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Complex Rupture of the 2014 Ms 6.6 Jinggu Earthquake Sequence in Yunnan Province Inferred from Double-Difference Relocation QINGDONG WANG,1 RISHENG CHU,1 HUI YANG,1 LIANGBAO ZHU,2 and YOUJIN SU3 Abstract—To study the seismogenic structure of the 7 October 2014 Ms 6.6 Jinggu earthquake, we use the cut-and-paste (CAP) method to obtain the focal mechanisms and depths of the mainshock and the two largest aftershocks with Ms [ 5. Then, we take advantage of waveform cross-correlations to obtain precise time difference data and apply the double-difference method to relocate the aftershocks between October 7 and December 31. We relocate 2076 earthquakes (approximately 73.6% of the total) with an average horizontal accuracy of approximately 150 m and a depth uncertainty of approximately 700 m. The Ms 6.6 mainshock epicenter originated at 23.378°N, 100.475°E at a depth of 15.38 km. The Jinggu earthquake sequence exhibited a linearly concentrated distribution in the northwest–southeast direction with obvious segmentation features and, thus, it can be divided into four branches spatially and two stages temporally. The aftershocks first appeared around the Ms 6.6 mainshock and then extended on either side of the mainshock along the NW–SE direction (the NW branch). The earthquake rupture direction experienced a slight clockwise deflection at the NW end and rotated clockwise by approximately 90° toward the SW (the NE branch) at the SE end. Then, the rupture propagated a short distance along the SW direction and rotated counterclockwise by approximately 90° into an SSE direction (the NNW branch). There is a small angle between the NW and NNW branches. The depths of the whole sequence with vertical dip angles were shallower toward the NW and deeper with two seismogenic layers toward the SE. According to the distributions of the earthquakes and nearby fractures, it is highly possible that the Jinggu earthquake sequence occurred along a hidden fracture section of the Wuliangshan fault in the NW direction. Moreover, we can confirm that the three large earthquakes all occurred along right-lateral strike-slip faults. Key words: Jinggu earthquake sequence, focal mechanisms, waveform cross-correlation, double-difference method.

1 State Key Laboratory of Geodesy and Earth’s Dynamics, Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China. E-mail: [email protected] 2 Key Laboratory of Geospace Enviroment and Geodesy, Ministry of Education, Wuhan University, Wuhan 430079, China. 3 Earthquake Administration of Yunnan Province, Kunming 650224, China.

1. Introduction An Ms 6.6 earthquake (hereafter referred to as the Ms 6.6 Jinggu earthquake) occurred in the city of Pu’er, Jinggu County, Yunnan Province, at 21:49 on October 7, 2014 (Beijing Standard Time). The hypocenter occurred at 23.39°N, 100.46°E at a depth of 5 km (China Earthquake Networks Center 2014). Then, on November 6, the two largest aftershocks of the event with magnitudes of Ms 5.8 (23.3°N, 100.5°E, 9 km) and Ms 5.9 (23.3°N, 100.5°E, 10 km) occurred. The Ms 6.6 Jinggu earthquake struck approximately 25 km away from Jinggu County and approximately 80 km away from the city of Pu’er (Fig. 1a). The Jinggu earthquake occurred in the southeast of the Tibetan Plateau where the Indian plate collides with the Eurasian plate and pushes the Tibetan Plateau to extrude to the east. The Jinggu County area is located between the Simao-Pu’er seismic belt and the Gengma-Lancang seismic belt, where the structure is complicated with a high fracture density. There are two networks of conjugate fracture systems striking NNW and NNE that intersect and restrict each other and form a large number of smaller faults (Fig. 1a). The main representations of these systems are the Lancang River fault that strikes NNW and the Wuliangshan fault that strikes NNW-NW (Wu et al. 2016). The epicenter of the Ms 6.6 Jinggu earthquake occurred 34 km to the east of the Lancang River fault at the northwestern extension of the western branch of the Wuliangshan fault along the Puwen fault (expressed as a dotted line in Fig. 2a). Within a radius of 100 km around the epicenter, 35 earthquakes with Ms [ 5 have occurred historically, 13 of which had Ms exceeding 6 (Li et al. 2014). The biggest

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Figure 1 Fault (a) and station (b) distribution map of the study area. NDHF Nandinghe fault, MGF Muga fault, LCJF Lancangjiang fault, WLSF Wuliangsan fault, HHF Honghe fault. Border: the China-Myanmar international border. The dashed box in a represents research area of this paper. The circle in b represents the distance range of 200 km

earthquake with a magnitude of Ms 7.4 occurred along the Muga fault on November 6, 1988. This earthquake killed 748 people and injured another 7751 and it was located approximately 90 km from the Jinggu earthquake epicenter. Geographically, the nearest historical earthquake with Ms [ 6 was the M 6.75 Simao earthquake that occurred 37 km to the southwest of the Jinggu earthquake on February 1, 1942. The most recent earthquake was the Ms 6.4 Ninger earthquake that was related to activity along the Wuliangshan fault and occurred on June 3, 2007 (China Earthquake Administration 2014; Liu et al. 2008). The Jinggu earthquake sequence exhibited long spans both temporally and spatially and it did not occur on a known fault. To study the occurrence and development of earthquakes is of great significance for understanding the causes of earthquakes and for developing disaster prevention and reduction measures. Earthquake focal mechanisms and aftershock distributions are important for understanding rupture processes of earthquakes and seismogenic structures of active faults (Wen et al. 2013; Zhao et al. 2013). Xu et al. (2015) used the P-wave first-motion polarity

and amplitude ratio method to derive the focal mechanisms and employed phase data with the double-difference method to relocate the Jinggu earthquake sequence. The results indicated that the major rupture plane was a right-lateral strike-slip fault with an NW nodal plane. The linearly shaped earthquake distribution and focal mechanisms vary with location on different segments with clear endpoints and transform segments. Chen and Chen (2016) used teleseismic P-wave data with the grid search method to invert the source mechanisms of the earthquakes and used near-field seismic data with the double-difference method to relocate the locations of the events, which agreed well with the results of the focal mechanism inversion. With the combination of these results, they concluded that this earthquake might suggest a new concealed seismogenic fault. The accuracies of absolute hypocenter locations are controlled by several factors, including the network geometry, the available phases, the arrival-time accuracy, and the prior knowledge of the crustal structure (Pavlis 1986; Gomberg et al. 1990). The temporal accuracy of phase data is relatively low. One way to improve the accuracy of relative arrival-

Complex Rupture of the 2014 Ms 6.6 Jinggu Earthquake Sequence in

Figure 2 The initial location distribution of the Jinggu Ms 6.6 earthquake sequence (the focal mechanisms come from the Global CMT catalog in Table 2). JGF Jinggu fault, LCJF Langcangjiang fault, PWF Puwen fault

time data is to use a waveform cross-correlation method. The relative timing precision can then reach approximately 1 ms and, thus, the relative location errors will range from only a few meters to a few tens of meters (Waldhauser and Ellsworth 2000). We, therefore, propose a new waveform cross-correlation method called the time domain multi-channel correlation detector function (MCC), which can improve the calculation efficiency and provide more stable and reliable waveform cross-correlation time difference data. The effectiveness of the MCC has been already verified in our previous studies (Wang et al. 2015). Waldhauser and Ellsworth (2000, 2002) proposed the double-difference earthquake location

method (hereafter referred to as the DD method), which can use accurate waveform cross-correlation travel-time difference data as input data and reduce the influence of the velocity model. The DD method is suitable for the relocation of large earthquakes and the corresponding aftershock sequences and can obtain accurate spatio-temporal distributions of hypocenters with small location errors (Yang et al. 2003; Huang et al. 2008; Wang et al. 2012, 2014; Fang et al. 2013, 2014; Su et al. 2013; Zhang et al. 2014; Waldhauser and Ellsworth 2002; Waldhauser and Schaff 2008; Waldhauser and Tolstoy 2011; Schaff and Waldhauser 2005; Lin et al. 2007; Hauksson et al. 2012; Matoza et al. 2013).

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In this article, we use the CAP method to obtain the focal mechanisms and the depths of the mainshock and the two largest aftershocks with Ms [ 5. We also take advantage of waveform cross-correlations to obtain precise time difference data and use the DD method to relocate the Ms 6.6 Jinggu earthquake sequence from October 7 to December 31 recorded by the Yunnan seismic network. The location results provide an important reference for seismogenic structure research and for the spatiotemporal evolutionary characteristics of aftershocks.

velocity structure still can affect the absolute position and the scale of the earthquake cluster (Huang et al. 2008). The Ms 6.6 Jinggu earthquake occurred at the western edge of the Lanping-Simao Basin along the eastern side of the Lancangjiang fault, where the crustal structure is very complicated. Deep seismic sounding methods can provide a precise velocity structure of the observation point. Over the past 20 years, several deep seismic sounding projects were performed in Yunnan and obtained a large quantity of observational data (Hu et al. 1986; Xiong et al. 1986, 1993; Yin et al. 1987; Wang et al. 2002). Combined with research results on the crustal velocity structure (Chen et al. 1990; Wang et al. 1994; He et al. 2004), many researchers obtained the horizontal velocity structure for 25 observation points. The Jinggu observation point (23.47°N, 100.7°E) is approximately 3 km away from the Ms 6.6 earthquake epicenter. We compared the observed phase travel times with the theoretical phase travel times calculated using the crustal velocity structure of the Jinggu observation point (Table 1). The difference in the P and S travel-time datasets is small when the epicentral distances are less than 200 km, indicating that the phase data and the velocity structure are reliable. Therefore, we use the velocity structure at the Jinggu observation point as the location velocity model (Table 1) and select the phase travel-time data with epicentral distances of less than 200 km.

2. Data 2.1. Stations and Original Data There are approximately 20 stations with epicentral distances of less than 200 km, including 16 permanent stations and 4 temporary stations that were deployed on October 8. The nearest station is station Jinggu (JIG) with an epicentral distance of approximately 31 km. These stations provide a good azimuthal coverage and constraints on the Ms 6.6 Jinggu earthquake sequence locations (Fig. 1b). The seismic catalog provided by Earthquake Administration of Yunnan Province (EAYP) shows that the Jinggu earthquake sequence did not show any obvious foreshocks. We, therefore, choose the earthquakes that occurred between October 7 and December 31 and their waveform data. It is required that the earthquakes must have ML C 1.0 and have 4 phase records within epicentral distances of less than 200 km. Finally, we obtain 3383 earthquakes (Fig. 2), including 13 earthquakes with ML C 4 and 125 earthquakes with ML between 3 and 3.9. The initial location results given by the Yunnan seismic network (Fig. 2) show that the aftershock sequence of the Ms 6.6 Jinggu earthquake exhibited a banded distribution along the north-northwest direction approximately parallel to the Puwen fault. 2.2. Velocity Model Although the DD method can reduce the influence of the crustal velocity structure during the event location by using relative time difference data, the

3. Method 3.1. The CAP Method The cut-and-paste (CAP) method is an effective method for obtaining the focal mechanisms, moment Table 1 Velocity model Depth (km)

VP (km s-1)

VS (km s-1)

Density (kg m-3)

0–3.5 3.5–12 12–22 22–31 31–38.5 38.5–46.6 46.6?

4.60 6.07 6.30 6.60 7.30 7.90 8.10

2.66 3.51 3.64 3.82 4.22 4.57 4.68

2.60 2.60 2.90 3.38 3.38 3.38 3.38

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Figure 3 Focal mechanisms and a comparison between the theoretical (red) and real (black) waveforms using the CAP method. a Ms 6.6; b Ms 5.8; c Ms 5.9

magnitudes and centroid depths of earthquakes using regional earthquake waveform data (Zhao and Helmberger 1994; Zhu and Helmberger 1996). In this method, three-component full waveforms are divided into both body waves and surface waves, which are then filtered in different frequency bands and inverted. This method desensitizes the timing between the principal crustal arrivals and reduces the dependence on a velocity model (Zhu and Helmberger 1996). The CAP method has been widely used in earthquake focal mechanism inversions (Tan et al. 2006; Chu and Helmberger 2013). In this study, we choose the three-component waveforms of earthquakes with epicentral distances of less than 5° (approximately 550 km) provided by the National Seismic Network, including 10 stations with an evenly distributed azimuthal coverage. The instrumental responses of the original three-component waveforms are removed and then converted into velocity components. The three-component waveforms are rotated into the great circle path. The waveform data are separated into Pnl wave segments with a 35-s window, 7 s before and 28 s after theoretical P arrivals, and surface wave segments with a 70-s window, 21 s before and 49 s after theoretical S arrivals. We choose a 4th-order

Butterworth bandpass filter with bandwidths of 0.05–0.13 Hz for the Pnl wave component and 0.02–0.08 Hz for the surface wave component. Theoretical seismograms must be calculated for a comparison with the real waveform. We use the frequency–wavenumber numerical computation method (Zhu and Rivera 2002) to calculate the Green’s functions for a one-dimensional velocity model (Table 1). A comparison between the observed (black) and synthetic (red) waveforms is shown in Figure 3. The number below each trace is the time shift of the theoretical seismogram relative to the real waveform and their cross-correlation coefficient. The station names are given on the left and the numbers below the stations are their epicentral distances and relative time shifts that may have been caused by an error in the earthquake location, an error in the earthquake origin time or an error in the theoretical velocity model. To obtain the variation characteristics of the focal mechanisms with depth, we plot the misfit-fitting curve between the focal mechanisms and the depths (Fig. 4). The black solid line is the best-fit curve. The focal sphere at a point of intersection between the curve and the vertical line is the optimum focal

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Figure 4 Mismatch and focal mechanism solutions as a function of focal depths for a Ms 6.6; b Ms 5.8; c Ms 5.9 earthquakes, respectively

Table 2 Best double-couple solutions of the Global CMT catalog Magnitude

Ms 6.6 Ms 5.8 Ms 5.9

Nodal plane 1

Nodal plane 2

Institution

Strike (°)

Dip (°)

Rake (°)

Strike (°)

Dip (°)

Rake (°)

329 151 346 167 339 161

81 70 81 69 71 73

174 174 162 174 163 172

60 243 79 259 71 252

84 90 72 85 84 90

9 20 9 19 19 16

mechanism solution at that depth. The number at the top of the focal sphere is the moment magnitude. The best-fit curve has an obvious trough, which suggests that the local earthquake data have good constraints on the depth. According to the distribution of focal mechanisms, there is a small change in the focal mechanism with depth. In addition, the inversion results are less dependent on the depth. The above analysis shows that the inversion results of the focal mechanisms in our study are reliable. We include the isotropic (ISO) and CLVD components in the inversion of focal mechanisms. The DC component of the Ms 6.6 earthquake is about 98.4%, and the ISO and CLVD components in the focal mechanism can be safely ignored. Table 2 shows the best double-couple (DC) solutions for the three large earthquakes in the Jinggu sequence given

GCMT CAP GCMT CAP GCMT CAP

both by the Global CMT catalog and by our study. The differences in the two results are within the range of allowable error. We note that the fault plane dips to opposite directions between GCMT and our results. It might be caused by the uncertainties of 15° of dipping angle inversion for near vertical faults. The focal mechanism solutions suggest that the three earthquakes occurred along strike-slip faults with high dip angles and that the two nodal planes are almost perpendicular. The rake angle of nodal plane 1 is close to 180°, suggesting that it is a right-lateral strike-slip fault. The rake angle of nodal plane 2 is close to 0°, suggesting that it is a left-lateral strikeslip fault. These findings using only focal mechanisms are unable to confirm the nodal plane that represents the earthquake plane because the two nodal planes are equivalent. However, the

Complex Rupture of the 2014 Ms 6.6 Jinggu Earthquake Sequence in

distribution of the aftershocks can provide complementary information for a determination of the earthquake plane.

Dm, which can minimize the double-difference dr, is the optimal solution. 3.3. Waveform Cross-Correlation Method

3.2. The Double-Difference Method To verify the results of the focal mechanism inversion and determine the fault planes of the earthquakes, we apply the DD method (Waldhauser and Ellsworth 2000) to relocate the Ms 6.6 Jinggu earthquake sequence. The DD method is a relative earthquake location method that uses travel-time differences to invert for the hypocenter locations. It allows for the simultaneous relocation of large numbers of earthquakes over large distances and can obtain accurate relative positions between earthquakes. Compared with traditional earthquake location methods, the location accuracy of the DD method is an order of magnitude higher and it can achieve an accuracy of one hundred meters in a small area. In the DD method, every two earthquakes within a certain distance (i.e., the hypocentral separation) form an earthquake pair. For an earthquake pair (i, j), the double-difference can be defined as the difference of observed and theoretical differential travel time between the two events at a station k: drijk ¼ r ik  r kj ¼ ðtik  tkj Þ  ðT ik  T kj Þ:

ð1Þ

where tik and Tik are the observed travel-time and the theoretical travel time of an earthquake i recorded by a station k, respectively. When the hypocentral separation between two earthquakes is small compared with the event-station distance and the length scale of the velocity heterogeneity, the two earthquakes have similar ray paths at a common station. Under this condition, the effects of velocity model errors can be ignored, and the former equation can be approximated as a linear system of equations of a partial shift in the event source parameters: drijk ¼

otki ot j Dmi  k Dm j : om om

ð2Þ

where m is the vector of the hypocentral model parameters and D denotes a perturbation to the model parameters. Using an appropriate least squares method to solve the equations, the final partial shift

The DD method uses travel-time difference data as input data. Usually, travel-time difference data can be calculated using the observed travel times of two events. However, we can further improve the location precision by improving the accuracies of the relative arrival-time picks using a waveform cross-correlation method. Two earthquakes produce similar waveforms at a common station if their source mechanisms are virtually identical and if their sources are collocated such that any signal scattering due to velocity heterogeneities along the ray paths is small (Waldhauser and Ellsworth 2000). Waveform cross-correlation methods have been applied previously by many investigators (Poupinet et al. 1984; Got et al. 1994; Waldhauser et al. 1999; Schaff et al. 2002; Rowe et al. 2002). Schaff and Waldhauser (2005) proposed the use of a correlation detector (obtained by padding real data) rather than a correlation function (obtained by zero-padding in the time domain) in order to recover time lags greater than half the window length. This improvement can produce robust delay time measurements in an efficient manner. Yang et al. (2009) developed a sliding-window cross-correlation (SCC) detection technique and applied it to continuous waveforms to detect aftershocks. The SCC method can be applied to three-component (e.g., BHZ, BHE, or BHN) waveform data simultaneously and obtain one detection time for each application. Integrating the advantages of the above-mentioned two methods, we propose a time domain MCC and use it to calculate the waveform cross-correlation time difference data. We have preliminarily verified the effectiveness of the MCC in previous studies on the Yiliang earthquake sequence that occurred in Yunnan in September 2012 (Wang et al. 2015). The calculation steps are as follows. First, calculate the correlation detector Cm of each component in the time domain (Schaff and Waldhauser 2005):

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Cm ðsÞ ¼

N 1 X

m ym 1 ðnÞy2 ðn  sÞ s 2 ðs; sÞ

ð3Þ

n¼0

where y represents the waveform data, s is the sliding quantity, s is the sliding range, n is the data point, N is the data length, and m denotes the seismic wave component. Then, calculate the normalized coefficient cm: " #1=2 N 1  N 1  X 2 X 2 m m m c ðsÞ ¼ y1 ðnÞ y2 ðn  sÞ ð4Þ n¼0

n¼0

Finally, we can obtain the multi-channel correlation detector function (Yang et al. 2009): , M M X X m CðsÞ ¼ C ðsÞ cm ðsÞ ð5Þ m¼1

m¼1

The maximum value of the function C is denoted as the normalized cross-correlation coefficient (CC), and the corresponding delay time s is denoted as the correlative correction value. The sum of the catalog time difference and the cross-correlation correction value is the waveform cross-correlation time difference: dtcc ¼ dtcat þ s

ð6Þ

The advantage of the MCC is that there will be only one CC and s for each measurement, and researchers can choose different wave components to calculate the cross-correlation time difference data for different phases (e.g., P and S). The MCC can improve the calculation efficiency and provide more stable and reliable time difference data. 3.4. Time Difference Data Calculation To find neighboring events, we set the minimum number of links required to define a neighbor and the minimum number of observations per pair (MINOBS) to 8, the maximum hypocentral separation between the two events to 10 km, and the maximum distance between each station pair to 200 km. We first converted the waveform data into an SAC format and wrote the necessary header information, including the earthquake location and origin time and the arrival times of the P and S waves, within the files. Then, we removed the mean, trend and instrumental response from the earthquake SAC

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files. The SAC data were bandpass filtered from 1 to 10 Hz. We examined the waveforms and selected the data with high signal-to-noise ratios for the next step. We calculated the azimuth angles between the earthquakes and stations from the original locations of the earthquakes and stations. According to the azimuth angles, we converted the north component (N) and east component (E) of each earthquake wave into a radial component (R) and a transverse component (T). Generally, within a layered homogeneous medium, the energies of the P and SV waves are mainly concentrated in the Z and R components of an earthquake, while the energy of the SH wave is mainly concentrated in the T component. The SV wave could be affected by the P wave, and its first motion may be relatively indistinct (Fig. 5). Hence, in this study, we chose to use the Z and R earthquake components to calculate the waveform time differences in the P waves and to use the R and T earthquake components to calculate the waveform time differences in the S waves. The waveforms of two earthquakes recorded at the same station were aligned according to their phase arrival times, manually picked by EAYP, and the phase windows were initially aligned around the phase. The length of the phase window should be approximately 2–3 wavelengths at least. We set the P-phase window from 0.5 s before the P phase to 1 s after the P phase, and we use the same settings for the S-phase window. Thus, the cross-correlation coefficient of the two phases can be compared directly. The magnitude of the window slide is an estimate of the observation error. We set two sliding ranges of ± 1 s and ± 1.5 s (Waldhauser and Schaff 2008; Matoza et al. 2013). Next, the MCC was used to calculate the data sets of the correlative correction value s and the crosscorrelation coefficient CC. Only the data sets with CC values greater than 0.5 were retained. Because we had two sets of sliding ranges, we were able to obtain two data sets for each station-event pair. If the values of s in the two data sets were very close (i.e., if the difference was less than several sample intervals), the data sets were accepted. This method can be used to judge whether the waveform time difference is correct (Waldhauser and Schaff 2008; Waldhauser and Tolstoy 2011).

Complex Rupture of the 2014 Ms 6.6 Jinggu Earthquake Sequence in

Figure 5 The earthquake waveforms recorded by station LIC (the magnitude is M4.6 and the epicentral distance is 71.1 km)

Equation (6) suggests that the correlative correction value s is the error in the catalog time difference data. In the statistical sense, the value of s should exhibit a Gaussian distribution (Fig. 6). To ensure the data quality, we require that the correlation coefficient of the cross-correlation data must be greater than 0.7 and that the value of the time difference data must be smaller than the largest forecasted time difference obtained from the following equation: jdtj  jDe =vj þ 0:5

ð7Þ

The right-hand side of Eq. (7) represents the largest forecast time difference, dt is the time difference data, De is the hypocentral separation of the station-event pair, and v is the reference wave velocity, which is generally set to the wave velocity of the first layer or the minimum wave velocity in the velocity model. After the MCC calculation, there are 1,432,888 points of cross-correlation time difference data, including 956,149 P-wave cross-correlation time difference data points and 476,739 S-wave cross-

correlation time difference data points. After selection, 730,297 points of cross-correlation time difference data are left, including 497,747 P-wave cross-correlation time difference data points and 232,550 S-wave cross-correlation time difference data points. Approximately, 49 percent of the data were removed.

4. Double-Difference Location Results 4.1. Input Data and Iterations There are 3383 earthquakes in the original catalog; after the selection process, the final data used for the relocation have 2819 earthquakes, 242,193 event pairs, and 730,297 waveform time difference data points, including 497,747 P-wave time difference data points and 232,550 S-wave time difference data points. The average hypocentral separation of the station-event pairs is 3.93 km, and every event has 172 neighbors on average. The cross-correlation coefficients are used as weights for the waveform time difference data during

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Figure 6 Histograms of the correlative correction value (gray represents the original data, black represents the selected data). a P-wave correlative correction value; b S-wave correlative correction value

the relocation process. Twenty-five iterations are used and are grouped into five sets on average. We use 6 times the standard deviation as the cutoff value in the second and third groups and four times the standard deviation in the fourth and fifth groups while excluding the data with large residuals during the inversion. We use the conjugate gradient method to solve the equations and obtain the damped least squares solution. If an earthquake is located in the air (i.e., an air-quake or AQ) during the iteration, the depth of that earthquake is reset to the depth obtained during the previous iteration and used in the subsequent iterations. On the screen output of the program hypoDD, the parameter RMSCC indicates the RMS residual; meanwhile, the parameters DX, DY, and DZ indicate the average absolute values of the change in the hypocenter location and DT denotes the origin time during each iteration. During the iteration process, the RMSCC is reduced from 246 to 9 ms and does not change throughout the final three iterations. The values of DX, DY, DZ, and DT are reduced from 498, 578, 947, and 103 ms to 3, 3, 31, and 1 ms, respectively. The values of DX, DY, DZ and DT are within the noise level of the data. The number of AQs is reduced from 14 to 1. These changes show that the iterations become increasingly stable and that the location results of the final iteration are reliable.

4.2. Location Results Ultimately, we obtain 2076 relocated earthquakes (approximately 73.6% of the total). After the relocation, the Ms 6.6 mainshock is located at 23.378°N, 100.475°E with a depth of 15.38 km. The shift in the earthquake position relative to the original location is approximately 1 km horizontally and 3.6 km vertically. Table 3 shows the original and relocated positions of the Ms 6.6 mainshock and the two largest aftershocks. Figure 7 shows that the relocated earthquake sequence distribution is consistent with the original location results given by the Yunnan seismic network (Fig. 2). However, the relocation results reflect a more concentrated linear distribution. Cross-section AA* is parallel to the strike of nodal plane 1 of the Ms6.6 earthquake, and cross-section BB* is parallel to the strike of nodal plane 1 of the Ms 5.8 earthquake (Table 2). The width of section AA* is the line BB* and the width of section BB* is the line AA* and the same for the section CC* and DD*. As seen from the epicenter distributions, the whole earthquake sequence can be roughly divided into two branches with a small angle (Fig. 7a). The earthquake cluster containing the mainshock has a banded distribution along the northwest direction (i.e., the NW branch) and is approximately

Complex Rupture of the 2014 Ms 6.6 Jinggu Earthquake Sequence in Table 3 Jinggu earthquake sequence source locations Magnitude

YN seismic network

Our study

GCMT

CAP

Ms 6.6

23.374°N, 100.465°E, 19 km

23.378°N, 100.475°E, 15.38 km

Ms 5.8

23.320°N, 100.490°E, 10 km

23.321°N, 100.493°E, 12.45 km

Ms 5.9

23.330°N, 100.500°E, 10 km

23.333°N, 100.507°E, 12.72 km

Mw 6.1 12.1 km Mw 5.6 12 km Mw 5.1 15.1 km

Mw 6.1 15.9 km Mw 5.6 11.3 km Mw 5.5 8.3 km

parallel to the extended line of the Puwen fault. The earthquake cluster containing the two largest aftershocks has a banded distribution along the northnorthwest direction (i.e., the NNW branch). Crosssections AA* and CC* indicate the strikes of those two branches. These two branches already appear in the original earthquake distribution (Fig. 2), but they are not very clear. However, a new branch emerges after the relocation. This third branch is located between the NW branch and the NNW branch and exhibits a banded distribution along the northeast direction (i.e., the NE branch). As shown in the focal depth profiles, the rupture length is approximately 26 km and the rupture width is approximately 5 km. Most of the aftershocks are mainly distributed in the depth range of 5–15 km throughout the earthquake cluster. A few earthquakes occurred in the shallow crust (Fig. 7). The mainshock occurred in the central-south part of the NW branch, which is approximately 20 km long and 3 km wide. The earthquakes were mainly distributed at either end and in the middle. From north to south, the distribution trend changes from NS to NW. The NE-striking Lancangjiang fault intersects the northern side of the NW branch. This might make the earthquake distribution appear to rotate clockwise. As shown in cross-section AA* (Fig. 7b), the earthquakes also have a linear distribution with depth. The depths of the earthquakes change along the profile; they are shallower in the north (between 6 and 10 km) with approximate depths between 10 km and 15 km in the south. As shown in cross-section BB* (Fig. 7c), there is no obvious slope in the depth distribution throughout the earthquake cluster. The mainshock is located at the bottom of the earthquake cluster. The NNW branch is approximately 10 km long and 3 km wide. Relative to the NW branch, the NNW

branch appears to display a clockwise deflection. Moreover, there is an obvious dividing line (a blank strip) between the NW branch and the NNW branch. The Ms 5.8 earthquake occurred in the middle of the NNW branch. As shown in cross-section CC* (Fig. 7d), the earthquake depth distribution appears to exhibit two layers. The upper layer is horizontal with a depth of 7 km. The lower layer slopes from north to south with an increasing earthquake depth. The depths of the earthquakes at the southeast end of the branch reach 17 km. This is very similar to the earthquake depth distribution of the NW branch. As seen from cross-section DD* (Fig. 7e), the depth distribution of the entire earthquake group is almost vertical. The Ms 5.8 earthquake is located in the middle of the lower layer of the earthquake group. The NE branch is approximately 5 km long and 2 km wide. The Ms 5.9 earthquake occurred in the middle of this branch. The line connecting the epicenters of the Ms 5.8 and Ms 5.9 earthquakes is also located in this branch. The depth distribution of the earthquakes at the southwest end (the D end of the cross-section in Fig. 7e) is mainly between 5 and 16 km, while that at the northeast end (the D* side in Fig. 7e) is mainly between 8 km and 15 km. These results are consistent with the depth distribution characteristics of the NNW branch (two layers) and the NW branch (deeper at the southeast end).

5. Discussion 5.1. Error Estimation We use a bootstrap method (Efron 1982; Billings 1994; Waldhauser and Ellsworth 2000) to evaluate the location errors and the correlations among the

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Figure 7 The hypocenter distribution of the Jinggu earthquake sequence after relocation (the focal mechanisms come from the CAP method in Table 2)

four source parameters. The original input data in Eq. (2) are randomly sampled. The number of samples is equal to the number of data points and,

thus, the size of the linear system of equations is not changed. We relocate all of the events using these bootstrap resampled data and unit weights to

Complex Rupture of the 2014 Ms 6.6 Jinggu Earthquake Sequence in

determine the shift in the locations relative to the resampled data vector. This process is repeated 200 times, and the events that are relocated more than 190 times are selected. We calculate the standard deviation of all of the location results for the same event, and we set the location error of that event as twice the standard deviation. Table 4 shows the average (median) location errors of all of the events and the location errors for the three earthquakes. The errors of the Ms 6.6 mainshock are much larger than those of the Ms 5.8 earthquake and the Ms 5.9 earthquake. Checking the relocation information file, we found that the position of the Ms 6.6 earthquake was only constrained by approximately 20 data points; however, the positions of the Ms 5.8 and Ms 5.9 earthquakes were constrained by approximately 100 and 150 data points, respectively. This is likely due to the fact that there were few earthquakes with waveforms similar to those of the Ms 6.6 earthquake because of their large magnitudes. Another reason for this is that there were only a few permanent seismic stations in service when the Ms 6.6 earthquake occurred. These two reasons might reduce the waveform time difference data associated with the Ms 6.6 earthquake and diminish the positioning accuracy. The location errors of the Ms 5.8 and Ms 5.9 earthquakes are very close to the average errors, indicating that a good data structure is very important. The positioning accuracy of the whole earthquake sequence is relatively high according to the median errors. The horizontal errors are typically less than approximately 100 m and have a concentrated distribution (Fig. 7). The errors in the east–west direction are slightly larger than the errors in the north–south direction, which is most likely due to the sparser station coverage in those areas. The depth errors are

Table 4 Location errors Source parameters

E–W (m)

S–N (m)

Depth (m)

O (s)

Average error Median error Ms 6.6 Ms 5.8 Ms 5.9

151.1 66.8 1138.7 147.5 216.4

128.1 51.7 849.0 290.1 154.9

685.5 323.8 1932.1 594.5 692.2

0.03 0.018 0.12 0.037 0.036

typically less than 300 m and have a wide distribution. The average depth error is approximately 4 times that of the average horizontal error. The determination of the focal depth is still relatively difficult. 5.2. Seismogenic Structure After the mainshock, aftershocks occur along the fault plane of the main earthquake and within its vicinity. Therefore, the spatial distribution of the aftershocks can precisely outline the shape and position of the fault plane. In this paper, we obtained the focal mechanisms and depths of the mainshock and the two largest earthquakes with Ms [ 5 using the CAP method. The results are shown in Table 2. The differences between the results in our study and those from the Harvard Global CMT catalog are very small. The focal mechanisms for the three earthquakes show that they occurred along strike-slip faults with high dip angles and two reference nodal planes that strike NNW and NEE. We also obtained the Jinggu earthquake sequence distribution using the DD method and waveform cross-correlation time difference data. The relocation results in addition to the strike direction and dip angle of the focal mechanisms fit very well. The strike and dip angles of nodal plane 1 for the Ms 6.6 earthquake are close to the distribution characteristics of the NW branch. Therefore, nodal plane 1 is believed to be the earthquake plane, and the Ms 6.6 mainshock occurred along a right-lateral strike-slip fault. We can also confirm that the Ms 5.8 earthquake occurred along a right-lateral strike-slip fault. The Ms 5.9 earthquake is more complicated because the two branches are mutually perpendicular. The strikes of the two nodal planes for the Ms 5.9 earthquake and the distribution characteristics of the two branches are correlative. Although the longitudinal extension of these aftershocks corresponds to that of an M 5.9 strike slip earthquake from scaling relations (e.g., Wells and Coppersmiths 1994), the spatio-temporal evolution characteristics of the Ms 5.9 earthquake require further analysis. There are two groups of conjugate fracture networks with strikes of NNW and NNE that intersect

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and restrict each other and form a large number of smaller faults in the Jinggu area. The Jinggu earthquake sequence occurred at the eastern end of the Lancangjiang fault along the northwest extension of the western branch of the Wuliangshan fault known as the Puwen fault (expressed as a dotted line in Fig. 2a). The strike of the Lancangjiang fault near the Jinggu area is NNE, and the dip angle is close to 90°. This segment of the Lancangjiang fault is a rightlateral strike-slip fault. The strike of the Puwen fault near the Jinggu area is NNW, and the dip angle is between 60° and 80°. This segment of the Puwen fault is a right-lateral strike-slip fault. The strikes of the Jinggu earthquake sequence are generally close to the strike of the Puwen fault. The distribution of focal depths of the Jinggu earthquake sequence is also consistent with the dip angle of the Puwen fault. However, there is a distinct distance between the Jinggu earthquake sequence and the Puwen fault. Therefore, the seismogenic structure of the Jinggu earthquake sequence might be a hidden fault that

belongs to the Puwen fault in addition to some secondary fractures that strike toward the NE. Other researchers have also studied the Jinggu earthquake sequence (Xu et al. 2015; Chen and Chen 2016), and their results are similar to our findings. According to the existing research results and our results, it can be determined that the main seismogenic structure of the Jinggu earthquake sequence belongs to a hidden fracture section of the Wuliangshan fault that strikes toward the NW. 5.3. Spatio-Temporal Evolutionary Characteristics To facilitate the analysis in this study, we set the origin time of the Ms 6.6 mainshock as the reference time and plot the origin times of the earthquakes in a histogram (Fig. 8). The Ms 5.8 earthquake occurred on day 59.2, and the Ms 5.9 earthquake occurred on day 59.85. There is a peak in seismic activity when the Ms 6.6 earthquake occurs and then declines slightly. Then, the largest aftershocks cause some small peaks of seismic activity.

Figure 8 Origin time distribution histogram (the reference time is the origin time of the Ms 6.6 mainshock, and the colored lines indicate the durations of the branches)

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Figure 9 The earthquake distribution within 37 day after the Ms 6.6 earthquake

1. The reference time is the origin time of the Ms 6.6 mainshock. Within 12 h after the mainshock, the aftershocks occurred along cross-section AA*. The aftershocks first appeared in the vicinity of the Ms 6.6 mainshock and then extended on both sides of the mainshock along the NW–SE direction, during which time the NW branch began to form.

Therefore, the Ms 6.6 Jinggu earthquake was mainly a bilateral rupture event, and the rupture propagated from the epicenter toward the northwest and southeast simultaneously. The aftershocks with ML C 4 mostly occurred to the southeast of the mainshock. The depths of the aftershocks with a linear distribution are shallower

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to the northwest, and the aftershocks are deeper to the southeast along cross-section AA*(Fig. 9). On approximately the fourth day after the mainshock, the rupture extended to the southeastern end of the NW branch (point A*), which is approximately 6 km away from the mainshock epicenter. Then, the rupture direction rotated clockwise by

approximately 90° into an NE direction, during which time the NE branch began to form slowly. The NE branch developed rapidly on day 31 and stopped on approximately day 33 (Fig. 9). The NNW branch began to form on day 38 and reached a peak on day 44. The two layers were shown at depth along cross-section CC*. The

Figure 10 The earthquake distribution between day 37 and day 59 after the Ms 6.6 earthquake

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Figure 11 The earthquake distribution within 24 h after the Ms 5.8 earthquake

upper layer is horizontal with a depth of 7 km. The lower layer slopes from north to south with increasing earthquake depths. During this period, the largest aftershock was the M4.5 earthquake that occurred on day 43 with a depth of 14.9 km. The NNW branch ceased growing on day 55.

Between days 56 and 59 (4 days before the Ms 5.8 earthquake occurred), most of the earthquakes occurred at the northern end of the NW branch. The rest of the region exhibited almost no earthquakes (Fig. 10).

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Figure 12 The earthquake distribution between day 1 and day 27 after the Ms 5.8 earthquake

2. The reference time is the origin time of the Ms 5.8 earthquake. The Ms 5.9 earthquake occurred at 15.6 h. The NNW branch entered a second development period between the origin time of the Ms 5.8 earthquake and the origin time of the Ms 5.9 earthquake. Compared with the first

development period, the NNW branch became longer. A common feature during this period is that most of the epicenters were located at the western end of cross-section CC* with two layers at depth (Fig. 11). The Ms 5.8 earthquake occurred in the lower layer.

Complex Rupture of the 2014 Ms 6.6 Jinggu Earthquake Sequence in

Within approximately 9 h after the Ms 5.8 earthquake, most of the aftershock epicenters were located at the eastern end of cross-section CC*, and the branch became shorter. Therefore, the original NNW branch can be divided into two branches. We call the branch at the western end of cross-section CC* the NNW-1 branch and the branch at the eastern end of cross-section CC* as the NNW-2 branch. The Ms 5.8 earthquake occurred along the NNW-1 branch, while the Ms 5.9 earthquake occurred along the NNW-2 branch, which is shorter. According to the aftershock distribution along the NNW-2 branch, nodal plane 1 of the Ms 5.9 earthquake mechanism is the fault plane. The Ms 5.9 earthquake occurred along a rightlateral strike-slip fault (Fig. 11). At approximately

hour 38 after the Ms 5.8 earthquake, the M 4.9 aftershock occurred at the southern end of the NNW1 branch at a depth of 15.44 km (Fig. 12). Based on the above analysis, the Ms 6.6 Jinggu earthquake sequence can be divided into four branches spatially (Fig. 13) and two stages temporally (Fig. 8). These four branches are the NW branch, the NE branch, the NNW-1 branch and the NNW-2 branch. The first stage constitutes the development period of the NW and NE branches from the origin time of the Ms 6.6 earthquake to day 58. The second stage constitutes development period of the NNW-1 and NNW-2 branches from day 38 after the Ms 6.6 earthquake to day 85 (which is also day 27 after the Ms 5.8 earthquake). These two stages

Figure 13 The four branches of the Jinggu earthquake sequence (the colored lines are just demonstrations)

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have an overlap because of the development period of the NW branch.

NNW-1 branch and the NNW-2 branch. After the mainshock occurred, the NW branch appeared first. This might have been due to the constraints of geological structures. The earthquake distribution turned at the southeastern end of the NW branch, thereby forming the NE branch. The earthquake distribution also turned at the southwestern end of the NE branch, thereby forming the NNW branch. A small angle also exists between the strikes of the focal mechanisms of the Ms 6.6 mainshock and the Ms 5.8 earthquake (or Ms 5.9 earthquake) between the NW branch and the NNW branch, and the NE branch is approximately perpendicular to the NW branch and the NNW branch. According to the banded distribution of the aftershocks and because of the constraints of the structural transition nodes at either end, the size of the main rupture zone of the mainshock was limited and could not expand along the original direction. The segmentation features of the banded distribution of the aftershocks reveal complex geological structure in the area. The complex fault system interacts with each other, which could be barriers to prevent occurrence of large earthquakes.

6. Conclusion In this paper, we obtained the focal mechanisms of three large earthquakes (Ms 6.6, Ms 5.8, and Ms 5.9) using the CAP method and the earthquake distribution of the Jinggu earthquake sequence using the DD method. The Ms 6.6 mainshock occurred at 23.378°N, 100.475°E at a depth of 15.38 km. Its focal mechanism solution shows that the earthquake occurred along a strike-slip fault. The strike, dip angle and rake angle of nodal plane 1 are 151°, 70° and 174°, respectively, and those of nodal plane 2 are 243°, 90° and 20°, respectively. The focal mechanisms of the Ms 5.8 and Ms 5.9 earthquakes show that they also occurred along a strike-slip fault. According to the earthquake distribution characteristics, we can confirm that the three earthquakes all originated along right-lateral strikeslip faults. According to the earthquake case summary, Gu et al. (1982) found that most of the aftershocks occurred at both ends of the fault and near the epicenter of the mainshock. The front end of the mainshock rupture is a stress singularity where strong aftershocks are most likely to occur. Therefore, the Ms 5.8 and Ms 5.9 earthquakes and several large aftershocks with ML C 4 occurred at the southeastern end of the Ms 6.6 earthquake rupture (the NW branch), where the ruptures intersected with one another. The Jinggu earthquake sequence was dominantly distributed along the northwest direction. The sequence has an obvious linear concentration both horizontally and vertically and is approximately 26 km long and 5 km wide. The depths of the earthquakes at the northwestern end are shallower (6–10 km) than those at the southeastern end, where the two layers are deeper (6–16 km). The dip angle of the cross-section is close to vertical. The mainshock is located at the bottom of the earthquake sequence. As viewed at a smaller scale, the earthquake sequence has obvious segmentation features. The earthquake sequence can be divided into four branches spatially and two stages temporally. These four branches are the NW branch, the NE branch, the

7. Data and Resources The waveforms used in location were obtained directly from the Yunnan regional seismic network and the waveforms used in the focal mechanism inversions were obtained from the National Seismic Network. The DD location method is provided by Professor F.Waldhauser and the CAP method is from http://www.eas.slu.edu/People/LZhu/home.html (last accessed December 2016). The Global Centroid Moment Tensor Project database was searched using www.globalcmt.org/CMTsearch.html (last accessed on August 2016).

Acknowledgements The National Seismic Network of the China Earthquake Administration and the Yunnan Seismic Network provided the data used in this study. The authors benefitted greatly from discussions with Dr.

Complex Rupture of the 2014 Ms 6.6 Jinggu Earthquake Sequence in

Sidao Ni of the Institute of Geodesy and Geophysics, Chinese Academy of Sciences. We thank the reviewers for their valuable advice. The research is supported by China Earthquake Science Experiment Project, China Earthquake Administration (Project Code 2017CESE0101) and by Natural Science Foundation of China through 41474049, 41661164035, and 41704066. REFERENCES Billings, S. D. (1994). Simulated annealing for earthquake location. Geophysical Journal International, 118, 680–692. Chen, H., & Chen, X. F. (2016). Focal mechanism inversion and relocation of the Yunnan Jinggu Mw 6.2 earthquake on 7 October 2014. Progress in Geophysics (in Chinese), 31, 1413–1418. https://doi.org/10.6038/pg20160401. Chen, P. S., Liu, F. T., Li, Q., et al. (1990). The transverse inhomogeneity of velocity structure in Yunnan region. Science in China Series B: Chemistry, 4, 431–438. China Earthquake Networks Center. (2014). A topic of the Ms6.6 earthquake in Yunnan Pu’er Jinggu Daiyi autonomous county, http://news.ceic.ac.cn/CC20141007214940.html. China Earthquake Administration. (2014). Historical disaster distribution map of the Ms6.6 Jinggu earthquake in Yunnan, http:// www.cea.gov.cn/publish/dizhenj/468/553/101360/101382/ 20141008220651458837896/index.html. Chu, R. S., & Helmberger, D. V. (2013). Source parameters of the shallow 2012 Brawley Earthquake, Imperial Valley. Bulletin of the Seismological Society of America, 103, 1141–1147. https:// doi.org/10.1785/0120120324. Efron, B. (1982). The jackknife, the bootstrap, and other resampling plans (p. 92). Philadelphia: SIAM. Fang, L. H., Wu, J. P., Wang, W. L., et al. (2013). Relocation of the mainshock and aftershock sequences of Ms 7.0 Sichuan Lushan earthquake. Chinese Science Bulletin, 58, 3451–3459. https://doi. org/10.1007/s11434-013-6000-2. Fang, L. H., Wu, J. P., Wang, W. L., et al. (2014). Relocation of the aftershock sequence of the Ms 6.5 Ludian earthquake and its seismogenic structure. Seismology and Geology, 36, 1173–1185. https://doi.org/10.3969/j.issn.0253-4967.2014.04.019. Gomberg, J. S., Shedlock, K. M., & Roecker, S. W. (1990). The effect of S-wave arrival times on the accuracy of hypocenter estimation. Bulletin of the Seismological Society of America, 80, 1605–1628. Got, J. L., Frtchet, J., & Klein, F. W. (1994). Deep fault plane geometry inferred from multiple relative relocation Beneath the South Flank of Kllauea. Journal of Geophysical Research: Solid Earth, 99, 15375–15386. https://doi.org/10.1029/94JB00577. Gu, J. C., Xie, X. B., & Zhao, L. (1982). On spatial distribution of large aftershocks of the sequence of a major earthquake and preliminary theoretical explanation. Acta Seismologica Sinica (in Chinese), 4, 380–388. Hauksson, E., Yang, W. Z., & Shearer, P. M. (2012). Waveform relocated earthquake catalog for Southern California (1981 to June 2011). Bulletin of the Seismological Society of America, 102, 2239–2244. https://doi.org/10.1785/0120120010.

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(Received January 8, 2018, revised May 30, 2018, accepted May 31, 2018)