## 2 The Coulomb Stress Triggering Hypothesis  
### Coulomb Failure Criterion  
The coulomb failure criterion is commonly adopted to quantify the effect of static stress change on a fault plane. The trend of rocks to rupture in a brittle manner is considered to be a function of both shear and confining stresses, commonly formulated as the coulomb failure criterion [8]. A seismogenic fault rupture permanently deforms the crustal medium and modifies the tectonic stress field, increasing or decreasing the stress on nearby faults as a function of the location, geometry, and slip direction. The coulomb failure stress (CFS) is defined as follows [31]:  
\[\text{CFS}=\tau-s-\mu(\sigma_{\text{n}}-p) \tag{1}\]  
where \(\tau\) is the shear stress along the fault plane (positive in the inferred direction of slip). \(s\) is cohesion, and \(\mu\) is apparent friction coefficient, which ranges from 0.6 to 0.8 for most intact rocks [31]. \(\sigma_{\text{n}}\) is the normal stress on the fault plane, and \(p\) is the fluid pressure, respectively. The coulomb failure stress change can be defined as follows:  
\[\Delta\text{CFS}=\Delta\tau+\mu^{\prime}\Delta\sigma_{\text{n}} \tag{2}\]  
where \(\Delta\tau\) is the shear stress change on a given failure plane (positive in the fault slip direction). \(\Delta\sigma_{\text{n}}\) is the normal stress change (positive for fault unclamping or compression). \(\mu^{\prime}=\mu(1-\beta)\) is the effective coefficient of friction, which includes the effects of pore pressure changes and generally ranges from 0 to 0.8. \(\beta\) is [PERSON]'s coefficient, and the range is from 0 to 1. The previous study showed that the \(\mu^{\prime}\) is typically found to be around 0.4 (\(\mu=0.75\), \(\beta=0.47\)) for subduction zones [28]. Previous studies have employed values of \(0.2\leq\mu^{\prime}\leq 0.75\) to compute coulomb stress changes and have discussed the robustness of the obtained conclusion for different settings of apparent coefficients of frictions [32; 33; 34]. In this paper, we investigated \(\mu^{\prime}=0.2\), 0.4, 0.6, and 0.8, respectively. The computed results show that there is no significant differences, which is consistent with previous conclusions. A priori, the models with \(\mu^{\prime}=0.4\) can minimize the uncertainty, as discussed by [PERSON] et al [8]. Here, we take the computation results with \(\mu^{\prime}=0.4\) for the following analysis and discussion. Positive values of the coulomb stress change promote rupture and negative values inhibit rupture. It seems that the coulomb stress increases as low as 0.1 bar can trigger the occurrence of subsequent aftershocks [7; 8].  
The coulomb stress change relies on the source model of an earthquake, the geometry, the slip direction of the receiver fault (fault receiving stress from a mainshock), and the effective coefficient of friction. Here, we utilize this model to estimate how the Ecuador \(M\) 7.8 mainshock transferred stress in the epicentral region. By assuming a [PERSON]'s modulus of 8.0 \(\times\) 10\({}^{5}\) bar and a Poisson's ratio of 0.25, we compute the coulomb stress change in an elastic half-space. The effective friction coefficient is 0.4. We make two complementary computations. First, we resolve coulomb stress changes on both nodal planes of each \(M\geq 6\) aftershock. Second, we compute the normal, shear, and coulomb stress changes in the focal source of each \(M\geq 6\) aftershock. The coulomb failure stress changes, produced by the Ecuador \(M\) 7.8 mainshock, is important for us to investigate the cause and mechanism of the larger aftershocks.