## 2 Tectonic Setting
### Slip Model  
[PERSON] et al. [36] showed that the combined area of asperities \(A_{\rm as}\) occupies 22% of the total rupture area on average.  
\[A_{\rm as} =0.22\times L\times W \tag{3}\]  
where \(L\) and \(W\) are the rupture length and width, respectively. The area of the largest asperity \(A_{\rm a1}\) is approximately 16% of the total rupture area, and the area of the other asperities \(A_{\rm a2}\) is 6%.  
\[A_{\rm a1} =0.16\times L\times W \tag{4}\] \[A_{\rm a2} =0.06\times L\times W \tag{5}\]  
The asperities and other rupture areas could be assigned different slips to appropriately represent the inhomogeneity of stress and slip on the rupture area. The average slip of the rupture area \(\bar{D}\) was calculated as follows [37]:  
\[\bar{D}=\frac{M_{0}}{\mu A} \tag{6}\]  
where \(\mu=3\times 10^{11}\) dyne/cm\({}^{2}\) is the average shear modulus of the crust, \(A\) is the rupture area, and \(M_{0}\) is the seismic moment. The seismic moment can be calculated based on the empirical relationship between the moment magnitude of the maximum credible earthquake and the seismic moment [38]:  
\[M_{\rm W}=\frac{2}{3}\log M_{0}-10.7 \tag{7}\]  
The ratio of the average slip on the asperities to the average slip over the whole rupture plane is independent of the seismic moment, and the average value for the events studied was approximately 2 [36]. Thus, the average slip on the asperities \(D_{\rm as}\) and on the other rupture areas \(D_{\rm bk}\) can be calculated as follows:  
\[D_{\rm as}=2.0\times\bar{D} \tag{8}\]  
\[D_{\rm bk}=0.71\times\bar{D} \tag{9}\]  
Based on the slip distribution data of 13 earthquakes from [PERSON] et al. [36] and additional data of 16 earthquakes, [PERSON] [39] obtained the characteristic parameters of asperities for shallow earthquakes. For a strike-slip fault, the semi-empirical relationship between the distance \(X_{\rm as}\) from the fault reference point to the center of the largest asperity along the strike direction and the rupture length is as follows:  
\[\log X_{\rm as}=\log L-0.30 \tag{10}\]The semi-empirical relationship between the distance \(Y_{\text{as}}\) from the top depth of a fault to the center of the largest asperity along the dip direction and the rupture width is as follows:  
\[\log Y_{\text{as}}=\log W-0.28 \tag{11}\]  
The empirical relationship between the length of the largest asperity \(L_{\text{as}}\) and the fault rupture length is as follows:  
\[\log L_{\text{as}}=\log L-0.66 \tag{12}\]  
The empirical relationship between the width of the largest asperity \(W_{\text{as}}\) and the fault rupture width is as follows:  
\[\log W_{\text{as}}{=\log}W-0.23 \tag{13}\]  
The results of different source models show that the random slip model is not suitable when conducting near-field ground-motion simulations of large earthquakes, while the asperity slip model can represent the maximum ground-motion scenario for some sites [26]. To calculate the maximum credible ground-motion parameters at the Longpan dam, the asperity source model was adopted. Referring to the above empirical relationships and existing research data, the size and center location of the largest and other asperities for the Daju-Lijiang, Xiaozhongdian-Daju, and Longpan-Qiaohou faults were obtained.