# Horizontal PGA Estimates for Varying Deep Geological Conditions--A Case Study of Banja Luka
## 4 PSHA Analysis for the Case Study Location in Banja Luka
The cumulative disaggregation for \(M\) and four different return periods is depicted in the top left plot of Figure 4:1 For the return periods of 95, 475, 975, and 2475, the magnitudes that contribute to 50% of the anticipated likelihood of exceedance are equal to 4.9, 5.2, 5.35, and 5.5, respectively. The three other plots in Figure 6 show the magnitude recurrence relations for the three most contributing source zones (in Figure 4, these three zones are designated with serial numbers). As can be seen from these plots, the real recurrence (return) periods of the earthquakes that contribute the most vary with the \"return period\", _Tr_, which represents just a reciprocal value of _N(a)_ (see Equations (6) and (10)). What is even more important, the real return periods are significantly shorter than the corresponding return periods, _Tr_. This is very important to understand, because Eurocode 8 [9] defines Types 1 and 2 spectra not in terms of maximum credible magnitudes but rather in terms of those magnitudes that \"contribute most to the seismic hazard defined for the site for the purpose of probabilistic hazard assessment\" (please refer to Eurocode 8 [9]: 3.2.2.1, (4), Note 2 and 3.2.2.2, (2)P, Note 1). The selection of the spectral type based on the most contributing earthquakes can be extremely confusing for average civil engineers. The type of spectrum is not specified in Bosnia and Herzegovina's National Annex to Eurocode 8 [14], and users are free to select it without being given access to the hazard disaggregation data. Given Banja Luka's history of experiencing earthquakes with magnitudes in excess of 6.0, it stands to reason that the majority of the contributing magnitudes would be greater than 5.5. However, Figures 5 and 6 show that the magnitudes of the most contributing earthquakes are smaller than 5.5, with the exception of the most contributing magnitude  
\begin{table}
\begin{tabular}{c c c c} \hline _P(pga)_ & _p(pga)_ [\%] & _p(pga)_ [\%] & _Tr(pga)_ = \(\frac{1}{\textit{Npqsd}}\)\(\simeq\)\(\frac{1}{\textit{Puga}}\)\(=\)\(\frac{1}{\textit{1-}\textit{U(  
for \(Tr\) = 2475 years. Even for \(Tr\) = 2475 years, this magnitude is equal to 5.5 or little less than 5.5. The seismic hazard curves for \(44^{\circ}46.5^{\prime}\) N, \(17^{\circ}15^{\prime}\) E (see Figures 1 and 4) were compared to the PGA values calculated based on regulations in former Yugoslavia (S  
Before we compare different hazard estimates, it is important to remember that the PGA values on the hazard maps provided in the National Annex to Eurocode 8 are for \"rock or comparable geological formations\" [9]. Under former Yugoslavian standards, official hazard maps were created for average local soil conditions, and the hazard was calculated using the MCS intensity scale degrees [43; 54; 55; 56]. The impact of deep geologic conditions was not explored in the creation of any of these maps. As shown in Figure 6, our PSHA estimates of horizontal PGAs are in fair agreement with those from 1990 macroseismic intensities [56] only for the return periods of 50 and 10,000 years. For all other return periods (100, 200, 500, and 1000 years), our estimates are much smaller. However, our estimates in the case of (deep) geological rock and stiff soil sites are in good agreement with the PGA values for Banja Luka from the 2018 official maps of Bosnia and Herzegovina [14].