## 3 Methods and Data  
We applied [PERSON]'s [5] well-known method (AH84) for estimating \(\kappa\) by analysing the S-wave spectra in this study following [PERSON] et al. [7; 11] guidelines. The total path attenuation  
Figure 2: Spatial distribution of earthquake locations in the investigated area (373 BC–2019, according to the Croatian Earthquake Catalogue-CEC, the updated version first described in [27]. Seismic zones are marked as: Zagreb-green, Novo Mesto-Krsko-red, Karlovac-Metlika-blue and Pokupsko-Petrinja-yellow. Faults are marked with black lines [28; 29]. of S-waves within the crust is separated into two attenuation parameters: the frequency-dependent quality factor \(Q(f)\) and the near-surface attenuation parameter \(\kappa\) (also termed site diminution parameter, \(\kappa_{0}\)) as shown in Equation (1) where _A(f,t)_ is acceleration spectrum that contains the effects of source, distance and local site effects. In Equation (1), \(t^{*}\) is attenuation time [4], \(f\) is frequency, \(R\) is distance, \(\beta_{0}\) is shear wave velocity of the Earth's medium:  
\[A(f,\;\;t)=A_{0}\exp(-\pi ft^{*})=A_{0}\exp\left[-\pi f\left(\frac{R}{Q(f) \beta_{0}}+\kappa_{0}\right)\right]=A_{0}\exp(-\pi\kappa f) \tag{1}\]  
[PERSON] and [PERSON] [5] observed a linear dependence between the calculated \(\kappa\) of the ground motion and the epicentral distance (\(R_{e}\)) of the recording station and proposed a mathematical formula (Equation (2)) that treats \(\kappa\) as a function of \(R_{e}\). In Equation (2), the zero-distance intercept \(\kappa_{0}\) represents the attenuation contribution to \(\kappa\) from geological structure beneath the site (near-site attenuation or site-kappa), and the distance dependent part in term of the slope (\(\kappa_{R}\)) is related to the regional attenuation:  
\[\kappa=\kappa_{0}+\kappa_{R}\cdot R_{e} \tag{2}\]  
Value of \(\kappa\) gradually increases with distance, and degree of the slope \(\kappa_{R}\) depends on the local and regional geology. Since its introduction, general observation of [PERSON] and [PERSON] [5] study that \(\kappa\) is a linear function of \(R_{e}\) has proven to be good approximation as shown in the recent studies that estimated \(\kappa\) (e.g., [1; 6; 7; 30; 31; 32; 33]). In the last decade relationship between estimated \(\kappa_{0}\) and measured \(V_{530}\) values were proposed; \(\kappa_{0}\) has lower values for sites on harder rocks (higher \(V_{530}\) values) and higher \(\kappa_{0}\) values are obtained on softer rocks (e.g., [11]). Two seismological stations included in this study are: Puntijarka (PTJ), located at the top of Medvednica Mountains and Zagreb (ZAG), located in the city area (Figure 1). A compiled ground motion data set is selected within \(M_{L}\geq 3.0\), \(R_{e}\leq 150\) km and a focal depth of \(h\leq 30\) km. Figure 3 evaluates the compiled ground motion dataset distribution of the epicentres (\(R_{e}\)) and focal depth with magnitudes (\(M_{L}\)) at each station. The number of recordings at each station depends not only on local seismicity and data selection that is the same for both stations, but also on the operational period of each station (from 2000) and usable frequency sampling rate. In this study we used 50 Hz seismograms recorded from 2004 to 2019 (PTJ), 127 recordings) and from 2007 to 2019 (ZAG, 92 recordings). Figure 3: Statistics of the compiled ground motion dataset. (**a**) \(R_{e}\)-\(M_{L}\) distribution of recordings at PTJ and ZAG stations. (**b**) \(h\)-\(M_{L}\) distribution of recordings at PTJ and ZAG stations. We calculated the parameter \(\kappa\) by using the classical [PERSON] and Hough [5] approach (Equations (1) and (2)) for all three components (north-south-NS, east-west-EW and vertical-Z) of weak motion seismograms with frequency sampling rate of 50 Hz. Figure 4 represents two examples of step-by-step \(\kappa\) calculation for seismograms recorded on ZAG and PTJ stations.