## 3 Validation of Effectiveness
### Ground Motion Simulation of the 2013 Lushan Earthquake
In Figures 13-18, the black line represents the observed record, the yellow line represents the simulation result with the constant rise time when the subfault division number is \(11\times 7\), the green line represents the simulation result with the modified rise time expression when the subfault division number is \(11\times 7\), the brown line represents the simulation result with the constant rise time when the subfault division number is \(44\times 28\), and the blue line represents the simulation result with the modified rise time expression when the subfault division number is \(44\times 28\). The results indicate that if the rise time is constant, the sag phenomenon of the simulated response spectra and amplitude spectra in the intermediate frequency band will not be obvious when the subfault division number is small, whereas the amplitude in the intermediate frequency band will show a significant decrease when \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Station** & **Latitude** & **Longitude** & \(R_{\text{rup}}\) **(km)** & \(V_{\text{s30}}\) **(m/s)** &
\begin{tabular}{c} **NEHRP Site** \\ **Classification** \\ \end{tabular} \\ \hline
51 BXZ & 30.5 & 102.9 & 15.6 & 393.9 & C \\
51 YAM & 30.1 & 103.1 & 13.3 & 600.4 & C \\
51 LSF & 30.0 & 102.9 & 4.1 & 517.4 & C \\
51 BXM & 30.4 & 102.7 & 22.5 & 398.0 & C \\
51 YAL & 29.9 & 102.8 & 14.9 & 535.0 & C \\
51 HYT & 29.9 & 103.4 & 43.8 & 437.2 & C \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Station information of the 2013 Lushan earthquake. (\(R_{\text{rup}}\) is the rupture distance, \(V_{\text{s30}}\) is the time-averaged shear-wave velocity of the upper 30 m). Figure 11: Fault location and station location of 2013 Lushan earthquake. (\(OXYZ\) is the overall coordinate system, \(O\) is the projection of the upper left corner of the fault plane on the surface, \(X\), \(Y\), and \(Z\) are the north, east, and vertical downward direction, respectively, _oxy_ is the local coordinate system of the fault plane, \(o\) is the upper left corner of the fault plane, \(x\) and \(y\) are the direction of fault length and width, respectively, \(Q\) is the rupture starting point on the fault plane, and \(d_{\text{t}}\) is the top depth of the fault plane. The black star marks the hypocenter, and the black triangles mark the locations of the stations.). the subfault division number is large. After using the modified rise time expression, the sag phenomenon that appeared in the intermediate frequency range is alleviated, and the simulation results are closer to the observed records. As the subfault division number increases, the decrease in amplitude in the intermediate frequency range is not as significant as the decrease when the rise time is constant. From a sensitivity perspective, for 51 BXZ and 51 BXM stations, the sensitivity of simulation results to the subfault division number is stronger than the rise time expression in almost the whole period range. For the 51 YAM station, the simulation results show stronger sensitivity to the rise time expression than the subfault division number in the period range shorter than 0.4 s, while the simulation results show stronger sensitivity to the subfault division number in the period range longer than 0.4 s. For the 51 LSF station, the simulation results show stronger sensitivity to the rise time expression than the subfault division number in almost the whole period range. For the 51 YAL station, the sensitivity of the simulation results to the subfault division number and the rise time expression is roughly similar in the whole period range. For the 51 HYT station, the sensitivity of the simulation results to the subfault division number and the rise time expression is roughly similar in the period range shorter than 0.3 s, while the simulation results show stronger sensitivity to the subfault division number in the period range longer than 0.3 s. The change in sensitivity may be related to the azimuth and site effects of the station. Figure 12: The source spectra of the 2013 Lushan earthquake.