## 3 Validation of Effectiveness
### Ground Motion Simulation of the 1994 Northridge Earthquake
As the acceleration time history of the ground motion is mainly concerned with the engineering seismic design, in this study, the acceleration time histories, acceleration response spectra, and displacement amplitude spectra of the synthesized 3D ground motions are compared with those of the observed records of the 1994 Northridge earthquake. Due to the uncertainty of fault parameters, propagation characteristics, and local site conditions, the simulated acceleration response spectra of the horizontal components are also compared with the prediction results obtained by the ground motion prediction equation (GMPE) ASK14 proposed by [PERSON] et al. [48], as shown in Equation (21): \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 L4B & 34.650 & \(-118.477\) & 31.69 & 523.54 & C \\ L09 & 34.608 & \(-118.558\) & 25.36 & 670.84 & C \\ ATB & 34.758 & \(-118.361\) & 46.91 & 572.57 & C \\ HOW & 34.204 & \(-118.302\) & 16.88 & 581.93 & C \\ CHL & 34.086 & \(-118.481\) & 20.45 & 740.05 & C \\ LV1 & 34.594 & \(-118.242\) & 37.19 & 499.31 & C \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Station information of the 1994 Northridge earthquake. (\(R_{\text{rup}}\) is the rupture distance, \(V_{\text{s30}}\) is the time-averaged shear-wave velocity of the upper 30 m). Figure 3: The source spectra of the 1994 Northridge earthquake. (The red solid line represents the source spectra of the large earthquake synthesized using the constant rise time, the blue solid line represents the source spectra of the large earthquake synthesized using the modified rise time expression, and the black dashed line represents the theoretical \(\omega^{-2}\) source spectrum.). \[ \begin{split}&\ln Sa(g)=f_{1}\big{(}M_{w},R_{rup}\big{)}+F_{RV}f_{7}(M_{w} )+F_{N}f_{8}(M_{w})+F_{AS}f_{11}\Big{(}CR_{jp}\Big{)}+f_{5}\big{(}\dot{S}a_{1180 },V_{s30}\big{)}+\\ & F_{HW}f_{4}\Big{(}R_{jp},R_{rup},R_{x},R_{y0},W,dip,Z_{TOR},M_{w} \Big{)}+f_{6}(Z_{TOR})+f_{10}(Z_{1.0},V_{s30})+Regional\big{(}V_{s30},R_{rup} \big{)}\end{split}  \tag{21}\]  
The specific meanings represented by the parameters in the equation can be found in the literature [48]. The comparison results are shown in Figures 4-9. In Figures 4-9, 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 36 \(\times\) 40). In Figures 4-9, 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 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,  
Figure 4: Simulation results of the L4B 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.