## 5 Discussion  
Earthquake interaction can change the stress state of faults, which is reflected in both earthquake activity rate and earthquake size distribution. The relationship between stress state and \(b\) value can be used to quantify the effect of large earthquakes that can significantly change the stress states and, therefore, the earthquake size distribution. In contrast to previous studies on the Wenchuan and Lushan earthquakes, our paper focuses on a quantitative analysis and discussion of the effect of the Wenchuan \(M_{\rm S}\) 8.0 and Lushan \(M_{\rm S}\) 7.0 earthquakes on the size distribution of the earthquakes along the Longmenshan fault at different times. Interpretation of the \(b\) value and its variability according to physical mechanisms has received considerable attention and discussion. In most cases, the observation of spatial and temporal \(b\) value variability can be caused by several factors: (i) Process of estimation: homogeneity of catalog and method of calculation can affect the results. All the data in this work are from the Longmenshan fault and its surroundings, and each event includes the time, location and magnitude depth. The maximum likelihood estimation and least-squares regression method [30; 41; 42; 43; 52; 53; 54; 55] are used to estimate the \(b\) value and its uncertainty, but the latter is excessively affected by the largest earthquake magnitude. [PERSON] et al. [56] measured the bias on \(b\) values caused by the magnitude binning and catalog incompleteness when the \(b\) value is estimated by the maximum likelihood estimation and provided guidance to reduce the likelihood of being misled by \(b\) value variation. (ii) Stress conditions: the \(b\) value and its variation represent stress buildup and release. The differential stress is inversely dependent on the \(b\) value has been observed in laboratory experiments [57; 58] as well as in the field [59; 60]. The stress acting on a fault may control the variation in the \(b\) value in space and time. [PERSON] et al. [61] calculated the regional Coulomb stress changes on major faults surrounding the rupture resulting from the Wenchuan \(M_{\rm S}\) 8.0 and showed that significant stress increased in the Lushan aftershock zone. Other studies obtained similar results [5; 6; 62]. The spatial variation in the \(b\) values throughout the Lushan aftershock zone decreased after the \(M_{\rm S}\) 8.0 mainshock (Figure 5i), and the same effect occurred in the southern part of the Wenchuan aftershock zone after the \(M_{\rm S}\) 7.0 event (Figure 5g). These findings suggest that the \(b\) value is negatively correlated with stress and indicate the effect of the earthquake interaction along the Longmenshan fault zone. (iii) Crustal tectonics: the variation in \(b\) value can be interpreted according to the tectonic characteristics, i.e., rock heterogeneity [63], focal depth [23], pore pressure [26], and fault types [24; 25]. Previous studies have shown that the \(b\) value in different types of faults is \(b\) (normal) \(>\) 1, \(b\) (strike-slip)-1, and \(b\) (thrust) \(<\) 1 [26; 64]. As shown in the spatial footprints in Figure 5, the \(b\) value of the southern part of the Longmenshan fault zone is lower than that in the northern part. This pattern is consistent with the tectonic characteristics of the Longmenshan fault, which is a strike-slip fault in the north and a thrust fault in the southern part [65; 66]. Stress changes seem to be a key factor that affects the \(b\) value and its variation. Excepting the approach of estimation, all other factors are secondary because they are directly or indirectly affected by the stress [67]. Therefore, the observed falls in the \(b\) values shown in Figure 5a,b was interpreted as changes in the related stress conditions, which could be precursors to large earthquakes. However, these temporal variations may occur over a timescale ranging from months to years, and the timeliness and effectiveness of this variability as an indicator are difficult to guarantee.