## 4 Probabilistic Seismic Hazard Analysis and Evaluation of Example Scenario Earthquake
### Seismic Hazard De-Aggregation for Selection of Scenario Earthquake  
Although a UHS is used for risk assessment, it does not indicate the specific magnitude or distance of a single earthquake. Therefore, a method of de-aggregating seismic hazards, an extension of PSHA, has been developed for selecting the input ground motion required for seismic risk assessment [33]. Seismic hazard de-aggregation calculates the contribution of magnitude-distance pairs (M-R bins) of earthquakes at a specific annual frequency of exceedance and spectral period. These contributions were grouped into their respective bins.  
If considering epsilon (\(\epsilon\)), which represents the number of standard deviations used to scatter ground motions about the median GMPE values, based on the calculated contribution, the combination of the dominant magnitude-distance-epsilon pairs (M-R-\(\epsilon\) bin) is defined as a probabilistic scenario earthquake [34; 35]. For instance, the conditional distribution of magnitudes is calculated as follows [24]:  
\[f_{M|Sa>y}(m,y)=\frac{1}{v(Sa>y)}\sum_{k}\sum_{j}v_{j}\iint f_{M,R,E}(m,r, \epsilon)P(Sa>y|m,r,\epsilon,GMPE_{k})d\textit{rde}P(GMPE_{k}) \tag{3}\]  
\begin{table}
\begin{tabular}{c c c} \hline \multicolumn{1}{c}{**Parameter**} & \multicolumn{1}{c}{**Value**} \\ \hline \multicolumn{1}{c}{Seismic Source Model} & \multicolumn{1}{c}{\(100\,\text{km}\times 100\,\text{km}\) single area source} \\ \hline \multirow{4}{*}{Gutenberg-Richter} & \(a\,\text{value}\) & 2.843 \\ \cline{2-3}  & \(b\,\text{value}\) & 0.95 \\ \cline{2-3}  & Min Magnitude & 5.0\(\,\text{Mw}\) \\ \cline{2-3}  & Max Magnitude & 7.0\(\,\text{Mw}\) \\ \hline \multicolumn{1}{c}{Ground Motion Prediction Equation} & [PERSON] and Boore (2006) [30] \\ \hline \multicolumn{1}{c}{Annual Frequency of Exceedance} & \multicolumn{1}{c}{\(0.2\times 10^{-4}\,(/\text{year})\)} \\ \hline \end{tabular}
\end{table}
Table 1: Seismic hazard parameters for PSHA.  
where each variable is defined in Equation (1). By adjusting the variables in Equation (3), the de-aggregation of distance and epsilon can be computed. The distribution for each magnitude-distance-epsilon bin pair is calculated to establish the contribution of each pair to the annual frequency of exceedance, and the magnitude-distance pair with the highest contribution is defined as the scenario earthquake. The spectral period of interest was set to 0.2 s in the de-aggregation process, considering that nuclear power plant structures typically have natural periods in the short period range of 0.1 to 0.25 s. The hazard curves in Figure 3a were de-aggregated for an annual frequency of exceedance of 0.2 \(\times\) 10\({}^{-4}\) at a spectral period of 0.2 s, with the de-aggregation results shown in Figure 4. Most hazard contributions were concentrated over a short distance of 20 km. Considering the low annual frequency of exceedance in hazard de-aggregation resulted in significant contributions from large magnitudes and short distances. At the same distance, as the magnitude approaches its maximum, the contribution to the hazard increases. The contribution to the hazard was greatest at the maximum magnitude or slightly lower. Most contributions fell within the positive epsilon bin, indicating that ground motions larger than the median value of the GMPE were considered. The magnitude-distance-epsilon pair (M-R-\(\varepsilon\) bin) with the highest contribution to the hazard is shown in Table 2. Based on the de-aggregation results expressed in bins, a moment magnitude of 6.5 and an epsilon of 0.75 were selected from Table 2 to specify the parameters of the scenario earthquake, with 10.0 km selected as the optimal distance value.