## 4 Uniform Hazard Spectra and Seismic Hazard Maps for Osijek  
In this section, we perform a probabilistic seismic hazard assessment (hereinafter, PSHA) analysis utilizing Equation (1) as the GMPE and coefficients from Table 1, assuming the deep soil sites and deep geological layers throughout the analyzed area. We also employ the SHARE Project's pan-European seismic source zone model [34; 35; 36]. The boundaries of the seismic source zones employed in this study's hazard calculations are depicted in Figure 6. The same figure also shows the radii of 123, 184, and 228 km, which show the epicentral distances that must be incorporated in the PSHA calculations for the 475-year return period to obtain 1% accuracy for computed spectral amplitudes at 0.05, 0.3, and 0.5 s, respectively. These radii show that the short-period spectral amplitudes are less sensitive to the occurrence of distant strong earthquakes and are dominated by the local seismic activity. Furthermore, the circle with a radius of 43 km designates the distances that contribute to 50% accuracy of PSHA calculations for the 0.5 s spectral amplitude. The epicenter of the largest historical (M 4.6, 1922) earthquake near Osijek, which is also shown in Figure 6, falls almost within this radius around the analyzed area. Figure 5: Correlation between regional horizontal pseudo-acceleration spectra recorded at deep soil sites (\(s_{L}=2\)) and the empirical predictions of Equation (1) and the coefficients in Table 2.  
The PSHA estimations were generated with REASSES V2.0 software [37], which is based on [PERSON] [38] and [PERSON]'s [39] methodology. According to this methodology, to calculate the mean yearly rate of occurrence, \(N(a)\), of seismic events that will cause a ground motion \(PSA\) amplitude \"\(A\)\" to exceed expectation \"\(a\)\", products of probabilities related to distance, magnitude recurrence, and GMPE predictions are integrated over all the considered magnitudes and distances and summed. If homogeneous Poisson distribution is assumed, the probability of at least one yearly exceedance of the expectation \(a\) can be calculated as follows [40]:  
\[P(a)=1-e^{-N(a)}. \tag{2}\]  
If a binomial distribution is additionally considered, the chance that \(A\) will surpass \(a\) at least once throughout \(t\) years can be estimated as follows [40]:  
\[p(a)=1-[1-P(a)]^{t} \tag{3}\]  
The so-called return period, \(Tr\), is then equal to \(N(a)^{-1}\) and does not (in general) correlate to any single engineeringly significant earthquake. Magnitudes and distances of earthquakes contributing to \(N(a)\) can be determined using a technique known as \"seismic hazard disaggregation\" [41]. In the disaggregation, we can additionally define the values of the number of standard deviations that \(\log(a)\) is distant from the median empirical estimate for each pair of magnitude and distance [42]. Figure 7 shows hazard disaggregation examples for the coordinates \(45^{\circ}32^{\prime}\) N, \(18^{\circ}23^{\prime}\) E. Top plots and the bottom-left plot in Figure 8 show cumulative disaggregation for distances and magnitudes. The magnitude recurrence curve for the most contributing seismic source zone surrounding Osijek is in the bottom-right plot. As can be observed, the real return periods of the most contributing earthquakes vary depending on the vibration period and are substantially shorter than the so-called return period \(Tr\), defined as a reciprocal value of the mean yearly rate of occurrence, \(N(a)\). This is significant because Eurocode 8 [16] does not define Types 1 and 2 spectra in terms of maximum credible earthquake magnitudes but rather in terms of magnitudes that \"contribute most to the seismic hazard defined for the site for the purpose of probabilistic hazard assessment\" (see Eurocode 8 [16]: 3.2.2.1, (4), Note 2 and 3.2.2.2, (2)P, Note 1). Figure 6: Boundaries of the seismic source zones used in the hazard calculations.