## 6 Selection of Seed Ground Motions for UHS and CMS
By selecting the case with the minimum total MSE value, the response spectrum of the synthesized ground motion time history at seismic station 2 with rupture starting point 5 was selected as the best match for the CMS. For the UHS, the response spectrum of the synthetic ground motion time history at seismic station 1, with rupture starting point 3, was selected. Figure 9 shows the acceleration response spectrum and time history selected based on the CMS, whereas Figure 10 shows those selected based on the UHS. The synthesized acceleration time histories selected to best match the CMS and UHS were used as seed ground motions to obtain spectrum-compatible ground motions for risk assessment. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\
\begin{tabular}{c} **Rupture** \\ **Starting Point** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Horizontal** \\ **Direction** \\ **Components** \\ \end{tabular} } & \multicolumn{5}{c}{**Virtual Seismic Station Number**} \\ \cline{3-7}  & & EW & 0.2048 & 0.1083 & 0.2539 & 0.0842 & 0.138 \\ \cline{2-7}  & NS & 0.1048 & 0.094 & 0.1175 & 0.0648 & 0.0604 \\ \hline \multirow{2}{*}{2} & EW & 0.1787 & 0.1291 & 0.2327 & 0.1002 & 0.0903 \\ \cline{2-7}  & NS & 0.1413 & 0.1412 & 0.2382 & 0.0548 & 0.0686 \\ \hline \multirow{2}{*}{3} & EW & 0.0837 & 0.2154 & 0.2976 & 0.125 & 0.2029 \\ \cline{2-7}  & NS & 0.0381 & 0.1698 & 0.2304 & 0.072 & 0.0672 \\ \hline \multirow{2}{*}{4} & EW & 0.2806 & 0.3341 & 0.5171 & 0.2514 & 0.1657 \\ \cline{2-7}  & NS & 0.2685 & 0.3338 & 0.5095 & 0.1642 & 0.0962 \\ \hline \multirow{2}{*}{5} & EW & 0.2082 & 0.0998 & 0.2416 & 0.0833 & 0.1183 \\ \cline{2-7}  & NS & 0.1179 & 0.0801 & 0.1139 & 0.0715 & 0.0756 \\ \hline \multirow{2}{*}{6} & EW & 0.1604 & 0.128 & 0.244 & 0.1056 & 0.0954 \\ \cline{2-7}  & NS & 0.1490 & 0.1198 & 0.2159 & 0.058 & 0.0574 \\ \hline \multirow{2}{*}{7} & EW & 0.1012 & 0.2263 & 0.3249 & 0.1149 & 0.1990 \\ \cline{2-7}  & NS & 0.0294 & 0.2725 & 0.2681 & 0.0782 & 0.0715 \\ \hline \multirow{2}{*}{8} & EW & 0.2753 & 0.3003 & 0.5439 & 0.2181 & 0.1645 \\ \cline{2-7}  & NS & 0.2056 & 0.2602 & 0.5095 & 0.1211 & 0.0788 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: MSE values for the two horizontal direction components between the response spectra of the synthesized time histories and the UHS. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\
\begin{tabular}{c} **Rupture** \\ **Starting Point** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Horizontal** \\ **Direction** \\ **Components** \\ \end{tabular} } & \multicolumn{5}{c}{**Virtual Seismic Station Number**} \\ \cline{3-7}  & EW & 0.1514 & 0.0857 & 0.1932 & 0.1122 & 0.1605 \\ \cline{2-7}  & NS & 0.0515 & 0.0552 & 0.0697 & 0.0823 & 0.0738 \\ \hline \multirow{2}{*}{2} & EW & 0.1469 & 0.0973 & 0.1661 & 0.1209 & 0.1202 \\ \cline{2-7}  & NS & 0.0654 & 0.0743 & 0.132 & 0.0619 & 0.0588 \\ \hline \multirow{2}{*}{3} & EW & 0.1036 & 0.1554 & 0.2099 & 0.1441 & 0.2932 \\ \cline{2-7}  & NS & 0.0434 & 0.0801 & 0.1222 & 0.0476 & 0.1317 \\ \hline \multirow{2}{*}{4} & EW & 0.2004 & 0.2161 & 0.3568 & 0.1777 & 0.1586 \\ \cline{2-7}  & NS & 0.1466 & 0.1974 & 0.3274 & 0.0803 & 0.0558 \\ \hline \multirow{2}{*}{5} & EW & 0.1613 & 0.0837 & 0.1849 & 0.1021 & 0.1272 \\ \cline{2-7}  & NS & 0.0569 & 0.055 & 0.0689 & 0.0869 & 0.085 \\ \hline \multirow{2}{*}{6} & EW & 0.1283 & 0.0997 & 0.1734 & 0.1305 & 0.1147 \\ \cline{2-7}  & NS & 0.0717 & 0.0612 & 0.1212 & 0.0743 & 0.0565 \\ \hline \multirow{2}{*}{7} & EW & 0.1406 & 0.154 & 0.2185 & 0.1168 & 0.2883 \\ \cline{2-7}  & NS & 0.0501 & 0.1671 & 0.15 & 0.0496 & 0.1411 \\ \hline \multirow{2}{*}{8} & EW & 0.1953 & 0.1952 & 0.3766 & 0.1695 & 0.1555 \\ \cline{2-7}  & NS & 0.1075 & 0.1436 & 0.3254 & 0.0532 & 0.0452 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: MSE values for the two horizontal direction components between the response spectra of the synthesized time histories and the CMS.