## 2 Methods and Data  
### Attenuation Model  
Ground motion is influenced by factors, such as the seismic source, propagation medium, and site conditions. The attenuation relationship simplifies the expression of these three main influencing factors [2]. The attenuation model refers to the functional form of the attenuation relationship of ground motion, and the ground motion prediction equation represents the functional relationship between ground motion parameters and factors, such as the magnitude, distance, and site conditions. For nonlinear fitting of the strong motion observation data and for obtaining the coefficients of the attenuation model, the selection of an appropriate attenuation model is the key step in establishing a ground motion prediction equation. The quality and quantity of the samples used for regression analysis primarily determine the advantages and disadvantages of establishing prediction equations based on empirical methods.  
Duke introduced the linear term of \"\(R\)\" in the attenuation model to quantitatively represent the energy attenuation attributed to absorption, providing a comprehensive model that accounts for geometric attenuation factors associated with source characteristics, propagation distance, and inelastic attenuation effects [15]. This Duke model has since become the predominant choice for attenuation modeling in subsequent regression analyses within the field, as follows:  
\[\lg(Y)=A_{1}+B_{1}R+C_{1}lg(R+R_{0})+D_{1}M+\varepsilon \tag{1}\]  
In this study, the surface wave magnitude (MS) was used as the magnitude parameter, and since the research was limited to the attenuation characteristics of the mainshock in Pazarcik, Turkriye, the source parameter was set as a constant term, namely 7.8. Regarding the distance factor, both geometric attenuation and non-elastic attenuation were considered. The following attenuation model was used in this research:  
\[\lg(Y)=A_{1}+B_{1}R+C_{1}lg(R+R_{0})+\varepsilon \tag{2}\]  
where Y represents the ground motion parameter, which refers to the relevant variable, specifically the peak ground motion parameter that reflects the intensity characteristics of ground motion. \(R\) stands for the fault distance, representing the independent variable. \(A_{1}\), \(B_{1}\), and \(C_{1}\) are unknown constants obtained through fitting, and \(\varepsilon\) denotes the random error. The term \(R_{0}\) is introduced to control the near-field ground motion and needs to be determined through a trial calculation. After determining the attenuation model, the least squares method is often employed to perform regression fitting on the seismic record data to determine the coefficients in the functional relationship.  
Referring to previous research results, \(R_{0}\) is usually selected within the range of 0 to 45 with intervals of 5. In this study, east-west PGA data were fitted using \(R_{0}=25\), which provided the best fitting effect after the comparative analysis. Owing to limitations in length, the trial calculation process is not further described. During the regression analysis, the value range for A1 was 0 to 20, and for B1, it was \(-1\) to 0. If B1 is determined to be 0 after the trial calculation, the B1R term in Model 2 is removed, and the model is adjusted to Model 3, represented by Equation (3), for further data fitting. The value range for \(C_{1}\) was \(-5\) to \(-0.1\).  
\[\lg(Y)=A_{2}+C_{2}\lg(R+R_{0})+\varepsilon \tag{3}\]  
The meanings of the parameters in Equation (2) are the same as those in Equation (1). In the following, prediction equations are presented for PGA and EPA parameters for the bedrock site and soil site, without considering site classification, for both horizontal and vertical directions.