井中地電阻影像探測法鏡像效應之研究與對策

Countermeasures for Symmetric Effect in Borehole Electrical Resistivity Tomography

王浩然(Hao-ran Wang)

指導教授 ： 林志平

國立交通大學/工學院/土木工程系所/碩士(2017年)

摘要

地電阻影像探測方法，尤其是地表電探的方法以及被成功地應用到很多領域。關於井孔地電阻方法的研究主要致力於應用，而忽略了在井孔電探方法中的一些理論問題。井孔電探主要包括井對地和跨孔兩種施測模式。由對稱形態的靈敏度所導致的鏡像效應是存在于井孔電探中的特殊的陰影效應。在本研究中，澄清了鏡像效應產生的根本原因，同時也提出了兩種方法來解決鏡像問題。
本論文首先對井孔電探進行了文獻回顧。當使用傳統電極排序時，鏡像效應會產生。並且它很難被消除即使使用加權反演的方法。基於內外靈敏度參數計算的聯合反演的方法能夠減小鏡像效應，但其計算方法以及選擇程序非常複雜。通過排序函數選擇出來的優化序列致力於提升解析度和靈敏度，而一些物理問題是無法被優化序列解決的。
在地對孔的部分，討論了幾乎所有可能的地對孔的序列。通過靈敏度的繪製以及每一個序列的反算結果，鏡像效應產生的根本原因被發現是一個電流極和一個電位極同時存在於孔內所造成。在本研究中，首次定義了一個參數來評估每一個地對孔的序列抵抗鏡像的能力大小。基於這個參數以及每個序列的特性，優化的資料組合被選擇來進行聯合反算，并得到了較好的結果。同時加權模型疊加也被用來解決鏡像問題，且不需要預備知識以及計算相關參數。
在跨孔的部分，同樣也討論了幾乎所有可能的跨孔序列。并將它們與前人提出的優化序列以及常用的Bipole-Bipole序列進行了比較。鏡像效應產生於跨孔中的原因與地對孔是一樣的，並且所提的方法同樣可以解決在跨孔中存在的鏡像效應。同時，跨孔的反算模式被重新檢核以及改進。通過一般反算模型與擴展的反算模型的結果的比較，修正了跨孔反算中的邊界條件。
總而言之，本研究揭示了鏡像效應的根本原因並且提出了解決的辦法。未來的研究應該要更多地考慮現地實作的雜訊的影響來提高資料品質。

關鍵字

井孔電探 ； 鏡像效應 ； 聯合反演 ； 加權模型疊加 ； 優化方法

並列摘要

Electrical resistivity tomography (ERT) method, especially surface ERT method has been successfully applied in many fields. Researches about the borehole electrical resistivity tomography (BHERT) method were mostly concentrated on the applications, while ignored the theoretical problems in the BHERT. BHERT method mainly consists of borehole-to-surface and cross-hole method. Symmetric effect which is caused by the symmetrical sensitivity pattern is a special type of shadow effect in the BHERT method. The root cause of the symmetric effect was clarified and two countermeasures for symmetric effect were proposed in this research.
Literatures about BHERT were reviewed in this research firstly. The symmetric effect exists when using the conventional configurations. And it was difficult to be removed even if the weighted inversion method was used. Combined data inversion method based on the in-panel/off-panel sensitivity calculation can reduce the symmetric effect, but the selection procedure was complex. Optimized arrays selected through special ranking functions were mainly focused on the enhancement of resolution and sensitivity, while some physical problems in the ERT method cannot be solved by using the optimized arrays.
In the part of borehole-to-surface ERT, almost all possible borehole-to-surface electrode configurations were discussed. Through the sensitivity plot and the inversion results of each configuration, it was found that the concurrently exist of one current pole and one potential pole in the borehole would lead to the symmetrical sensitivity pattern in the inverted profile. And it was the root cause of the symmetric effect. An index was firstly defined in this study to evaluate the capability of each borehole-to-surface configuration to resist the symmetric effect. Based on this index and the characteristics of each configuration, optimal dataset was selected to conduct the combined data inversion, and then better results were obtained. Weighted model stacking technique which did not need the pre-knowledge of the subsurface was also proposed to solve the symmetric effect.
As for the part of cross-hole ERT, discussions were also performed on all possible cross-hole configurations. And these configurations were compared with the optimized dataset proposed by previous researchers and the mostly used Bipole-Bipole array generated from the AGI software. The root cause of symmetric effect was found to be the same as in the borehole-to-surface measurements and the proposed countermeasures also worked in cross-hole method. Meanshile, inversion scheme of cross-hole ERT was examined and modified in this study. From the comparison of the general and the extended inversion model, the boundary condition in the inversion process was corrected.
Above all, this research unveiled the root cause of symmetric effect and proposed effective countermeasures. Further investigations should consider the field noise in order to enhance the data quality.

並列關鍵字

borehole ERT ； symmetric effect ； combined inversion ； weighted model stacking ； optimization

參考文獻

Bellmunt, F., Marcuello, A., Ledo, J. and Queralt, P., 2016. Capability of cross-hole electrical configurations for monitoring rapid plume migration experiments. Journal of Applied Geophysics, 124, pp.73-82.

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LaBrecque, D.J., Ramirez, A.L., Daily, W.D., Binley, A.M. and Schima, S.A., 1996. ERT monitoring of environmental remediation processes. Measurement Science and Technology, 7(3), p.375.

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