## 3 Seismotectonic Setting, Data Selection, and Analysis
### Post Seismic Time Series Analysis  
The post seismic displacement evolution is made up of two contributions: the displacement \(u(t)\) due to the relaxation one on the fault zone and the long term \(\mathrm{V_{pst}}\)\(t\), where \(\mathrm{V_{pst}}\) is the long term loading velocity a long time after the earthquake when the system has reached a new equilibrium state. In our case, \(\mathrm{V_{pstEast}}\) = (17.48 \(\pm\) 0.07) mm/yr, \(\mathrm{V_{pstNorth}}\) = (3.72 \(\pm\) 0.07) mm/yr, and \(\mathrm{V_{pstUp}}\) = (-0.44 \(\pm\) 0.18) mm/yr, which was removed from the observed postseismic data. To apply our approach, we analyzed the post seismic relaxation observed after the 17 November 2015 Mw6.5, Lefkas island earthquake. In Figure 5, the North-South displacement, which was the event's predominant post seismic displacement, presented as a function of time for a period 1000 days after the event. For energy reasons, the minimum relaxation time \(\tau_{min}\) cannot be equal to zero in order to have a converged relaxation function. From Figure 5, the transition from the linear to logarithmic part is observed, permitting the estimation of \(\tau_{min}\approx\) 3-5 days. Since the longest relaxation time \(\tau_{max}\) is the time where the relaxation stops, from Figure 5, we estimate \(\tau_{max}\approx\) 350 days. The aforementioned estimations of \(\tau_{min}\) and \(\tau_{max}\) result in a value \(R_{o}\approx\) 4.2 to 4.7. Using the observed values of \(u(t)\), we estimate that an average value of displacement in the range from 300 to 600 days is about \(-\)26 mm, a value that could be used to approximate \(u_{\infty}\). In Figure 5, the observed displacement, along with the theoretical one, calculated using Equation (1), with \(S\) = 4.8 mm, \(u_{\infty}=-\)26 mm, \(\tau_{min}\approx\) 3.5 days, and \(\tau_{max}\approx\) 350 days (i.e., \(R_{o}\approx\) 4.6), is presented as a very good agreement. Furthermore, the time evolution of displacement suggests a slope \(F_{2}\approx-4.21\) for the logarithmic part and an approximate value \(F_{1}\approx-1.09\) for the short linear early part of deformation. Comparing the above estimation with Equations (10) and (13), we conclude that, since \(\tau_{min}<<\tau_{max}\), the scaling of the slopes leads to \(\tau_{min}\approx\) 3.8 days, in agreement with our estimation from Figure 5.  
A function to present the slow dynamics of postseismic relaxation could be defined in terms of the asymptotic long-term value \(u_{\infty}\) as [59]:  
\[\Omega(t)=\frac{u(t)-u_{\infty}}{u_{o}-u_{\infty}} \tag{15}\]  
Substituting Equation (10) in (15) leads us to:  
\[\Omega(t)=\frac{R(t)}{R_{o}} \tag{16}\]  
In Figure 6, the experimentally estimated \(\Omega(t)\) function for the first 400 days of the post-seismic relaxation after the Lefkas main event is given, along with the calculated one using Equation (16) for \(\tau_{min}\approx 3.5\) days and \(\tau_{max}\approx 350\) days, respectively. A comparison of the observed and calculated values is given in Figure 7, along with a dichotomous line.  
Furthermore, we note that \(\int_{0}^{\infty}\Omega(t)dt=\frac{\tau_{max}-\tau_{min}}{R_{o}}\), which, after using the experimental values of \(\Omega\), leads to \(\tau_{max}~{}\approx 360\) days in quite good agreement with the value used in Figures 5 and 6. We note that the law values of \(\frac{R(t)}{R_{o}}\) in Figure 7 correspond to the logarithmic part of relaxation, while the high values are related with the part just after the rupture where the uncertainty in the estimated displacement is higher.  
Figure 5: The observed displacement, along with the theoretical calculated using Equation (1) (see text), with \(S\) = 4.8 mm, \(u_{\infty}=-26\) mm, \(\tau_{min}\approx 3.5\) days, and \(\tau_{max}\approx 350\) days (i.e., \(R_{o}\approx 4.6\)) is presented as a very good agreement.