Time Series Inversion And Monitoring Method Of Cross-hole Electrical Resistivity Tomography Based On Extended Kalman Filter

During the construction of major underground projects in China,we often encounter geological disasters such as water inrush and the resulting groundwater environmental damage and other issues.Therefore,the dynamic monitoring and forecasting of the state of occurrence,migration path,and the affected areas of groundwater bodies is of great significance for follow-up disaster prevention and control work.DC resistivity method has the advantage of higher sensitivity to water,and it has been widely used in the monitoring of groundwater activity in recent years.However,for the monitoring of the rapid migration process of groundwater bodies,the existing resistivity monitoring and inversion methods have problems such as insensitivity to fast-changing processes,poor inversion performance,and inability to predict effectively.It is urgent to carry out targeted research work.In view of the above issues,this paper focuses on the study of resistivity-based timing inversion based on extended Kalman filtering,and theoretical analysis,numerical inversion,model tests and field tests are used.for the study of the prediction model and observation model of the cross-hole resistivity CT monitoring system based on the extended Kalman filter,and the theoretical study of the time sequence inversion method.Numerical simulation experiments are used to test the performance of the time-series inversion method,and the imaging characteristics of low resistivity gradients and abrupt changes in the process of simulated groundwater migration are summarized.On this basis,the experimental study of water body diffusion and migration monitoring model and field experiments are carried out to verify the effectiveness and reliability of the proposed method.The main research work and achievements of this paper are as follows:e(1)An optimization method of Kalman filtering resistivity prediction method based on grey prediction theory.Aiming at the problem that the traditional Kalman filter resistivity prediction model can not predict the non-linear variation trend of resistivity effectively by simple random walk model or linear evolution model,this paper introduces the grey prediction theory to improve and optimize the resistivity prediction model.Based on a limited historical resistivity model,a new model sequence with a certain regularity is created through the "accumulated gray generation" method,and the implicit resistivity change trend is revealed.At the same time,in the process of continuous monitoring and prediction,the optimal estimated resistivity model at the current moment obtained by the Kalman filtering method is added to the historical resistivity model series,and the database is updated to improve the accuracy of prediction at the next moment.(2)An optimization method of Kalman filtering observation model based on cross-hole resistivity CT quadrupole joint observation method.An all-quadrupole joint observation method is proposed as the Kalman filter observation model.This method can not only obtain more abundant data volume,but also has a better model sensitivity distribution pattern,and has a better resolution in terms of geological anomaly morphology imaging and positioning.(3)A Kalman filtering initial model correction method based on least squares reversal.When the underground medium changes rapidly in a short time,the priori estimated state obtained from the previous moment's prediction model often does not include these change information,and using it as an initial model of the Kalman filter will lead to a large error in the result.To solve this problem,this paper proposes a modified Kalman filter initial model,which takes the priori estimated state as the initial model,and first uses the observation data obtained at the current moment to perform a least squares inversion.The inversion result obtained this time is used as the initial model of Kalman filter,and on this basis,the Kalman filter is used to estimate the optimal value.The obtained inversion result is used as the initial model of Kalman filter,and the Kalman filter optimal estimation is performed on the basis of this model.Since the latest data information is incorporated,as well as the reliability of the initial model is improved,the result of the Kalman filter can be effectively improved,and the non-uniqueness of the inversion can be reduced.(4)An inversion method of single time-step multiple Kalman filtering.The process of traditional Kalman filtering method to solve the optimal estimation value is often only filtered once.Numerical simulation experiments show that the results of one filtering are different from the real model for the data processing of the rapidly changing process of subsurface media.To solve this problem,this paper proposes a scheme for filtering multiple times in a single time step,and takes the convergence allowable error RMS as a condition for controlling the number of filtering times.The numerical simulation experiment in this paper shows that the multi-filtering scheme is more similar to the real model for imaging the rapid change process of subsurface media.(5)Based on the above research,this paper independently develops a cross-hole resistivity CT monitoring inversion program based on Kalman filtering,and carries out numerical simulations of multi-groups of low-resistivity gradient and abrupt geoelectric models,and summarizes the response characteristics and imaging law of low resistance body in different motions.Monitoring experiments and field tests of groundwater diffusion processes are conducted to verify the validity and reliability of the proposed method in this paper.