## 3 Results
### Qc Averaged  
To improve the quality of the \(Q_{c}^{comp}\) dataset, we removed all those \(Q_{c}^{comp}\) estimates with off-scaled values to avoid the invidation of the average \(Q_{c}\). The removed \(Q_{c}^{comp}\) outliers represent 5% of the initial \(Q_{c}^{comp}\) dataset. The error on each \(Q_{c}^{comp}\) was computed from the error \(\Delta m\) on the slope \(m\) of the linear regression: \(\Delta Q_{c}^{comp}=\left|\frac{Q_{c}^{comp}}{\Delta m}\right|\Delta m\). \(Q_{c}\) was then computed from a weighted average, by using the inverse square of \(\Delta Q_{c}^{comp}\) as weights. The results are plotted in Figure 5, and it can be observed that \(Q_{c}\) regularly increases at  
Figure 4: Number of \(Q_{c}^{comp}\) estimates, versus the central frequencies \(f_{c}\), for each lapse time \(t_{L}\). Figure 3: (**a**) Original three-component record (count/s) at station SGRT (IV network) with origin O, P-wave and S-wave arrival markers. (**b**) Energy envelope (count/s) filtered around \(f_{c}\) = 6 Hz, with \(T3\) and \(T4\) markers (see the text for explanation). a fixed \(f_{c}\) for an increasing \(t_{L}\), and at the same \(t_{L}\) for increasing \(f_{c}\), indicating a satisfying regularization of the data. The observed correlations between \(Q_{c}\) vs. \(f_{c}\) and \(Q_{c}\) vs. \(t_{L}\) are in total agreement with previous studies conducted in the same area [23] or in other tectonic areas as, for instance, in the central Apennines [39]. Taking the logarithm of Equation (3), we get:  
\[\ln Q_{c}=\ln Q_{0}+\alpha\ln f_{c}. \tag{7}\]  
Through the linear regression of \(\ln Q_{c}\) versus \(\ln f_{c}\), we obtained \(Q_{0}\) from the intercept and \(\alpha\) from the slope. We performed this analysis for all single-trace seismograms to obtain average \(Q_{0}\) and \(\alpha\) values for the different lapse times \(t_{L}\). The results are reported in Table 1, together with a comparison with other studies in the same area or in other worldwide areas. The increasing trend of \(Q_{0}\) vs. \(t_{L}\) in Table 1 reflects the size of the Earth's volume, sampled by seismic waves. By adopting the simplifications of [PERSON] and [PERSON] [1], it is possible to define an order of magnitude of the investigation depth. Estimating a mean value of \(v_{s}=3.86\) km/s for the Gargano crust [33], we computed the radii of the spherical volumes (and therefore the maximum depths investigated) for all the considered lapse time windows (Table 1). The average \(Q_{c}\) for each station, named \(Q_{c}^{st}\), is plotted vs. \(f_{c}\) in Figure 6a-g. These plots exhibit the pattern of variation of the quality factor \(Q_{c}^{st}\) with central frequencies \(f_{c}\) at different lapse times \(t_{L}\). The station \(Q_{c}^{st}\) trend versus \(f_{c}\) is irregular for \(t_{L}=10\) s, for which the least number of \(Q_{c}\) estimates is available; for \(t_{L}>20\) s, more regular trends are observed. \begin{table}
\begin{tabular}{c c c} \hline \(t_{L}\) & **This Study** & **Radius of Investigation (km) 1** \\ \hline
10 s & \(Q_{0}=11\pm 9\); \(\alpha=0.96\pm 0.07\) & 19.3 \\ \hline
15 s & \(Q_{0}=24\pm 15\); \(\alpha=0.80\pm 0.11\) & 29.9 \\ \hline
20 s & \(Q_{0}=31\pm 15\); \(\alpha=0.88\pm 0.10\) & 38.6 \\ \hline
25 s & \(Q_{0}=34\pm 13\); \(\alpha=0.97\pm 0.09\) & 48.2 \\ \hline
30 s & \(Q_{0}=40\pm 14\); \(\alpha=1.00\pm 0.10\) & 57.9 \\ \hline
35 s & \(Q_{0}=49\pm 16\); \(\alpha=1.00\pm 0.11\) & 67.5 \\ \hline
40 s & \(Q_{0}=63\pm 20\); \(\alpha=0.95\pm 0.15\) & 77.2 \\ \hline \end{tabular} \({}^{1}\) Assuming the relations of [PERSON] and Chouet [1].  
\end{table} 
Table 1: For each lapse time \(t_{L}\), \(Q_{0}\) and \(\alpha\) estimates, with their errors and the radius of investigation in the Earth lithosphere, are reported. Figure 5: Average \(Q_{c}\) versus \(f_{c}\) at all the \(t_{L}\). The error bars quantify the average percentage errors on \(Q_{c}\). Figure 6: \(Q_{c}^{St}\) estimates for each central frequency \(f_{c}\), for all the recording OT and IV stations.