# Horizontal PGA Estimates for Varying Deep Geological Conditions--A Case Study of Banja Luka
## 3 GMPEs for Horizontal PGA and Varying Deep Geology  
The northwestern Balkans are one of the few areas in the entire world with available information on deep geological conditions from numerous recording stations. Several researchers used those regional strong motion data to develop GMPEs that take into consideration both local soil (up to 100 m in depth) and deep geology [7; 25; 26]. The GMPEs were employed in a series of recent microzonation studies and shown to be in great agreement with recorded macroseismic intensities [6; 57; 58; 59; 60; 61; 62; 63; 64; 65]. We are now going to present regional empirical equations for estimating PGA values that account for both local soil conditions and deep geological site environment. The attenuation equations will be defined in this mathematical form:  
\[\log[\text{PGA}]=c_{1}+c_{2}\cdot M+c_{3}\cdot\log(\sqrt{R^{2}+R_{0}(T)^{2}} )+c_{4}\cdot S_{L1}+c_{5}\cdot S_{L2}+c_{6}\cdot S_{G1}+c_{7}\cdot S_{G2}+ \sigma_{\log}\cdot P. \tag{2}\]  
In Equation (2), PGA denotes horizontal peak ground accelerations (in \(g\)), \(M\) is the earthquake magnitude (refer to [66] for more information on magnitude type), and \(R\) is the epicentral distance. Equations for the hypocentral distance were also developed in our previous studies [57; 58; 59; 60]. \(S_{L1}\) and \(S_{L2}\) are categorical variables for local soil, while \(S_{G1}\) and \(S_{G2}\) are for deep geological conditions. Table 3 summarizes these categorical variables. In Table 3, we use the same values for the categorical (dummy) variables (\(S_{L1}\), \(S_{L2}\), \(S_{G1}\), and \(S_{G2}\)) and site parameters (\(s_{L}\) and \(s\)) as defined in [8]. We assumed that the data had a log-normal distribution. Consequently, \(\sigma_{\log}\) is the standard deviation of the common logarithm of PGA, and \(\varepsilon\) is equal to 0 for the median estimate and \(\pm 1\) for the median \(\pm 1\)\(\sigma_{\log}\) estimates. The database for prediction equations includes 436 horizontal components of strong-motion accelerograms from 112 earthquakes with a magnitude of \(3<M\leq 6.8\). Our analysis is predominantly based on the EQINFOS database [67], which contains records from earthquakes in the northwest Balkan region. The authors of the database used the \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: & \(S_{L1}=S_{L2}=0\) & Geological rock: & \(S_{G1}=S_{G2}=0\) \\ \(s_{L}=0\) & & \(s=2\) & \\ Stiff soil sites: & & Intermediate (or complex) & \\ \(s_{L}=1\) & \(S_{L1}=1\) and \(S_{L2}=0\) & sites: & \(S_{G1}=1\) and \(S_{G2}=0\) \\  & & & (Deep geological) \\ Deep soil sites: & \(S_{L1}=0\) and \(S_{L2}=1\) & sediments: & \(S_{G1}=0\) and \(S_{G2}=1\) \\ \(s_{L}=2\) & & \(s=0\) & \\ \hline \end{tabular}
\end{table} 
Table 3: Categorical variables used in this study for different types of local soil and deep geological site settings. \(M_{L}\) magnitude as defined by [PERSON] et al. [66] for all events with a magnitude smaller than around 6.0, while only for the strongest earthquakes, they used the \(M_{S}\) magnitude. They purposefully chose the local magnitude, \(M_{L}\), for the majority of events, since it was thought to be most suited for the so-called \"strong motion\"--the frequency content between 0.1 and 30 Hz that civil engineers are most interested in [68]. According to a subsequent study that converted the \(M_{L}\) magnitudes of the earthquakes in Croatia and the adjacent areas to moment magnitudes (\(M_{W}\)) [69], the difference between \(M_{L}\) and \(M_{W}\) was less than 2% for magnitudes between 3.5 and 6.5. Furthermore, [PERSON] [70] found that the gap between \(M_{S}\) and \(M_{W}\) magnitudes is roughly 0.2% for magnitudes between 6.2 and 7.0.