## 1 Introduction  
Following the Wenchuan \(M_{5}\) 8.0 earthquake on 12 May 2008, the Longmenshan fault zone was struck by the 20 April 2013 \(M_{5}\) 7.0 Lushan earthquake. The Longmenshan fault zone is composed of several almost parallel thrust faults, forming a boundary fault between the Sichuan Basin and Tibetan Plateau, and controls the seismicity of the Longmenshan region (Figure 1). The epicenters of the Wenchuan and Lushan earthquakes were approximately 87 km apart, and the focal mechanism of both events showed a thrust rupture [1]. According to the characteristics of the Wenchuan and Lushan earthquakes, whether the \(M_{5}\) 7.0 Lushan event was a strong aftershock of the \(M_{5}\) 8.0 Wenchuan earthquake or a new and independent event has been a topic of debate. For example, some researchers suggest that the two large earthquakes were independent events. The reasons are as follows: (1) there is no overlapping area between the Wenchuan and Lushan earthquake rupture zones [2]; (2) the Wenchuan and Lushan earthquakes were generated in different faults in the Longmenshan fault zone [3]; (3) the rupture processes of the Wenchuan and Lushan earthquakes were different, and the aftershock zones of the two events were nearly 45 km apart [4]. Alternatively, some scientists propose that the Wenchuan and Lushanearthquakes were a mainshock-aftershock sequence and note that the Lushan event struck in an area where Coulomb stress was increased due to the Wenchuan earthquake [5; 6]. The controversy over the relationship between the Wenchuan and Lushan earthquakes highlights the complexity of earthquake interaction in the Longmenshan fault zone. It is widely accepted that earthquake interactions can be understood by identifying changes in static and dynamic stress states around faults [7; 8; 9]. The most observable effect of this stress change is a significant increase in seismicity rate, which is generally considered an aftershock phenomenon [10; 11; 12]. Statistically, aftershock activity is classically described by \(n(t)=K/(t+c)p\), where \(n(t)\) is the number of aftershocks after time \(t\) and \(K\), \(c\), and \(p\) are constants that describe the aftershock productivity [13]. [PERSON] [14; 15] described aftershock activity as a multigenerational branching process and proposed the epidemic-type aftershock sequence model, which is a stochastic point process model of self-exciting point processes. Changes in stress can impact the seismicity rate and the frequency size distribution, which is alternatively known as the frequency-magnitude distribution (FMD) [16] or Gutenberg-Richter (G-R) law [17] and is expressed as log\(N=a-b\)\(M\), where \(N\) is the number of events in a given time period with magnitude greater than \(M\), \(a\) describes the seismicity of a given seismogenic volume, and \(b\) is the slope of the FMD. Previous studies showed that \(b\) values fall within the range of 1.02 \(\pm\) 0.03 on a large scale for a long time [18; 19]. For regions on a smaller scale, the \(b\) values show a broad range of spatial and temporal variations. For example, the \(b\) value ranged from 0.5 to 2.5 in the Andaman-Sumatra region and California [20]. Interpretation of the variation of \(b\) values is based on several factors, including stress state [21; 22], focal depth [23], faulting style [24; 25], fluid pressure [26], and so on. The earthquake size distribution generally follows a power law, with a slope of \(b\) values, which characterizes the relative occurrence of large and small events. A low \(b\) value indicates a larger proportion of large earthquakes and vice versa. [PERSON] et al. [27]  
Figure 1: **The topographic and tectonic map of the Longmenshan fault zone and its surrounding region. ** Blue beach ball represents the focal mechanism of the Wenchuan \(M_{S}\) 8.0 earthquake. Pink beach ball represents the focal mechanism of the Lushan \(M_{S}\) 7.0 earthquake. Red circles represent epicenters of earthquakes (\(M_{S}\geq 4\)) from 1 January 2000 to 1 January 2019.