The Resistivity Inversion Based On Geostatistics And Its Application In Karst Exploration

Karst landform is widely distributed in China,and the karst development is very complicated and has caused great potential problems for the constructions of road and bridges and hydraulic and hydro-power engineerings.Therefore,the exploration of karst cave,the investigation of groundwater resources and water pollution in karst area has always been a hot and difficult point in hydrological geophysics.Due to the influence of karst development,the distribution of resistivity in karst area is very uncertain.Therefore,the apparent resistivity calculated by the traditional modeling method is often not consistent with the measured data in karst exploration.In order to reflect the electrical characteristics of karst medium more truly,on the basis of previous studies,this paper constructs a two-dimensional random model which is more consistent with the karst geology by selecting appropriate autocorrelation functions,autocorrelation length,mean and variance.The forward calculation of theoretical and experimental models shows that the forward modeling results of stochastic medium models are closer to the measured abnormal forms compared with the results of ordinary models.Therefore,it is necessary to use random model to simulate the resistivity forward modeling in karst area.On the one hand,it can better simulate the actual geoelectric structure;on the other hand,it helps to improve the understanding of people for the anomalous form of apparent resistivity under the complex medium and the identification and analysis of the observed apparent resistivity anomalies.When 2D or 3D geological bodies are revealed,geophysical workers often encounter serious problems of multiple solutions and huge computation time.In this paper,based on the theory of geostatistical inversion,the variogram function model which can reflect the characteristics of the resistivity distribution in the region is fitted through multiple sampling of the exploration area.The fitted variogram model can be transformed into a covariance function that reflects the correlation between the points in the space by specific mathematical relations.Then we can solve the system of cokriging equation constructed by the covariance function,so that we can achieve successive iterations of sequential linear estimator inversion until the result reachesthe convergence standard.In order to verify the inversion effect,several groups of typical geological bodies including random and non random models were set up.The results are almost the same as those obtained from the non random model forward data,and the results are basically in accordance with the real situation of the model setting.This shows that the sequential linear estimator inversion can flexibly combine the geological prior information(such as geological body direction,spatial scale,etc.)into the inversion equation as constraints to improve the accuracy and reliability of the inversion.It is also shown that the random disturbance of medium has less interference on sequential linear estimator inversion,and the inversion algorithm has good practicability.