## 4 Results and Analysis of Three-Dimensional Forward Modeling
### Detection of Water-Bearing Trap Columns by Cross-Hole EM with Multiple Grounded-Wire Source  
In practical exploration, multiple boreholes are typically present within roadways. These boreholes can be used to deploy receivers for the 2D observation of anomalies, as illustrated in Figure 14. The survey consisted of five lines, arranged in a fan-shape within the x-z plane, with a 15\({}^{\circ}\) angular separation between adjacent lines. Each line had 41 electrodes, spaced 2 m apart. The grounded-wire source, 85 m in length, was positioned at a 60\({}^{\circ}\) angle to the survey plane. Between the grounded-wire source and the survey lines lay a dome-shaped trap column, with a resistivity of 1 \(\Omega\cdot\)m, a height of 20 m, and a top and bottom radius of 6 m and 12 m.  
Figure 11: Multi-channel and difference curves for cubic anomalies (**a,d**) close to the transmitters; (**b,e**) on the inner side and close to the survey line; and (**c,f**) on outer side and close to the survey line. Figure 12: The positioning of the two anomalies (**a**) along the centerline between the grounded-wire source and the survey line and (**b**) near the survey line. We present contour maps of the electric field responses for the five survey lines at different time steps, based on two models: the full-space model (Figure 15a-f) and the trap column model (Figure 15g-l). Both models share the same color bar for each time channel, with the locations of the trap columns indicated by white dashed lines. As the survey lines diverge from the grounded-wire source, the distance between them increases along the receiver coordinates. In the full-space model, the electric field decrease as the distance increases. However, in the trap column model, the presence of the water-bearing trap alters the electric field distribution, creating a low-value band in the trap column and generating high-value anomalies beyond the boundary. This effect becomes more pronounced over time, leading to a broader range of electric field response values. Figure 14: Model of water-bearing trap column and three-view drawing. Figure 13: Multi-channel electric field and differential curves for two cubic anomalies: (**a,d**) aligned along the centerline between the grounded-wire source and survey line; (**b,e**) located near the survey line with both anomalies of low resistance; (**c,f**) located near the survey line with one anomaly of low resistance and the other of high resistance. Similarly, we performed differential calculations of the electric field in Figure 16. For the full-space model, the color bar has a broad range of values, resulting in differential results with minimal variation. In contrast, the electric field parameters from the trap column model more clearly delineate the location of the low-resistance anomaly, which appears as a negative center, with positive regions on either side. This differential analysis demonstrates that the anomaly boundary could be more precisely localized through first-order differential calculations. In this study, comparisons with other configurations were also considered. However, due to the need to control for a single variable, direct comparisons between MTEM and STEM methods were not straightforward. To address this, we adopted the RBTEM method, which is based on boreholes. In this setup, the transmitting coil (orange line) was placed in the roadway, with a side length of 5 m, as shown in Figure 14. The measuring electrodes remained positioned in the borehole, and the location of the water-bearing trap column was consistent with that in the previous example. As a result, we obtained the contour maps of the EMF. Figure 17a-f display the responses for different time channels for the full-space model without anomalies, while Figure 17g-l show the responses of the water  
Figure 16: Contour plots of first-order difference in electric field obtained by (**a–f**) full-space model and (**g–l**) water-bearing trap column model.