The2D Forward Modeling And Inversion Of Direct Current Resistivity Method Based On Correction For Singularity And Boundary Condition

The advantage of finite element method is its ability to handle topography. Direct current resistivity method uses a artificial current sources, the potential falls off rapidly near a source. Thus, leading the simulated results in the places near the source locations performs a bigger error phenomenon. The simulated potential at grid nodes cannot be able to represent the change features of real electrical field. This phenomenon is called source singularities. Therefore, to reduce the influence of source singularities, this paper introduces a correct algorithm called BC/singularity correction algorithm. This correct algorithm not only can improve the accuracy near source electrode, but also can reduce errors associated with boundary condition. Based on the governing equation of stable electrical current flow field, variational equations corresponding to boundary value problems are obtained. The integral area is discretized into rectangle elements. The potential value of grid nodes solved from equation formed by the forward operator matrix is corresponding to a wavenumber. The regularization value directly affects the stable and accuracy of the inversion process. A higher value will generate a smoother model and cannot reflect small structure, while a lower value will generate a rougher model and possibly introduce untrue geological structure. It needs perform inverse Fourier transform to calculate the potential in the spatial domain. The wavenumber and corresponding weight coefficient is obtained by optimization method. Least square smooth constraint method is used to invert the DC resistivity data. In the process of inversion iteration, we use active constraint balance (ACB) method to calculate the value of regularization parameter. The regularization parameter value is adjusted according to the model resolution matrix and the number of iteration. Thus the artificial factors can be avoided. The basic principle of ACB is assigning a relative larger value of Lagrangian multiplier to parameter which performs poor resolving power, and assigning a relative smaller value of Lagrangian multiplier to parameter which performs high resolving power. In this paper, we complete least-squares adaptive regularization smoothness constraint inversions for DC resistivity data. Numerical experiments with synthetic data and field data demonstrate the validity and accuracy of the forward and inversion scheme.