## 6 Selection of Seed Ground Motions for UHS and CMS  
Another important aspect of the procedures in this study was to determine whether differences in the target spectrum used to select the ground motion time histories affected the generation of earthquake input ground motions for risk assessment. Although the selection of the ground motion time histories based on the CMS is appropriate considering the consistency with hazard de-aggregation, the differences in selection based on the UHS, which is used for risk assessment, need to be analyzed. Therefore, the CMS obtained for a 0.2 s target period, corresponding to the UHS, and the UHS were used as the target spectra for selecting the ground motion time histories. The time history selection criteria were based on the mean squared error (MSE) between the response spectra of the ground motion time histories and the target spectra, as given by Equation (7). The assumption of a fundamental spectral period of 0.2 s is used; however, shorter period ranges owing to higher vibration modes and longer period ranges owing to nonlinear structural behavior can affect the dynamic behavior of structures. Therefore, the MSE was calculated for the range of 0.01 to 2.0 s from a structural engineering perspective. \[MSE=\frac{\sum_{i=1}^{n}\left(\left(\ln Sa_{SYN}(T_{i})-\ln Sa_{CMS_{w}UHHS}(T _{i})\right)^{2}\right.}{n} \tag{7}\]  
where \(n\) refers to the overall number of spectral periods assessed, and \(Sa_{SYN}(T_{i})\) represents the acceleration response spectral value of the synthesized ground motion time history at the \(i\)-th period, as determined by the EGFM. \(Sa_{CMS_{w}UHHS}(T_{i})\) represents the acceleration spectral value of the CMS and UHS at the \(i\)-th period. A smaller MSE indicates a better match between the two response spectra. The results of calculating the MSE for the response spectra of the 40 ground motion time histories in each direction in Figure 7 are listed in Tables 4 and 5. Table 4 presents the MSE values for the response spectra of the synthesized ground motion time histories compared with those of the UHS, while Table 5 presents the MSE values compared with those of the CMS. The total MSE values for the analysis were calculated as the sum of the MSE values of the two horizontal components. Figure 8 shows the total MSE values according to the hypocentral distance presented in Tables 4 and 5. Comparing the MSE values, the response spectra of the time histories synthesized from the finite fault of the EGFM were lower in the CMS (as shown in Figure 8b) than in the UHS (in Figure 8a). The ground motion synthesized using the finite fault model of the EGFM is expected to preserve the actual seismic characteristics. This was supported by the fact that the CMS was closer to the response spectra of the recorded ground motions than the UHS. Despite having the closest distance from the fault to the seismic station, a large deviation in the MSE was obtained. This deviation may occur because of forward or backward directivity effects. The directivity of seismic waves depends on the rupture direction and direction of seismic wave propagation. Therefore, the MSE values for station 3 in Figure 8 are strongly related to the hypocentral distance because this station is located in the direction of the fault plane. Accordingly, when the seismic station is determined first, the directivity effect must be considered based on the trends shown in Figure 8a,b. If the closest distance to the fault is the same and the hypocentral distance is the largest, the rupture direction aligns with the direction of the seismic wave propagation, and a high directivity effect is expected. The forward directivity effect caused larger amplitudes in long-period motion, resulting in the smallest MSE in this example model. A virtual seismic station and rupture starting point were selected based on the minimum value of the total MSE according to the target spectrum for ground motion selection.