# Characterization of HVSR and VRSR in the Loess Plateau of China Based on Strong-Motion Data
## 5 Conclusions  
This study analyzes the key characteristics of the average Fourier amplitude spectrum, power spectrum, HVSR, and VRSR based on strong-motion records from the Loess Plateau region. The findings are as follows. (1) Under seismic activity, the Fourier amplitude spectrum exhibits certain regularities, with both \(F_{max}\) and \(T_{f}\) increasing as the magnitude rises. The epicentral distance significantly impacts the horizontal components \(F_{max}\) and \(T_{f}\), with horizontal components generally exceeding the vertical component (UD direction). (2) The power spectrum is also influenced by the magnitude and epicentral distance. As the magnitude increases, both \(P_{max}\) and \(T_{p}\) rise, with the exception of the magnitude range between 7.1 and 8, where the differences between the horizontal and vertical components of \(P_{max}\) and \(T_{p}\) become insignificant. Epicentral distance has a large effect on the power spectrum, but when the epicentral distance exceeds 200 km, the differences between the horizontal and vertical components decrease. (3) The values of \(A_{0}\) and \(T_{0}\) for HVSR and VRSR show variations depending on seismic factors. The average \(A_{0}\) for the Loess Plateau region is about 3, and \(T_{0}\) is around 0.4 s, which is consistent with the theoretical results. \(A_{0}\) is stable around 3, with little influence from the magnitude, epicentral distance, or focal depth, while \(T_{0}\) varies significantly, with ranges of 0.14-0.57 s, 0.18-0.66 s, and 0.17-0.45 s for magnitude, epicentral distance, and focal depth, respectively. (4) The average HVSR and VRSR values are closely related to the loess thickness. As the loess thickness increases, \(A_{0}\) rises while \(T_{0}\) decreases. However, when the thickness exceeds 20 m, \(A_{0}\) begins to decline and \(T_{0}\) increases, reflecting the complex impact of loess thickness on the site.  
The unique structure of loess and the rarity of strong earthquakes have limited the availability of strong-motion records, hindering research in this field. This data shortage has prevented the comprehensive development of engineering recommendations, such as understanding the extent of loess's influence on seismic motion and the validity of its dynamic parameters. Several issues remain to be addressed, including the impact of loess on seismic motion and the suitability of dynamic parameters for loess.  
Methodology, Q.L. and J.B.; Software, Q.L.; Formal analysis, Q.L.; Data curation, Q.L.; Writing--original draft, Q.L.; Writing--review & editing, Q.L., J.B. and D.P. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China grant number U1939209 and Scientific Research Fund of Institute of Engineering Mechanics, China Earthquake Administration grant number 2020 EEEVL0201. The APC was funded by 2020 EEEVL0201.  
Not applicable.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{\(H\) (m)} & \multicolumn{2}{c}{**HVSR**} & \multicolumn{2}{c}{**VRSR**} & \multirow{2}{*}{**Number**} \\ \cline{2-2} \cline{4-5}  & \(A_{0}\) & \(T_{0}\) (s) & \(A_{0}\) & \(T_{0}\) (s) & \\ \hline
0–5 & 3.68 & 0.60 & 2.72 & 0.47 & 11 \\
5–10 & 3.59 & 0.37 & 2.95 & 0.38 & 21 \\
10–20 & 4.84 & 0.21 & 3.69 & 0.28 & 13 \\ \(\geq\)20 & 2.58 & 0.45 & 2.93 & 0.43 & 8 \\ \hline \end{tabular}
\end{table}
Table 8: List of HVSR and VRSR \(A_{0}\) and \(T_{0}\) periods for different loess thickness subgroups.  
Data Availability Statement: The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors declare no conflict of interest.