed.Compared with their respective responses,it also reflects the effect and difficulty of inversion of parameters at the same time.In the inversion,the data space OCCAM method is used,which not only fits the measured data,also includes the smoothness of the vertical and horizontal directions of the model.Finally,the partial derivative of the data body(impedance)to theparameters of the Cole-Cole model is obtained,that is the sensitivity matrix.Because of the large difference in the partial derivative matrix of the impedance to each parameter.The specific weighting method is to determine the Lagrange factor of each parameter by using the ratio of norm of Jacobian matrix of each parameter.Then,the iterative formula of the parameters of the model with different sensitivity is deduced from the objective function,.In addition,The range of parameters determined by the physical properties of the Cole-Cole model limits the parameters and reduces the multiple solutions to realize the inversion.Theoretical examples show that the forward and inversion methods adopted in this paper are basically feasible.