2.5-d Dc Resistivity Modeling By The Adaptive Finite-element Method With Unstructured Triangulation

The commonly used finite-element method in DC resistivity modeling generally leads to the following deficiencies.First, the model discretizaiton is implemented mostly by the artificial work, i.e.,the accuracy is determined greatly by the author's experiences.Then, the generally employed finite element is hexahedron for 3-D model,rectangle for 2-D model or hexahedron based tetrahedral and rectangle based triangle.Bu using the above mentioned elements,the accuracy can achieve the requirement when the geology structure is not complex.Once the complicated topography or the irregular heterogeneity is considered, the large discretizaiton error cased by using these regular elements will greatly decline the accuracy. Finally, the traditional way for model discretizaiton makes the local refinement, for instance, around the source point, inflexible.This problem will be more obvious when modeling the large-scaled problem, since the refinement from one direction may incur many new nodes generated by which the efficiency will be greatly deduced.Aiming at solving the above problems,the rigorous unstructured triangulation is used for modeling discretizaiton to make the simulation more flexible.Moreover, since the potential field decreases sharply around the source point, the refinement is necessary to perform to guarantee the accuracy. The gradient-based a-posteriori error estimator is employed to predict the new element size for the optimal mesh.Through combing the unstructured triangulation and this error estimator the efficiently adaptive refinement is accomplished.To validate our algorithm, some synthetic models are tested.From the visualized meshes,it is seen that the areas like near the source point is greatly refined.By contrast, the node distribution far away from the source points is correspondingly sparse by which the accuracy is distinctively improved without inserting too much nodes.In addition, the numerical results show that using the error estimation will make the finite-element solution converge to the analytical solution in a few iterations (generally no more than 3).Thus the accuracy and efficient of our algorithm are distinctively demonstrated. The whole iteration process does not need any manual control which makes our algorithm more universal.Based on the above validation, the impact of discrete wavenumbers to the accuracy is addressed in the following section. By analyzing the errors calculated using the commonly used wavenumbers, an improved algorithm for the selection of the wavenumbers is proposed. Through comparison, it is found that our enhanced technique is much superior to the conditional method by which its reliability is certified.