## 4 Discussion
### Scaling Relation
As Figure 6b shows, fitting raw and corrected data can create some estimation problems. The reason for this can be that one of the sensors was rotated by several degrees during the observation, and its registrations were disturbed by a deviation from the main geographic direction. However, errors of this type should affect the total recorded data. Thus, we can assume that a better fit would be obtained in terms of another estimation mode, which will depend on the exact ranges of recorded values--rotational or translational. Still, it cannot be taken for granted that one estimated model can be applied to all registration ranges. Based on recent research [21], in the case of the scaling relation between the vertical PRV and horizontal PGV, the function's slope is linked to the complexity of the local geology. The more excellent slope value should produce a higher value of the PRV for a given PGA of vertical component and, therefore, describe a more complicated surface geology [53]. Thus, considering our research, the potential connection of the \(a\) parameter with the complexity of the local geology cannot be excluded. Recent studies [5; 11; 26; 45] connected the \(a\) parameter with the local surface geology. Considering that the presented scaling relation was obtained for the peak values of the S-wave signal part, \(a\) should be linked to the apparent SH wave phase velocity [21]. Considering similar studies [21], the estimated apparent SH-wave phase velocity \(c\) equaled 379 m/s, with a standard deviation of 114 m/s. In the case of our study, \(a\) is proportional to \(1/(2c)\). Considering the results obtained for directly registered peak values and the model without intercept, the SH-wave phase velocity for the IMI and PLA stations was 1101 m/s and 982 m/s, respectively. However, the correction by an amplification value caused the SH-wave phase velocity for the IMI and PLA stations to reach 496 m/s and 387 m/s, respectively. The analyzed total models (Figure 5a,b) showed regression parameters similar to those for the separate IMI and PLA data. The question is whether these total models are universal. The location of the stations suggested similar geotechnical conditions due to the similar Vs30 value. Therefore, the obtained total models were expected to be a good approximation and match the empirical data. However, detailed visual inspection revealed that the model did not intersect the center of the points but generally emphasized points on the periphery. Therefore, the presented total model, obtained for two data sets with similar Vs30, cannot be treated as one model. Figure 8: Comparison of the scaling relation models between peak values of the rotational velocity and translational acceleration [5; 26; 45]. The above discussion can be summarized as follows:  
1. Correction of the data set by measured amplification value increases the approximation of the scaling relation model to the data by removing the local site effect from the data. 2. The scaling relation model without an intercept better approximated the data. 3. Correction by the amplification resulted in a lowered value of the apparent SH-wave and suggested a correlation of the function slope to the complexity of the local geology.