## 4 Discussion  
### Determination of Damage Zone  
The statistical results indicate that the fracture frequency and rock strength on both walls of the XSHF hold an obvious relationship with the distance from the fault core (Figure 4). By observing the rock outcrops in the field, power-law function fitting, and comparing the rock properties in the damage zones with the rocks of the same type but undeformed (protolith zone) [50; 51], we can determine the extents and boundaries of the different types of damage zones associated with the XSHF (Table 1). When the fracture frequency of the rock mass is less than or equal to 20-30 fractures per cubic meter, such rock mass would be considered outside of the actual fault zone.  
In the TDZ (Profile V), the inclination of the rock on the NE wall within the range of 0-17.1 km changes from steep to gentle and the completeness of the rock mass changes from fragmented to blocky, indicating that the level of tectonic activity on the NE wall of the LHS has significantly decreased within the range. On the SW wall, due to the superimposed disturbance of the GZ-YSF and LHS, the fracture frequency has remained at a relatively high level within a distance of 20.8 km from the LHS (Figure 4c), and the rock is also fragmented (Figure 3a,c). Therefore, we believe that the boundary of the fracture zone on the SW wall of the XSHF tip is at about 20.8 km (Table 1). The damage zone boundary associated with the LDZ is more uniform, the fracture frequency decreased to less than 20 per cubic meter at distances of 16.1 \(\pm\) 0.1 km (Figure 4(b1,b2)) and 14.6 \(\pm\) 1.1 km (Figure 4(b1,b3)) from the SW wall and NE wall, respectively (Table 1). On both walls of WDZ, there is a composite  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multirow{2}{*}{**Profile ID**} & \multicolumn{2}{c}{**SW Wall**} & \multicolumn{2}{c}{**NE Wall**} \\ \cline{3-5}  & & **Width (km)** & \(n\) & **Width (km)** & \(n\) \\ \hline Wall damage zone & I & 16.1 & 0.39 & 12.7 & 0.42 \\ \hline \multirow{3}{*}{Linking damage zones} & II & 16 & 0.42 & 15.7 & 0.44 \\  & III & 16.2 & 0.30 & 13.5 & 0.34 \\  & IV & \textgreater{}8.9 & 0.31 & 15 & 0.36 \\ \hline Tip damage zone & V & \textgreater{}20.8 & 0.25 & 17.1 & 0.38 \\ Total & & \textgreater{}20.8 & 0.335 \(\pm\) 0.085 & 17.1 & 0.39 \(\pm\) 0.05 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The boundary of the damage zones of XSHF.  
disturbance of ZDS and YLS (Figure 2a), but the distance between the NE boundary and the KDS is 12.7 km, which is less than the 16.1 km of the SW wall (Table 1). This seems to indicate that the different damage widths of the two walls are affected by the fault activity, as the activity rate of the YLS is 1.05 \(\pm\) 0.45 mm/yr [52], which is smaller than that of ZDS, which is 4.1 \(\pm\) 0.7 mm/yr [53].  
We can see that there are obvious differences in the widths of different damage zones and damage zones in the two walls of the _XSHF_, i.e., TDZ \(>\) LDZ \(>\) WDZ and SW wall \(>\) NE wall (Table 1). Previous studies have indicated that the asymmetry of the damage zone may include the deformation history [54; 55], geometrical spreading [4], seismic rupture [56], stratigraphic lithology [57], and so on. Considering the difficulty in calculating the surface rupture caused by frequent earthquakes along the XSHF, as well as the fact that the lithology of hard rocks such as sandstone and granite is relatively single, we discussed the differential distribution of the damage zones of the XSHF caused by stress distribution and fault activity.