## 7 Temporal Properties of the Aftershock Sequence
### Scaling of the Aftershocks Focal Zone with Time
Since the estimated co-seismic Coulomb stress field \(\Delta\)CFS (Equation (3)) can be significantly different from the \"real\" one, ref. [103] suggested a mean Coulomb stress gradient to be used. In this case, Equation (15) becomes:  
\[\langle\Delta L_{a}(t)\rangle=A^{\prime}\times\langle\left(-\frac{\partial \Delta CFS}{\partial x}\right)^{-1}\rangle ln\left(\frac{t}{t_{i}}\right)= \zeta A^{\prime}\frac{l_{c}}{\Delta\sigma}ln\left(\frac{t}{t_{1}}\right) \tag{16}\]  
In the latter equation, \(l_{c}\) is the radius of the co-seismic rupture, \(\Delta\sigma\) the mean value of the mean co-seismic stress drops and \(\zeta\) a constant. For an idealized Coulomb stress field, \(\zeta\) takes the value of 2.77 [103]. In the light of the previously described model, we investigated the scaling properties of the aftershock focal zone with time for the Arkalochori aftershock sequence. In the analysis, we used the relocated catalog for the events with \(M\geq M_{c}=2.5\) to estimate the mean distance of aftershocks from the mainshock \(\langle\Delta L_{a}(t)\rangle\) with time \(t\), along the horizontal dimensions. The result is shown in Figure 18, as a function of the logarithm with time. The expansion of the aftershocks zone becomes apparent, as \(\langle\Delta L_{a}(t)\rangle\) grows systematically with time after the surpass of one day from the mainshock. This growth can well be described by the afterslip front (Equation (16)) for over a period of one hundred days (R\({}^{2}=0.97\)). We note that the logarithmic time dependence starts almost after the first day from the main event, possibly suggesting that after that time the system starts to be driven by an afterslip process. Furthermore, from Equation (16) the rheological parameter \(A^{\prime}\) can be determined once the slope \(s_{a}\) of the afterslip front is known. From Figure 18, we obtain \(s_{a}=0.320\pm 0.003\). Then, from Equation (16), \(s_{a}=\frac{d(L_{a}(t))}{dint}=\zeta A^{\prime}\frac{l_{c}}{\Delta\sigma}\), where \(l_{c}\) is the radius of the co-seismic rupture and \(\Delta\sigma\) the co-seismic stress drop. For a simple model of circular rupture, \(l_{c}\) can approximately be determined as \(l_{c}=\left(\frac{7}{2}\frac{M_{c}}{\Delta\sigma}\right)^{1/3}\)[51]. The average stress drop for normal fault earthquakes in Greece is \(\Delta\sigma=5.5\pm 1.5\) MPa [108; 109], while the mainshock's seismic moment is M\({}_{\rm o}=1.1\times 10^{18}\) Nm (Table 4) [21; 22; 23]. Then, we estimate the value of \(l_{c}\approx 8.9\) km for the co-seismic rupture. For \(\zeta=2.77\), the rheological parameter \(A^{\prime}\) takes the value of \(A^{\prime}\approx 0.71\) MPa, which is within the range 0.1-1 MPa of \(A^{\prime}\) values that are  
Figure 18: The average expansion (in km) of the aftershock zone as function of the logarithm of time (symbols) for Central Crete 2022, Mw6.0 aftershock sequence. The solid line represents the logarithmic growth of the aftershocks zone. usually found [97; 98; 103]. This value is considerably higher than other \(A^{\prime}\) values that were estimated for recent normal fault mainshocks in Greece, as [97] estimated \(A^{\prime}\approx\) 0.041 MPa for the 2020 Mw7.0 Samos earthquake, while [98] estimated the value of \(A^{\prime}\approx\) 0.29 MPa for the 2021 Mw6.3 Northern Thessaly earthquake.