Anomaly edge enhancement and topographic correction technology of linear source 3D borehole-to-surface electrical method
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摘要: 基于非结构网格有限元方法开展了三维复杂地电模型的线源井地电法的高效正演模拟研究，探讨了通过求取电场响应导数来刻画目标体边界范围、采用差异场地形校正技术来消除地形影响等措施对井地电法成像的效果和精度的影响。并通过对比与解析解，验证了本文数值解算法的有效性。模型计算结果表明：积水巷道的空间位置和走向均会引起视电阻率的显著变化，视电阻率变化率的极值准确且清晰地指示了巷道边界的位置；电位的归一化总水平导数极大地提高了井地电法对目标体复杂边界位置的识别能力；地形对井地电场分布的影响也很大，其视电阻率响应与地形形状近似呈对称关系，利用差异场技术能有效地削弱地形对井地电法高精度成像的影响。Abstract: Based on the finite element method of unstructured grid, the efficient forward modeling of the borehole-to-surface electrical method derived by the linear current source under the condition of the 3D complex geoelectric model was carried out. The effects on the effectiveness and accuracy of the borehole-to-surface electrical method imaging were discussed by obtaining the electric field response derivative to characterize the boundary range of the target body, and using the difference field topography correction technology to eliminate the topographic influence. And the comparison between the numerical solution and the analytical solution verifies the effectiveness of the algorithm in this paper. The model calculation results show that the spatial position and direction of the roadway with water accumulation cause significant changes in the apparent resistivity, and the extreme value of the apparent resistivity change rate accurately and clearly indicates the boundary position of the roadway. The normalized total horizontal derivative of the electric potential greatly improves the ability of the borehole-to-surface electrical method to identify the complex boundary position of the target body. Moreover, the influence of topography on the distribution of borehole-to-surface electrical field is also serious, and its apparent resistivity response is approximately symmetrical to the shape of the topography. The difference field technique can effectively weaken the influence of topography on the high-precision imaging of the borehole-to-surface electrical method. The research results have important theoretical and practical significance for improving the data interpretation level and application effect of the borehole-to-surface electrical method.
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图 1 均匀半空间模型的电极布设及计算结果
（a） 电极布设；（b） 数值解与解析解对比及其相对误差；（c） 电流密度lgJ （单位为A/m2）分布
Figure 1. Electrode layout and calculation results of uniform half-space model
（a） Electrode layout；（b） Comparison of numerical solution with analytical solution and their relative error； （c） Distribution of current density lgJ （unit in A/m2）
图 2 模型的剖面（a）和平面（b）以及测点分布（c）示意图
Figure 2. Schematic diagram of profile （a） and plane （b） of the model and distribution of measuring points （c）
图 4 模型的剖面（a）和平面（b）示意图
Figure 4. Schematic diagram of profile （a） and plane （b） of the model
图 5 巷道模型地表视电阻率平面等值线图（白色方框代表巷道在地表的投影）
（a） 模型1；（b） 模型2；（c） 模型3；（d） 模型4
Figure 5. Contour maps of apparent resistivity on surface of roadway model where the white box represents the projection of the roadway on the surface
（a） Model 1；（b） Model 2；（c） Model 3；（d） Model 4
图 6 巷道模型视电阻率一阶导数曲线图
Figure 6. Curves of the first-order derivative of apparent resistivity of the roadway models
图 7 巷道模型3的视电阻率二阶导数曲线图
Figure 7. Curve of the second-order derivative of apparent resistivity of the roadway model 3
图 9 平面等值线图
（a） 电位；（b） 视电阻率；（c） 异常电位；（d） 电位总水平导数的负对数；（e） 电位的归一化总水平导数
Figure 9. Plane contour maps
（a） Electric potential；（b） Apparent resistivity；（c） Abnormal electric potential；（d） Negative logarithm of the total horizontal derivative of the electric potential；（e） Normalized total horizontal derivative of the electric potential
图 10 地形模型的剖面（a）和平面（b）示意图
Figure 10. Schematic diagram of profile （a） and plane （b） of the topographic model
图 11 当地垒（a，c）和地垫（b，d）深为20 m （上）和40 m （下）时纯地形模型地表视电阻率等值线图
Figure 11. Surface apparent resistivity contour maps of pure topography model with horst （a，c） and graben （b，d） being 20 m （upper panels） and 40 m （lower panels） deep
图 13 带地形模型的剖面（a）和平面（b）示意图
Figure 13. Schematic diagram of profile （a） and plane （b） of the topography model
图 14 地垒（a）和地堑（b）地形未校正的地表视电阻率等值线图
Figure 14. Contour maps of surface apparent resistivity for uncorrected horst （a） and graben （b）
图 15 地形校正之后以及水平地表模型的视电阻率等值线图
（a） 地垒地形校正后；（b） 地堑地形校正后；（c） 水平地表模型
Figure 15. Apparent resistivity contour maps after topography correction and without topography
（a） After topography correction for horst；（b） After topography correction for graben； （c） Model results without topography
图 17 地形校正前（a，c）、后（b，d）的视电阻率（上）和视电阻率归一化总水平导数（下）
Figure 17. Apparent resistivity （a，c） and normalized total horizontal derivative of apparent resistivity （c，d） before （upper panels） and after （lower panels） topographical correction
表 1 巷道规模及位置
Table 1. Roadway scale and location
模型 巷道规模 巷道左侧距源/m 长/m 宽/m 高/m 1 200 20 10 100 2 200 20 10 0 3 20 200 10 100 4 500 20 10 −200 
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