## 3 Validation of Effectiveness
### Ground Motion Simulation of the 2013 Lushan Earthquake  
In order to further verify the effectiveness of the improvement proposed in this study, the ground motion of the 2013 Lushan Ms 7.0 earthquake in China is simulated below. The epicenter of the Lushan earthquake was located at 30.3\({}^{\circ}\) N, 103.0\({}^{\circ}\) E, with a focal depth of  
Figure 7: Simulation results of the HOW 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). 10.2 km. According to the inversion results of [PERSON] et al. [49], the fault parameters used in this study are listed in Table 3. The quality factor \(Q_{K}(f)\) is expressed as follows [50]:  
\[Q_{K}(f)=274.6f^{0.423} \tag{22}\]  
Figure 8: Simulation results of the CHL 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). \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Fault Parameter** & **Parameter Value** \\ \hline \hline  & Strike, dip, rake & 205\({}^{\circ}\), 38.5\({}^{\circ}\), 88.8\({}^{\circ}\) \\  & Fault length and width & 66 km, 35 km \\  & Rupture area & 2310 km\({}^{2}\) \\  & Depth at the top of the fault & 0 km \\ Macroscopic fault & Stress drop & 6.0 MPa \\ parameter & Seismic moment & 3.61 \(\times\) 10\({}^{19}\) N-m \\  & Average slip & 0.43 m \\  & Medium density near the source & 2.8 g/cm\({}^{3}\) \\  & S wave and P wave velocity near the source & 3.6 km/s, 6.2 km/s \\  & Rupture propagation velocity & 2.88 km/s \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Fault parameters of 2013 Lushan earthquake. The fault location and station location of the 2013 Lushan earthquake are shown in Figure 11.  
Firstly, using the two methods described in the previous section, the source spectra of the 2013 Lushan earthquake are synthesized with subfault division numbers of \(11\times 7\)