# An Analysis of the 2008 \(M_{\rm s}\) 8.0 Wenchuan Earthquake's Aftershock Activity
## 4 Results  
### Statistical Characteristics of Aftershock Sequence  
Figure 4 shows the relationship between the magnitude and cumulative frequency of the Wenchuan aftershock sequence. The largest aftershock of the Wenchuan earthquake was \(M_{\rm s}\) 6.4 on 25 May. The least squares method was used to estimate the \(a\)- and \(b\)-values in the G-R relation and their standard deviations. According to Section 1, the data were best fit when the lower limit of the completeness magnitude \(M_{c}\) was 2.5, which is within the range of the variation in \(M_{c}\) in Figure 2. The calculations yielded \(a\) = 6.33 and \(b\) = 0.89 \(\pm\) 0.02. This \(b\)-value is relatively small. The calculation of the \(b\)-value is easily affected by the magnitude interval, upper limit of the magnitude, sample size, and algorithm applied [12]. In addition, the incompleteness of the catalog is a major factor leading to errors in the \(b\)-value, and the magnitude-frequency distribution of a complete earthquake sequence is generally thought to conform to the typical G-R distribution with a \(b\)-value of one [15]. Thus, the small \(b\)-value of the Wenchuan aftershock sequence obtained in this study may be related to the absence of some small earthquakes in the catalog. The decay of the Wenchuan aftershock activity over time is shown in Figure 5. Based on the modified Omori model [2; 3], three parameters, \(p\), \(c\), and \(k\), were obtained using the maximum likelihood estimation method, with \(M_{\rm min}\) = \(M_{c}\) = 2.7 and \(T_{\rm start}\) = 0.05. The calculated \(p\)-value was 1.05 \(\pm\) 0.02, and the \(c\)-value was 2.823 \(\pm\) 0.288. The decay pattern of the Wenchuan aftershocks conforms well to the Omori law (Figure 5), and compared with the value obtained in other studies, the \(p\)-value is normal, indicating that the background seismic activity had a minor influence on the decay of the Wenchuan aftershocks. The reason for this finding is that the magnitude and fault rupture area of the Wenchuan mainshock were both large. The seismic activities around the Wenchuan earthquake area were influenced by the ruptured fault of the mainshock over a long period. Figure 4: Frequency–magnitude distributions of Wenchuan aftershock sequence. [PERSON] et al. [3] showed that the \(p\)-value does not depend on the selection of \(M_{\min}\), while the \(c\)-value is closely related to \(M_{\min}\). Hence, we calculated the values of \(p\) and \(c\) for different combinations of \(T_{\text{start}}\) and \(M_{\min}\) (Table 1). The \(p\)-value varied little with \(M_{\min}\), whereas the \(c\)-value drastically changed with \(M_{\min}\). Some seismologists think that the aftershocks are so dense immediately after the mainshock that some of them overlap with each other. As a result, not all of the aftershocks can be recorded, which leads to the incompleteness of the aftershock catalog in the initial period after the mainshock, resulting in a large \(c\)-value. The \(c\)-value for a complete aftershock catalog should be zero [16]. In this study, we obtained a \(c\)-value of 2.823 \(\pm\) 0.288, which is relatively large due to the incomplete aftershock catalog in the initial period after the mainshock (Figure 5). Furthermore, the complexity of the earthquake rupture process can lead to a large \(c\)-value [17]. Therefore, the large \(c\)-value in this study also suggests the complexity of the fault rupture process of the Wenchuan earthquake to a certain extent.