## 3 Validation of Effectiveness
### Ground Motion Simulation of the 2013 Lushan Earthquake
\begin{table}
\begin{tabular}{c c c} \hline  & **Fault Parameter** & **Parameter Value** \\ \hline  & Number of asperities & 3 \\  & Area of the first asperity & 120 km\({}^{2}\) \\  & Slip of the first asperity & 0.613 m \\  & Area of the second asperity & 300 km\({}^{2}\) \\  & Slip of the second asperity & 1.069 m \\  & Area of the third asperity & 210 km\({}^{2}\) \\  & Slip of the third asperity & 0.78 m \\  & Area of the background & 1680 km\({}^{2}\) \\  & Slip of the background & 0.26 m \\ \hline \end{tabular}
\end{table} 
Table 3: _Cont._  
Figure 9: Simulation results of the LV1 station. (The comparisons of acceleration time histories are shown in the top row, the comparisons of acceleration response spectra are shown in the middle row, and the comparisons of displacement amplitude spectra are shown in the bottom row. The simulation results in the NS, EW, and UD directions are shown from left to right. The black line represents the observed record, the red line represents the GMPE, the yellow line represents the simulation result with the constant rise time when the subfault division number is 9 \(\times\) 10, the green line represents the simulation result with the modified rise time expression when the subfault division number is 9 \(\times\) 10, the brown line represents the simulation result with the constant rise time when the subfault division number is 36 \(\times\) 40, and the blue line represents the simulation result with the modified rise time expression when the subfault division number is 36 \(\times\) 40). 22 \(\times\) 14, and 44 \(\times\) 28, respectively, and they are compared with the theoretical \(\omega^{-2}\) source spectrum, as shown in Figure 12.  
The results indicate that when assuming a uniform rise time distribution on the fault plane, as the subfault division number increases, the sag phenomenon of the source spectrum in the intermediate frequency band becomes more and more significant, and the frequency range where the sag phenomenon occurs is also expanding. After improving the rise time expression, as the subfault division number increases, the amplitude change in the source spectrum is not significant. Next, six stations are randomly selected around the 2013 Lushan earthquake fault, and the ground motions at these stations are simulated with subfault division numbers of 11 \(\times\) 7 and 44 \(\times\) 28, respectively. According to the results of [PERSON] [51], Table 4 lists the basic information of these stations. The rupture distances of these six stations range from 4 km to 44 km, with four stations located on the hanging wall and two stations located on the foot wall of the fault. According to the NEHRP code [47], the site types of these stations are all class C sites. Figure 10: The simulation misfit of the ground motion of the Northridge earthquake. (The yellow line represents the simulation misfit with the constant rise time when the subfault division number is 9 \(\times\) 10, the green line represents the simulation misfit with the modified rise time expression when the subfault division number is 9 \(\times\) 10, the brown line represents the simulation misfit with the constant rise time when the subfault division number is 36 \(\times\) 40, and the blue line represents the simulation misfit with the modified rise time expression when the subfault division number is 36 \(\times\) 40). In this study, the acceleration time histories, acceleration response spectra, and displacement amplitude spectra of the simulated 3D ground motions are compared with those of the observed records at these stations in the 2013 Lushan earthquake. The comparison results are shown in Figures 13-18.