Three-Dimensional Forward And Inversion Of Direct Current Resistivity Method For Finite Volume Target

To develop better non-destructive detection technology,we implemented direct current resistivity(DCR)modeling approach to detect the finite volume target electrical structure in threedimensional.However,the application of electrical tomography technology to the non-destructive testing of concrete and other materials is rare in our country.As a vital branch theory of electrical exploration,DCR still plays an essential role in geology,minerals,hydrogeology,engineering,environment,archaeology,and other exploration fields closely related to human social life.However,the current application of DCR to the electrical structure detection and imaging of the finite volume target conductive medium is seldom.Therefore,to solve the above problems,we have developed the DCR to detect the 3D electrical structure of the limited volume target forward modeling and inverse research.If we want to solve the forward problem,we must establish the correct boundary value problem.Since the surface of the target is in contact with the air,we choose the Neumann boundary condition.After establishing the boundary value problem,I implemented the unstructured Finite Element Method to direct current resistivity forward modeling in three-dimensional.In this way,we can get the electric potential distribution of the entire observation field.Taking the cube model as an example,I compared my forward calculation results with adam’s forward calculation results,and,subsequently,established a different resistance model.We can see that the electric potential has recovered to a certain extent,indicating that the algorithm is effective.Calculating the forward response of the high-resistance model,low-resistance model,and 3D complex combination model provides the basis for 3D Inversion.The 3D inversion adopts the L-BFGS based on unstructured grids.The L-BFGS inversion is a regularization inversion,which constrains the model space,adopts a new model smoothing strategy,derives the smoothness operator on the unstructured grid in the finite element,and introduces the L2 norm to define the smoothness of the model.The L-BFGS inversion method improves the inversion effect,mainly reflected in saving calculation space,accelerating the calculation speed,and excellent imaging results.The development of the forward and inverse algorithm of this subject finally provides a new method for detecting the electrical structure of a finite target body and a new way for the development and application of the resistivity method.