## 5 Finite-Fault Modeling for Scenario Earthquake Utilizing Empirical Green's Function Method  
The magnitude of the scenario earthquake for risk assessment was determined to be 6.5, and the distance was determined to be 10.0 km, respectively. The use of recorded ground motion time histories for magnitudes and distances consistent with the scenario earthquake is recommended as the input ground motion for seismic risk assessment. However, the Korean Peninsula is characterized by low to moderate seismic activity, and strong earthquakes rarely occur. The largest recorded ground motion accelerogram was from the 912 Gyeongju Earthquake, which had a moment magnitude of 5.5 and occurred in 2016. When strong ground motion records are absent, scaling or modifying moderate-magnitude ground motion time history records from the site can be used as an alternative. However, simple intensity scaling cannot reflect the earthquake magnitude characteristics corresponding to the annual frequency of exceedance. Accordingly, the EGFM, which utilized the similarity of the seismic source scaling law, was used to adjust the ground motion of the recorded 912 Gyeongju Earthquake to match the magnitude and distance of the scenario earthquake. The EGFM was first developed to estimate large-magnitude mainshocks using small-magnitude aftershocks [37; 38]. This method utilizes the similarity law of large and small earthquakes [39] and the characteristics of two earthquakes recorded at close distances with similar fault characteristics, path effects, and site effects [40]. The equation for synthesizing a large-magnitude earthquake by superposing small-magnitude earthquakes is given in Equation (5):  
\[U(t)=C{\sum_{i=1}^{N}\sum_{j=1}^{N}\frac{r}{r_{ij}}F\big{(}t-t_{ij}\big{)}*u(t)} \tag{5}\]  
where \(U(t)\) is the ground motion time history of the synthesized large-magnitude earthquake (main-event), \(u(t)\) is the small-magnitude earthquake (i.e., element-event) used for superimposition, and * indicates the convolution. \(C\) is the stress drop ratio between large and small magnitude earthquakes, and \(N\) is the ratio of the fault dimensions between large and small magnitude earthquakes. Here, \(i\) and \(j\) represent the increased dimensions in the strike and dip directions of a large-scale fault, respectively, compared with a small-scale fault. Parameters \(r\) and \(r_{ij}\) denote the hypocenter distance to the seismic station of a small and large magnitude earthquake, respectively. \(F(t)\) is the correction function for the difference in slip velocity time between large and small magnitude earthquakes. Parameters \(t\) and \(t_{ij}\) denote the rise times of large and small magnitude earthquakes, respectively. As demonstrated in Equation (5), the synthesized main event from the EGFM preserves the characteristics of the actual faults and path effects by utilizing the recorded ground motion as an element event in the finite fault model. Accordingly, many studies have focused on large-magnitude earthquake synthesis or estimation of seismic source parameters and wave propagation using EGFM [3]. In this study, the limitations due to the lack of recorded ground motions were addressed using EGFM. The generation of the scenario earthquake ground motion in accordance with the de-aggregation of the PSHA is presented. To synthesize the ground motion time histories suitable for the PSHA de-aggregation results presented in Figure 4 and Table 2, a finite fault model was constructed as shown in Figure 6. The fault parameters for the 912 Gyeongju Earthquake [22] and EGFM are listed in Table 3.