## 3 GMPEs for Vertical PGA Values for Varying Deep Geology  
We will next present empirical GMPEs for estimating vertical PGA values when local soil and deep geology effects are to be considered together. The equations will be expressed in the following mathematical form:  
\[ \begin{split}\log[PGAvert]=& c_{1}+c_{2}\cdot M+c_{3} \cdot log(\sqrt{R^{2}+R_{0}(T)^{2}})+c_{4}\cdot S_{L1}+c_{5}\cdot S_{L2}\\ &+c_{6}\cdot S_{G1}+c_{7}\cdot S_{G2}+\alpha_{log}\cdot P.\end{split}  \tag{2}\]  
In Equation (1), \(PGAvert\) is the vertical maximum acceleration (in \(g\)), \(M\) represents the earthquake magnitude, and \(R\) represents the epicentral distance. Equations for hypocentral distance were also generated in our prior studies [2, 14, 15, 16]. Table 4 lists the categorical factors \(S_{L1}\), \(S_{L2}\), \(S_{G1}\), and \(S_{L1}\). The local soil conditions were classified as per [PERSON] et al. [11, 12], and the deeper geological conditions were in line with [PERSON] and [PERSON]'s classification [10]. Before we proceed to discuss the magnitude types we used, we should reiterate that the EQINFOS database [18], which includes records from earthquakes in the northwest Balkan region, serves as the foundation for our analysis. For the largest events (magnitudes that exceeded 6.0), the database's authors employed the \(M_{S}\) magnitude; for all other events, they employed the \(M_{L}\) magnitude as specified by [PERSON] et al. [40]. The local magnitude, \(M_{L}\), was deliberately selected for the majority of events, as it was deemed most suitable for \begin{table}
\begin{tabular}{c c c c} \hline
**Local Soil** & **Local Soil** & **Deep Geology** & **Deep Geology** \\
**Parameters** & **Categorical Variables** & **Parameters** & **Categorical Variables** \\ \hline “Rock” soil sites: & & & \\ \(s_{L}=0\) & \(S_{L1}=S_{L2}=0\) & \begin{tabular}{c} Basement (geological) rock: \\ \(s=2\) \\ Intermediate (or complex) \\ sites: \\ \(s_{L}=1\) \\ \end{tabular} & \(S_{L1}=1\) and \(S_{L2}=0\) & \
\begin{tabular}{c} Basement (geological) rock: \\ \(s=2\) \\ Intermediate (or complex) \\ sites: \\ \(s=1\) \\ \end{tabular} & \(S_{G1}=S_{G2}=0\) \\ Deep soil sites: & & (Deep geological) & \(S_{G1}=1\) and \(S_{G2}=0\) \\ \(s_{L}=2\) & \(S_{L1}=0\) and \(S_{L2}=1\) &
\begin{tabular}{c} Basement (geological) rock: \\ \(s=2\) \\ \end{tabular} & \(S_{G1}=0\) and \(S_{G2}=1\) \\ \hline \end{tabular}
\end{table} 
Table 4: Categorical variables from Equations (2)-(4) for shallow and deeper geological site conditions. \begin{table}
\begin{tabular}{c c} \hline
**Eurocode 8 [1] Ground Types** & **Vertical PGA** \\ \hline Eurocode 8, Type 1 Spectrum (\(M_{S}>5.5\)), all ground types [1] & \(a_{\text{g}}\,\times\,0.900\) \\ Eurocode 8, Type 2 Spectrum (\(M_{S}\leq 5.5\)), all ground types [1] & \(a_{\text{g}}\,\times\,0.450\) \\
1964 code of former Yugoslavia [36] & \(a_{\text{g}}\,\times\,0.330\) \\
1981 code of former Yugoslavia [39] & \(a_{\text{g}}\,\times\,0.700\) \\ GMPEs for California, USA [19], geological rocks & \(a_{\text{g}}\,\times\,0.760\) \\ GMPEs for California, USA [19], intermediate geological sites & \(a_{\text{g}}\,\times\,0.718\) \\ GMPEs for California, USA [19], geological sediments & \(a_{\text{g}}\,\times\,0.681\) \\ GMPEs for former Yugoslavia [22], all deep geology types & \(a_{\text{g}}\,\times\,0.720\) \\ \hline \end{tabular}
\end{table} 
Table 3: The vertical PGA according to various design codes and researchers based on the horizontal PGA value, \(a_{\text{g}}\), as provided for the analyzed site on the corresponding seismic hazard map. the so-called \"strong motion\"--the frequency content between 0.1 and 30 Hz that civil engineers are most interested in (see, for example, the related discussion in [41]). A later study that converted the \(M_{L}\) magnitudes of the earthquakes in Croatia and the surrounding regions to moment magnitudes (\(M_{W}\)) revealed that the difference in magnitudes between 3.5 and 6.5 was less than 2% [42].