## 4 Results  
In the present work we applied original the [PERSON] and [PERSON] [5] linear formulation (Equation (2)) to a pair of individual \(\kappa\) values with epicentral distances \(R_{e}\) for all records at each station. Figure 4: Example of \(\kappa\) calculation. (**left**) Station PTJ. \(M_{L}\) = 4.2, \(R_{e}\) = 34 km, NS component. (**right**) Station ZAG: \(M_{L}\) = 3.5, \(R_{e}\) = 128.5 km, EW component. We estimated the value of site-specific (near-site) attenuation parameter \(\kappa_{0}\) based on proposed \(\kappa\) model as a function of epicentral distance. Calculated individual \(\kappa\) values for EW and NS components we combined into an average value of \(\kappa_{hor}\) for each recording. In certain cases where they differ significantly from each other (difference \(>\) 25%), the recording is excluded for further regression analysis to obtain the site kappa value (e.g., [7,11]). 81 usable pairs of \(\kappa\) and \(R_{e}\) data for \(\kappa\) models were finally chosen (from the initial 92) for the ZAG station and 118 (from the initial 127) for the PTJ station. In this study, both \(\kappa\) models (\(\kappa_{hor}\) and \(\kappa_{ver}\)) as a function of epicentral distance are proposed to estimate site-specific parameters \(\kappa_{hor}\) and \(\kappa_{0 ver}\) using linear least-square regression (e.g., [7]). Both variables, \(\kappa\) and \(R_{e}\) are imperfectly known and errors in \(R_{e}\) could have impact on the final \(\kappa_{0}\) value and the slope of regression \(\kappa_{R}\). Therefore, instead of using the traditional linear least-squares regression, we performed linear regression suitable for data with errors, following the method by [PERSON] et al. [35]. This allowed us to test how the existence and correlation for the observational errors in two coordinates (\(R_{e}\) and \(\kappa\)) affect values of \(\kappa_{0}\) and \(\kappa_{R}\), and if there exists a significant difference regarding the standard linear regression. Typically, we set the standard error for \(R_{e}\) to vary \(\pm\)2, 5 and 10 km and error in \(\kappa\) set to be \(\pm\)1 or 2 standard deviations based on observed empirical data. A regression test showed that differences between standard and error-in-variables linear regression \(\kappa_{0}\) and \(\kappa_{R}\) values vary mostly between 1-5% (Table 1). Highest differences up to 9% are within standard error in \(R_{e}\pm\) 10 km and smallest below 1% within standard error in \(R_{e}\pm\)2 km with respect to \(\pm\)1 or 2 standard deviations in \(\kappa\). However, \(\pm\)1 standard deviations in \(\kappa\) is too small to be consider representative as can be seen by data scatter in Figure 5. We choose to evaluate final \(\kappa_{0}\) and \(\kappa_{R}\) values using errors for epicentral distances to be in order of 5 km with errors in \(\kappa\) to be \(\pm\)2 standard deviations as shown in Figure 5. Summarized results and differences between standard linear regression and errors-in-variables regression are shown in Table 1.  
Figure 5: Least-square linear regression of and \(R_{e}\) data pairs. PTJ station: (**a**) horizontal model, (**b**) vertical model. ZAG station: (**c**) horizontal model, (**d**) vertical model. Fit regression line shown by thick lines. \(\pm\)1 standard deviation-dashed lines. \(\pm\)2 standard deviation-dotted lines. Vertical error-bars show the uncertainty of \(\kappa\) values and horizontal error-bars show uncertainty in epicentral distances with standard error set to \(\pm\)5 km. Estimation of individual kappa values is very sensitive as can be observed on Figure 4. This is particularly important to consider when kappa is estimated by different users and different computational procedures as described in [7].