## 4 Effect of Seismic Parameters on Vertical DRFs
### The Effect of Distance  
Figure 8 shows the variation in the mean DRFs at damping ratios (\(\xi\)) equal to 1%, 3%, 10%, 15%, 20%, 30%, and 40% for two source-site distance groups. The first group corresponds to less than 30 km, and the other is higher than 30 km.  
Figure 8 shows that the DRFa is less sensitive to the damping ratio at a distance higher than 30 km compared to the DRFd and DRFv. Figure 8c,d show that the DRFd is equal to unity for very short period values, and it tends to move away from unity as the rupture distance increases for long ranges of structural periods. This tendency is consistent with the studies carried out by [PERSON] et al. [29]. The results in Figure 8e,f indicate that the DRFv curves approach unity, especially for short periods (T < 0.02 s). Then, the DRFv values diverge from unity until reaching 0.1 s. After 1.0 s, the DRFv values approach unity again for long structural periods and R\({}_{\rm rup}\)\(\leq\) 30 km.  
Figure 8: The variation in the median DRFs for different damping ratios by rupture distance; (**a**,**c**,**e**) R\({}_{\rm rup}\)\(\leq\) 30 km, (**b**,**d**,**f**) R\({}_{\rm rup}\)\(>\) 30 km.  
Figure 7: Effect of moment magnitude (M\({}_{\rm w}\)) on DRFs calculated for different damping ratios; (**a**–**d**) DRFa, (**e**–**h**) DRFd, and (**i**–**l**) DRFv.  
In Figure 9, the difference between the DRF curves of the distinct distance bins (i.e., \(\mathrm{R_{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{ \mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{}}}}}}}}}}}}}}}} \leq 30\) and \(\mathrm{R_{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{ \mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{ }}}}}}}}}}}}}}} >30\) km) is compared at different damping ratios. The figure indicates that the DRFa values are almost the same for all the distance groups up to periods of 0.02 s, 1.5 s, 0.9 s, 0.7 s, 0.5 s, 0.4 s, and around 0.3 s for damping ratios of 1%, 3%, 10%, 15%, 20%, 30%, and 40%, respectively. Beyond these periods, the differences become more evident at high damping and for longer periods.  
The figures for the DRFd (see Figure 9e-h) and the figures for the DRFv (see Figure 9i-l) clearly indicate that the DRF values are greater than unity at damping ratios lower than 5% and lower than unity under the opposite conditions for both of these types of DRFs. It can be also said that the DRFs calculated for \(\mathrm{R_{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{ \mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{ \mathrm{ \mathrm{ \mathrm{ }}}}}}}}}}}}}}}}}} >30\) km are higher than the DRFs calculated for \(\mathrm{R_{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{ \mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{ \mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{  \mathrm{   \mathrm{    }}}}}}}}}}}}}}}}} >30\) km in general. This difference becomes more pronounced as the damping and the structural period increase. This trend has also been observed by [PERSON] and [PERSON] (2019). In general, it can be considered that the DRFd and DRFv are not influenced by the rupture distance parameter.