Source parameters inversion of the 2013 Lushan earthquake by ...

SCIENCE CHINA Earth Sciences • RESEARCH PAPER •

July 2013 Vol.56 No.7: 1177–1186 doi: 10.1007/s11430-013-4640-3

Source parameters inversion of the 2013 Lushan earthquake by combining teleseismic waveforms and local seismograms XIE ZuJun1,2, JIN BiKai1,2, ZHENG Yong1*, GE Can1,2, XIONG Xiong1, XIONG Cheng1,2 & HSU HouTze1 1

State Key Laboratory of Geodesy and Earth's Dynamic, Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China; 2 College of Earth Sciences, University of Chinese Academy of Sciences, Beijing 100049, China Received April 27, 2013; accepted May 6, 2013; published online June 8, 2013

On April 20, 2013, a magnitude Ms7.0 earthquake occurred in Lushan, Sichuan Province, China, and caused heavy casualties and economic losses. Based on the local broadband waveforms in Sichuan and adjacent provinces regional networks and teleseismic broadband records from IRIS stations, the focal mechanism and the focal depth are determined by the CAP (Cut And Paste) and its upgraded methods, CAPtele and CAPjoint, respectively. The results show that the focal mechanisms and depth from different methods are steady, and the best double couple solution derived from the joint inversion is 210°, 44°, and 91° for strike, dip, and rake angles respectively for one nodal plane and 29°, 46°, and 89° for another with 16 km focal depth and Mw6.66 moment magnitude. In order to verify the reliability of the results, a number of tests are performed based on local seismograms with different velocity models. They indicate that there is about 10 degree’s fluctuation in focal mechanisms and about 2 km variation in focal depth with a complex velocity structure. Furthermore, inverted by re-sampling the teleseismic waveforms on the basis of epicentral distance, the solutions are consistent with each other, which manifests that the teleseismic records are effective for constraining source parameters of the Lushan earthquake. Lushan earthquake, focal mechanism, focal depth, CAP method Citation:

Xie Z J, Jin B K, Zheng Y, et al. Source parameters inversion of the 2013 Lushan earthquake by combining teleseismic waveforms and local seismograms. Science China: Earth Sciences, 2013, 56: 1177–1186, doi: 10.1007/s11430-013-4640-3

According to the reports of CENC (China Earthquake Networks Center, CENC), a strong earthquake (Ms7.0) struck Lushan, Ya’an of Sichuan province at 08:02 Beijing time on April 20, 2013. As of 15:00 April 21, this quake had caused serious damages to the source region, at least 180 people were killed and more than tens of thousands were injured. According to the epicenter location of this event determined by CENC, this quake occurred on the south segment of the Longmenshan Fault Zone (LFZ), which is only about 100 km away from the epicenter of the Wenchuan earth-

*Corresponding author (email: [email protected])

© Science China Press and Springer-Verlag Berlin Heidelberg 2013

quake (2008/05/12). It is the largest earthquake occurred in this region after the Wenchuan earthquake. After the main shock, as many as 1165 aftershocks had been recorded as of 8:00 April 21 (Beijing Time). The number of events with M>3.0 is up to 67 (0 events with mag6.0–6.9, 3 events with mag5.0–5.9, 16 events with mag4.0–4.9, and 48 events with mag3.0–3.9). The precise locations and focal depths of these aftershocks will provide important constraints for the analysis of the fault’s strike, dip, and centroid depth of the main shock. Some organizations, such as Harvard University, USGS and Institute of Geophysics, China Earthquake Administration (IGP-CEA), quickly determined and reported the moearth.scichina.com

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ment tensor solution of this event. Many other researchers in China had also shown their initial results about the source parameters of this earthquake, such as the focal mechanism and rupture process [1–4]. All of these results consistently indicate that this earthquake is dominated by the thrust dislocation, although there are some discrepancies among them. The mechanism of the earthquake provides the basic information for the characteristics of earthquake source and tectonic stress [5]. It also plays a key role in the fault geometry determination, the rupture process inversion [6] and the research of Coulomb stress changes [7, 8]. So, the accurate determination of the source mechanism is a very important project. Among all the parameters, the centroid depth should be paid more attention to. The depths determined by different institutes range from 10 to 21.8 km. This kind of large discrepancy causes some difficulties for determining the magnitude, source property and tectonics environment. In order to further study this quake’s property (such as dynamic rupture process and aftershock distribution tendency) and better meet the demands of earthquake relief, it is necessary to determine the focal depth and source mechanism of the earthquake precisely. In order to obtain the source parameters of earthquakes with different magnitudes, several models have been proposed (IPS, Isotropic Point Source; CMT, Centroid Moment Tensor; FMT, Finite Moment Tensor; Finite Fault Model) with different complexities [9]. For the moderate earthquakes, because the CMT model contains only 10 parameters (6 moment components, 3 location parameters, and 1 source time parameters), it can effectively describe the main source property, although it lacks the information of rupture directivity. For most earthquakes, this model with six independent moment components can be simplified as a double couple model with only three parameters, and then the 10 parameters in total are reduced to 8, so that the time spend on the inversion will be shorter, and the geometry and kinematic characteristics of the earthquake [10, 11] can be obtained quickly. In order to better constrain the parameters of the double couple model, Zhao and Helmberger [12] proposed the CAP (Cut and Paste) method to fit the seismograms. Specifically, the body wave and surface wave are cut or fitted separately with different filters. Many researches from both China and abroad have validated the reliability of this method in the inversion of source mechanism [5, 13–20]. Moreover, because different segments of the seismograms are fitted separately and the body wave segment is sensitive to centroid depth, the CAP method has an advantage in the centroid depth determination, which has been approved both theoretically and practically. Besides, the local and regional seismograms are less distorted by the three-dimension (3D) structure model than the teleseismic seismograms, while the teleseismic seismograms contain some depth phases (such as pP, sP, sS). Therefore, the former should constrain the source mechanism better while the latter is more suitable for determining the focal depth of

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moderate earthquake. Due to these characteristics, the joint inversion of regional and teleseismic seismograms should be capable of constraining both the depth and source mechanism well. In this study, we choose the abundant seismograms and use the CAP and its upgraded methods to determine the source mechanism and depth of Lushan earthquake. The regional seismograms are taken from the broadband seismograph network of Sichuan and nearby provinces and the teleseismic seismograms are downloaded from IRIS stations. Then, in order to validate the robustness and reliability of the inversion, we tested the structure dependence for the regional seismograms inversion and the azimuth dependence of teleseismograms inversion by re-sampling the teleseismic stations on the basis of epicentral distance.

1 Methods In this work, the CAP method is employed to determine both the depth and source mechanism [12, 13]. Since the magnitude of this earthquake is large, the point source approximation in CAP may be not accurate enough for the regional inversion although it is still valid for the teleseismic inversion. In order to fully study the depth and mechanism, the regional (CAP), teleseismic (CAPtele), and joint (CAP joint) inversion will be applied respectively. The idea of CAP method is to separate the seismogram into two parts: body wave (Pnl) segment and surface wave segment. The objective error function can be calculated by fitting two segments of observed seismogram and synthetic seismogram (generated from double couple model). The optimal solutions of centroid depth, source magnitude and mechanism can be obtained by grid searching in the defined parameter space. The frequency-wavenumber (F-K) [21] method is adopted to calculate the synthetics used in the inversion. In the F-K method, the integrals of frequency and wavenumberare calculated separately, and wave propagation matrix is also used to get full waveform of displacement including body wave and surface wave. Moderate to strong earthquakes can be monitored by the global stations. Thus the teleseisic seismograms can provide the data to study the source mechanism and depth. The CAPtele method uses the teleseismic waveforms to constrain the source mechanism and centroid depth [15, 17]. Because of its longer distance, the teleseismic surface wave is distorted more seriously by the structure effects than the regional and local surface waves. So the CAPtele method only fits the P and SH wave, but not the surface wave [22]. The program for calculating the Green function of teleseismic waveform is upgraded from that Kikuchi and Kanamori [23] initially developed. The calculation of the Green’s function contains two major parts: the wave propagation in the stratified structure near the source and the travel effects in the mantle. The former factor is extracted by the propaga-

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tion matrix method and the latter includes the geo-spreading and attenuation factors. As for the inversion, the error objective function (the same as that for CAP) for two components are calculated and the optimal solution with the minimum error is searched in the defined parameters domain. The weight ratio of teleseismic P wave to SH wave (wP:wS) is defined by the following formula to balance the contributions from different components to the inversion:

wP : wS 

rmsS rmsP : , nS nP

(1)

where P and S represent the P and SH wave respectively. The rms (Root Mean Square) is the second moment norm error between the observation and synthetics of all components used, and the variable n in the left-hand side is the number of records used. Chen et al. [17] named the joint inversion of teleseismic and regional seismograms CAPjoint for short. CAPjoint method combines the teleseismic and regional seismograms, with the appropriate weights of the teleseismic and regional data used to avoid the bias caused by the strong amplitude regional waveforms. Their weight ratio can also be described by eq. (1), but here “S” and “P” represent the regional and teleseismic data, respectively. In this paper, some improvements are made in the practical application of CAPjoint method. Specifically, taking into account the frequency contents and attenuation difference between the regional and teleseismic data, we use the different time windows, band range of filters, and the attenuation factors for them.

2 2.1

Data and models Data

There is a dense local network in the Longmenshan region, which can provide abundant broadband waveform data for this event [24]. Since the number of stations is not crucial for the CAP method, and the main purpose of this work is to do efficient inversion for the focal mechanism and focal depth, we choose 12 local stations based on their signalto-noise ratio (SNR), azimuthal coverage, and P wave polarities. The teleseismic waveforms are provided by IRIS, and the seismic stations used in this paper are shown in Figure 1. For the local waveforms, after removing the instrument response and rotating the two horizontal components to radial and transverse components, we pick the P arrival manually and cut the waveform into two parts: one for Pnl segment with 35 s window length and the other for surface segment with 70 s window length. For keeping higher SNR singals, a 4th order Butterworth bandpass filter is applied to the Pnl segment in the long period band (0.05–0.2 Hz), and

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to the surface segment in the long period band (0.05–0.1 Hz). In these bands, the earthquake information can be picked out and accurate magnitude can be inversed by avoiding noise scattered from fine structure of the crust and high frequency signals [26]. After the same filters are applied to the synthetic waveforms, the optimal source parameters with minimum errors can be found by grid-searching in the space of earthquake magnitude, focal mechanism (strike, dip and rake) and focal depth [13]. To avoid the problem that the closest station dominates the weight of the inversion, and to compensate for the amplitude decay due to geometrical spreading and attenuation, a distance range scaling factor is introduced and the misfit error is defined as the following [13]: r e    us ,  r0 

(2)

where, r is the distance and r0 is the reference distance and is set as 100 km in this paper. P is the scaling factor with 1 for Pnl segment and 0.5 for surface segment. u and s are observed seismograms and synthetic waveforms, respectively. For the teleseismic records, the Green’s Functions are calculated by tel3 program. A 4th order Butterworth bandpass filter is utilized for P wave segment in the long period band (0.01–0.05 Hz) with 50 s length time window, and the same filter for SH wave segment in the long period band (0.01–0.04 Hz) with 120 s length time window. The inelastic attenuation factor t* is used to calculate synthetic teleseismic waveforms. t* is a constant [27] and is independent from epicentral distance. According to Wei [22], the best waveform-fitting results with minimum errors can be found with tP*=1 for P wave segment and tSH*=5 for SH wave segment. We compute the synthetic teleseismic waveforms by using the same factor following Wei [22] to simulate the inelastic attenuation [23]. And there is a weight factor between local records and teleseismic records to give the local records the same weight as teleseismic records in CAPjoint inversion. 2.2

Velocity model

The geological structure is complicated in Longmenshan region, with crustal velocity and thickness variations in horizontal directions [28], which may cause some deviations in the inversion for focal mechanism and focal depth. So an accurate velocity model is required for improving the inversion accuracy. Many researches [29, 30] have focused on the velocity structure in this region after 2008 Wenchuan earthquake, which provide us several reference models for our research. Since only 1D layered model can be used in CAP method, the velocity model should be built by considering these reference models. Zheng et al. [5] constructed an average lay-

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Figure 1 Epicenter location, station distribution (a), and velocity model (b). Star represents the epicenter, while triangles indicate the local and telesiesmic stations. The used velocity model (model 1) is shown on the lower-right inset in (b) and the model 2 consists of three areas with different velocity models, divided by the dash line, labeled with digital ①，② and ③. f1 is Pengxian-Guanxian fault; f2 is Ya’an fault; f3 is Beichuan-Yingxiu fault [25].

ered velocity model of this region by combing Crust2.0 model and field measure work in Beibei-Heishui profile in Sichuan, which was supported by a field work team of the Chinese Academy of Sciences in the 1990s. Based on this model, Yi et al. [31] inversed the focal mechanisms of Wenchuan aftershocks. With the studies in this region [32–36] taken into consideration, the velocity model (model 1) is built as shown in Figure 1. For the teleseismic inversion, the velocity model of the source region should be horizontal layered model. The model used for local inversion is also utilized in teleseismic inversion, and mantle model is extracted from PREM [37]. Since the CAP method is not sensitive to the velocity model under the stations, the same model is also picked as the crustal model used in the teleseismic inversion.

3 Results and analysis 3.1

Focal depth and focal mechanism

Based on model 1 and local waveforms as shown in Figure 1, the fitting misfit reaches the minimum around the depth 17 km (Figure 2(a)) by utilizing CAP method with global grid searching in depth. At this depth the best estimate of the magnitude is Mw6.67 and the corresponding optimal focal mechanism is (216°/45°/90°) (representing strike/dip/ rake here and after) for one nodal plane and (36°/45°/90°) for another. The CAPtele inversion of the teleseismic waveforms, shown in Figure 2(b), indicates that the best solution is around 16 km for depth and Mw6.66 for magni-

tude. The correspondent focal mechanism solution is (209°/ 44°/91°) and (28°/46°/89°) for the two nodal planes, respectively. And the CAPjoint inversion of local and telesismic data shows that the focal mechanisms is (210°/44°/91°) and (29°/46°/89°) for the two nodal planes, respectively, with the magnitude Mw6.66 and the depth 16 km, as shown in Figure 2(c). From Figure 2, the inversion results of focal mechanism are consistent and robust in different depth, dominated with thrust dislocations. At the depth of 16 km, both local and teleseismic waveforms are matched very well with synthetic seismograms (Figure 3). From Figure 3, the cross correlation coefficients are larger than 60%, indicating the result is acceptable. The waveforms fitness in the CAP and CAPtele results are both similar to Figure 3 with lager cross correlation coefficients. As concluded in Table 2, the results by CAPjoint method are close to those by CAPtele method, but differ slightly from those by CAP method. It should be noted that the similarity is a coincidence between CAPtele and CAPjoint results, not meaning the malfunction of local seismic data in joint inversion. In fact, through the adjustment of weight factors, the local data and teleseismic data contribute equally to the joint results. Chen et al. [17] have tested the importance of local seismic data in the joint inversion by Bootstrap method, which could improve the robustness and reliability of the inversion 3.2

Model sensitivity test

Although reliable source estimates can be achieved with rough velocity model by CAP method, an accurate velocity

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Figure 2 Inversion misfit used different inversion method versus centroid depth. The result inversed by CAP method (a), CAPtele method (b) and CAPjoint method (c).

model will make the result more reliable. The Longmenshan region has a complex geological structure, acting as a geographical transition zone, with elevation and crustal thickness varying from 500 m and 40 km, respectively, in the Sichuan Basin to higher than 4000 m and about 60 km, respectively, in the Songpan-Ganzi Block. There is a huge difference among the west, east and south side of Longmenshan Fault Zone (LFZ). Since the LFZ is narrow, it is reasonable to divide the whole region into three areas with different crustal structure. We build the model 2 with three unique crust models (Figure 4(a)) [38–42]. The areas are divided by the dash line, labeled with digital ①, ②, ③ as shown in Figure 1. Since the earthquake mainly locates at the intersection of the three parts, the Green’s Functions for each station can be calculated based on the crustal structure beneath the station. The misfit error that varies with focal depth is shown in Figure 4(b). The minimum error can be found near 15 km depth with focal mechanism of 214°/54°/89° and magnitude of Mw6.66. The fitness between the observations and the synthetic seismogram is similar to that in Figure 3, and the cross-correlation coefficient is also very high. The results of model 2 are different from those from model 1, and the discrepancy of dip angle is as big as 10°. Based on the previous researches [5, 12, 14], the change of focal mechanism is about 5°–10° (the same search step with this work) among different models. So, such kind of differences may not be caused by crustal structural complexity only. Other factors, especially the point source model simplification in the local inversion, should be responsible for the inversion difference. According to the scaling law of magnitude and rupture length, and the moment rate function from Liu et al. [6], the rupture process is dominant in the first 10 s, which is also the duration time used in this paper, and the rupture length is longer than 20 km. Thus, the rupture length cannot be treated as a point in this duration time, which will lead to variable

source time functions and duration times for different stations based on their azimuth [43]. With different models applied in the three parts, more rupture details may be inversed in the results, leading to the mismatch with that from model 1. The results based on model 1 are preferred for obtaining the principal rupturing information, although that model 2 results can exhibit more details of the earthquake because of its more accurate crustal model. For further testing the reliability of results derived from model 1, we build model 3 in which the crustal model is constructed by averaging the crustal models from part ① and ③ in model 2 (Figure 4(c)). As shown in Figure 4(d), the inversed focal depth is 16 km, and the focal mechanism solution is 220°/47°/96° and the magnitude is Mw6.68. The differences between the results from model 1 and 3 are about 1 km in focal depth, 0.01 in magnitude, and 4°/2°/6° in mechanism, and are in the range of searching step (5°), indicating that the results are reliable and imperfect velocity model can work very well with CAP method. 3.3

Reliability test on teleseismic stations re-sampling

In order to verify the stability of CAPtele results, the teleseismic stations are re-sampled to get several CAPtele results inversed from different subsets, and then the results are used to make a statistical analysis for reliability. Chen et al. [17] applied Bootstrap method to analyze the results from subsets inversed by local data, and confirmed the robust of the CAPjoint method. However, the Bootstrap method is not suitable for verifying the stability of CAPtele results in this work, since there are 68 tele-stations, 5 times more than the stations used in their test. For instance, to randomly pick 30 tele-stations from all 68 tele-stations will lead to more than 1×1019 possible cases, which is too huge to be calculated in a short time. And the randomly picked stations may distribute unevenly in azimuth, which will

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Figure 3 The CAPjiont inversion results including the focal mechanism and the comparison between observed (the black lines) and synthetic waveforms (the red lines) based on the velocity model 1. The top line illustrates the fault planes of the earthquake, the moment magnitude and the fit error, and the beachball shows the focal mechanism of the event. The first column tells the azimuth (°), the station name and the epicentral distance (km). The numbers on the other 5 columns, the synthetic and observed seismograms, are the time shifts (s) (left) and cross-correlation coefficient in percent (%) (right). Positive time shifts mean that the synthetics have been delayed or shifted the observed.

contribute some bias in inversion since all picked stations share the same off angle. So, in this work the teleseismic stations are divided into four groups based on their distance:

3000–6000 km, 6000–7000 km, 7000–8000 km and 8000–8800 km, as listed in Table 1. From Table 1 we can see that the results of the magnitude and focal depth

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Table 1

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The inversion solutions based on different teleseismic waveforms subsets on the basis of epicentral distance

Epicentral distance (km) 3000–6000 6000–7000 7000–8000 8000–8800 Total

Strike (°)

Dip (°)

Rake (°)

Magnitude (Mw)

Best depth (km)

Stations number

220 203 207 219 209

43 43 43 46 44

98 92 88 98 91

6.69 6.65 6.64 6.65 6.66

15 18 16 17 16

8 13 28 19 68

Figure 4 Inversion misfit with different inversion velocity model versus centroid depth. (a) Velocity model 2; (b) the inversion result with model 2; (c) velocity model 3; (d) the inversion result with model 3.

in the four groups are close to each other, even for the extreme case (group a) which only contains 8 stations. This test confirms that the focal mechanism and focal depth can be well constrained by teleseismic stations. 3.4

Results comparison

The focal mechanism and focal depth of the Lushan earth-

quake are listed in Table 2, derived from different methods with three crustal velocity models. For comparison, the results from other organizations are also listed. As shown in Table 2, the focal mechanisms are roughly consistent with each other. The principal source properties of this event could be picked out through the best double-couple solutions inverted by CAP method and its modifications. Nevertheless, there is a somewhat large discrepancy of the cen-

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Table 2 Comparison of source parameters derived from different organizations and researchers Origin Model 1 CAP Model 2 Model 3 CAPtele CAPjoint Harvard WPhase USGS Body-Wave Centroid Liu et al. [1] Zeng et al. [4]

Nodal plane I 216°/45°/90° 214°/54°/89° 220°/47°/96° 209°/44°/91° 210°/44°/91° 210°/38°/96° 218°/39°/103° 216°/47°/93° 198°/33°/71° 214°/39°/100° 212°/47°/93°

troid depth among results from different organizations. But the focal depths derived from the CAP, CAPtele and CAPjoint method are in consistence and are concentrated around 16 km. Because the teleseismic waveforms contain some depth phases like pP and sP which are sensitive to focal depth, the focal depth can be well constrained. Furthermore, because of the large distance, the Lushan earthquake could be simplified as a point source in teleseismic inversion, so that the centroid depth could be determined more accurately by teleseismic waveforms. Based on these advantages, we adopt the results inversed from the CAPjoint method. Soon after the occurrence of the Lushan earthquake, Liu et al. [1] and Zeng et al. [4] also published their initial results，which are also listed in Table 2. Liu et al. [1] obtained the source parameters by local broadband waveforms with CAP method. The magnitude discrepancy between Liu et al.’s work [1] and our results could be attributed to the different rupture duration time used in the inversion. Zeng et al. [4] also applied the CAPjoint method and P wave polarities to inverse the parameters of this event based on local and teleseismic waveforms. However, only the P segment of teleseismograms with large signal to noise ratio (SNR) and long period radial and vertical components of local S wave and surface wave with simple propagation path were used in the inversion in Zeng et al. [4]. From the Table 2, except for the centroid depth, our results are consistent with Zeng et al. [4]. The depth difference probably is caused by the differences of the dataset and the filtering band used in the inversions.

4 Discussion and conclusions In this study, focal mechanism solution and focal depth of Lushan earthquake, occurred on April 20, 2013, have been determined with local and teleseismic waveforms using CAP and its upgraded methods, CAPtele and CAPjoint. According to the work of Liu et al. [6] the appropriate fault rupture duration time and filtering frequency band have been chosen by performing a number of tests. Then we ap-

Nodal plane II 36°/45°/90° 36°/46°/91° 31°/43°/84° 28°/46°/89° 29°/46°/89° 22°/53°/85° 22°/52°/80° 32°/43°/87° 40°/59°/102° 21°/52°/82° 28°/43°/87°

Magnitude (Mw) 6.67 6.66 6.68 6.66 6.66 6.6 6.6 6.5 6.6 6.37 6.7

Best depth(km) 17 15 16 16 16 21.8 11 19 10 19 12

ply three different velocity models to estimate the effect of the velocity structure on the focal mechanisms and depth. And through re-sampling the teleseismic data, the stability of the results for data selection is tested. The results derived from various methods with different velocity models are steady and consistent. The best double-couple fault plane solution of Lushan event, based on the average velocity model of Longmenshan region and the CAPjoint inversion method, is 210°, 44°, and 91° for strike, dip, and rake angles respectively for one nodal plane, and 29°, 46°, and 89° for another, with uncertainty less than 10°. The velocity structure in the seismogenic zone is very complex, presenting significant differences in both sides of the LFZ. The focal mechanisms inversed by applying different velocity models in different areas show a slight difference compared with the other results inversed by using average model. This indicates that velocity models have certain influence on the result when employing the CAP method, and the results based on these models would probably reflect the complex nature of earthquakes, particularly like this event. In the complex tectonic regions, using simple 1D model may only be able to obtain the first approximation results, and it is worthy of considering quasi 2D model or 3D model in the future study. Besides, in the inversion of source parameters, how to choose fault rupture duration time also has influence to some extent on the inversion result, especially for the events with magnitude larger than 6.5, because the large scale and long duration of the fault rupture would take prominent effects on the inversion results. In this study, 10 s was chosen as the fault rupture duration time according to the result of Liu et al. [6]. In addition, by searching the duration with the CAPjoint method, we found that when the duration is 5 s, the inversion error reaches the minimum. Compared with those based on the 10 s duration, the fitness between observed seismograms and synthetics based on the 5 s duration time is somewhat better for both local and teleseismic seismograms, and the time shifts that synthetics shift relative to the observed waveforms are also less than 5 s for both datasets. However, the magnitude based on 5 s dura-

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tion is about 0.1 and 0.2 smaller for teleseismograms and local data respectively than those inversed with 10 s duration. Based on the CAP method program, the amplitude of the source time function increases when the duration decreases, which is closer to the point source assumption but is deviated from the fact of the true rupture process. For this reason, in the inversion of source parameters for moderate and strong events, the selection of the duration time should be based on the seismic scaling law and the seismic moment rate function of rupture model. Taking the rupture length and the scale of the Lushan earthquake into consideration, we prefer to use 10 s as the source duration. Large earthquake usually has a certain rupture size and its source depth is distributed in a certain range. Based on three kinds of inversion methods, we obtain a consistent focal depth of ~16 km. Since the teleseimic data contain depth phases like pP and sP, the result of focal depth may be more creditable than just using local data. Moreover, through the way of extracting combination stations, we found that the focal depth searched by the CAPtele is more stable. So we believe that the focal depth is around 16 km within 2 km error. In order to constrain the focal depth or deep distribution of the fault, we need to do further research and analysis on the aftershock sequence. Meanwhile, another available approach is to use depth phases to determine the initiation rupture depth of the event accurately. We plan to do such work in the near future. This study was supported by National Natural Science Foundation of China (Grant Nos. 41174086, 41074052 and 41021003), Special Project Seismic Commonweal research (Grant No. 201308013) and Key Development Program of Chinese Academy of Science (Grant No. KZZD-EW-TZ05). We thank the anonymous reviewers for their important suggestion and comments. Thanks are due to the Data Backup Centre of China Seismograph Network at the Institute of Geophysics, China Earthquake Administration and the Sichuan Seismological Bureau for providing the local seismograms. In addition, the facilities of the IRIS Data Management System, Harvard and USGS were used to access teleseismic data and source parameters required in this study. We also thank Prof. Ni Sidao and his student Chen Weiwen for constructive criticism of an early draft. The figures in this paper were drawn with GMT. 1

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