*4.3. Discussion*

2D ERT assumes that the geological formation is a 2D semi-infinite space. However, in the real state of geological formation, the electric current flows in the 3D (X, Y, Z) direction, therefore, the object in the non-2D section has a certain degree of disturbance to the ground resistivity electric field, thus causing some irregular resistivity and noise on the 2D profile [8], which is called the 3D effect. Many scholars have adopted indoor sandbox experiments to conduct 2D ERT. As a result, a space with boundary constraints is formed. The current transfer is affected by the boundary, and causes some irregular resistivity and noise on the 2D profile, which is called the boundary effect. Most scholars will often choose to evade the 3D effect and boundary effect when performing 2D ERT. Few scholars had made in-depth discussions on the 3D effect and boundary effect. Mei, Xing-Tai used a homogeneous thickness model made from dough to explore the indoor test method and criteria for 2D ERT where. The results of this study and that of Mei, Xing-Tai (2001) both found that the 2D resistivity profile had a boundary effect. Mei, Xing-Tai found that the sandbox experiment needed to have twice the distance of spread to avoid the boundary effect. This study found that the boundary effect had a distance of about 6–8 m. Yang and Lagmanson used a numerical simulation to build a model with three different resistivity blocks, and placed a 2D and 3D survey line on the surface of the model. The results showed that the 2D resistivity profile was mapped by surrounding resistivity blocks and exhibited an irregular resistivity distribution; however, the 3D resistivity profile was not affected [8]. The results of this study and that by Yang and Lagmanson (2006) both showed that the 2D resistivity profile had a 3D effect. After deeper analysis, the study found that the influence distance was 8–6 m, and that the three-dimensional effect was not obvious after the distance limit of 8 m. Lin et al. conducted 2D ERT at the Hsin-Shan Earth Dam in Taiwan where during the measurements, it was found to be affected by the changes of the nearby stratum and geocenter as well as the curtain grouting wall of the Hsin-Shan Earth Dam, which was at 45 degrees with the survey line. As the 2D resistivity profile had a 3D effect, the authors established the 3D forward modeling of the Hsin-Shan Earth Dam, and compared the differences between the 2D resistivity profile after inverse computing and the Hsin-Shan Earth Dam model. The results showed that the 2D resistivity profile was indeed affected by the 3D effect and had an irregular resistivity distribution [10]. Both the results of this study and Lin et al. (2013) found that the 2D ERT had a 3D effect. However, the results of this study explored the effects of various influencing factors on the 3D effect and boundary effect in depth, and should be avoided as much as possible in future detection.

In summary, most of the studies that have explored the 3D effect and boundary effect have mostly been to discover and confirm the existence of the 3D effect and boundary effect, or to explore the effects of the 3D effect and boundary effect on a single parameter. As a result, this study explored the effects of the 3D effect and boundary effect on 2D ERT through the parameters of the resistivity ratio, pipeline size, embedding depth, influence distance, and electrode spacing under different conditions and summarized these changes as conclusions and discussed them in detail. In this study, the 3D effect and boundary effect of the 2D resistivity profile were explored through numerical simulation. From the simulation results, good results were obtained, and the relevant results can be used to provide a reference for future detection.

#### **5. Conclusions and Suggestions**

ERT can provide the stratum 2D or even 3D resistivity profile to further understand the situation of stratigraphic change, but it is a big challenge to engineer the data interpretation of the ERT spatial resolution and testing result. One important phenomenon in the 3D effect that was observed whilst exploring the pipeline stratum model was the mapping phenomenon of the 3D effect of the pipeline stratum, which will produce an illusion of high and low resistivity in the 2D resistivity profile. The boundary effect will cause the resistivity value of the 2D profile boundary to abnormally increase, reduce resolution, and increase interpretation error. Through the model established in this study, it was found that there was roughly similar influence trend in the parameter analysis of the 3D and boundary effects. The following are suggestions for future testing.


Currently, the scope of this study is only to establish a numerical model. In the future, we will try to confirm the results of the numerical simulation through in situ testing.

**Author Contributions:** Conceptualization, C.-P.L.; Methodology, C.-P.L.; Modeling Y.-C.H.; Software, Y.-C.H. and C.-T.L.; Data analysis Y.-C.H.; Conclusions, C.-P.L. and Y.-C.H.; Electrology consultation, C.-T.L. and K.-W.W.

**Funding:** This study has no funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
