## 7 Spectral Matching of Seed Ground Motions to Risk Assessment Spectrum  
To utilize the ground motion time history generated using the EGFM as the input ground motion for seismic risk assessment, a spectral matching procedure is necessary to modify its response spectrum to be compatible with the UHS. In the spectral matching process, compatibility with the target spectrum and preservation of the seed ground motion characteristics in the time domain are important. For this purpose, the spectral matching method that adjusts wavelets in the time domain proposed by [PERSON] and [PERSON] (2010) [42] was used to preserve the non-stationary characteristics of the original acceleration time history. As in the selection step of the synthesized ground motion time history from finite fault modeling using the EGFM, the range of 0.01 to 1.0 s spectral period was considered during the spectral matching. In general, the spectral matching process in the frequency domain is effectively performed. However, in the time domain, it may not perform well in some cases, depending on the selection of the seed motion. To evaluate the effectiveness of selecting ground motion matched to the UHS or CMS as seed motions, a matching process was conducted using the seed motion time histories from the two previously selected cases. The matching conditions were identical in both cases. In the first case, the ground motion time history presented in Figure 9, which was selected based on the CMS, was matched to be compatible with the UHS shown in Figure 11. In another case, the ground motion time history presented in Figure 10, which was selected based on the UHS, was matched to be compatible with the UHS shown in Figure 12. As shown in Figure 11, the acceleration time histories are closely compatible with the UHS  
Figure 10: Selection of acceleration time histories with a response spectrum to best match the UHS: (**a**) Comparison of acceleration response spectra selected from the EGFM synthetic ground motion time histories; (**b**) Acceleration time histories recorded at MKL station from the 912 Gyeongju Earthquake; (**c**) Acceleration time histories synthesized using the EGFM. after only the first iteration. However, when selected based on the UHS (Figure 12a), the EW component did not change before or after matching with the first iteration. That is, at least the second iteration is necessary for spectral matching to proceed. In addition, 15 iterations were conducted to analyze the convergence of compatibility with the UHS across iterations. The degree of compatibility with the UHS is represented by the MSE using Equation (7). Figure 13a,b show the MSE for each of the EW and NS components for the time histories selected based on the UHS and CMS, respectively, as the number of iterations increased. Regardless of the selected ground motions, the MSE converged remarkably around the fourth iteration of matching and almost converged after the eighth iteration. However, there was a difference in the converged MSE values between the two seed motion selection methods. Figure 14a,b show the response spectra for the EW and NS components, respectively, when spectral matching corresponding to the fourth iteration in Figure 13 was performed. Figure 11: Acceleration response spectra and time histories before and after the matching for the ground motion time histories selected based on the CMS. The solid blue line represents the case before the matching, whereas the solid green line represents the case after the matching with the first iteration: (**a**) EW component; (**b**) NS component. Figure 12: Acceleration response spectra and time histories before and after the matching for the ground motion time histories selected based on the UHS. The solid blue line represents the case before the matching, whereas the solid green line represents the case after the matching with the first iteration. (**a**) EW component (**b**) NS component.