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

Zhitao Xiong,Weizhong Qiu,Xingong Tang,Lianqun Zhang,Chunyan Zhao

doi:10.1109/access.2019.2961806

Abstract

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.

Highlights

The borehole-to-surface electric potential method possesses the advantages of both ground surface and borehole electrical prospecting methods
The calculations made use of the new method of the total field potential synthesized from the pure anomaly field and the analytic solution of the background field
This investigation led to the following important conclusions after studying the roles of the length of the line source, the vertical and horizontal size of the low-resistivity anomaly, the volume fraction of water in the gob, and the burial depth

Summary

INTRODUCTION

The borehole-to-surface electric potential method possesses the advantages of both ground surface and borehole electrical prospecting methods. Li et al [10] completed the calculation of the 3D borehole-to-surface potential response with terrain using the finite-element method of unstructured mesh and simulated the anomalous surface potential distribution for different locations of the point source relative to the anomaly. Wang et al [33], [34] succeeded in inverting the borehole-to-surface potential model with an inequality-constrained, nonlinear conjugate gradient method and simulated the response features of apparent resistivity and apparent polarization of a line source 2D borehole-tosurface model with terrain using the finite-element method with unstructured mesh. We use a finite-element method with unstructured mesh to study the effects of line source length, horizontal and vertical scale change of the model, and the percentage of water in the gob on the detection of anomalous bodies, and discuss the potential and apparent resistivity response characteristics of.

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CONCLUSION