# Seismological Research Letters

- © 2014 by the Seismological Society of America

*Online Material: *Figures comparing calculated Coulomb Failure Stress changes.

## INTRODUCTION

The 20 April 2013 Lushan earthquake, *M*_{s} 7.0 (China Earthquake Data Center [CENC]) or *M*_{w} 6.6 (U.S. Geological Survey [USGS]), with 196 people killed, and more than 10,000 injured according to the local government’s official report, was the strongest earthquake after the 12 May 2008, *M*_{s} 8.0 (CENC) or *M*_{w} 7.9 (USGS), Wenchuan earthquake in Sichuan province, China. This earthquake occurred in the southwestern part of the Longmen Shan fault zone, which also was the same causative fault zone of the 2008 Wenchuan earthquake (Fig. 1). The epicenter and focal depth of the Lushan earthquake were at 30.308° N, 102.888° E, and 14.0 km, according to the location of USGS (http://comcat.cr.usgs.gov/earthquakes/eventpage/usb000gcdd#summary, last accessed August 2013). The focal mechanism of the Lushan event showed a thrust rupture which was similar to that of the southwestern part of the Wenchuan earthquake rupture (Fig. 1). The slip distribution of the Lushan earthquake was concentrated at the hypocenter, and did not rupture to the surface (Zhang *et al.*, 2013, 2014).

The disastrous Wenchuan *M*_{s} 8.0 earthquake occurred on the same Longmen Shan fault zone, with at least 69,000 people killed and tens of thousands injured. The source inversion of the Wenchuan event showed rupture of two faults (Beichuan and Pengguan) and the mechanism showed a predominant thrust movement on its southwestern part and a predominant right‐lateral slip on its northeast part (Hu *et al.*, 2008; Shen *et al.*, 2009; Wang *et al.*, 2008a, 2011). The Wenchuan event generated a 240 km long and a 72 km long surface rupture along the Beichuan and Pengguan faults, respectively (Xu *et al.*, 2009). The rupture of the Wenchuan earthquake mostly propagated northeastward, and left abundant aftershocks around its source faults (Fig. 1).

According to the related characteristics of the Lushan and Wenchuan earthquakes, some scientists proposed that the Lushan earthquake was the strongest aftershock of the Wenchuan earthquake. Chen *et al.* (2013) argued that, if it is regarded as the strongest aftershock of the Wenchuan earthquake, then the magnitude of the Lushan earthquake was in accordance with Båth’s law, which states that the largest aftershock is typically 1.1–1.2 magnitude units smaller than the mainshock, in the median (Båth, 1965). There were no earthquakes on the Longmen Shan fault zone within the 40 years prior to the Lushan earthquake, except the 2008 Wenchuan earthquake and its aftershocks. Furthermore, the Lushan earthquake occurred in an area with an increased Coulomb Failure Stress (CFS) induced by the Wenchuan earthquake (Parsons *et al.*, 2008; Shan *et al.*, 2009; Jia *et al.*, 2012; Parsons and Segou, 2014). Wang *et al.* (2013) also considered the Lushan earthquake as a strong aftershock of the Wenchuan earthquake.

Alternatively, some scientists held the converse opinion. The reasons include: (1) even though the Wenchuan earthquake promoted the occurrence of the Lushan earthquake, neither the epicenter of the Lushan earthquake was within the aftershock zone of the Wenchuan earthquake (Zhou, 2013b), nor the rupture ranges of those two earthquakes overlapped (Fig. 1) (Xu, 2013); (2) there was a gap between the fault segments of those two earthquakes that did not fail (Ji, 2013); (3) these two earthquakes occurred on different fault branches of the Longmen Shan fault zone (Zhou, 2013a); and (4) the rupture process and aftershock spatial distributions of the Lushan and Wenchuan earthquakes were significantly different (Du *et al.*, 2013).

Meanwhile, Shen (2013) stated that the occurrence of the Lushan earthquake consisted of both independent and aftershock ingredients, and that the aftershock ingredient was dominant. He estimated that the aftershock ingredient of the Lushan earthquake was about 80%, from the ratio of advanced time of the Lushan earthquake impacted by the Wenchuan earthquake (about 20 years) (Wan and Shen, 2010) to the five years’ of tectonic loading.

An outstanding question is: Is the Lushan earthquake an aftershock of the Wenchuan earthquake or not? To answer these questions, first, we should know the definition of aftershock. Aftershocks are defined as “smaller earthquakes following a large earthquake (the mainshock) in the same rupture area” by Liu and Stein (2011). Using this definition, we have three key characteristics of aftershocks. First, aftershocks must be smaller than their mainshock. Second, aftershocks occur after the mainshock. Third, aftershocks occur in the same rupture area where the mainshock fails. The first key point is definite, however, the second and third points are not so clear. The time intervals and distances differentiating aftershocks from independent earthquakes are not well defined. The durations of aftershock sequences could be about 10 years for plate‐boundary earthquakes (Parsons, 2002), and may last hundreds of years or even longer within slowly deforming continents (Stein and Liu, 2009). Typically, aftershocks occur within the mainshock rupture area. However, in many cases, aftershocks could occur off the main rupture surface (Robinson and Zhou, 2005). Earthquakes remotely triggered by dynamic seismic waves of the mainshock are also regarded as aftershocks (Gomberg and Johnson, 2005). So, the ambiguity of the definition of aftershocks still exists, and dominates the debate over the Lushan earthquake event.

In this study, we analyze the background seismicity in the Lushan region from a statistical viewpoint using the epidemic‐type aftershock sequence (ETAS) model and the stochastic declustering method to determine the relationship between the Wenchuan and the Lushan earthquakes. Furthermore, to examine the mechanism between the Wenchuan and Lushan earthquakes, we calculate the evolution of the CFS change by considering the viscoelastic relaxation of the lower crust and upper mantle in the focal region of the Lushan earthquake induced by the Wenchuan earthquake. Through these two different approaches, we derive our conclusion.

## BACKGROUND POSSIBILITY OF THE LUSHAN EARTHQUAKE

The space–time ETAS model introduced by Ogata (1998) combines the Omori–Utsu law, productivity law, and Gutenberg–Richter law, in which any earthquake has a magnitude‐dependent ability to trigger its own aftershocks.

According to the space–time ETAS model, given the observations before *t* the expected number of earthquakes above a magnitude threshold *M*_{c} in a unit space–time window centered at time *t* and spatial location (*x*,*y*), can be composed as (1)in which *μ*(*x*,*y*) represents the background seismicity rate, and (2)is the expected number of aftershocks generated from an event of magnitude *m*; (3)is the probability density function of the time‐interval distribution of aftershocks; and (4)is the probability density function of the relative locations between aftershocks and a mainshock. Equations (1)–(4) are according to Ogata (1998), Ogata and Zhuang (2006), Zhuang (2011), and Zhuang *et al.* (2005). The parameters *A*, *α*, *c*, *p*, *D*, *q*, and *γ* can be estimated through the maximum likelihood method.

The ETAS model provides a promising tool to distinguish triggered earthquakes from their aftershocks, especially when they are swarm‐like (Hill and Prejean, 2007; Peng *et al.*, 2012). The stochastic declustering method, proposed by Zhuang (2011; also in Zhuang *et al.*, 2002, 2005) is used to obtain the background probability of each event.

Obtaining the model parameters, we can simply calculate the quantity: (5)which can be interpreted as an estimate of the background probability for the *j*th event, in which *μ*(*x*_{j},*y*_{j}) is the background seismicity rate at the location of the *j*th event, and *λ*(*t*_{j},*x*_{j},*y*_{j}) is the expected number of earthquakes at the occurrence time and location of *j*th event.

If the background seismicity is constant in time, the declustered process, that is, the output of the stochastic declustering procedure, is close to a Poisson process that is stationary in time even if it is inhomogeneous in space. If the thinned outcomes for the background events do not appear uniform in time, then this should indicate some departure from the base assumption for the clustering effects. For example, some studies have shown that the background seismicity increased (decreased) with the increased (decreased) Coulomb stress (Stein, 1999; Toda *et al.*, 2005; Cocco *et al.*, 2010; Deng *et al.*, 2010; Ishibe *et al.*, 2011).

An advantage of the stochastic declustering method is that it allows uncertainties in the declustering process. Using the ETAS model and stochastic declustering method, we analyze the background seismic activity of Lushan region. The catalog used in this study is from CENC, and has been revised, correcting some errors.

To avoid influence of other main faults or large earthquakes and to ensure that the number of earthquakes within the study region is large enough for statistical analysis, a polygon region for model fitting and a study region (Lushan region) are carefully selected (white and blue polygon regions, respectively, shown in Fig. 1). We use the maximum likelihood method to estimate the model parameters in the time interval from 1 January 1990 to 20 April 2013 and the spatial region enclosed by the white polygon shown in Figure 1. The completeness of magnitude is 4.0 because of the absence of small earthquakes (*M*≤4.0) in the catalog immediately after the Wenchuan earthquake (Fig. 2a). The estimates of model parameters are , (events), (day), , , , , and . Then, we calculate the background probability of each event in the catalog above completeness magnitude and within the space–time range.

Through the stochastic declustering method, the aftershocks of the Wenchuan earthquake are effectively removed (Fig. 2b,c) and the background probabilities (equation 5) of each event in the catalog above magnitude completeness (Fig. 2a), and within the fitting space–time range are obtained (white polygon shown in Fig. 1). Table 1 lists the background probabilities for the Lushan earthquake and other events with *M*≥6.0. The background probability of the Lushan earthquake is 88%, and its aftershock probability is 12%, assuming that the ETAS model is a good model of the process.

Let the cumulative background probabilities of earthquakes, defined by Zhuang *et al.* (2005), be denoted by *S*(*t*), in which (6)

Figure 2d clearly shows that in the Lushan region (blue polygon region shown in Fig. 1), *S*(*t*) increased after the Wenchuan earthquake, indicating that the Wenchuan earthquake indeed changed the background seismicity in the Lushan region. Hence, the Wenchuan earthquake affects the Lushan earthquake in two ways, immediate triggering (resulting in aftershocks of the Wenchuan earthquake), and indirect triggering through changing the local background seismicity. We fit the data with two straight lines using the time of the Wenchuan earthquake as the turning point of the background seismicity. From Figure 2d, we can see that the background probability of the Lushan earthquake consists of indirect triggering of the Wenchuan earthquake and the original background seismicity, with a ratio of about 1.3:1 between them. Multiplying the percentage of indirect triggering (1.3/(1.3+1)=57%) by 88%, we determine that the indirect triggering probability is 50%. Thus, the contribution of the Wenchuan earthquake to the occurrence of the Lushan earthquake is 62% (50%+12%), and the remaining 38% is part of the original background seismicity.

## COULOMB FAILURE STRESS CHANGE

To understand how the Wenchuan earthquake influenced the stress field in the focal region of the Lushan earthquake, we calculate the CFS changes induced by the Wenchuan earthquake. We use a model of finite triggering sources embedded in a mixed elastic/viscoelastic layered half‐space, to calculate the evolution of CFS change considering viscoelastic relaxation of the lower crust and upper mantle. The Earth media structure consists of a layered elastic upper crust, a viscoelastic lower crust, and a viscoelastic upper mantle (Xiong *et al.*, 2010; Jia *et al.*, 2012). The viscosities of the lower crust and upper mantle are set to be 1×10^{18} and 1×10^{20} Pa·s, respectively.

Ji and Hayes (2008) swiftly published their inversions of the rupture processes of the Wenchuan *M*_{s} 8.0 earthquake using teleseismic broadband waveforms. Using high‐resolution geodetic data, Wang *et al.* (2011) provided a more recent inversion of the rupture model of the Wenchuan earthquake. We use their inverted results as the source models and the PSGRN/PSCMP code (Wang *et al.*, 2006) to calculate the evolution of CFS change. Earthquake triggering is considered as a mixture of static, dynamic, and viscoelastic processes (Steacy *et al.*, 2005). In this study, we focus on static stress triggering immediately after the Wenchuan earthquake and viscoelastic triggering five years after the Wenchuan earthquake. Dynamic stresses triggered by the seismic waves of the Wenchuan earthquake are neglected.

First, we calculate the evolution of CFS change along the slip direction at the initial rupture point (30.308° N, 102.888° E, depth 14.0 km), based on the location result of the USGS (http://comcat.cr.usgs.gov/earthquakes/eventpage/usb000gcdd#summary, last accessed August 2013) of the Lushan earthquake using different source models and friction coefficients (Fig. 3). Different models show differences in magnitudes of CFS change, but still show the same increased trends. The CFS change using a higher‐friction coefficient is smaller than that using a lower‐friction coefficient, but the differences between them are small. The focal mechanism of the Lushan earthquake used here is from Global Centroid Moment Tensor (CMT) (strike, 210°; dip, 38°; rake, 96°), is similar to the results of Wang *et al.* (2013) and Zhang *et al.* (2013). We project the stress‐change tensors on their fault planes, the patterns of calculated results of CFS changes are quite close to each other ( supplementary Fig. S1). We also project the stress‐change tensors at different depth (5.0, 10.0, 19.5 km), the patterns and magnitudes of the CFS changes are similar to the case of projecting them at depth of 14 km ( supplementary Fig. S2).

Then, we resolve the CFS change at 14 km depth around Lushan county, using two different models assuming *μ*=0.8 (Fig. 4). The coseismic (immediately after the Wenchuan earthquake) CFS changes at the hypocenter of the Lushan earthquake using the rupture models of Wang *et al.* (2011) and Ji and Hayes (2008) are 0.06∼0.09 and 0.10∼0.12 bar, respectively, and the postseismic (right before the Lushan earthquake) CFS changes using those two rupture models are 0.25 and 0.31∼0.37 bar, respectively. Increased coseismic and postseismic CFS changes at the hypocenter of the Lushan earthquake implied that the Lushan earthquake was promoted by the Wenchuan earthquake. The postseismic CFS change increased at least 0.4 bar and the combined CFS change increased about 0.5 bar in region between surface ruptures of the Wenchuan and Lushan earthquakes, where there was no failure in the Wenchuan and Lushan earthquakes. Thus, the postseismic CFS change induced by the Wenchuan earthquake could not be ignored because it might be larger than or at least at the same level as the coseismic CFS change about five years after the Wenchuan earthquake. Considering aftershocks barely occurred in the area where combined CFS change increased, we should pay more attention to this area.

Both models show that the CFS changes induced by the Wenchuan earthquake promote the failure of the Lushan earthquake (Fig. 4). Parsons *et al.* (1999) proposed low‐friction coefficients on faults with large cumulative slip, and high‐friction coefficients on faults with limited slip. Although the source fault of the Lushan earthquake is unknown until now, we could assume the friction properties of the source fault are similar to those of nearby faults. As slip rates of the Beichuan and Pengguan faults are low, and the shortening rate across Longmen Shan fault range is lower than 3 mm/yr (Chen *et al.*, 2000; Shen *et al.*, 2005; Wang *et al.*, 2008b), the assumption of *μ*=0.8, which indicates a higher‐friction coefficient of the source fault of the Lushan earthquake, is reasonable. Thus, the coseismic CFS changes immediately after the Wenchuan earthquake calculated using the models of Wang *et al.* (2011) and Ji and Hayes (2008) are 0.06∼0.09 and 0.10∼0.12 bar, respectively. Those values are comparatively similar to previous studies (Parsons *et al.*, 2008; Toda *et al.*, 2008; Shan *et al.*, 2009; Wan and Shen, 2010; Wang *et al.*, 2014). In addition, the combined CFS changes at the origin time of the Lushan earthquake based on the models of Wang *et al.* (2011) and Ji and Hayes (2008) are 0.31∼0.34 and 0.41∼0.49 bar, respectively, which are increased by a factor of 4. We propose that the dramatic changes in background seismicity in the Lushan region were caused by the elastic and viscoelastic stress transfer from the Wenchuan earthquake.

## CONCLUSION

Our statistical analysis, using the projected cumulative background probabilities (Fig. 2d), shows that the local background seismicity of the Lushan region was greatly changed by the Wenchuan earthquake. The occurrence of the Lushan earthquake consists of not only the contribution from the original background seismicity (38%), but also the aftershock effect and static indirect triggering of the Wenchuan earthquake, with proportions of 12% and 50%, respectively.

Considering the viscoelastic relaxation of the lower crust and upper mantle, we calculate the evolution of CFS change induced by the Wenchuan earthquake at the initial rupture point of the Lushan earthquake. The CFS changes increased from 0.06∼0.09 (origin time of the Wenchuan earthquake) to 0.31∼0.34 bar (origin time of the Lushan earthquake), and 0.10∼0.12 to 0.41∼0.49 bar, using the rupture models of Wang *et al.* (2011) and Ji and Hayes (2008), respectively (Fig. 3). Through the CFS changes, we show that the dramatic change in background seismicity in the Lushan region was probably due to the Wenchuan earthquake.

Is the Lushan earthquake an aftershock of the Wenchuan earthquake? The answer to this question depends on whether we utilize the 50% increment contribution to the occurrence of the Lushan earthquake, from the increment of background seismicity rate caused by the CFS changes due to the Wenchuan earthquake. If this increment is not taken into account, then the probability that Lushan is an aftershock of the Wenchuan earthquake in the traditional sense of the ETAS model is as low as 12%. If we regard the seismicity indirect triggered by the Wenchuan earthquake as aftershock effect in a more general sense, then the Lushan earthquake was more likely a strong aftershock of the Wenchuan earthquake with probability 62%.

## ACKNOWLEDGMENTS

We appreciate the Editor H. Yao, Z. Peng and two anonymous reviewers for providing insightful comments that greatly improved the manuscript. We thank J. Wu for providing the relocation results of the Wenchuan and Lushan aftershocks. We are grateful to Y. Zhang and W. Wang for providing us the rupture models of the Wenchuan earthquake. We are thankful to R. Wang for providing us the PSGRN/PSCMP code. We also appreciate helpful discussions with D. Harte. This research is jointly funded by the National Natural Science Foundation of China (Grant Number 41074030 and 41274052) and the “Scientific Investigation of April 20, 2013 *M*_{s} 7.0 Lushan, Sichuan Earthquake” from China Earthquake Administration. Some figures are prepared using Generic Mapping Tool mapping software (Wessel and Smith, 1991).