Research On Three-Dimensional Modeling Of Cross-hole Induced Polarization

The crosshole induced polarization(IP)method which observation device is placed underground deeply can effectively improve the exploration depth and the ability to find deep targets.With the study of deep prospecting methods and the development needs of well exploration,3D crosshole inversion has gradually become a new trend.Due to the limitation of computational efficiency and applicability of 3D forward and inversion,the data processing is still based on 2D inversion mostly,and 3D inversion is not widely used.Using the 2D crosshole inversion the underground structure can be obtained by the collected data of two adjacent wells.However,there are some shortcomings.First,the electric field response received by the well is from the 3D space,while the electric field record simulated under the 2D condition does not fully reflect the crosshole electric field information in the 3D space.In particular,the cross-hole electric field imaging in the 2D can only obtain the electrical structure of the plane where the two wells are located,rather than the lateral ones.That makes negative factors to interpret and evaluate the three-dimensional electrical structure.Second,two-dimensional imaging is only using two adjacent wells and the information of multiple wells distributed in three-dimensional space is not utilized,that causes the low utilization rate of the space well.In view of the above problems,this paper will carry out research on numerical simulation and inversion method of three-dimensional IP based on multi-hole data,which will help to obtain the true three-dimensional electrical structure and make up the shortcomings of current two-dimensional imaging.That will provides more realistic and accurate information for crosshole IP exploration,and also provides a basis for the data interpretation.In this paper,the research on three-dimensional forward and inversion of cross-hole IP based on finite element method is carried out.The finite element method is used to realize the forward calculation of the cross-hole IP.The non-uniform hexahedral meshing method is adopted,and the generated mesh is further refined by tetrahedron to improve the calculation accuracy.In the process of stiffness matrix synthesis,Comparing the computational efficiency of different strategies,the authors optimized the synthesis strategy of the stiffness matrix.For the finite element method to form large sparse linear equations,the iterative calculation of SSOR-CG is realized,and the calculation of 3D IP forward is completed.Considering the computational problem of large sparse linear equations formed in 3D modeling,the algebraic multigrid method is implemented to improve the calculation efficiency of large sparse linear equations.This paper presents a calculation process of RS roughening strategy on algebraic multigrid method and the calculation methods of interpolation operator,constraint operator,coefficient matrix and smooth iteration of virtual grids.Numerical experiments show the relationship among the convergence efficiency,the connected threshold and coarsening layers of the grids,which optimizes the parameters selection.The computational efficiencies of the SSOR-CG,AMG,AMG-CG and AMG-BCGSTAB algorithms are compared by numerical experiments,thus I find that AMG-CG and AMG-BCGSTAB algorithm have the highest computational efficiency,this indicates that the algebraic multigrid method can be a preconditioner of the traditional iterative method with higher computational efficiency and stability.For the inversion study of the crosshole IP,the L-BFGS optimization algorithm is introduced into 3D inversion.At first,the paper establishes of the inversion objective function,analysis selection and calculation problem of the model constraints and the regularization factor of the objective function.For the influence of grid on the inversion stability and computational efficiency,coarse mesh inversion and fine mesh modeling are implemented,which also improve the stability of inversion and computational efficiency.The computational problem of Jacobian matrix of objective function is analyzed.By adopting the method of “approximate forward modeling”,the computational resources are saved and the efficiency of inversion calculation is improved.In the L-BFGS algorithm,the strong Wolfe-Powell criterion is used to calculate the step size so as to achieve good results.Aiming at the multi-source problem,the Jacobian matrix calculation process of objective function and the algorithm of L-BFGS in multi-source problem are analyzed,which provides guidance for the realization of parallel computing.The MPI parallel strategy is used to realize the master-slave mode inversion with parallel computing.Through numerical experiments,the efficiency of MPI parallel algorithm for modeling and inversion is analyzed.When the computational core reaches 10 cores,the inversion acceleration ratio is up to 5.7 times.Finally,the correctness of the inversion procedure is verified by numerical calculations of several models.For the effect analysis of inversion from multi-source and multi-hole observations,it is found that the vertical resolution of this method is better,and the longitudinal position and shape of the anomalous body can be accurately inverted.The horizontal direction method is not as good as the vertical direction method,but it is also clearly inverted the position and shape of the anomalous body;for a low-resistance complex model,the basic shape of the anomalous body can be inversed,but there is an extra structure appears around the anomalous body.