1 Introduction

An earthquake sequence including the Ms4.8 mainshock (Changning earthquake for short) shocked Changning, Sichuan, on April 25, 2013, which injured dozens and resulted in economic losses amounting to about 300 million RMB (Fig. 1). The Chinese Earthquake Network Center reported that both the Ms4.8 mainshock and the strongest aftershock occurred at a depth of 4 km. (http://www.cenc.ac.cn/manage/html/402881891275f6df011275f971990001/__SUBAO/_content/13_04/25/13e3e2158b900.html), while the USGS National Earthquake Information Center determinated the mainshock is a M5.3 event occurring at 10-km depth (http://comcat.cr.usgs.gov/earthquakes/eventpage/usb000gfau#summary). Such divergence increases more interest in improving accuracy of focal parameters.

Fig. 1
figure 1

Historical seismicity (M > 2.0) between 2009 and 2013 at Changning. The red star denotes location of salt mine

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Most deconstructive and felt earthquakes in Sichuan occur at major fault systems such as the Longmenshan Fault system. However, the epicenter of Changning earthquake is about 40 km away from the Huayingshan Fault that is a major fault in eastern Sichuan basin. Since the thickness of sediment in southern Sichuan depression ranges from 6 to 8 km (Song and Luo 1995), the Changning earthquake was eventually an earthquake occurring in sediment. Because the strength of rock in shallow crust is too weak to accumulate enough strain, most earthquakes occur in the middle crust except in the area with anomaly geothermal flow (Shi and Zhu 2003; Klose and Seeber 2007). Therefore, there are only a few articles about deconstructive earthquakes occurring in shallow crust (<5 km) in India and Austria cratons (Dawson et al. 2008; Gupta et al. 1996). Luo et al. (2011) reported a deconstructive event occurring in Mesozoic sediment at the center of Sichuan basin. The 2010 Christchurch earthquake is also another recent example (Kaiser et al. 2012). Such cases provide an opportunity to study strain accumulation and failure in weak rock.

In recent years, production of shale gas experienced a great boom in the US, and many countries proposed ambitious plans for shale gas exploration and production. Because the permeability of shale or other tight rocks is very low, engineers pump huge volumes of pressurized mix of water, chemicals, and sand to create and hold open fractures. Seismicity events induced by fluid injection in geothermal sites (e.g., Eberhart-Phillips and Oppenheimer 1984) and wastewater disposal sites (e.g., Healy et al. 1968) have been reported in the recent decades. Several moderate and felt earthquakes (up to Mw5.7, Keranen et al. 2013) occurred in shale-gas fields in the US midcontinent, and such a situation was proposed to be posing a higher risk (Ellsworth 2013). There are several articles on induced seismicity in gas field (Zhu et al. 2007; Long et al. 2010) and salt mine (Lu et al. 2009). Changning–Weiyuan field is the first shale-gas production area of China. The historical seismicity concentrates in the range of 10–20-km depth. Therefore, the Changning earthquake is a rare case study to analyze seismic hazard caused by shallow event.

Due to sparsity of the sample, uncertainties of source parameters of shallow earthquake determinated with traditional methods are sizable. For travel-time location except nearby stations, sparse samples of takeoff vector in upper hemisphere increase uncertainty introduced by tradeoff between depth and origin time (Mori 1991). For first motion inversion, uncertainties of the depth and velocity model also introduce large errors. Methods based on waveform could use more information taken from later phases to constrain fault plane and centroid depth. In this article, we adopted waveform inversion method to obtain focal mechanism including centroid depth, and then used local and teleseismic depth phases and amplitude ratio of body wave and surface wave to determinate the focal depth.

2 Focal mechanism

The cut and paste (CAP for short) method is a popular waveform inversion method, which uses regional three-component records of body wave and surface wave to constrain fault plane and centroid depth (Zhao and Helmberger 1994; Zhu and Helmberger 1996). Recently, the teleseismic waveform was also introduced into CAP to provide more constraint for thrust event (Ni et al. 2010; Chen et al. 2012). We collected three-component records at stations within 200 km (Fig. 2a; Zheng et al. 2009) and adopted Sichuan basin velocity model obtained from short-period surface-wave dispersion inversion (Fig. 2b; Xie et al. 2012). Velocity increases with the depth in sediment, and the total thickness of the crust reaches 40 km. Synthetic seismograms of arbitrary faults are built from those of the three basic faults that were computed with FK method (Zhu and Rivera 2002). Both synthetic and observed waveforms were bandpass filtered (0.02–0.15 Hz for body wave and 0.02–0.1 Hz for surface wave). Grid search scheme was employed to seek the best solutions at different depths, and the misfit function reaches the minimum at 3 km as the best centroid depth (3 km; Fig. 3a), while the magnitude of moment is 4.5. The fault planes of the best solution are 128°/42°/83° (plane I) and 317°/48°/96° (plane II) for strike, dip, and rake, respectively. Figure 3b shows comparison between the filtered synthetic and observed waveforms. Most cross-correlation coefficients of Pnl Segment are larger than 0.8 except CQT and WAS stations that are further away from the epicenter. For surface-wave segment, the synthetic waveforms best fit observations at ROC and YAJ stations, and the cross-correlation coefficients are larger than 0.7. Strike of fault plane I is consistent with the Changning Anticline, and it is close to fault planes of historical events obtained from the amplitude ratio method (Ruan et al. 2008). Consequently, the fault plane I is possibly the rupture plane.

Fig. 2
figure 2

a Epicenteral and seismic stations used in this study. Star denotes epicenter, while triangles show stations. Faults are shown in solid lines, b basin velocity model. Dashed line denotes shear wave, while Vp is shown in solid line

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Fig. 3
figure 3

a Waveform misfit versus focal depth, b waveform comparison between synthetic (red) and observed waveforms (black line)

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3 Depth phases

The depth phases are reflected at free surface upper hypocenter, and the paths of depth phase and reference phase are close to each other except the reflected segment. Hence, the differential time between two phases is dominated by depth, and it is slightly affected by heterogeneity along propagation path. Benefiting from radiation pattern of thrust event, the global seismic network provides high-quality records of the Changning earthquake. We selected broadband records at Global Seismographic Network. After removing instrument response and lowpass filtering (<1 Hz), we chose three high signal–noise-ratio records at different azimuths (Fig. 4a). When the focal depth is small, the pP and sP signals may be contaminated by direct P wave, and manual picking is difficult. The waveform modeling method, which best fits observation with synthetic waveforms of different focal depths, is a better choice. The synthetic waveform was computed with three steps involving effects of mantle, source, and receiver-side crust (Kikuchi and Kanamori 1982). The source-side crust model is the same as the previous one, and the velocity model in the mantle is that of PREM model. The t* (1.0 for P wave) was adopted to take into account the effect of inelastic attenuation. Figure 4b shows the comparison between the filtered observations and the synthetic waveforms of different focal depths. All traces were filtered and aligned with direct P arrival. The differential time between P and pP shows a clear growth trend in synthetic waveforms, and the preferred depth is around 1–2 km.

Fig. 4
figure 4

a Teleseismic stations map, b waveform comparison between the teleseismic synthetic (red) and the observed (black) ones

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We also analyzed depth phases as recorded by the regional network. The sPL phase is an effective one for determining focal depth at near distance, and it has been widely used in several moderate earthquake studies (Luo et al. 2010; Chong et al. 2010). The dominant frequency of sPL is lower than direct P wave, and the radial component is much stronger than the vertical one. Three-component records of JLI pertain to the removed instrument response, and velocity records were integrated into displacement. Both the synthetic and observed waveforms are bandpass filtered between 0.05 and 1.0 Hz. As Fig. 5a shows, the sPL signal at the radial component is much stronger than the one at the vertical component. The synthetic waveforms of 2 and 3 km fit the observation better than other ones. The sPL is also clear for records of Ms4.2 aftershock, and the differential time between sPL and P suggests that depth of this aftershock is close to that of the mainshock (Fig. 5b).

Fig. 5
figure 5

a sPL waveform fitting at JLI station for Ms4.8 mainshock, b sPL waveform fitting at JLI station for Ms4.2 aftershock. Red the synthetic vertical component: gray the synthetic radial component; and blue the observed radial component

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4 Short-period surface wave

At regional networks, we observed strong short-period surface wave that is an index of shallow earthquake. Tsai and Aki (1970) proposed that spectrum of surface wave could be used to constrain focal depth with the well-constrained fault plane. The short-period Rg wave also is considered as an important characteristic of shallow event (Kafka, 1990; Luo et al. 2011). Both the 90-degree phase differences between radial and vertical components and dispersion are helpful to us to identify Rg wave. Figure 6 shows clear Rg wave signals at HWS and LZH stations. In general, the Rg wave could be observed when epicentral distance exceeds by about five times of focal depth (Luo et al. 2011). Consequently, the Rg wave at HWS (distance = 31 km) suggests that the focal depth of the Changning earthquake may be not larger than 6 km. The amplitude ratio of the body wave and the surface wave is also sensitive to the focal depth (Luo et al. 2011). We compare the different ratios at the synthetic waveform and observation, as shown in Fig. 6. As Fig. 6 shows, deeper focal depth results in weaker Rg wave. At HWS, the best depth is about 2–4 km, while the other one is about 3–5 km at LZH. Most of the energy of the short-period Rg wave was trapped in sediment where inelastic attenuation is much stronger than that at middle crust. While path of the body wave bends toward the middle crust, inelastic attenuation of the body wave slightly increases with the distance. Therefore, amplitude ratio between Rg and body wave at farther stations will be smaller than the one measured at closer station.

Fig. 6
figure 6

a Observed (black) and synthetic (red) short-period surface waves at HWS, b observed (black) and synthetic (red) short-period surface waves at LZH

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5 Discussion and conclusions

As mentioned above, the Changning earthquake is a thrust event on ESE fault plane, while theestimated focal depth is between 2 and 4 km. The preferred depth of 3 km was obtained from CAP inversion, and it is supported by both depth phases and short-period surface observations. In the southern Sichuan depression, thicknesses of Paleozoic and Mesozoic sediments are about 7 km (Song and Luo 1995), and so the hypocenter is positioned in the Paleozoic Dengying Formation. The most-deconstructive earthquake occurs in the crystalline basement, and Horton et al. (2005) reported a rare case of a Mw4.2 earthquake that occurred in Paleozoic sediment in Kentucky, U.S.A. The number of fellable earthquake at Changning has been significantly increasing since 2006 (Ruan et al. 2008). In October 2007, Earthquake Administration of Sichuan Province installed two temporal broadband seismometers to monitor microseismicity. The location result shows that most small earthquakes are shallower than 3 km, while stronger events occurred at greater depths, while the centroid of earthquakes between October 18, 2007 and November 12, 2007 lies at about 10 km east of the salt mine. The semi-major axis of the earthquake cluster is close to that of the fault plane I of this study’s result. The focal mechanism solution indicates the axis of the compressive principal stress along NE. This result is similar to the previous result (Ruan et al. 2008), but it is different from the result of the regional tectonic stress field (Zhu et al. 2007). Mckenzie (1969) pointed out that the stress axes obtained from a few earthquakes might deviate from that of the regional tectonic stress. Another potential interpretation is that the present tectonic stress is different from the one in geological time. The rupture fault was formed in different tectonic stresses, and a strong horizontal stress induced the thrust sliding.

Changning–Weiyuan region is one among the first pilot shale-gas fields of China. Since hydraulic fracking increases concern on seismic hazard, the Changning earthquake provides a case to study the mechanism of earthquake in sediment that will be helpful to us to understand induced seismicity. The salt mining is a historical industry in Sichuan basin, and previous studies proposed that fluid injection during the salt mining induced microseismicity (e.g., Lu et al. 2009; Long et al. 2010). At Changning, the salt deposit is about 2,400–2,900 m deep, and the deepest injection well is about 3,000 m (Ruan et al. 2008). The number of felt earthquake shows similar variation with the net injected fluid volume (Ruan et al. 2008). Injected fluid not only induces seismicity around well but also possibly diffuses to nearby fault and results in the increase of pore pressure. The induced seismicity in Arkansas shows that the fluid injection increases the potential of deconstructive earthquake at blind faults (Horton 2012) even tens of kilometers away. Flows in the lower crust and the upper mantle may enhance stress in the upper crust, and it leads to the seismogenic fault reaching critical state (Zoback and Townend 2001). The lower mantle flow beneath Sichuan basin has been reported in recent decades, and high-frequency-induced seismicity in Rongchang region also supported the fact that faults are in critical state. Therefore, even a small stress perturbation caused by injected fluid could induce earthquake. Induced seismicity such as that occurred in the Changning earthquake raises public concern on seismic hazard.

Since the Changning earthquake occurred only 5 days after the April 20, Lushan Ms7.0 earthquake and separation between two earthquakes is <300 km, the Changning earthquake raised concern on whether the Lushan earthquake would trigger strong earthquake in adjacent region. There are two main potential mechanisms about earthquake trigger: static and dynamic triggering mechnisms. Coseismis static displacement changes strain at nearby faults, and the resulting effect could be described as change of Coulomb failure stress (ΔCFS). Positive ΔCFS means that risk of earthquake increases, and the ΔCFS threshold of triggering is about 0.1 MPa (King et al. 1994). The coseismic static displacement decreases with distance as 1/r–1/r2. For example, in the Mw7.3 Landers earthquake, the ΔCFS is only about 0.003 MPa at 200 km far away (Hill et al. 1993). Shan et al. (2013) show that ΔCFS caused by the Lushan earthquake at Huayingshan fault is less than −0.01 MPa. Therefore, the possibility of static trigger is very low. The amplitude of surface wave excited by large earthquake decreases with distance, as such displacement could induce strong stress perturbation. Therefore, the dynamic triggering is still significant at far field. For example, the maximum dynamic stress perturbation caused by the Mw7.9 Denali earthquake is up to 0.12 MPa at 3,000 km far away (Pankow et al. 2004). Most dynamic triggered events occurred in a few minutes after arrival of surface wave. However, Brodsky and Prejean (2005) proposed the fluid migration is a potential mechanism of dynamic trigger, and delay time would be affected by permeability and diffusion coefficient (Glowacka et al. 2002). The delay time ranges from seconds to days (Mohamad et al. 2000; Hough 2005). After fluid injection in past decades, rock in sediment may have been saturated and easier to be triggered. However, there is not clear creditable clue of triggering.

In summary, focal mechanism of the Changning earthquake was obtained from waveform inversion, and the fault plane I (128°/42°/83°) is possibly the rupture plane. The focal depth (2–4 km) was determinated with the depth phases and amplitude ratio of body wave and surface wave. Such shallow earthquake in Paleozoic sediment is possibly induced by fluid injection rather than triggered by the Lushan earthquake.