基于非结构网格有限元的三维井地电阻率法任意各向异性正演模拟

地层介质的电各向异性增加了井地电阻率法响应的复杂性, 开展基于电各向异性介质模型的井地电阻率法响应规律研究对于正确解释各向异性显著地区的观测数据特征至关重要.针对垂直线源井地电阻率法的任意各向异性响应模拟问题, 本文提出了一种基于非结构网格有限元三维正演算法, 通过引入3×3的对称正定张量来表征任意各向异性的电导率, 采用非结构四面体网格有限元方法来离散电位的边值问题, 通过将垂直线源等效为一系列点源问题, 进而实现了任意各向异性介质中井地电阻率法的高效数值计算.通过与三个地电模型的解的对比, 验证了本文数值解算法的精度和有效性.针对线源远离和垂直穿过异常体的两类模型, 分别考察了当围岩或异常体为各向异性介质时的井地视电阻率响应特征.结果表明, 对于各向异性地层, 围岩和异常体的主轴电阻率值和旋转角均会对井地视电阻率的幅值及分布产生显著的影响.研究结果对于提高井地电阻率法的认识和资料解释水平具有重要的理论和实际意义.

Arbitrarily anisotropic forward modeling of the 3D borehole-to-surface resistivity method based on unstructured grid finite element

The electrical anisotropy of the formation medium increases the complexity of the response of the borehole-to-surface resistivity method. It is of great importance to study the response law of the borehole-to-surface resistivity method based on the electrical anisotropy medium model to correctly interpret the characteristics of the observed data in the areas with significant anisotropy. Aiming at the simulation problem of arbitrary anisotropy response of vertical line source borehole-to-surface resistivity method, this paper proposes a three-dimensional (3D) forward modeling algorithm based on the unstructured grid finite element. A 3×3 symmetrical positive definite tensor is introduced to characterize the electrical conductivity of any anisotropy. The unstructured tetrahedron grid finite element method is used to discretize the boundary value problem of the electrical potential. By equating the vertical line source to a series of point source problems, highly efficient numerical calculation of the borehole-to-surface resistivity method in any anisotropic medium is further realized. The accuracy and effectiveness of the numerical solution algorithm of this paper are verified by comparing with the solutions of three geoelectric models. For the two types of models where the line source is far away from and vertically passes through the anomaly body, the response characteristics of the borehole-to-surface apparent electrical resistivity are investigated when the surrounding rock or the anomaly body is an anisotropic medium, respectively. The results show that for the anisotropic formation, both the main axis electrical resistivity value and the rotation angle of the surrounding rock and anomaly body have a significant impact on the amplitude and distribution of the borehole-to-surface apparent resistivity. The above research results have important theoretical and practical significance for improving the understanding and the data interpretation of borehole-to-surface resistivity method.