## 1 Introduction
We will also examine the ratios of the vertical to horizontal spectra. Table 1 presents the formulas for computing vertical to horizontal \(PSA\) ratios for Ground Type C using the spectra of Types 1 and 2 of Eurocode 8 [1]. As can be seen, the vertical to horizontal \(PSA\) ratio changes non-linearly with the vibration period, \(T\), with a general tendency to become lower with \(T\). For short periods, the so-called damping correction factor, \(\eta\), also influences this ratio. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Type 1 Spectrum: “Most Contributing” Earthquakes with \(M_{5}>5.5\)**} \\ \hline Vibration periods, \(T\) [s] & Vertical to Horizontal \(PSA\) Ratios \\ \hline
0.00–0.05 & 0.782 \(\times\) [1 + (\(\eta\times 3.0-1\)) \(\times\) T/0.05]/[1 + (\(\eta\times 2.5-1\)) \(\times\) T/0.2] \\
0.05–0.15 & 2.348 \(\times\) [1 + (\(\eta\times 2.5-1\)) \(\times\) T/0.2] \\
0.15–0.20 & 0.352 \(\times\) n/1/1 + (\(\eta\times 2.5-1\)) \(\times\) T/0.2]/T \\
0.20–0.60 & 0.141/T \\
0.60–1.00 & 0.235 \\
1.00–2.00 & 0.235/T \\
2.00–4.00 & 0.117 \\ \hline \hline \multicolumn{2}{c}{**Type 2 Spectrum: “Most Contributing” Earthquakes with \(M_{5}\leq 5.5\)**} \\ \hline Vibration periods, \(T\) [s] & Vertical to Horizontal \(PSA\) Ratios \\ \hline
0.00–0.05 & 0.3 \(\times\) [1 + (\(\eta\times 3.0-1\)) \(\times\) T/0.05]/[1 + (\(\eta\times 2.5-1\)) \(\times\) T/0.1] \\
0.05–0.10 & 0.9 \(\times\) n/1/[1 + (\(\eta\times 2.5-1\)) \(\times\) T/0.1] \\
0.10–0.15 & 0.36 \\
0.15–0.25 & 0.054/T \\
0.25–1.00 & 0.216 \\
1.00–1.20 & 0.216/T \\
1.20–4.00 & 0.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Vertical to horizontal \(PSA\) estimates for Types 1 and 2 of Eurocode 8 [1] spectra for Ground Type C.  
Figure 2: Empirical regional vertical \(PSA\) attenuation curves for four different vibration periods, \(T\) = 0.05 s, 0.10 s, 0.30 s, and 0.50 s, calculated using Equation (1), for deep soil sites (\(S_{L}=2\)) and for different deep geology parameters (\(S=2\) for geological rock sites, \(S=1\) for intermediate geological surroundings, and \(S=0\) for deep sediments). Solid lines show median empirical predictions obtained by using coefficients developed for all epicentral distances, while dashed lines show the predictions obtained by using coefficients developed for distances smaller than 30 km. The GMPEs that will be generated in this study will account for the effects of deep soils and deep geological sediments on the vertical spectra, which is a unique feature of this research. Most other GMPEs for vertical spectra only address local soil conditions via the V5,30 parameter [19; 20; 21; 22; 23]. However, strong motion predictions based on scaling equations that account for local soil conditions (up to depths of 100 m and more) as well as deep geology, have been proven to be very accurate when compared to recorded ground motions and observed intensities in the north-western Balkans [24; 25]. In addition, a series of recent regional seismic microzonation studies [26; 27; 28; 29; 30; 31] found that changes in deep geological site conditions can considerably increase seismic hazard estimates when compared to hazard estimates based simply on local soil effects.