## 3 Empirical Scaling Equations vs. Real Records
However, for larger vibration periods, there is no de-amplification. For example, as shown in the bottom right-hand side plot in Figure 4, the \(PSA\) (0.50s) at deep soil sites is going to be \(10^{0.238}=1.73\) times larger than the value for rock soil sites. Figure 3: Empirical GMPE for four different vibration periods, \(T=0.05\), 0.10, 0.30, and 0.50 s, calculated using Equation (1) and coefficients from Table A1, 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 geological sediments). The solid lines represent median empirical predictions based on coefficients created for all source-to-site distances, whereas the dashed lines represent predictions based on coefficients developed for distances less than 30 km. The coupled effect of deep soils and deep geological sediments can be assessed by considering both \(c_{5}\) and \(c_{7}\) from Tables A1 and A2. For example, \(PSA\) (0.05 s) at deep soil atop deep geological sediments will be \(10^{-0.058}\)\(\cdot 10^{-0.143}\) = 0.63 of the value for rock soil atop the geological rock when coefficients from Table A1 are considered. This indicates even larger de-amplification than when only deep soil effects (i.e., only \(c_{5}\)) are analyzed. On the other hand, the amplification of \(PSA\) amplitudes will occur for vibration periods between \(\sim\)0.3 s and \(\sim\)1 s. For \(PSA\) (0.50s), the amplification for deep soil atop deep geological sediments will be equal to \(10^{0.238}\)\(\cdot 10^{0.136}\) = 2.37. The only GMPEs we can compare our results to (as they also simultaneously consider effects of deep soils and deep geological sediments) are the ones developed for California based on 1482 strong-motion records from earthquakes in the western United States [21]. Moreover, the author of these GMPEs used the same categorical variables as we did (see Table 2) [21], and the site amplification can also be assessed simply by analyzing corresponding scaling coefficients. For the vibration period of \(T\) = 0.04 s, for example, Californian GMPEs indicate 30% lower \(PSA\) amplitudes at the deep soil atop deep geological sediments than at the rock sites, which is very similar to what we obtained for \(T\) = 0.05 s. Furthermore, according to the Californian GMPEs [21], the amplification exists for the vibration periods longer than 0.3 s, and the maximum amplification is \(\sim\)1.7, which is somewhat smaller than what we obtained. The spectra of both orthogonal horizontal components of 15 accelerograms recorded at deep soil sites are compared in Figure 5 to the empirical predictions defined by Equation (1) and the scaling coefficients from Table A2. The actual and predicted spectra exhibit a great degree of agreement, as is shown. Figure 4: Median, median \(\pm\) 1 \(\sigma_{\text{log}}\), and median \(\pm\) 2 \(\sigma_{\text{log}}\) (shaded area) empirical \(PSA\) estimates for the deep soil sites (\(s_{L}\) = 2), and median estimates for rock soil (\(s_{L}\) = 0) and stiff soil (\(s_{L}\) = 1) sites. Several recent regional microzonation investigations [9; 10; 11; 12; 13; 14] have also demonstrated that empirical predictions based on scaling equations that take into consideration both the deep geology and local soil are in excellent agreement with recorded ground motions in the region. Therefore, despite the limitations of the used strong-motion data, we employ the scaling equation derived in this study for the probabilistic hazard analyses for Osijek, just as we did for vertical spectra [19]. It is easy to update the empirical scaling equations and redo the hazard estimations as the number of acceleration records grows.