## 2 Materials and Methods
### Source Model
#### 2.2.2 Slip Model 2  
The scaling relationships of earthquake rupture models are based on a relatively small set of events, and there must be uncertainty in establishing a source model based on empirical relationships. Therefore, we needed to identify an asperity on a rupture plane to overcome our inability to accurately predict slip models of future earthquakes. Determining earthquake recurrences, fault slip accumulation patterns, and offset accumulation patterns based on geographic evidence can assist in identifying asperities. To determine its fault activity characteristics, [PERSON] et al. [40] conducted geological field and geomorphological surveys of the F1-3 segment. They found a series of relatively intact linear reverse fault scarps and large earthquake surface fractures along the length of the fault. A digital elevation model image clearly showed offsets along the F1-3 fault, including visibly sinistral offset rivers and gullies and T2 terraces. Therefore, it could be reasonably estimated that the target fault was active in the recent period. They also excavated a trench, whose location is shown in Figure 1b. They determined that four events had occurred on the F1-3 fault that had offset sediments deposited during the Holocene. The radiocarbon-14 dating results for the trench samples indicated that the elapsed time of the latest event was approximately 1670 a, which is close to the characteristic earthquake recurrence interval of 2000 a [40]. The geological and geomorphological results presented in [40] revealed that the southwestern segment of the F1-3 fault is the most active, and there is a high seismic risk of large earthquakes on this fault in the future. Therefore, we set the largest asperity to be in this location. On 20 July 2007, the Xinjiang Tekesi \(M_{\text{S}}\) 5.9 earthquake occurred in the eastern part of the F1-3 fault (see Figure 1b). Based on the tectonic stress field and the focal mechanism solution of the Tekesi \(M_{\text{S}}\) 5.9 earthquake, [PERSON] et al. [41] ascertained that the NEE-trending Kalawengquan fault was the seismogenic structure for this earthquake, specifically where the fault is inclined toward the southeast with a dip angle greater than 50\({}^{\circ}\). There is an earthquake gap near the source, which may be due to the relatively complete medium in this area. The F1-3 fault exhibits strong tectonic activity with high stress accumulation [59]. The absence of \(M_{\text{S}}\) > 4.0 aftershocks in the Tekesi earthquake sequence may indicate that the energy accumulated in the F1-3 fault has not been fully released, and there is a risk of strong earthquakes in the future. \begin{table}
\begin{tabular}{c c c c} \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Fault strike & N64\({}^{\circ}\)E & \begin{tabular}{c} Average slip of rupture \\ area (m) \\ \end{tabular} & 1.85 \\ \hline Inclination & Southeast & Slip of asperity (m) & 3.7 \\ \hline Fault dip angle (\({}^{\circ}\)) & 80, 85, 90 & Slip of background (m) & 1.29 \\ \hline Fault rupture length (km) & 82 & \begin{tabular}{c} Depth from upper fault \\ boundary (km) \\ \end{tabular} & 0 \\ \hline Fault rupture width (km) & 22 & S-wave velocity (km/s) & 3.6 \\ \hline Fault rupture area (km\({}^{2}\)) & 1804 & \begin{tabular}{c} Average crustal \\ density (g/cm\({}^{3}\)) \\ \end{tabular} & 2.8 \\ \hline Moment magnitude & 7.3 & Stress drop (bar) & 30.0, 60.0 \\ \hline Seismic moment & \(1.0\times 10^{20}\) N \(\cdot\) m & Geometrical spreading & \(1/R\) \\ \hline d\(l\) (km) & 2 & Quality factor & \(Q(\prime)=460.7\)\({}^{0.52}\) \\ \hline d\(w\) (km) & 2 & \(\kappa_{0}\) (s) & 0.015, 0.025, 0.035 \\ \hline Maximum asperity area (km\({}^{2}\)) (Slip Model 1) & 288 & \
\begin{tabular}{c} Other asperity area \\ (km\({}^{2}\)) (Slip Model 1) \\ \end{tabular} & 112 \\ \hline Maximum asperity area (km\({}^{2}\)) (Slip Model 2) & 264 &
\begin{tabular}{c} Other asperity area \\ (km\({}^{2}\)) (Slip Model 2) \\ \end{tabular} & 140 \\ \hline \end{tabular}
\end{table}