Research On Forward And Inversion Of Induced Polarization In Borehole And Application

The borehole induced polarization(IP) method is one of the most popular and effective borehole geophysical methods to detect solid minerals, especially for the deep blind ore resources. The surface-borehole 5-direction measurement and borehole-surface sctioning are two most widely used ways in the borehole IP. However, these two measurements couldn’t always meet the practical needs, as the theories of the forward modeling and inversion still need to developed,the corresponding research results are insufficient, and the interpretation of the field data are not convincing sometimes. Focused on these problems,this thesis studied the forward and inversion strategy of the borehole IP developed some methods and get some research results.For the forward problem, this thesis provides the 3-D boundary value problem and variation equation satisfied for the electrical field from the partial differential equation and boundary condition satisfied for the 3-D point source steady electrical field, and solves the forward simulation of the borehole IP with finite element method (FEM)The discretization of the domain is realized by applying the unstructured tetrahedral meshes,this can decrease the amounts of the meshes and save the memory space.The developed numerical simulation software GID is applied to generating the unstructured tetrahedral meshes which can greatly increase the efficiency of the discretization.The implementation principle and specified steps of GID have been shown in details in this thesis.For the Sparse coefficient matrix of the linear equations developed from the finite element method, the compressed storage strategy is conducted. When storage the stiffness matrix, As the storage format CSR needs to konw the location information of the storage elements, there is no enough memory space for converting the stiffness matrix of the 3-D inversion process into CSR format. So this thesis simplifies the process of compression storage by using the storage format COO in transition, and then converting into the storage format CSR. And the thesis solves the final system of linear equations by using Krylov subspace methods and preprocessing technology.For the inversion problem, this thesis discusses the theories and implement methods of different inversion algorithms, and applies the results of the nonlinear conjugate gradient inversion method into the 3-D borehole IP inversion.Choose the BFGS correction formula of the Newton method to produce the preconditioner,and thus the diagonal elements can be calculated from the gradient of the object function and last iteration result.Under the strong Wolfe-Powell conditions, the number of the forward calculation iteration for the search step length.Use the advantage of the NLCG that only need to calculate the product of the patial derivatives and vectors, the method can greatly save the memory space and improve the speed of the inversion calculation.The thesis attempt to set the value range of the medium resistivity as the prior information and constraint condition.and apply the inequality constraint of model parameter range as the penalty function into the NLCG objective function. Compared with the ordinary 3-D resistivity inversion objective function,this method adds an inequality constraint which is simple and easy to be accomplished. the method effectively remove the redundant structure of the inversion images and reduce the multiplicities of the solutions. The inversion calculation results of different synthetic models shows that it’s more precise when applying the prior information of structural location into the 3-D inversion objective functions.The inversion accuracy is better when the inequality constraint of model parameter range is more accurate.In the surface-borehole 5-direction survey, as the data obtained by each measurement is not sufficient, the 3-D inversion show great multiplicity of solutions and couldn’t get the accurate inversion result. A more general inversion method is to optimize with some particular parameters by fitting the forward calculations. Thus this thesis will apply the joint inversion into the surface-borehole 5-direction survey data, which aims to increase the amount of measured data and reduce the multiplicities of the inversion results. Proved by the model simulation, the joint inversion can effectively reduce the redundant structures and improve the accuracy of inversion, but the resistivity and polarizability of the final inversion results are quite different from the true value, and the range of anomalous body matches not well with the real situation. Hence, the 3-D accurate inversion of the surface-borehole survey needs more measured data and prior information.The main innovative points of this thesis show as below,(1) when storage the sparse stiffness matrix, the thesis simplifies the process of compression storage by using the storage format COO in transition, and then converting into the storage format CSR. And the thesis solves the final system of linear equations by using Krylov subspace methods and preprocessing technology.(2) The thesis applies the research results of the nonlinear conjugate gradient inversion method into the 3-D borehole IP inversion,and completes the 3-D inversion program with FORTRAN language. Set the value range of the medium resistivity as the prior information and constraint condition,and apply the inequality constraints of model parameter range as the penalty function into the NLCG objective function, the method effectively remove the redundant structure of the inversion images and reduce the multiplicities of the solutions.(3) The joint inversion with surface-borehole 5-direction survey data can improve the accuracy of the 3-D surface-borehole inversion result...