## 3 Empirical Results and Analysis
### The Attenuation Characteristics of Bedrock Sites and Soil Sites  
Site conditions are one of the most important factors that influence seismic attenuation. Owing to the influence of the site effects, ground motion can exhibit considerable variations within a small range. Hence, it is necessary to establish ground motion prediction equations for different site types. In this study, the PGA attenuation relationships for bedrock and soil sites were fitted separately according to Model 2. The fittings included both horizontal and vertical components. For the vertical attenuation fitting of soil sites, Model 3 was employed, allocating a zero value for B. The fitting processes were carried out using the orthogonal distance regression method, and the values of the parameters are presented in Table 6.  
The PGA attenuation fitting curves for horizontal bedrock sites and soil sites, along with the PGA records from strong motion events on these sites, are shown in Figure 7a. The dataset for horizontal soil sites consisted of 204 samples, while the dataset for horizontal bedrock sites consisted of 76 samples. The PGA attenuation fitting curves for vertical rock and soil sites are exhibited in Figure 7b, based on a dataset of 88 records from soil sites and 34 records from rock sites. Figure 7a indicates that the attenuation fitting curves for bedrock and soil sites match well with the original data, reflecting the attenuation trend of the original data. However, the horizontal attenuation relationship fitting for bedrock sites had slightly larger errors due to the limited number and discrete distribution of near-field effective records obtained from bedrock sites. \begin{table}
\begin{tabular}{c c c c c} \hline
**Type** & **A + \(\sigma\)** & **B + \(\sigma\)** & **C + \(\sigma\)** & **Adjusted R-Square** \\ \hline Bedrock Horizontal & 5.204 \(\pm\) 0.978 & \(-\)0.00113 \(\pm\) 0.00234 & \(-\)1.646 \(\pm\) 0.585 & 0.992 \\ Soil Horizontal & 5.323 \(\pm\) 0.363 & \(-\)0.000627 \(\pm\) 0.000815 & \(-\)1.671 \(\pm\) 0.217 & 0.998 \\ Bedrock Vertical & 4.778 \(\pm\) 1.339 & \(-\)0.000907 \(\pm\) 0.00359 & \(-\)1.537 \(\pm\) 0.818 & 0.996 \\ Soil Vertical & 5.683 \(\pm\) 0.215 & / & \(-\)1.994 \(\pm\) 0.111 & 0.999 \\ \hline \end{tabular}
\end{table} 
Table 6: Coefficients of horizontal PGA prediction equations. Figure 6: Scatter plot of the vertical-EPA-to-horizontal-EPA ratio. An analysis of Figure 7 reveals that under the same fault distance conditions, the horizontal PGA for soil sites is greater than that for bedrock sites. This is attributed to the stronger ground-motion-amplification effect in softer soil layers. The vertical characteristics exhibited some differences compared to the horizontal characteristics, with significant amplification effects in the vertical soil layers observed only within the fault distance range of 0 to 100 km. Beyond 100 km, the vertical PGAs for both bedrock and soil sites were almost similar. To quantitatively represent the ground-motion-amplification effect of soil sites, we calculated site amplification factors based on the fault distance (Table 7). The site amplification factor is the ratio of the PGA calculated using the soil site PGA prediction equation to the PGA calculated using the bedrock site PGA prediction equation at the corresponding distance point [22]. Overall, using the bedrock site PGA as a reference, the average amplification factor for horizontal site effects was 1.46, while that for vertical soil site effects was 1.12, indicating a substantially stronger seismic effect in soil layers compared to bedrock. This helps us to explain the more severe seismic damage to structures on soil sites compared to those on bedrock sites at the same fault distance. It is worth mentioning that the seismic-motion-amplification effect of soil was largely manifested in the horizontal direction, while no significant seismic-motion-amplification effect was observed in the vertical direction. As the fault distance increased, the horizontal amplification effect of soil became increasingly prominent.