# Characterization of HVSR and VRSR in the Loess Plateau of China Based on Strong-Motion Data
## 4 Results and Discussion
### Characterization of the HVSR and VRSR Mean Curve Features
#### 4.3.2 HVSR and VRSR Mean Curves Versus Magnitude, Epicentral Distance, and Focal Depth  
(1) HVSR and VRSR mean curves versus magnitude  
Using the strong-motion record distribution and magnitude groupings outlined in Section 4.1.1, the mean HVSR and VRSR curves for each magnitude group were calculated, as shown in Figure 12a,b. The corresponding \(A_{0}\) and \(T_{0}\) values derived from these mean curves for the different magnitude groups are provided in Table 5.  
As shown in Figure 12a,b and Table 5, the \(A_{0}\) values for both HVSR and VRSR are generally stable and remain around 3, with minimal variation across different magnitudes. However, the \(T_{0}\) values are notably influenced by magnitude, ranging from 0.14 s to 0.47 s.  
(2) HVSR and VRSR mean curves versus epicenter distance  
Using the distribution of strong-motion records and the epicentral distance groupings from Section 4.1.2, the mean HVSR versus epicentral distance curve and the mean VRSR versus epicentral distance curve were computed for each group, as shown in Figure 13a,b. The corresponding \(A_{0}\) and \(T_{0}\) values derived from these mean curves for the different epicentral distance groupings are presented in Table 6.  
Figure 12: (a) Curve of mean HVSR versus magnitude in the Loess Plateau region. (b) Curve of mean VRSR versus magnitude in the Loess Plateau region.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\(M_{avg}\)} & \multicolumn{2}{c}{**HVSR**} & \multicolumn{2}{c}{**VRSR**} & \multirow{2}{*}{**Number**} \\ \cline{2-2} \cline{5-6}  & \(A_{0}\) & \(T_{0}\) **(s)** & \(A_{0}\) & \(T_{0}\) **(s)** & \\ \hline
3.1–4 & 7.49 & 0.44 & 3.43 & 0.34 & 8 \\
4.1–5 & 3.94 & 0.22 & 3.47 & 0.22 & 47 \\
5.1–6 & 3.36 & 0.21 & 2.76 & 0.14 & 21 \\
6.1–7 & 3.21 & 0.31 & 2.97 & 0.47 & 11 \\
7.1–8 & 3.08 & 0.36 & 3.19 & 0.37 & 72 \\ \hline \hline \end{tabular}
\end{table}
Table 5: List of HVSR and VRSR \(A_{0}\) and \(T_{0}\) values for different for different magnitude subgroups.  
As seen in Figure 13a,b and Table 6, the \(A_{0}\) values for both HVSR and VRSR are largely unaffected by epicentral distance, consistently remaining around 3 with minimal variation. In contrast, the \(T_{0}\) values are strongly influenced by epicentral distance, varying between 0.18 s and 0.66 s.  
HVSR and VRSR mean curves versus focal depth  
Focal depths were classified into four ranges, namely, 4-8 km, 9-13 km, 14-15 km, and 16-21 km, according to the distribution of strong-motion records. The mean HVSR and VRSR curves for each range plotted against the focal depth are shown in Figure 14a,b. The \(A_{0}\) and \(T_{0}\) values derived from these curves for the different focal depth groupings are presented in Table 7.  
It can be observed from Figure 14a,b and Table 7 that the \(A_{0}\) values for both HVSR and VRSR are generally stable, remaining around 3 with minimal variation across different  
\begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{\(\mathbf{R}\) (km)} & \multicolumn{2}{c}{**HVSR**} & \multicolumn{2}{c}{**VRSR**} & \multirow{2}{*}{**Number**} \\ \cline{2-2} \cline{5-6}  & \(\mathbf{A_{0}}\) & \(\mathbf{T_{0}}\) **(s)** & & \(\mathbf{A_{0}}\) & \(\mathbf{T_{0}}\) **(s)** & \\ \hline
0–20 & 4.56 & 0.66 & 3.10 & 0.41s & 13 \\
20–50 & 3.07 & 0.36 & 3.18 & 0.37s & 43 \\
50–200 & 3.87 & 0.22 & 3.36 & 0.31 & 30 \\ \(\geq\)200 & 3.12 & 0.21 & 3.06 & 0.18 & 73 \\ \hline \end{tabular}
\end{table}
Table 6: List of HVSR and VRSR \(A_{0}\) and \(T_{0}\) values for different epicenter distance groupings.  
Figure 13: (**a**) Curve of mean HVSR versus epicentral distance in the Loess Plateau region. (**b**) Curve of mean VRSR versus epicentral distance in the Loess Plateau region.  
focal depths. In contrast, the \(T_{0}\) values are notably influenced by the focal depth, varying between 0.17 s and 0.45 s.