Three-Dimensional Anisotropic Forward Modelling And Axial Anisotropy Inversion Research For Resistivity Method

Resistivity method is widely used in the fields of metal ore,environment,engineering,shallow hydrology,etc.Under normal circumstances,the underground target body is represented as a three-dimensional electrical structure,and the anisotropy of the medium is also objective.For the geo-electric model whose electrical distribution is anisotropic,it will inevitably cause great errors or even wrong results to analyze such problems using isotropic theory,which may mislead people's understanding of the real geological conditions.The data simulation of resistivity method at home and abroad is basically based on isotropic media,and the inversion and interpretation of anisotropic data is still in the study of one-dimensional or two-dimensional special models.There is very little research on general three-dimensional complex media.Therefore,it is very necessary to carry out three-dimensional forward and inverse study of resistivity anisotropy problem.For the forward modelling of the resistivity method,numerical calculations have been implemented using finite element method and finite difference method.The introduction of anisotropy changes the scalar resistivity in isotropic theory to tensor resistivity.The tensor resistivity is calculated using three principal axial resistivity defined in the spindle coordinate system of anisotropy and three Euler angles.The finite element splitting unit will directly affect the computing efficiency and accuracy of forward modeling.In this paper,three-dimensional finite element numerical simulation of resistivity model with arbitrary anisotropy is achieved based on an unstructured grid.Unstructured grids can adapt to complex geologic models and can achieve local encryption at the same time,which has outstanding performance in improving calculating accuracy and reducing memory loss.Great progress has been made in the three dimensional isotropic study of resistivity method.However,anisotropic problem is very complex.One reason is that there exist many inversion parameters and the other is the consequent non-uniqueness of the inversion result Therefore,the study of three-dimensional inversion of anisotropic resistivity data is quite rare.In this paper,we begin with the three-dimensional inversion of isotropic resistivity data and introduce borehole observation(borehole-surface and borehole-borehole)to improve the inversion result.Then we apply this well-to-well acquisition device to the three-dimensional anisotropic inversion.Besides,the paper also discusses the feasibility of interpreting anisotropic data using three-dimensional isotropic inversion algorithm;Then,on the basis of isotropic inversion,the objective function and Jacobian matrix in the inversion are modified,the gradient of the objective function and the “pseudo-forward” process are re-derived,and the anisotropy inversion of the principal axis of the resistivity method is finally completed.