## 3 GMPEs for Vertical PGA Values for Varying Deep Geology
Additionally, according to [PERSON] [43], for magnitudes between 6.2 and 7.0, the difference between \(M_{S}\) and \(M_{W}\) magnitudes is approximately 0.2%. We therefore think that we can utilize our GMPEs in seismic hazard calculations with the seismic source zones determined by using the \(M_{W}\)-based seismicity data, taking into account the other constraints of the given database. Here, we must note that even the \(M_{W}\) magnitude has significant restrictions. As shown in recent studies by [PERSON] et al. [44] and [PERSON] and [PERSON] [45], the \(M_{\text{agg}}\) scale should be used to adjust the seismicity data in order to improve the accuracy of seismic hazard estimates. In our future research, we plan to modify our calculations by using other magnitude scales. However, this will wait until additional regional seismicity and strong motion data are collected, and further discussions on this topic will have to be left out of the purview of this study. The database used to derive equations for scaling _PGAvert_ consists of 218 vertical components of ground motion records from the region of the former Yugoslavia from 112 earthquakes of magnitude \(3<M\leq 6.8\)[18; 46; 47]. Detailed descriptions of the data can be found in [2; 15; 17]. The database has no records from events with magnitudes above 7, and less than 20% of the data is from events with magnitudes greater than 6.0. As a result, the generated predictive equations will be most useful in areas with low to moderate seismic activity. However, a comparison to real records from a 6.8 magnitude earthquake [17] demonstrates that these equations can be generalized to zones of moderate-to-high seismicity, assuming that magnitudes do not exceed 7. It should also be noted that the proposed attenuation equations do not account for potential _PGAvert_ variations as a function of fault rupture directionality (relative to the investigated site). As shown in a recent study, the directivity phenomenon (the presence of high-velocity pulses) can have a significant impact on low- and mid-rise masonry structures like those found in Banja Luka [48]. However, due to the limited quantity of near-fault pulse data in regional strong motion records, this will stay outside the scope of our current research. We conducted multiple linear regression analyses to compute the scaling coefficients, with \(R_{0}\) systematically adjusted to lower the root mean squared error. Since the majority of the data was obtained over short distances, we performed a supplementary analysis that only included data acquired at epicentral distances of less than 30 km. Finally, because we also conducted regression analyses for the pseudo-spectral accelerations at 61 vibration periods (and in both horizontal and vertical directions), in all our analyses the scaling coefficients were smoothed in MATLAB(r) (version 8.5, release 2015a) by \"weighted linear least squares and a second degree polynomial model\" [49; 50; 51]. We utilized a log-normal distribution for all regression analyses, with \(\sigma_{log}\) being the standard deviation of the decadic logarithm of PGA and \(\varepsilon\) being equal to 0 for median estimations. The resulting scaling equation for the _PGAvert_, based on the data recorded at all distances, is as follows:  
\[ \begin{split}\log[PGAvert]=&-1.6833+0.3947\cdot M-1.3 186\cdot\log(\sqrt{R^{2}+16.8^{2}})+0.1575\cdot S_{L1}\\ &-0.0165\cdot S_{L2}-0.1204\cdot S_{\text{G1}}-0.0678\cdot S_{ \text{G2}}+0.2428\cdot P,\end{split}  \tag{3}\]  
while based solely on the data recorded at distances of not more than 30 km, we got the following equation:  
\[ \begin{split}\log[PGAvert]=& 3.9665+0.4045\cdot M-4.5446\cdot\log(\sqrt{R^{2}+40.0 ^{2}})+0.1328\cdot S_{L1}\\ &-0.0165\cdot S_{L2}-0.1949\cdot S_{\text{G1}}-0.0630\cdot S_{ \text{G2}}+0.2506\cdot P.\end{split}  \tag{4}\]As illustrated in Figure 2, both deep geology and local soil influence _PGAvert_.