Research On Time-domain Spectral Induced Polarization Method Forward Modeling And Optimal Calculation Of Spectral Characteristic Parameters

In recent years,with the renewal of geophysical prospecting equipment and methods,the time spectrum observation of the time domain induced polarization method has been paid more and more attention,and the time spectrum induced polarization method(TSIP)has become the main development direction of the time domain direct current induced polarization method.At present,most researchers obtain time-domain expressions containing gamma function and time-domain expressions based on digital filtering algorithm through frequency-time conversion based on Cole-Cole model.When using these two expressions to study TSIP forward or inverse,there are errors in the calculation results and the calculation efficiency is low.At the same time,the current conventional induced polarization instruments have less observation time,which leads to the problem of strong versatility in the optimal calculation of spectral characteristic parameters.This paper introduced the Gaver-Stehfest(G-S)inverse Laplace transform algorithm to perform frequent-time conversion on the Cole-Cole model in the frequency domain,and compared the results of digital filtering algorithm to verify the effectiveness of the G-S inverse Laplace transform algorithm.Using the time-domain expression based on the G-S inverse Laplace transform algorithm to study the time-spectrum characteristics of different spectral characteristic parameter theoretical models.At the same time,based on the mirror principle of TSIP,the expression of secondary potential difference attenuation considering charging time is constructed,and the time-varying characteristics of secondary potential difference attenuation under different charging time of uniform medium model are studied by using this expression,which provides a basis for the optimization of the characteristic parameters of apparent spectrum.Then,based on the forward modeling of the time spectrum of the excited electric field,the optimization of the characteristics of the visual spectrum is studied.The time domain expression based on the G-S inverse Laplace transform algorithm and the expression of the potential difference attenuation of the secondary field considering the charging time are used to construct the objective function through the ratio form of the observation data of different channels Using gradient method and Barzilai-Borwein step size,the optimization algorithm of spectral characteristic parameters was written.The feasibility of the optimization algorithm was verified by the uniform medium theoretical model,and the applicability of the expression considering the attenuation of the potential difference of the secondary field under different charging time conditions was verified to calculate the spectral characteristic parameters.The simulation data of simple medium model and field measured data are processed by using the optimization algorithm of spectral characteristic parameters to verify the feasibility of the method of searching for abnormal underground polarization bodies by spectral characteristic parameters in this paper.Based on the above research,this paper draws the following conclusions: The timedomain expression based on G-S inverse Laplace transform algorithm has certain applicability,and this expression has the advantages of simple structure,pure real number operation and small computation;Trial calculations of theoretical models have verified that different spectral characteristic parameter models have different time-varying characteristics;Based on the expression of secondary field potential difference attenuation considering charging time,the attenuation law of secondary field potential difference under different charging time can be better reflected;In the study of the optimization of spectral characteristic parameters,the objective function constructed by this ratio form can reduce the multi-solution by reducing the solving parameters;According to the optimization results of the apparent spectrum characteristic parameters of uniform media,it is proved that the optimization algorithm of the apparent spectrum characteristic parameters written in this paper is feasible,and the expression of the secondary field potential difference introduced in this paper considering the charging time has stronger applicability to calculate the apparent spectrum parameters of different charging time;According to the data processing results of the simple medium model and application examples,it is found that the use of spectral characteristic parameters can identify subsurface polarization anomalies,which proves that the method of searching for underground polarization anomaly by spectral characteristic parameters in this paper is feasible.