## 4 Results
Additionally, by restricting the distance range for kappa we ensure that local site attenuation at zero distance is overwhelmed by the path component at larger distances [36; 37]. Figure 6 shows comparison of results from different methods to estimate \(\kappa_{0}\) for the PTJ and ZAG stations. It can be observed that \(\kappa_{0}\) values are constrained for shorter distances to catch mainly upper local site conditions and data ranges are similar within errors. \(\kappa_{0}\) values estimated from the extrapolation to zero distance (preferably using error-in-variables regression) are within the range of the uncertainty (\(\pm 1\) standard deviation) with a constrained \(\kappa_{0}\) value (Figure 6, Table 2). At larger distances, variations between empirical kappa values are scattered among similar distances due to heterogeneity along the paths between different sources and stations. It is possible to compare estimated values of frequency-dependent \(Q\)(_f_) for the high-frequency range with frequency-independent \(Q\) estimated from \(\kappa\)[5; 7; 11; 32]. The \(Q\) value is inversely proportional to slope \(\kappa_{R}\) as a regional attenuation contribution, \(Q(\kappa_{R})=1/\beta\)-\(\kappa_{R}\) (typical value of \(\beta=3.5\) km/s is used \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Station**} & \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**HOR**} & \multicolumn{2}{c}{**VER**} & \multicolumn{2}{c}{**Vs30**} \\ \cline{3-6}  & & \(\kappa_{0}\) (s) & **SE-\(\kappa_{0}\)** & \(\kappa_{0}\) (s) & **SE-\(\kappa_{0}\)** & **ECS Site Class** \\ \hline \multirow{3}{*}{**PTJ**} & LSE & **0.0283** & 0.0028 & **0.0249** & 0.0024 & 800 m/s \\  & Error-in-variable regression & **0.0298** & 0.0026 & **0.0261** & 0.0026 & A \\  & Constrained \(\kappa_{0}\) & **0.0360** & 0.0097 & **0.0311** & 0.0084 & \\ \hline \multirow{3}{*}{**ZAG**} & LSE & **0.0411** & 0.0032 & **0.0391** & 0.0026 & \multirow{3}{*}{360-800 m/s} \\  & Error-in-variable regression & **0.0426** & 0.0030 & **0.0402** & 0.0030 & B \\ \cline{1-1}  & Constrained \(\kappa_{0}\) & **0.0475** & 0.0092 & **0.0445** & 0.0077 & B \\ \hline \end{tabular}
\end{table} 
Table 2: Summarized \(\kappa_{0}\) values estimated within different approaches compared with local site conditions based on the EC8 [41] site classification (based on approximation via correlation to topographic slope [39; 40]. The range of the uncertainty with constrained \(\kappa_{0}\) value is set to \(\pm 1\) standard deviation. Figure 6: Comparison of results from different methods to estimate \(\kappa_{0}\). PTJ station: (**a**) horizontal model, (**b**) vertical model. ZAG station: (**c**) horizontal model, (**d**) vertical model. Thick green line indicates constrained \(\kappa_{0}\) value at shorter distances. Zero-distance regression line indicate the \(\kappa_{0}\) value estimated from Figure 5. Yellow range shows \(Q\) models for different slopes applied within \(\pm 2\) standard deviations (dotted lines) at larger epicentral distances for a fixed \(\kappa_{0}\) value. as an average shear wave velocity of the crust). To compare two independent attenuation studies, frequency-dependent attenuation, the \(Q(f)\) value, is adopted from [34] as \(Q_{c}(f)=78f_{c}^{0.69}\) for the PTJ and \(Q_{c}(f)=45f_{c}^{0.92}\) for ZAG stations for a time lapse equal to 30 s. For the high-frequency range 10-20 Hz this yields to \(Q_{c}(f=10\)-20 Hz) = 382-616 for PTJ and \(Q_{c}(f=10\)-20 Hz) = 374-708 for ZAG. Common regional effects \(Q(\kappa_{R})\) averaged for high frequency attenuation and azimuthal changes, estimated from the slope \(\kappa_{R}\) for both components (horizontal and vertical) are: \(Q(\kappa_{R})=913\)-1120 for PTJ and \(Q(\kappa_{R})=1143\)-1348 for ZAG. Differences in the frequency independent \(Q(\kappa_{R})\) are probably the result of higher local site attenuation effects at ZAG station compared to PTJ station, azimuthal differences and data quality between stations.