## 1 Introduction  
Rotational ground motion is described by three components: torsion, as motion around a vertical axis, and rocking--around two horizontal axes [1]. Generally, rotational seismology is used to study the effects of natural seismicity [2, 3, 4, 5, 6], but the influence of anthropogenic seismicity has also been taken into consideration in the last decade [7, 8, 9]. Separate topics concern the rotation-to-translation scaling relations or transformations [10, 11] and the generation of a specific sequence of translational and rotational motions in anisotropic media [12, 13]. In addition, one should note that concerns about the effects of rotational motions on civil structures [14, 15, 16, 17] and their potential responsibility for the instability of the failure mechanism of landslides and slopes [18, 19] have increased significantly over the past two decades. Nevertheless, one poorly documented issue still needs to be addressed: the relation between rotation and site conditions. Regarding the translations, the site effect parameters can be estimated using the horizontal-to-vertical (H/V) spectral ratio method [20]. Further research has shown that the H/V method can be used to estimate the rotational site effect parameters after rewriting the equations [11, 21, 22, 23, 24]. The new formula assumes the torsion-to-rocking spectral ratio (TRSR) estimations, which correspond to the horizontal rotation spectrum to the vertical rotation spectrum [11, 21, 22, 23, 24]. The explanation for rewriting the original H/V formula is motivated by the fact that torsion represents motion in the horizontal plane, while rockings are motions in the vertical plane [21]. In the literature, one can find comparisons of the rotational and translational amplification spectrum performed for the rotation of the registered components [23] and related to estimating the spectrum ratio [24]. However, given that the amplification effect and the resonance of the wave in the ground affect the observed translational and rotational signals [22; 23; 24], the parameters of the scaling relation between the rotational and translational peak values should also be affected by the site effect [4; 5; 9; 11; 25; 26; 27]. The main contributions of the current research are as follows:  
1. Investigated the possibility of estimating the site effect parameters of rotational motion using the rewritten horizontal-to-vertical spectral ratio method and comparing the obtained results to the translational motion.
2. Estimated the scaling relation between the maximum peak values of horizontal ground acceleration (PGA) and vertical rotational velocity (PRV) for two models, y = ax and y = ax + b, checking whether the intercept b is significant and what physical meaning it may have.
3. Analyzed the influence of amplification on the scaling relation function by re-estimating the models for amplification factor-corrected data sets.  
The rest of the manuscript is arranged as follows: Section 2 presents a detailed description of the site conditions, seismic data characteristics, and applied methods; Section 3 presents the results of the analysis; Section 4 explores the discussion part of the paper; and finally, Section 5 concludes the study.