# Compatible Ground Motion Models for South Korea Using Moderate Earthquakes
## 3 Results
### Comparing Residuals  
Residuals were calculated based on Equation (1), comparing GMMs, and plotted along distance for familiarization. For plotting purposes, the residuals are based on spectral acceleration at T = 0.2 s. Moreover, specific V\({}_{\text{S30S}}\) were taken from Table 2 in calculations. Figure 8 plots the relative residuals for each recording relative to NGA West GMMs for all events considered in this study. Figure 8a shows the variability in the residuals for the 2016 Gyeongju event, with a majority of the relative residuals within two lognormal standard deviations at distances less than 200 km. After 200 km, the figure shows that the relative residuals for three of the five NGA-West GMMs (AS08, BA08, CB08) continue to increase, signifying a pattern of underprediction, while one of the five NGA-West GMMs (CB08) continued to decrease, signifying a pattern of overprediction. For the 2017 Pohang event shown in Figure 8b, the NGA-West GMMs generally show overprediction at distances less than 100 km. One of the GMMs (CB08) consistently overpredicted across the distances considered. Similar to the 2016 Gyeongju event, three of the five NGA-West GMMs underpredicted at distances greater than 100 km. Figure 8c shows similar patterns of increasing scatter at larger distances. Interestingly, all NGA-West GMMs overpredicted the Pohang aftershock event at distances less than 100 km, even though two GMMs have built-in considerations for aftershocks. The GMM estimates increasingly scattered with distance after about 130 km. Results for the offshore Ulsan earthquake are shown in Figure 8e. The scatter is considerable, going across 4 log normal standard deviations. Figure 8: Distribution of resultant z-scores for NGA-West GMM spectral accelerations at T = 0.2 s for the (**a**) Gyeongju, (**b**) 2017 Pohang, (**c**) 2016 Gyeongju foreshock, (**d**) 2018 Pohang aftershock, and (**e**) Ulsan earthquakes. For comparison, Figure 9 shows the results when NGA-West2 GMMs are applied to the earthquakes under study in a similar format to Figure 8. Figure 9 shows the same patterns as NGA-West GMMs for each event. However, the variability appears to tighten per recording when NGA-West2 GMMs are considered. This is due, in part, to the higher standard deviations in the NGA-West2 suite. Relative residuals were also calculated for both M\({}_{\text{W}}\) 5.5 events using the subset of NGA-East GMMs and are shown in Figure 10. This plot suggests that both DASG15 and PZCT18 GMMs performed relatively well at long distances, especially the DASG15 GMM. For the 2017 Pohang aftershock, the GMMs also show a similar tendency to overestimate earthquake ground shaking but perhaps not as variable as the M\({}_{\text{W}}\) 5.5 events. Table 5 presents the relative residual scores for each GMM compared at SA(T = 0.2s). What is somewhat simultaneously surprising and unsurprising is that both NGA-East GMMs considered herein outperformed their NGA-West and NGA-West2 GMMs in the South Korean region. It is surprising because NGA-East GMMs incorporated simulated results into their regressions, which were local to CENA conditions, most likely different from the Korean peninsula. What is unsurprising is the relative improvement, from the perspectives of residuals, that NGA-East GMMs have over NGA-West and NGA-West2 GMMs as they were later derived from active crustal regions, which the Korean peninsula is  
Figure 9: Distribution of resultant z-scores for NGA-West2 GMM spectral accelerations at T = 0.2 s for the (**a**) Gyeongju, (**b**) 2017 Pohang, (**c**) 2016 Gyeongju foreshock, (**d**) 2018 Pohang aftershock, and (**e**) Ulsan earthquakes. not, at least not yet. However, the I08 and I14 GMMs did well for all moderate earthquakes considered, which is perhaps not surprising as the original intent of that GMM was to revolve around rock sites, i.e., sites with relatively higher V\({}_{\text{S30}}\).