## 2 Methods and Simulation of Boulder Detection Using Cross-Hole ERT
### Multi-Configuration Combination, Based on Weighting Factor  
According to the analysis of [PERSON] and [PERSON] [23], the signal of the bipole-bipole array is stronger and sensitive, even for a relatively small target. However, when the environment becomes more complex, the resolution of the array can be reduced. While, the resolution of the pole-tripole array is excellent, even in a complex environment, but the results of some studies featured many artifacts. Furthermore, [PERSON] and [PERSON] [18] found that a disadvantage of the dipole-dipole array is that the potential difference measured by this array is smaller and more easily masked by noise, which in turn decreases the resolution.  
Considering the cumulative factors of these three measurement techniques, the electrical resistivity measurement chosen was a multi-configuration combination, consisting of the three cross-hole configurations as described above, including a dipole-dipole array, bipole-bipole array, and pole-tripole array. The electrode spacing of the dipole-dipole array varied within the interval, which was guaranteed to collect more overall data. Moreover, the spacing of the electrodes of the bipole-bipole array was 2 m, while for the pole-tripole array it was 1-3 m. The test applied this multi-configuration combination, featuring the superposition of all three cross-hole configurations, to perform the numerical calculations.  
At the same time, in order to equalize the participation of the data of each configuration, a particular weighting factor was introduced to improve distinguishability [24]. The magnitude of the weighting factor was based on the Jacobian matrices, \(J_{A}\), \(J_{B}\) and \(J_{C}\), of the three configurations. Following previous research, in this study, the sum of the ratios between \(J_{j}^{A}\) and \(J_{j}^{B}\) gives the magnitude of the weighting factor, which is defined as Equation (1):  
\[J_{j}^{A}=\frac{\sum_{i=1}^{N_{A}}\left|J_{ij}^{A}\right|}{N_{A}},\ J_{j}^{B}= \frac{\sum_{i=1}^{N_{B}}\left|J_{ij}^{B}\right|}{N_{B}},\ J_{j}^{C}=\frac{\sum_ {i=1}^{N_{C}}\left|J_{ij}^{C}\right|}{N_{C}} \tag{1}\]  
\[b=\sum_{j=1}^{M}\frac{J_{j}^{A}}{J_{j}^{B}}(j\ =\ 1,2\dots M),\ c=\sum_{j=1}^{M} \frac{J_{j}^{A}}{J_{j}^{C}}\ (j\ =\ 1,2\dots M) \tag{2}\]  
\[J_{B}=J_{B0}*c,\ J_{C}=J_{C0}*c \tag{3}\]  
Figure 2: Sensitivity distribution of cross-hole ERT configurations: A and B represent the current electrodes, and M and N represent the potential electrodes: (**a**) dipole-dipole array; (**b**) bipole-bipole array; and (**c**) pole-tripole array.  
where \(A\) is the bipole-bipole array, \(B\) is the pole-tripole array, and \(C\) is the dipole-dipole array. By comparison of the numerical simulation tests, the results of selecting the bipole-bipole array as \(A\) were more accurate. Thus, \(b\) is the weighting factor of the pole-tripole array, and c is the weighting factor of the dipole-dipole array. Meanwhile, the weighting factor for the bipole-bipole array is 1. In this process, \(J_{j}^{A}\) are the average values of the absolute value of \(J_{ij}^{A}\), which is every element in one column of the bipole-bipole array; while \(J_{ij}^{B}\) are the average values of the absolute value of \(J_{ij}^{B}\), which is every element in one column of the dipole-dipole array or pole-tripole array. Finally, the Jacobian matrices were multiplied by the weighting factor, to balance the contribution of each of the arrays, as in Equation (2).