Two-dimensional Anisotropic Forward Modeling And Axial Anisotropy Inversion For Resistivity Method

The processing and interpretation of electrical prospecting data is mainly qualitative analysis in the early stage.With the gradual maturation of two-dimensional and three-dimensional inversion techniques and the practical application,quantitative inversion has become the main means for the interpretation of measured data.As we all know,the current geophysical electrical prospecting is all based on the underground isotropic media,and based on this it has made many achievements in many aspects.For example,it has been widely used in geological prospecting,hydrogeological surveys,groundwater surveys,engineering surveys,environmental pollution surveys and treatment,etc.However,the electrical anisotropy is objectively existing in the underground.Compared with isotropic media,its influence on the distribution of underground current density is more complicated.Therefore,it is difficult to explain the anisotropic data with the isotropic theory and even difficult to explain.For isotropic resistivity,a scalar is generally described,and the anisotropic resistivity is usually represented by tensor.Due to the complexity of the theory of resistivity anisotropy,so far,both domestic and overseas are mainly based on the isotropic medium model to process and interpret the data collected from electrical prospecting.The research on the theory of anisotropy is still relatively small,and most of them still study the simple anisotropic models such as one-dimensional medium,and the research on complex conditions is still relatively small.While the actual underground medium is multi-dimensional and complex.Therefore,the two-dimensional anisotropic problem of resistivity method is studied in this paper.In this paper,the anisotropic resistivity is introduced in the forward algorithm study.Compared to the traditional scalar resistivity,the anisotropic resistivity is a tensor,which is calculated from the three principal axis resistivity and the three Euler angles.Then based on the basic equations of underground potentials,the differential equations and boundary conditions for potentials are deduced.The boundary value problem is transformed by Galilean method and finally solved by the finite element method.Through the solution of the TTI model example,the correctness of the forward algorithm is verified.Through several sets of forward modeling examples of anisotropic models,the influence of dips and anisotropic coefficients on the forward response was demonstrated.In the inversion algorithm,the two-dimensional inversion of resistivity method based on the same-homogeneous media is very mature.However,due to the complexity of the anisotropy,there are many inversion parameters,which leads to a strong multiplicity of inversion.Therefore,there are still few studies at home and abroad.Based on this,this paper considers only the inversion of the three electric spindles.Because the data space Occam method has a small amount of calculation and fast iteration,this paper uses this method for inversion research.And using this method to achieve the resistivity method of two-dimensional spindle anisotropy inversion algorithm.By using two sets of theoretical data to synthesize the model,the inversion effect of the algorithm is shown.Comparing with the calculation results of the isotropic media inversion algorithm,it shows that it is unreasonable to use the isotropic codes to invert the anisotropic data.