A Multi-Mesh Approach for 3-D Arbitrary Anisotropic Inversion of Direct Current Resistivity Method

The three-dimensional arbitrary anisotropic inversion algorithm for direct current (DC) resistivity method is developed based on unstructured meshes and L-BFGS optimization, enabling the simultaneous recovery of all independent anisotropic parameters. To enhance robustness and decrease inversion non-uniqueness, distinct meshes are employed for forward modeling and inversion. A novel mesh-assignment strategy is introduced, where inversion meshes for individual anisotropy parameters are aligned specifically with the directional resolution inherently provided by the surficial data. This approach eliminates the conventional requirement for symmetric surficial configurations in three-dimensional DC resistivity anisotropic inversion based on unstructured meshes. Furthermore, to stabilize inversion updates, a volume-weighted method is implemented to compute the objective function gradient on the coarse inversion mesh by aggregating contributions from the finer mesh. This prevents the gradient of one particular parameter from dominating the optimization process due to unbalanced accumulation, a common issue in traditional direct summation strategy, resulting in a more reasonable update of anisotropy parameters and ensuring the reliable recovery of principal resistivities and orientation angles. Five anisotropic inversions with distinct mesh strategies were performed for each model. Comparative analysis based on synthetic data confirms the effectiveness of the proposed approach in improving anisotropic inversion accuracy and resolution, especially in distinguishing between principal resistivities and angle. These results validate both the practicality and reliability of the proposed approach.