Forward And Inverse Research Of Borehole-to-surface Mixed Source Based On Finite Element-infinite Element Coupling

Borehole-to-surface potential is a highly efficient exploration method using power supply in the well and surface observation,as a finite long-line current source to deploy power supply electrodes in the well,it can achieve the ideal exploration depth which is difficult to be achieved by traditional ground-ground observation method,and alleviate the limitation that the resolution of surface electric method decreases sharply with the increase of distance from electrodes,which becomes the residual oil exploration in high water-bearing period oil fields,the second opening of old mines and hidden ore bodies in crisis.In order to further improve the well electrical exploration method,we have developed a new method for the exploration of residual oil in high water-bearing fields.In order to further improve the theoretical system of well geopotential exploration and to improve the speed and accuracy of 3D inversion of well geopotential,this paper conducts an in-depth study on the 3D positive and negative inversion algorithm of well geopotential.In order to balance the3 D inversion accuracy and computational efficiency of well geopotential,this paper develops a finite element-infinite element coupling algorithm for3 D well geopotential from any line source,and carries out the analysis of the accuracy of total and anomalous potential inversion from any line source.To address the nonlinear characteristics and discomfort of well ground potential inversion,this paper constructs point-based,vertical line source and multi-well hybrid source observation methods,and discusses in detail the conventional regularization constraint,hybrid regularization constraint strategy and Gaussian noise in well ground potential inversion of 3D complex models.In this paper,the following work is carried out.(1)A coupled finite-element-infinite element inverse algorithm based on an unstructured grid is proposed to achieve an efficient and accurate inverse of the borehole-to-surface potential for a complex model with arbitrary line sources.The algorithm adopts the variational method to construct the generalized function polar problem of the three-dimensional Poisson equation,and combines the finite element based on the trilinear interpolation basis function and the infinite element strategy based on the special coordinate mapping function and interpolation shape function to realize the potential integration at infinity instead of the traditional boundary conditions.Compared with the mixed boundary condition finite element,the coupled finite-infinite element method has the advantages of high accuracy,the coefficient matrix does not vary with the source term compared with the mixed boundary condition finite element,the finiteelement infinite-element coupling method has the advantages of high accuracy and the coefficient matrix does not vary with the source term,which improves the orthogonal accuracy of small-scale models.(2)The surface anomalous potential response of borehole-to-surface potential under different observation methods,such as multi-point source,line-point source,line-line source and multi-well hybrid source,is studied.The results show that when the positive and negative excitation sources are used,the spatial location of anomalous potential densities and anomalies coincide more closely,which is more favorable to the accurate tracing of anomalies.(3)A borehole-to-surface potential inversion algorithm based on a hybrid regularization constraint strategy is proposed.The mixed regularization constraint combines Tikhonov regularization and Total variation(TV)regularization,and the inexact Gaussian Newton method is used to solve the mixed regularization objective function.The test results show that the algorithm combines the advantages of Tikhonov regularization and TV regularization,with high stability and strong noise immunity,and improves the iteration efficiency,inversion accuracy and adaptability of 3D inversion of borehole-to-surface potential in complex geological structure models.(4)The borehole-to-surface single-source and multi-well mixed-source borehole-to-surface potential inversion tests were carried out to unify the borehole-to-surface potential and ground electrical data for inversion,and trial calculations were performed for different theoretical models.The mixed-source inversion has good adaptability to complex geological formations.(5)The inversion algorithm was applied to the measured data,and good results were obtained,laying the foundation for further research.