## 3 GMPEs for Vertical PGA Values for Varying Deep Geology
The coefficients of the variables \(S_{L}\) and \(S_{G}\) can be used to compute the differences in the PGA calculated for different site conditions. For example, if the deep geology parameters remain constant and Equation (3) is utilized, the PGA value for stiff soil sites is \(10^{0.1575}=1.44\) times that for rock sites and \(10^{-0.0165}=0.96\) times that for deep soil. In other words, for deep soil, seismic waves are de-amplified as energy dissipation outweighs local soil amplification. Likewise, if the local soil type remains the same, the PGA values will be lower at geological sediments and intermediate sites than at geological rock sites, since short-period waves travel more easily through compact hard rocks like granites or basalts. Specifically, the PGA estimates at geological rock will be \(1/10^{-0.1949}=1.57\) times larger than at intermediate locations, and \(1/10^{-0.0630}=1.16\) times larger than at geological sediment locations. All of these statistics demonstrate not only that site conditions have a significant impact on _PGAvert_ but also that the deep geology effects are even greater than the local soil effects. For the epicentral distance of 10 km, Figure 2 shows _PGAvert_ ranges estimated with Equation (1) (median \(\pm\) one standard deviation) for VIII \({}^{\circ}\)MCS. The intensity of VIII \({}^{\circ}\)MCS was predominant during the 1969 earthquake in Banja Luka, and the epicenter was at a distance of around 10 km. We can see that only the combination of stiff soil and deep geology rocks may produce a median empirical _PGAvert_ equivalent to that associated with VIII \({}^{\circ}\)MCS. Figure 3 compares 18 _PGAvert_ values recorded at the four different accelerograph stations in Banja Luka [18] (see the red circles in the bottom plot of Figure 1) with the median and median \(\pm\sigma_{log}\) empirical estimates, which were obtained using Equation (3). The empirical estimates for _PGAvert_ are in good agreement with the actual records in Banja Luka, as Figure 4 illustrates. Figure 2: The empirical GMPEs for _PGAvert_, defined by Equations (3) (solid lines) and (4) (dashed lines), for different deep geology and local soil combinations (see Table 4). The gray area shows the 95% confidence interval (median \(\pm\) 2\(\cdot\sigma_{log}\) empirical _PGAvert_ estimates) for \(s_{L}=2\). Figure 4: VHPga values for source-to-site distances up to 100 km and different deep geology and local soil types, calculated by using Equations (3) (solid lines) and (4) (dashed lines), and corresponding equations for the horizontal direction [51]. Figure 3: The _PGAvert_ values recorded by four different accelerograph stations in Banja Luka (see the red circles in Figure 1) vs. the median and median \(\pm\sigma_{\text{log}}\) empirical _PGAvert_ estimates, which were calculated using Equation (3). The 95% confidence interval (median \(\pm\) 2\(\cdot\sigma_{\text{log}}\) empirical _PGAvert_ estimates) is displayed by the gray area. Figure 4 displays the VHpga for different site conditions and distances. The VHpga values, as shown, are influenced by deep geology, local soil, source-to-site distance, and the probability level of empirical estimates. For distances up to 100 km, the empirical VHpga ranges from 0.30 to 0.66 for the rock soil sites, from 0.30 to 0.65 for the stiff soil sites, and from 0.36 to 0.78 for the deep soils.