Research On Weight Inversion Algorithm For The Determination Of Cole-Cole Parameters Using Real And Imaginary Parts Of Spectral Induced Polarization Data

Spectral induced polarization(SIP)has the ability to evaluate anomalous bodies by multiple parameters(Cole-Cole parameters)which can provide more informations.Because the number of the Cole-Cole model parameters in SIP inversion are more than others in other inversion methods,and the sensitivity of each parameter is different,and SIP includes both the induced polarization effect and the electromagnetic effect,and Induced polarization effect and Electromagnetic effects coexist in SIP,all of these restrict the research of SIP inversion.The inversion is the ultimate means to explain the geoelectric structure,so it is very important to study a SIP inversion algorithm based on the forward in the simultaneous consideration of the induced polarization effect and the electromagnetic induction effect,which has the ability to inverse four Cole-Cole model parameters at the same time.Based on the one dimensional SIP forward in consideration of the electromagnetic induction effect and the induced polarization effect,the one dimensional SIP the least square inversion has been finished.The idea of joint inversion of real and imaginary parts of SIP data is adopted by this paper.By this method,the inversion domain is changed from the complex domain to the real domain to depress the character of multi-results of inversion.In this paper,the least squares inversion algorithm for joint inversion of Cole-Cole model parameters using the real and imaginary parts of SIP data has been derived.In order to better inverse the frequency dependence and time constant with low sensitivity,the idea of weight inversion of real and imaginary parts is proposed for the first time,that the objective function of the real part and imaginary part is weighted when the objective function isdefined.By this method,the inversion result of each parameter is improved by controlling the proportion of real part and imaginary part in inversion.The results of model experiments indicate that this weight inversion method not only has a good ability to invert the resistivity and the chargeability,but also remarkably improve the results of the inversion of the frequency dependence and the time constant.In the aspect of 3D inversion,based on the finite difference SIP forward in consideration of the induced polarization effect and the electromagnetic effect,using NLCG Technology,the three dimensional SIP inversion algorithm which can inverse simultaneously four Cole-Cole model parameters has been finished.The joint inversion of the real and imaginary parts of the electric field is used in three dimensional SIP inversion to reduce the character of multi-results of inversion.Because of the joint inversion of the real and imaginary parts of the electric field,the sensitivity matrix expression of the real part and imaginary part of the electric field is derived.The method of calculating the real part and imaginary part of the sensitivity matrix by the pseudo-forward is proposed,greatly reducing the computational cost,avoiding the problem that direct calculation of the sensitivity matrix cost too much time and the computer memory is not enough.In order to solve the problems that some parameters has low sensitivity and are difficult to inverse,the method of weighting the real part and imaginary part is used in the inversion.By the experiment of theoretical model,the feasibility,superiority and stability of the algorithm are proved.