Earthquake Research in China  2019, Vol. 33 Issue (3): 403-417     DOI: 10.19743/j.cnki.0891-4176.201903007
The Longnan MS5.5 Earthquake on September 12, 2008: A Very Shallow Event Probably Triggered by the Wenchuan Earthquake
LUO Xinyu1, ZENG Xiangfang2, DONG Peiyu3, ZHOU Yong4,5, WEI Xing6, CHENG Huihong2,7
1. School of Earth and Space Sciences, University of Science and Technology of China, Hefei 230026, China;
2. State Key Laboratory of Geodesy and Earth's Dynamics, Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China;
3. Hubei Earthquake Agency, Wuhan 430071, China;
4. Department of Earth and Space Sciences, Southern University of Science and Technology, Shenzhen 518055, China;
5. School of Geodesy and Geomatics, Wuhan University, Wuhan 430072, China;
6. China Earthquake Networks Center, Beijing 100045, China;
7. CAS Key Laboratory of Computational Geodynamics, University of Chinese Academy of Sciences, Bejing 100049, China
Abstract: The 2008 Wenchuan earthquake has a significant impact on the seismicity of nearby regions. The Longnan earthquake which occurred on September 12, 2008 in Gansu Province was out of the aftershock zone. Reliable source parameters are essential for understanding the seismogenic process of this earthquake. Therefore, three approaches are adopted to study the source parameters of this event. The focal mechanism is obtained with the gCAP method that takes non-Double-Couple (non-DC) component into account. The two fault planes are NP1:150°/45°/81° and NP2:342°/45°/98°, while the non-DC component is about 53%. The focal depth is 1.6km, which indicates the Longnan earthquake is a shallow event. Furthermore, this result is also in good agreement with results obtained with two other approaches:amplitude spectra of Rayleigh wave and surface displacement from InSAR measurement. To analyze the cause of the event, coulomb failure stress change caused by the Wenchuan earthquake on the Longnan earthquake fault plane is calculated. The result shows that coulomb stress change is 30kPa around the Longnan earthquake hypocenter, which exceeds the typical triggering threshold of 10kPa. The research indicates that the Wenchuan earthquake probably promote the happening of the Longnan earthquake.
Key words: Longnan earthquake     Source parameter     Rayleigh wave amplitude spectra     Surface displacement     Coulomb failure stress

INTRODUCTION

The MW7.9 Wenchuan earthquake occurred on May 12, 2008 caused significant impact on adjacent areas. The seismicity changes of the nearby faults have become the focus of many researches. Previous studies based on Coulomb stress change theory show that the earthquake risk for the main active faults in the northeastern end of the Wenchuan earthquake aftershock zone (e.g. the Qingchuan fault) increased after the Wenchuan earthquake (e.g. Shan Bin et al., 2009; Shao Zhigang et al., 2010; Shi Yaolin et al., 2010). Although there is no identified surface rupture in the northeastern end (Xu Xiwei et al., 2010), aftershocks are relatively frequent. The source parameters of several strong aftershocks occurred in the area are significantly different. The focal depths range from 5km to 18km, whereas both thrust and strike-slip events are reported (e.g. Zheng Yong et al., 2009; Lü Jian et al., 2012).

 Fig. 1 (a) The M-T diagram of the seismicity in northeastern end of the Wenchuan earthquake aftershock zone. (b) Aftershocks of the Wenchuan earthquake and focal mechanisms of large events in northeastern end (location from Chen Jiuhui et al. (2009); focal mechanism from Global CMT) Fig. 1(a) events in M-T figure denote the earthquakes with surface wave magnitude ≥5.0, the blue line denotes the Longnan MS5.5 earthquake, red line denotes the Wenchuan earthquake. In Fig. 1(b), red lines delineate surface rupture of the Wenchuan earthquake. Green and black circles denote aftershocks with magnitude ≥3.0. Black circles show the aftershock happened in 3 days following the main shock. Green circles show the aftershock 3 days after the main shock. Red square denotes Shazhou Town, which is the division of early quakes and later quakes. Yellow star denotes the Longnan earthquake. Blue dashed box outlines the northeastern area corresponding to the Fig. 1(a). The beach balls show the focal mechanism of relatively large earthquakes in northeastern region

Among the earthquakes at the northeastern end of the Wenchuan earthquake aftershock zone, the Longnan MS5.5 earthquake that occurred on September 12, 2008 is a very special one. First, according to the hypoDD relocation result (Chen Jiuhui et al., 2009; Lü Jian et al., 2008), the Longnan earthquake is about 15km north to the aftershock zone (Fig. 1). The fact that the Longnan earthquake and the aftershock zone are not adjacent implies the Longnan earthquake is different from other aftershocks, and it might be an off-fault earthquake. Second, the Longnan earthquake is the largest aftershock in the northeastern end. Third, this event occurred at a relatively long time after the Wenchuan earthquake, so it holds great significance to study the triggering effect of the main shock. Moreover, there are two large destructive historical earthquakes happened in this region (Hou Kangming et al., 2005; Yuan Daoyang et al., 2007; in Fig. 2). The focal mechanisms of the Longnan earthquake also provides information about the regional stress field that helps to understand seismic hazard in this region.

 Fig. 2 Location of destructive historical earthquakes in vicinity of Longnan Symbols of Longnan earthquake and the two large historical earthquakes are given in the legend. Extreme seismic damage zones of both earthquakes are delineated with dash lines. Faults information from Ji Xingzhong(2016)

However, the source parameters of the Longnan earthquake are still uncertain. The focal mechanisms of the Longnan earthquake from Global CMT are Nodal Plane 1:155°/49°/88°, Nodal Plane 2:339°/41°/93°. Whereas, Guo Xiangyun et al.(2010) provided the focal mechanism as NP1:169°/69°/90°, NP2: 349°/21°/89°. Later, Luo (2018, personal communication) used the waveform inversion method and obtained the focal mechanism as NP1: 191°/69°/124°, NP2: 308°/39°/33° (Table 1). Although focal mechanisms of different sources indicate the earthquake to be a thrust event, there are still significant discrepancies among those results. At the same time, these earthquake depth solutions significantly differ from each other. Both arrival time method from China Earthquake Networks Center and long period surface wave method from Global CMT show the depth of the earthquake to be 12km, whereas the waveform inversion using local stations shows the result of nearly 2km (Luo, 2018, personal communication). Additionally, the CLVD component (47%) from the Global CMT solution is significantly larger than the average value (20%), which reveals the existence of large non-DC component and the earthquake's complexity(Frohlich C., 1994). So it might be insufficient to inverse the Longnan earthquake mechanism only using the double couple component.

Table 1 Focal mechanisms and depths from different sources

As mentioned above, there are significant discrepancies between solutions of the focal mechanism of the Longnan earthquake in current research. Consequently, the uncertainty of focal mechanism will result in significant uncertainty in calculated theoretical coulomb stress change on the fault plane of the Longnan earthquake (Zhan Zhongwen et al., 2011). Thus, it is necessary to obtain the accurate focal mechanism of the Longnan earthquake. Recently, Zhu Lupei et al.(2013) developed the gCAP method to utilize full moment tensor in focal mechanism inversion, which is more effective than previous double-couple-only CAP when applied to a complicated event that has significant non-double couple component. Compared to long period surface wave that the Global CMT utilized, the local seismic waveform used by gCAP has a better resolution of the focal depth (Yang Kai et al., 2018). Besides only using waveform, Jia Zhe et al. (2017) proposed that depth of earthquakes can be better constrained by incorporating Rayleigh wave amplitude spectra information of only few stations.

In recent years, InSAR observations have also played an important role in the study of earthquakes, and have been particularly helpful in the study of shallower crust sources (Sun Jianbao et al., 2008; Dawson J. et al., 2008; Ni Sidao et al., 2018). For the Longnan earthquake, InSAR also observed significant surface deformation that can further constrain the focal depth.

In this paper, firstly the gCAP method is used to obtain the moment tensor based on the inversion of local waveforms. Then, we use two stations that have clear surface wave signals to perform the focal depth inversion with the amplitude spectra to further confirm the focal depth of the Longnan earthquake. Furthermore, the InSAR observation on the surface displacement helps to ascertain the depth as well. Finally, the influence of Wenchuan earthquake on this earthquake is analyzed via the Coulomb stress change computation.

1 SOURCE PARAMETERS INVERSION BASED ON LOCAL WAVEFORM 1.1 Method

For source parameter inversion, we use the gCAP method (Zhao Lianshe et al., 1994; Zhu Lupei et al., 1996; Zhu Lupei et al., 2013), which is based on local seismic waveform fitting. In the gCAP method, the broadband seismic waveform is divided into two parts—Pnl wave and surface wave for waveform fitting separately, which can be filtered by different frequency bands. Meanwhile, gCAP allows different time shift for Pnl and surface wave, making it possible to obtain a relatively accurate focal mechanism even with a less accurate velocity model (Meng Qingjun et al., 2014). In order to be able to perform full moment tensor inversion, Zhu et al. proposed the dimensionless parameter of the isotropic (ISO) component and the compensated linear vector dipole (CLVD) component of the moment tensor based on Chapman's moment tensor decomposition method (Chapman C. H. et al., 2012; Zhu Lupei et al., 2013).

1.2 Data and Velocity Model

There are some clear waveform records at several local stations for the Longnan earthquake. Seven stations with high signal-to-noise ratios within 120km (Fig. 3(a)) are utilized. The azimuth distribution of the stations is relatively even, which is beneficial to the inversion of source parameters. The original waveforms are converted into velocity records after removing instrument response and the horizontal components are rotated to radial and tangential records according to the station and seismic location. The velocity model was modified from the eastern model of the Qinghai-Tibetan Plateau, which was obtained by Fan Wenyuan et al. (2015) through using ambient noise tomography method.

 Fig. 3 (a) Seismic stations used in the gCAP inversion. (b) Seismic stations for the Rayleigh wave amplitude spectra extraction

Table 2 Velocity model
1.3 Result

We calculate theoretical seismograms by the frequency-wave number (f-k) method based on propagation matrix (Zhu Lupei et al., 2002). The bandpass-filter for Pnl wave is 0.03-0.2Hz, and for the surface wave is 0.02-0.1Hz. Since the earthquake caused by pure shear faulting should not cause volume change, we limit the ISO component to 0 in the gCAP inversion, that is, the dimensionless parameter ζ is set to 0; the dimensionless parameter of CLVD χ between -0.5 and 0.5 is searched.

The focal depth search range is set from 1km to 12km with a step of 1km. In order to display the minimum value more accurately, the depth interval of the inversion between 1km and 3km is set to be 0.2km. Fig. 4 shows the depth residual obtained by gCAP inversion. The depth with minimum residual of the inversion is 1.6km. The waveform fitting at the optimal depth is shown in Fig. 5. The cross-correlation coefficients between theoretical waveforms and observed waveforms of most stations are close to 0.9. The two nodal planes of the solution are NP1: 150°/45°/81°, NP2: 342°/45°/98°. The non-DC component is 53%, which indicates that the ruptured plane is relatively complex. Two possible explanations are the rupture might occur on two fault planes that are not parallel to each other, or might occur on curved faults (Frohlich C., 1994). Two perturbed velocity models (±10%) were used to test effect of uncertainty of velocity model on the source parameters (e.g. Zheng Yong et al., 2009). The optimal focal depths are same while the changes of fault planes solution also falls into reasonable range (< 15 degrees).

 Fig. 4 Waveform fitting residuals at different depths

 Fig. 5 gCAP waveform fitting result Red lines are synthetic waveforms, black lines are observed waveform. Numbers above waveforms are time shifts and numbers below waveforms are cross-correlation coefficients. Corresponding station names, network, azimuth angle and epicenter distance are given on the left side
2 DEPTH INVERSION BASED ON RAYLEIGH WAVE AMPLITUDE SPECTRA 2.1 Method

In order to further confirm the focal depth, we also used the inversion method based on Rayleigh wave amplitude spectra. Tsai Y. B. et al., (1970) pointed out that amplitude spectra of the fundamental mode Rayleigh wave are sensitive to earthquake centroid depth. Jia Zhe et al. (2017) proposed that the Rayleigh wave amplitude spectra of few regional stations could effectively constrain the focal depth. Here, we use the inversion method proposed by Jia Zhe to invert the depth. This method utilizes the residual of amplitude spectra fitting as the objective function. The residual of the Rayleigh wave amplitude spectra fitting of a station at a given depth is represented by the following equation:

 $E{s_{{\rm{sta}}}}(h, i) = \sum\limits_{r = {T_{{\rm{start}}}}}^{{T_{{\rm{end}}}}} {\frac{{\left| {{{\log }_{10}}\left({\frac{{{A_{{\rm{obs}}}}(T)(i)}}{{{A_{{\rm{syn}}}}(T)(i)}}} \right)} \right|}}{n}}$ (1)

Where h is the source depth, i is the station number, Tstart and Tend refer to the shortest period and the longest period of the amplitude spectra, and n refers to number of sample periods. Aobs (T)(i) and Asyn (T)(i) are the observed and synthetic Rayleigh wave amplitude spectra values at periods T, respectively. The residual of the amplitude spectra fitting at a given depth is the sum of the residuals of all stations, i.e.

 $Es(h) = \sum\limits_{i = 1}^m E {s_{{\rm{sta}}}}(h, i)$ (2)

Where m denotes the number of stations, the depth corresponding to the minimum value of this objective function is adopted.

2.2 Rayleigh Wave Confirmation

The two stations used to extract the Rayleigh wave amplitude spectra are shown in Fig. 3(b). The two stations are BTA station and FXI station. These two stations' epicentral distances are more than 500km. Thus, the travel time difference between surface wave and S-wave is sufficient to separate these two phases, thus prohibiting the S-wave signal from mingling in surface wave and affecting the surface wave amplitude spectra extraction. In order to confirm the Rayleigh surface wave signal, we perform Hilbert transform on radial components, which can eliminate the 90-degree phase difference between the radial and vertical components of the Rayleigh wave. As shown in Fig. 6, the transformed R components generally overlap with Z components in the dashed box. This feature is consistent with the elliptical polarization characteristic of the Rayleigh wave.

 Fig. 6 Hilbert transform of R-component, original R-component and Z-component Blue lines represent transformed R-component waveforms, red dashed lines represent original R-component waveforms, black lines represent original Z-component waveforms. Each Black line and blue line generally coincide with each other in the black dashed box, indicating surface waves are observed at these two stations
2.3 Result

We extract the Rayleigh wave amplitude spectra of the two stations using the multiple-filter method provided in the Computer Programs in Seismology (CPS) software package (Herrman R. B., 2013). Then, we use the modal summation program in CPS to synthesize the amplitude spectra at 1-5km for BTA and FXI stations, and compare it with the observed spectra. We also consider the quality factor so that the Rayleigh wave attenuation during propagation could be taking into account as well. For BTA station, its surface wave traveled across the Qinghai-Tibetan plateau. The Q-value is relatively small and is around 200 (Li Guangpin et al., 2000). For FXI station, its surface wave traveled across the Sichuan basin. The Q-value is relatively large (Cheng Xianqiong et al., 2011). Here we test the Q-value of 200 and 500 for both BTA and FXI station during inversion.

The observed and synthetic Rayleigh wave amplitude spectra of two stations with two typical Q values are shown in Fig. 7. For the BTA station record, the spectra curve computed with Q=200 and depth=1km fitsthe observed spectra well (Fig. 7(a)). All theoretical spectra curves computed with Q=500 cannot explain the observation (Fig. 7(c)). The result of BTA station suggests that the focal depth is 1km, and the Q-value for this path is approximately 200. For the FXI station record, theoretical spectra curves predicted with Q=500 fit the observation better than the ones with Q=200 and the optimal focal depth is 1km (Fig. 7(b) and (d)). Additionally, there are minimal points (spectral null) on all the theoretical spectra curves when the focal depth is deeper than 1km and the frequency of the spectral null decreases with the depth (Langston C.A., 1980). However, there is no spectra null in the observed amplitude spectra, indicating that the earthquake occurred at a very shallow depth of 1km and thus produced a spectral null with a period too small to detect. The residual of inversion, which is summation of two stations' residual, is shown in Fig. 8. The optimal depth of amplitude spectra inversion is 1km, which is consistent with the previous inversion results, further confirming that the Longnan earthquake is a shallow event.

 Fig. 7 Rayleigh wave amplitude spectral fitting Red dots denote amplitude spectra from observed waveform. Solid lines represent synthetic amplitude spectra with different depth. Each synthetic curve is labeled with its source depth

 Fig. 8 Residuals of Rayleigh wave amplitude spectra fitting
3 DEPTH INVERSION BASED ON INSAR

If this event is indeed a M5.0 earthquake with depth around 1km, ground displacement might be up to a few centimeters which should be observable with InSAR data. We processed ALOS SAR data of path 471 on July 16, 2008 and July 19, 2009 with standard procedures. The quality of InSAR ground motion is worse than that observed by Dawson J. et al., (2008) for a M4.7 earthquake in Western Australia, where topography relief is much reduced as compared to the mountainous regions in this study. After unwrapping of the interferograms, we find coherent displacement along line of sight up to 7cm in an area about 2km by 2km (Fig. 9(a)).

 Fig. 9 (a) InSAR observed dislocation (b)-(d) synthetic dislocation of different source depths

To further determine the depth of the earthquake, synthetic surface displacement of several source depths are calculated with the programs EDGRN and EDCMP provided by Wang Rongjiang et al. (2003). The program can compute displacement for layered velocity model, and then transform the dislocation from xyz-direction to Line of Sight with equation (1) in Sun Jianbao et al. (2008). The velocity model used here is the same with the one used in the source parameters inversion. According the InSAR observation, the strike direction should be along the southeast direction. Therefore, the nodal plane 1 of the gCAP result is used to calculate synthetic displacement. According to the scaling law, the length, width and uniform slip of the source are set as 2.78km, 2.78km, and 0.14m, respectively (Kanamori H. et al., 2004). Three depths of 1.0km(Fig. 9(b)), 1.5km(Fig. 9(c)) and 4.5km(Fig. 9(d)) are used in this study.

The surface displacement decreases as the source depth increases from 1km to 4.5km (Fig. 9(b)-(d)). The maximum displacement (about 7cm) with the source depth of 1km is closest to the observation. When the source depth is at 1.5km, the maximum displacement of 5cm is slightly smaller than the observation. When the source depth is at 4.5km, the maximum displacement of 2cm is far smaller than the observation. Results show that the source depth is around 1km.

4 COULOMB FAILURE STRESS CHANGE ANALYSIS

Previous methods have confirmed that the Longnan earthquake is a very shallow event. To understand how this shallow event occurred, the impact of Wenchuan earthquake on the Longnan earthquake is studied. Coulomb stress change can indicate whether the stress impact from Wenchuan earthquake will hinder or facilitate Longnan earthquake's happening. Method of Coulomb stress calculation in homogenous half space is used (Wang Rongjiang et al., 2003). The velocity model from Crust 2.0 and Wenchuan fault model (Wang Qi et al., 2011) is used to calculate Coulomb stress change. According to InSAR observation, nodal plane 1 (150°/45°/81°) is the actual fault plane, so the Coulomb fault stress change is calculated for this nodal plane. Fig. 10(a) shows the Coulomb stress change on the plane. The Coulomb stress change is positive within 8km of the shallow area of the Longnan earthquake. The stress change is about 30kPa at 1.6km, which exceeds the Coulomb stress trigger threshold of 10kPa (Stein R. S. et al., 1994). The result indicates that the Wenchuan earthquake has strong triggering effect on the shallow part of the area, which possibly facilitated the Longnan earthquake. Furthermore, the triggering effect is still solid and reliable even when the friction coefficient varies to some extent (even up to 50%).

 Fig. 10 (a) Coulomb stress change corresponds to NP1. (b) Projection of fault plane NP1 on surface Black star in (a) represents earthquake centroid. The 3km×3km green rectangles represent the approximate rupture area according to earthquake scaling law
5 DISCUSSION

The focal mechanism solution of the Longnan earthquake we obtained is close to Global CMT's. There are some differences between previous studies and ours. These differences may be attributed to the inversion methods or structural complexity. The topographic variation around the Longnan earthquake is quite obvious, and the velocity structure is relatively complicated (Deng Wenze et al., 2014), which may cause deviation in gCAP inversion (Meng Qingjun, 2013). A more accurate inversion result might be obtained when waveform simulating methods such as spectral element method take 3-D velocity structure and topography into account (Liu Qinya et al., 2004). The focal depth obtained in this paper by gCAP method is 1.6km. This result is shallower than the depth of 12km given by Global CMT and China Seismic Network. And it is close to the depth of 2km given by Luo Yan. The source depth obtained by Rayleigh wave amplitude spectra method and InSAR data confirms that the earthquake is a shallow event as well. According to Coulomb stress change, the event is also possibly triggered by the Wenchuan earthquake. Besides this event, shallow triggered event cause has been reported before (Seeber L. et al., 1998).

The Longnan region locates in the eastern side of Bayan Har block. The region's stress is rapidly released since 1879. After the Wenchuan earthquake, the seismicity has increased, it is possible for big event to happen (Wen Xueze et al., 2009). The Gannan-Wudu-Wenxian fault zone, where the Longnan region locates, have a high seismicity even before the Wenchuan earthquake happened. Historically, there was a magnitude 8 earthquake happened in 1879 and a magnitude 7.0 earthquake happened in 186 B.C. The extreme shake zone is close to the Longnan region.

The Longnan MS5.5 earthquake, occurred in this region after the Wenchuan earthquake, is a thrust earthquake. The fault strike is along southeast direction. The fault locates near the Tongqianba-Fengxiangyuan fault. But the fault strike direction is almost perpendicular to the Tongqianba-Fengxiangyuan fault (Fig. 2), indicating that the earthquake occurred on an unknown fault. In addition, an MS5.2 earthquake happened at about 10km south of the Longnan earthquake on September 19, 2009. That earthquake has a strike of north to south, which is quite different from the nearby Qingchuan fault. These two earthquakes indicate that there are certain possibility of earthquake happening in the northeast area where blind faults may exist. Thus, the further study of effect of Wenchuan earthquake on Longnan and its surrounding region is necessary.

According to the earthquake scaling law, the rupture area of the Longnan earthquake is approximately the area within the green box (Fig. 9(a)). In this area, the Coulomb stress gradually increases from the bottom to the top. If the fault strength is uniform in the area, the rupture is more likely to initiate at the bottom, and the rupture extends from the bottom to the top. This is in consistence with the thrust rupture characteristics summarized by previous research (Das S. et al., 1983; Olson E. L. et al., 2005; Mai P. M. et al., 2005), but this inference requires more information, such as rupture directivity. In recent years, the newly proposed depth phase method may be able to further determine the rupture directivity of the earthquake, so that a better understanding of this earthquake can be achieved (He X. et al., 2017).

6 CONCLUSION

We studied the source parameters of the Longnan MS5.5 earthquake, an event located in the northeastern end of the Wenchuan MW7.9 earthquake aftershock zone, and investigated the relationship between this event and the Wenchuan earthquake. The focal mechanism and depth of Longnan earthquake were inverted by the gCAP method. The gCAP focal mechanism solution is NP1: 150°/45°/81°, NP2: 342°/45°/98°, and depth is 1.6km. Similarly, the RWAS inversion shows that the earthquake is a shallow event, with 1km focal depth. Moreover, InSAR observation confirms this earthquake is a shallow event. Finally, the Coulomb stress change on the fault plane was calculated. The result shows that the Coulomb stress change (30kPa) exceeds the triggering threshold, which indicates that the Longnan earthquake is likely a triggered event.

ACKNOWLEDGEMENT

The authors would like to show their thanks to the two anonymous reviewers for their constructive comments.

REFERENCES