## 5 Spatial Footprint of Coulomb Stress Changes  
Numerous studies of strong earthquakes show a correlation between the positive lobe of Coulomb stress changes and the locations of the majority of the most significant aftershocks, (e.g., [48; 49]). A moderate earthquake of magnitude Mw = 4.9 occurred on 24 July 2021, 02:07:37 (UTC) accompanied by many aftershocks, before the main and catastrophic earthquake of magnitude Mw = 6.0 and its major aftershock of magnitude Mw = 5.3, which took place on 27 September 2021, 06:17:21 (UTC) and 28 September 2021, 04:48:08 (UTC), respectively. Herein, we examine the co-seismic static stress changes with respect to the aftershock spatial distribution during the event of Mw = 4.9, the Mw = 6.0 main event as well as the Mw = 5.3 major aftershock. The \(\Delta\)CFS changes were determined via Coulomb3.3 software [50] in an elastic half-space and a uniform slip on the rupture planar surfaces. The Coulomb Failure Stress changes (\(\Delta\)CFS) are given by the Equation (3):  
\[\Delta\text{CFS}=\Delta\tau-\mu_{\text{f}}\,\Delta\sigma \tag{3}\]  
where \(\Delta\tau\) and \(\Delta\sigma\) are the in-shear stress and normal stress, respectively, while the \(\mu_{\text{f}}\) is the effective friction coefficient [51; 52; 53]. For the shear modulus and Poisson's ratio, we used the values of 3.3 MPa and 0.25, respectively, and a mean value for the coefficient of friction equal to \(\mu_{\text{f}}=0.4\)[54]. To calculate the subsurface fault's width and length, we used the empirical relations of [55] for each modeled earthquake. In addition, we used the available focal mechanism solutions from various agencies, and we present our preferred models for this study in Table 5.  
Figure 12 shows the determined co-seismic \(\Delta\)CFS changes caused by the event of magnitude Mw = 4.9 at a centroid depth of 8.0 km and the vertical cross-sections AB and CD. The spatial distribution of the \(\Delta\)CFS reveals a stress decrease towards NW and SE and a stress increase towards NE and SW of the ruptured fault. The aftershocks during this period and before the main event of Mw = 6.0 are distributed mainly along and under the fault up to 20 km depth. The \(\Delta\)CFS values at the hypocenters of the Mw = 6.0 and Mw = 5.4 events were calculated, and the results provide \(-\)0.104 MPa and +0.0169 Mpa, respectively. The co-seismic Coulomb stress variations caused by the strong earthquake of Mw = 6.0 and its major aftershock (Mw = 5.4) at centroid depths of 10.0 km and 9.0 km, respectively, as well as the spatial distribution of aftershocks, are presented in Figures 13 and 14. For both seismic events, the same pattern on the spatial distribution of the \(\Delta\)CFS is observed, which indicates a stress decrease towards NW and SE and a stress increase towards NE and SW of the ruptured faults. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Date** & **Hour** & **Minute** & **Lat.** & **Long.** &
\begin{tabular}{c} **Depth** \\ **(km)** \\ \end{tabular} & **Mw** & **Strike** & **Dip** & **Rake** & **Agency** & **Length** & **Width** & **Mo (Num)** \\ \hline
24 July 2021 & 2 & 7 & 35.1676 & 25.2286 & 8 & 4.9 & 214 & 52 & \(-\)95 & NOA & 2.3 & 2.56 & \(9.116\times 10^{55}\) \\ \hline
27 September 2021 & 6 & 17 & 35.1421 & 25.2734 & 10 & 6.0 & 218 & 57 & \(-\)85 & GFZ & 7.61 & 10.3 & \(1.1\times 10^{48}\) \\ \hline
28 September 2021 & 4 & 48 & 35.1356 & 25.2312 & 9 & 5.3 & 182 & 22 & \(-\)95 & UOA & 4.41 & 4.88 & \(1.30\times 10^{17}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Focal parameters of Mw = 4.9, Mw = 6.0 and Mw = 5.4 events. Figure 12: **(Up)** Coulomb stress changes distribution due to Mw = 4.9 event (yellow star) at centroid depth of 8.0 km. The red rectangle indicates the fault model for the kinematics of Mw = 4.9, while the blue one is the projection of the fault model of Mw = 6.0 main shock (listed in Table 3). (**Down**) Coulomb stress changes along the vertical cross-section AB.