## 3 Empirical Results and Analysis  
### Establishment of Prediction Equations of Peak Ground Motion  
#### 3.1.1 PGA Prediction Equation  
Peak ground acceleration (PGA) represents the maximum value of inertial forces caused by ground motion and is measured based on cm/s\({}^{2}\) (also known as gal) or m/s\({}^{2}\) or in terms of gravitational acceleration (g). In this study, gal was used as the unit of PGA. PGA reflects the high-frequency characteristics of ground motion. It is important to note that the PGA attenuation relationships presented in this section are derived from the fitting of data without distinguishing different site conditions. Through a comparative analysis, we found that the orthogonal distance fitting method outperformed the optimization algorithm in fitting the PGA attenuation relationship. The results of the fitting using Model 2 are presented in Table 3, which exhibits high goodness of fit values for each direction. However, coefficient B is zero, and coefficients A and C have large standard deviations, indicating the need for further fitting. BR represents the non-elastic attenuation term within the medium. It arises from the energy absorption in the propagation medium, leading to the energy attenuation of seismic waves. Given the relatively limited impact of the non-elastic attenuation, it is often simplified in engineering applications by amalgamating its effects into geometric attenuation, thereby omitting the BR term. To achieve better fitting results, the data of PGA in each direction were refitted using Model 3. The obtained coefficient values are presented in Table 4. The goodness of fit for the horizontal PGA attenuation relationship improved to 0.99411, and the standard deviation of coefficient A decreased from 0.38454 to 0.16406. The standard deviations of the fitting parameters for all four prediction equations also decreased, demonstrating a better fitting performance that could reflect the attenuation trend of the original data. The PGA values and attenuation curves for the east-west (EW) and north-south (NS) components of each station's records are shown in Figure 2a. For the same fault distance, the calculated values of the NS PGA equation were slightly larger than those of the EW PGA equation. Based on the analysis of 194 strong-motion records, the NS PGA was on average 1.0057 times the EW PGA. The ratio of the NS PGA to EW PGA ranged from 0.44 to 1.82, with 91 stations having ratios greater than one and 103 stations having ratios smaller than one. The PGA values and attenuation curves for the horizontal and vertical components of each station's records are displayed in Figure 2b. Overall, both the recorded and calculated values of the horizontal PGA were larger than those of the vertical PGA. The attenuation rates for horizontal and vertical components were generally similar, with a slightly faster decay observed in the vertical direction. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type** & **A + \(\sigma\)** & **B** & **C + \(\sigma\)** & **Adjusted R-Square** \\ \hline East–West PGA & 5.709 \(\pm\) 0.232 & / & \(-1.913\)\(\pm\) 0.113 & 0.994 \\ \hline North–South PGA & 5.750 \(\pm\) 0.233 & / & \(-1.927\)\(\pm\) 0.114 & 0.994 \\ \hline Horizontal PGA & 5.730 \(\pm\) 0.164 & / & \(-1.920\)\(\pm\) 0.0800 & 0.994 \\ \hline Vertical PGA & 5.691 \(\pm\) 0.274 & / & \(-2.011\)\(\pm\) 0.139 & 0.994 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Modified coefficient table of PGA prediction equation.