## 5 Finite-Fault Modeling for Scenario Earthquake Utilizing Empirical Green's Function Method
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Parameter** & **912 Gyeongju Earthquake** & **EGFM Finite Fault Model** \\ \hline \hline \multirow{2}{*}{Focal Mechanism} & & 5.5 Mw & 6.5 Mw \\ \cline{2-3}  & Strike & 26\({}^{\circ}\) & 26\({}^{\circ}\) \\ \cline{2-3}  & Dip & 67\({}^{\circ}\) & 67\({}^{\circ}\) \\ \cline{2-3}  & Rake & 175\({}^{\circ}\) & 175\({}^{\circ}\) \\ \hline \multirow{2}{*}{Fault dimension} & Width & 4.0 km & 12.0 km \\ \cline{2-3}  & Length & 4.0 km & 16.0 km \\ \hline \multirow{2}{*}{Hypocentral Depth} & \multirow{2}{*}{12.0 km} & (Min) 8.5 km, (Max) 12.2 km \\ \hline \multirow{2}{*}{S-wave Velocity} & \multirow{2}{*}{3.5 km/s} & 3.5 km/s \\ \cline{2-3}  & Rupture Velocity & 2.8 km/s & 2.8 km/s \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of fault geometry between the 912 Gyeongju earthquake and the EGFM finite fault model. Figure 6: Finite fault model using the empirical Green’s function method and the location of the seismic station where the ground motion time histories are synthesized: (**a**) The geometry of the fault plane of the hypothetical main event and the fault of the 912 Gyeongju Earthquake as the element event; (**b**) The side view of the fault plane of the main event; (**c**) The location of the rupture starting point considered on the fault plane of the main event. The size of the finite fault model that matches the PSHA de-aggregation results is calculated by converting it to the rupture area-moment magnitude relationship [41]:  
\[\log_{10}A=M_{W}-4.25 \tag{6}\]  
Parameters \(A\) and \(M_{W}\) correspond to the fault rupture area (km\({}^{2}\)) and the moment magnitude of the earthquake, respectively. The element event used in the EGFM was the fault rupture area of the 912 Gyeongju Earthquake. The fault rupture area with a moment magnitude of 6.5, which was the result of PSHA de-aggregation, was estimated to be approximately 177.83 km\({}^{2}\) using Equation (6). In consideration of the element event rupture area of 16.0 km\({}^{2}\), which can be assumed to be a 4 km \(\times\) 4 km square shape, the finite fault model can be converted into a fault with a width of 12.0 km in the dip direction and a length of 16.0 km in the strike direction, as shown in Figure 6a. The converted finite fault rupture area was determined to be 192.0 km\({}^{2}\), which is slightly different from 177.83 km\({}^{2}\). Nonetheless, this corresponds to a moment magnitude of 6.5 according to Equation (6), indicating that finite fault modeling is reasonable. The strike and dip angle of the finite fault were determined using fault values from the 912 Gyeongju Earthquake. The estimated crustal thickness of Korea is about 15.0 km, and the width of the finite fault model in the deep direction is 12.0 km. Therefore, the depth at the top of the fault in this study was determined to be 3.0 km, as shown in Figure 6b. Assuming that the rupture starts at the bottom of the finite fault model according to the EGFM, eight rupture starting points can be considered, as shown in Figure 6c. As shown in Figure 6b, the distance to each finite seismic station was considered the closest distance to the coseismic fault rupture plane, and this distance was determined to be 10 km by PSHA de-aggregation. Five virtual seismic stations were positioned at the same closest distance to the coseismic fault rupture plane, as shown in Figure 6a,c, to consider the directivity effect of the seismic wave propagation. Forty ground motion time histories with different characteristics for each direction were synthesized for the two horizontal components from the finite fault using the EGFM. Figure 7 shows the response spectrum of the ground motion time histories synthesized using the EGFM modeled in Figure 6, with the 912 Gyeongju Earthquake as the element event. Figure 7: Response spectra of the ground motion time histories synthesized using the EGFM.