## 5 Results and Discussion
### Influence of Earthquake Magnitude on the Horizontal and Vertical Response Spectra  
We investigated the dependency of earthquake magnitude, one of the most important components of seismic sources, by grouping earthquake magnitudes according to their magnitude levels: ML 6.0-7.3 (4 earthquakes), ML 5.3-5.8 (6 earthquakes), and between ML 4.6-5.0 (5 earthquakes). Accordingly, we investigated the influence of earthquake magnitude on the horizontal response spectra. Furthermore, we extended the investigation of dependence on the magnitude to all eight stations and events. Similar to the previous case, all events were classified into three levels based on the earthquake magnitude. Based on the magnitude distribution of the 15 Kumamoto earthquakes, the earthquakes in this study were divided into three groups according to the earthquake magnitude: ML 6.0-7.3 (4 earthquakes), ML 5.3-5.8 (6 earthquakes), and ML 4.6-5.0 (5 earthquakes). Figure 7a shows three horizontal responses for the three magnitude levels. The responses increased as the magnitude of the earthquake increased in the frequency band below \(\sim\)1 Hz. Further, no significant difference was observed among the responses of the  
Figure 6: Normalized horizontal response spectra at (**a**) JJU1, (**b**) JJU2, (**c**) SGP1, and (**d**) SGP2 using Kumamoto and Pohang earthquakes series. three groups in the frequency band of 1-9 Hz. Lastly, all three responses decreased rapidly in the frequency band above \(\sim\)9 Hz and converged to similar values. The amplitudes and locations of the maximum responses for the first, second, and third groups were -4.9 (3.3 Hz), 4.6 (\(\sim\)2.6 Hz), and \(\sim\)4.6 (\(\sim\)2.2 Hz), respectively. The maximum responses and corresponding frequencies were in the range of 4.6-4.9 and 2.2-3.3 Hz, respectively, indicating no significant differences in the amplitudes and frequency bands of the groups. Therefore, the dependence of the response spectrum on the earthquake magnitude is limited to the low-frequency band below \(\sim\) 1 Hz. According to the extended and point seismic source models ([PERSON], 1970, [PERSON], 1976, [PERSON], 1998, [PERSON], 2003, [PERSON], 2015), earthquakes of ML between 6.0 and 7.3 exhibit a seismic source spectrum much higher in amplitude and broader in frequency than those of earthquakes of smaller ML ([PERSON] and [PERSON], 2015, 2016, 2017, 2018). In addition, as the epicenter distance increased, the seismic energy in the higher and lower  
Figure 7: Normalized (**a**) horizontal and (**b**) vertical response spectra of three groups of earthquake magnitude (15 events): M\({}_{\rm L}\) 6.0–7.3 (black solid), 5.3–5.8 (red solid), and 4.6–5.0 (blue solid), respectively. frequencies decreased rapidly and gradually, respectively, and then those of lower frequencies propagated farther. Therefore, as the epicentral distance increases, larger earthquakes exhibit higher responses in lower frequency bands, as shown in Figure 7a,b), and as suggested by previous studies ([PERSON] and [PERSON], 2007, [PERSON] and [PERSON], 2014, [PERSON] et al., 2018, [PERSON] et al., 2019) [15; 16; 28; 29]. Owing to the similarities in the effects of the site and wave propagation path ([PERSON] et al., 1999) on the shapes of the response spectra, the seismic source, that is, the distribution of larger magnitude, is essential in determining the characteristics of the response spectrum, especially in the low-frequency region, as suggested in previous studies ([PERSON] and [PERSON], 2007, [PERSON] and [PERSON], 2014, [PERSON] et al., 2018, [PERSON] et al., 2019), including recent studies ([PERSON], et al., 2017, [PERSON]; and [PERSON], 2011) [15; 16; 28; 29; 30; 31]. When establishing the response spectra representing an arbitrary region while compensating for the conservativeness in the low-frequency band, it is necessary to consider a number of fairly large magnitudes of earthquakes (e.g., ML 6.0 or larger). The historical earthquake records show over 10 earthquakes of magnitude 6.0 or greater in the Korean Peninsula.