## 2 Methods and Simulation of Boulder Detection Using Cross-Hole ERT
### Numerical Examples  
This algorithm was applied to a synthetic resistivity model, which was designed to obtain knowledge about the value of the weighting factor for the detection of boulders. The model included two boreholes, 8 m apart and 30 m in depth, located in a 100 \(\Omega\)-m homogeneous half-space. One cable with 60 electrodes was installed in each borehole, and the electrode spacing was 0.5 m. Considering that boulders are characterized by high resistivity, the model was set up for targets of 1000 \(\Omega\)-m within the half-space. Following this, the inversion results showing whether the weighting factor should be added or not were contrasted to show whether the distinguishability had been improved. According to actual engineering situations, the side length of abnormal bodies buried below 10 m is usually no more than 1 m, while the side length of abnormal bodies buried above 15 m is usually about 2 m. Based on this, we design three numerical simulation examples. In each figure that follows, the geoelectrical models were obtained by the multi-configuration combination and weighted inversion of a multi-configuration combination. We placed four targets in the first example. Two square targets with a side length of 1 m were placed at 5 m, and the other two square targets with a side length of 2 m were placed at 16 m and 19 m. The results, which include the four targets, is presented in Figure 3. Comparing Figure 3b,c, the deepest target can be identified by increasing the weight factor, and the boundary of the deep boulders is clear. Furthermore, we can see that the resistivity inversion of the shallow anomalous body was about 280 \(\Omega\)-m and that of the deep anomalous body was more than 500 \(\Omega\)-m. Figure 4 presents the geoelectrical models with three targets with a side length of 1 m set at 3 m, 6 m, and 9 m, and three targets with a side length of 2 m are set at 15 m, 18 m, and 21 m. Comparing the result with no weighting factor (Figure 4b) and the result when using the weighting factor (Figure 4c) showed that the resolution was improved. When no weighting factor was added, the target bodies near-surface could not be clearly distinguished from the background and the result could not identify the boundaries of the three deep targets. Contrastingly, the model using the weighted inversion (Figure 4c) showed the approximate position of each of the six targets and identified the boundary of the three deep targets' bodies. In addition, we found that the resistivity of the deeper anomaly was higher than that of the shallow anomaly in the simulation result. Similarly, the resistivity model, including six targets, with two scattered bodies near the surface and the other four deeper agimated bodies, is shown in Figure 5a. Two targets with a side length of 1 m were set at 3 m and 6 m, and four targets with a side length of 2 m were set at 15 m, 17 m, and 22 m. Only a deep body and a bar object can be seen in the result with no weighting factor (Figure 5b). Moreover, considering the volume effect of the electrical exploration and sensitivity distribution, the cross-hole ERT has good vertical resolution and weak horizontal resolution, and the resolution of the multiple targets at the same horizontal position is limited (Figure 5c). Figure 4: Simulation result with six targets, which included three near the surface and others deeper: **(a)** model (background: 100 \(\Omega\)-m; simulated boulder (high resistivity anomaly): 1000 \(\Omega\)-m); **(b)** the results of the multi-configuration combination; and **(c)** the results of the weighted inversion of the multi-configuration combination. Figure 5: Simulation result, including six targets, with two near the surface and the other four deeper: **(a)** model (background: 100 \(\Omega\)-m; simulated boulder (high resistivity anomaly): 1000 \(\Omega\)-m); **(b)** the results of the multi-configuration combination; and **(c)** the results of the weighted inversion of the multi-configuration combination.