## 4 Discussion
### Scaling Relation  
The tested linear models, with and without the intercept, showed a perfect fit assessment with R2 \(>\) 0.85 and low values of SEE \(<\) 2.5 \(\times\) 10\({}^{-5}\). However, the models without the intercept provided the highest R2 values. This suggests that the model of PRV = aPGA seems to be more accurate than the model with intercept. Nevertheless, the analysis showed that all obtained models are reliable. According to previous research [11], the Vs30 significantly influences the regression parameters; however, the models (for IMI and PLA station) obtained for the raw data seem to be convergent, and comparable Vs30 values cause this similarity in both cases. So far, the presented scaling relations have not considered the amplification phenomenon in the near-surface layer. The scaling relations in the recent studies [4; 5; 11; 26; 45] were performed for the natural events registered in a greater epicentral distance than in the case of our study. Therefore, it is tough to ignore the possibility that the peak values were registered at the group of the surface waves, while in the case of our study, they were registered at the S-wave part. Therefore, the \(a\) coefficient should be considered as a slowness of the S-wave, while in the case of the recent studies [4; 5; 11; 26; 45], the \(a\) coefficient is connected with the slowness of the Love waves and denoted as the \(c\). Therefore, the models presented in our study should be treated separately due to differences in estimating the scaling relation for the peak values registered at the group of the surface waves. Nevertheless, the primary issue is still connected with the site effect impact on the determined scaling relations. In the presented study, the estimated peak values of the H/V ratio were used to correct the peak values of the signals and, consequently, remove the site effect impact on the estimated scaling relation. Moreover, the peak values of the signals were divided by the single amplification value, which was allowed due to the generation of the single clear peak of the amplification on the H/V spectrum. In the case of multiple amplification peaks on the H/V spectrum, this procedure should be changed to dividing signal peak values respective to that event H/V spectrum. The designation of the general peak of the H/V ratio in case of multiple peak occurrences can be done by estimating the H/V ratio using the response spectrum method, which should present one general peak [43]. Taking into account the research carried out for the same database [22; 23], the H/V ratio obtained from the response spectrum method presented identical general peaks for the same database, as was given during that research. Therefore, the obtained general peak values of the H/V ratio can be used to reduce the impact of amplification on the signal peak values. The new models converge (Figure 8), confirming their universal application for the USCB area. If they were different, something else would influence their trend apart from amplification and local geological conditions. The other worldwide models presented in Figure 8 differ from models from this study, which is an effect of the studied scaling relation for the signal peak values obtained for the surface waves. The presented scaling relations are based on two linear models: with and without the intercept. The function without the intercept has an explanation resulting from Equation (4). Nevertheless, some authors [5; 26; 45] used the function with the intercept \(b\). The physical nature of the parameter is unknown; it is only mathematical. The calculated _b_-values were low and can be assumed to be negligible. However, the non-zero _b_-value suggests that the rotation peak can exist without a translation motion. Forcing the _b_-value to 0 improved the statistical fit of the observational data to the model and increased the slope, resulting in an insignificant _a_-value modification. Using the function with intercept b also has another limitation.