New Algorithm for Three-Dimensional Borehole-to-Surface Apparent Resistivity Imaging Based on Unstructured Mesh Finite-Element Method

In this paper, a finite-element method with unstructured mesh is used to numerically simulate the line source model of three-dimensional borehole-to-surface electrical potential method. A new total field potential is synthesized using the calculated anomalous field potential and the analytic solution of the background field. In solving for the original total field potential and background potential, this method can guarantee a small near-field error in the new total field potential without the need to densely mesh the region with the source. By comparing the synthesized total field and analytic solution, the high accuracy of the numerical solution is verified. The results of model calculation show that the detection effectiveness of the borehole-to-surface electrical method depends on the length of the line source. The detection effectiveness increases substantially with increasing length of the line source within a certain range. However, when the line source is excessively long, the increase in detection effectiveness for anomalies is insignificant. For a low-resistance anomaly of a given volume, the borehole-to-surface electrical method is more sensitive to changes in the lateral area than to changes in the thickness. When the gob contains only a small amount of water (e.g., Model IV containing 5% of water by volume), it will appear as a low-resistance anomaly. In addition, the detection of a water-logged gob by the borehole-to-surface electrical method depends on the depth and size of the gob. The borehole-to-surface method can accurately delineate the profile boundary of an anomaly, even though the side closer to the source is susceptible to the effect of source current. These results are significant for guiding the field exploration of the borehole-to-surface electrical method, improving result interpretation, and assisting the application.