## 4 Discussion  
The PGAs recorded from 130 stations during the 2017 Pohang Earthquake are presented in Figure 8. Of these records, the PGAs at 20 stations within a source-to-site distance range of 11.56 to 99.8 km are used to validate the artificially generated earthquakes proposed in this study. While sufficient empirical data would enable more accurate PGA estimations, regions like the Korean Peninsula continue to face data limitations. This scarcity complicates direct comparisons between the PGAs of empirical records from actual earthquakes and those of artificial earthquakes.  
The close alignment between the median PGAs of the artificial and the recorded earthquake data, as shown in Figure 6, is attributed to the effective sampling of the randomly paired \(f_{c}\) and \(M_{0}\) sets. This representative sampling ensures consistency between the simulated and empirical medians, even with the limited number of available empirical records. By using consistent geological and seismological parameters across all distances and ensuring that the randomly sampled pairs reflect realistic physical characteristics, the  
Figure 8: Source-to-site distance versus observed PGAs for the 2017 Pohang Earthquake recorded at 130 stations.  
Figure 7: Probability density histograms and corresponding probability distribution curves for PGAs at a source-to-site distance of (**a**) 10 km, (**b**) 25 km, (**c**) 50 km, and (**d**) 75 km. Each distribution curve, depicted by a solid line, was fitted with a lognormal distribution.  
model provides reliable predictions of actual ground motions. Moreover, according to Table 4, the percentage differences between the median PGAs of the empirical data and the artificial earthquakes are 11.76%, 8%, 22.22%, and 20.34% for the source-to-site distance ranges of 10, 25, 50, and 75 km, respectively, with an overall average difference of 15.58%.  
Although the dataset expands as the source-to-site distance increases, the percentage difference between the empirical records and simulations does not necessarily decrease. However, a Mann-Whitney U test, which compares the distribution of PGAs rather than just their medians, yielded \(p\)-values of 0.84, 0.84, 0.09, and 0.10 for each case. These results, showing no significant statistical difference between the empirical and simulated PGA distributions (\(p>0.05\)), indicate that the overall distributions and median PGAs of both the empirical records and the artificial earthquakes exhibit a high degree of similarity. This similarity reinforces the predictive accuracy of the present stochastic model, as more empirical data become available, enhancing its reliability as a consistent estimator. This correspondence with actual ground motion distributions provides a basis for further validating the proposed method.  
Furthermore, the stochastic approach utilized in this study effectively models the probability distribution of PGA as a lognormal distribution, in agreement with findings from [45], which suggest that peak values of strong motion parameters are likely to follow a lognormal distribution. Figure 7 demonstrates that the PGAs from the artificial earthquakes generated in this study also exhibit this lognormal behavior. It supports the accuracy of the lognormal fittings applied and further illustrates the effectiveness of the stochastic approach for predicting PGA behavior in seismic analysis. By validating the model's ability to generate reliable PGA probability distributions, the evidence underscores the robustness of the proposed method in accurately capturing realistic seismic behavior patterns.