Three-Dimensional Anisotropic Inversion for Direct Current Resistivity Method Using Unstructured Tetrahedral Discretization

Abstract

Many rocks exhibit electrical anisotropic characteristics, leading to artifacts in isotropic inversion of dc resistivity data. To mitigate this issue, we employ the flexible unstructured finite element (FE) method for 3-D anisotropic forward modeling and anisotropic inversion for dc resistivity data. Synthetic inversions further validate algorithm feasibility. The code not only replicates the inversion of principal axis resistivities accomplished by previous researchers but also reconstructs challenging all angle parameters. Comparative analysis of inversion using isotropic and arbitrary anisotropic assumptions reveals that anisotropic inversion accurately recovers the parameters. Models comprising conductive and resistive targets, respectively, are utilized to stimulate two realistic scenarios. The angle parameters of conductive target are challenging to recover compared to a conductive one with the same anisotropy. We conduct comprehensive experiments to assess the results across various data types. Borehole-generated data enhances the principal resistivities resolution, aligning with the direction of the lines connecting to the boreholes, rather than all ones, whereas conventional surface configurations are unable to accurately capture discrepancies between principal resistivities and Euler angles. Moreover, the investigations confirm the resolvability of each anisotropy component, especially angle parameters, which depend on borehole distribution. These experiments on data-acquisition configurations greatly enhance the practical possibility of successfully collecting data containing anisotropy information, achieving reconstruction of angular parameters, and obtaining better images of principal axis resistivity in practical applications. Even with the correct anisotropic assumption, unreasonable data-acquisition configurations produce inversion results with distortion. Testing with the model containing multiple anisotropic targets further confirms the algorithm’s effectiveness.