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Spatio-temporal rupture process of the 2008 great Wenchuan earthquake

ZHANG Yong1,2, FENG WanPeng2, XU LiSheng2†, ZHOU ChengHu3 & CHEN YunTai1,2*

1 School of Earth and Space Sciences, Peking University, Beijing 100871, China; 2 Institute of Geophysics, China Earthquake Administration, Beijing 100081, China; 3 Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China

Focal mechanism and dynamic rupture process of the Wenchaun Ms8.0 earthquake in Sichuan province on 12 May 2008 were obtained by inverting long period seismic data from the Global Seismic Network (GSN), and characteristics of the co-seismic displacement field near the fault were quantitatively ana- lyzed based on the inverted results to investigate the mechanism causing disaster. A finite fault model with given focal mechanism and vertical components of the long period P-waves from 21 stations with evenly azimuthal coverage were adopted in the inversion. From the inverted results as well as after- shock distribution, the causative fault of the great Wenchuan earthquake was confirmed to be a fault of strike 225°/dip 39°/rake 120°, indicating that the earthquake was mainly a thrust event with right-lateral strike-slip component. The released scalar seismic moment was estimated to be about 9.4×1020― 21 2.0×10 Nm, yielding moment magnitude of Mw7.9―8.1. The great Wenchuan earthquake occurred on a fault more than 300 km long, and had a complicated rupture process of about 90 s duration time. The slip distribution was highly inhomogeneous with the average slip of about 2.4 m. Four slip-patches broke the ground surface. Two of them were underneath the regions of Wenchuan-Yingxiu and Beichuan, respectively, with the first being around the hypocenter (rupture initiation point), where the largest slip was about 7.3 m, and the second being underneath Beichuan and extending to Pingwu, where the largest slip was about 5.6 m. The other two slip-patches had smaller sizes, one having the maximum slip of 1.8 m and lying underneath the north of Kangding, and the other having the maximum slip of 0.7 m and lying underneath the northeast of Qingchuan. Average and maximum stress drops over the whole fault plane were estimated to be 18 MPa and 53 MPa, respectively. In addition, the co-seismic displacement field near the fault was analyzed. The results indicate that the features of the co-seismic displacement field were coincident with those of the intensity distribution in the meizo- seismal area, implying that the large-scale, large-amplitude and surface-broken thrust dislocation should be responsible for the serious disaster in the near fault area.

Wenchuan earthquake, earthquake rupture process, co-seismic displacement

As reported by China Seismograph Network Center buildings, including houses, roads and bridges (Satellite

(CSNC), an earthquake of Ms8.0 occurred near Yingxiu images in Figures 1(d) and (e)), were destroyed or col- town (31.0°N, 103.4°E, focal depth: 15 km) of Wen- lapsed, causing nearly 90000 dead and missing. chuan County, Sichuan Province, at 14: 28: 04 (Beijing Received July 25, 2008; accepted December 2, 2008; published online December 18, 2008 Time), 12 May 2008. The earthquake resulted in doi: 10.1007/s11430-008-0148-7 large-scale landslides and debris flows, silting of rivers, †Corresponding author (email: [email protected]) and more than 3000 barrier lakes (Satellite images in * Equal contributor (email: [email protected]) Supported by the National Basic Research Program of China (Grant No. Figures 1 (a), (b) and (c)), and seriously damaged more 2004CB418404-4) and the National Natural Science Foundation of China (Grant Nos. than one hundred of cities and towns. A large number of 40574025 and 40874026)

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Figure 1 Slides, debris flows and barrier lakes ((b),(c)), damaged towns, a large number of destroyed houses, roads and bridges ((d),(e)) along Long- menshan fault zone caused by the great Wenchuan earthquake shown by the images of MODIS satellite. Light yellow toothed lines in (a) are the thrust faults and the directions of sawtooth denote the dip directions of the faults. 1, Maoxian-Wenchuan fault; 2, Yingxiu-Beichuan fault; 3, Pengxian-Guanxian fault.

Epicenter of the great Wenchuan earthquake is lo- in recent years[2]. In contrast, there were strong seismic cated in the Longmenshan fault zone, on the eastern activities outside the Longmenshan fault zone, even in edge of Tibet Plateau. The Longmenshan fault zone is a Southwest China, with a number of large earthquakes large one striking NE-SW, about 500 km long and 30 km occurring not only in history but also in last decades[3,4] to 50 km wide, and fault movements are dominated by (Figure 2). However, magnitudes of the earthquakes thrust with right-lateral strike-slip component[1]. The never exceeded 8, and the largest one was the 1933

Longmenshan fault zone consists of the rear-Longmen- Diexi Ms7.5 earthquake. The Wenchuan earthquake was shan fault (Maoxian-Wenchuan fault), middle-Long- an abrupt energy release after being accumulated within menshan fault (Yingxiu-Beichuan fault) and fore- Longmenshan fault zone for many years. Longmenshan fault (Pengxian-Guanxian fault) from Focal mechanism and rupture process of the Wen- west to east (Figure 2). All these are thrust faults with chuan earthquake were quickly determined using long minor right-lateral strike-slip component, and more period seismic data from the Global Seismograph Net- right-lateral strike-slip component appears in northeast- work (GSN) in a few hours after the occurrence of the ern segment of the Longmenshan fault zone[1]. No major earthquake (http://www.cea-igp.ac.cn/special_issue/ earthquake with magnitude larger than 7 was recorded earthquake_situation/preliminary_results(1).pdf) and historically while moderate and small earthquakes (M<7) reported on the second day, which provided important occurred frequently inside the Longmenshan fault zone information for rescue work on the field. The inverted

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Figure 2 (a) Epicenter (white aniseed star) location of the 2008 great Wenchuan earthquake, main faults (modena lines) in epicentral area, historical earthquakes (yellow circles), and main cities (white circles) along Longmenshan fault zone. Lilac rectangle denotes the projection on ground surface of the fault plane model adopted in this study. “Beach ball” represents the lower hemisphere projection of focal mechanism (strike 225°/dip 39°/rake 120°) of the great Wenchuan earthquake obtained in this study. (b) The tectonic settings of the great Wenchaun earthquake. results indicated that the fault was about 300 km long, northeast of the epicenter, the earthquake rupture dura- and rupture initiated at 15 km underneath Yingxiu town tion time was about 90 s, and the maximum dislocation of Wenchuan County and stopped at Qingchuan County, occurred in vicinity of Wenchuan County and Beichuan

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County. seismic recordings in order to reserve source informa- In this article we present the focal mechanism and tion as complete as possible. Green’s functions used dynamic rupture process of the great Wenchuan earth- were calculated by reflectivity method[6] based on the quake obtained by inverting long period seismic data by global standard velocity model[7]. means of the inversion method based on a finite fault model[5], and quantitatively analyze the characteristics of 2 Determination of fault parameters co-seismic displacement field of this great earthquake Harvard University (http://www.globalcmt.org/CMT based on the inverted results. search.html), USGS, (http://earthquake.usgs.gov/ eqcenter/eqinthenews/2008/ us2008 ryan/# scitech) and 1 Data Chen et al. (http://www.cea-igp.ac.cn/special_issue/ Long period P waveform data from the stations with earthquake_situation/preliminary_results(1).pdf) deter- epicentral distances of 55° to 90° was selected and in- mined and released the seismic moment tensor solution verted for focal mechanism and rupture process of the (Table 1) timely after the earthquake. All the three re- great Wenchuan earthquake. To ensure stations to have sults show consistently that the Wenchuan earthquake evenly azimuthal coverage, we adopted 21 stations was mainly a thrust event with a minor right-lateral (Figure 3) with minimum azimuth interval of about 5°. strike-slip component. However, those results were ob- tained under the assumption that the source time func- tion was a triangle function, neglecting complexity of source time history. To take into account the complexity of source time history, we adopted a new method devel- oped by Zhang[8] to directly invert waveform data for six elements of the moment tensor and source time function describing the complexity of source time history under a condition of merely assuming the six elements of mo- ment tensor have the same time history, and then deter- mine the fault parameters[9]. The inverted results (Table 1) show that the scalar seismic moment released in the great Wenchuan earth- quake was about 2.0×1021 Nm, corresponding to a mo-

ment magnitude of Mw8.1. The best double couple solu- tion is strike 220°/dip 32°/rake 118° for nodal plane I, and strike 8°/dip 63°/rake 74° for plane II. This result is in agreement with the global centroid moment tensor Figure 3 Epicenter (white aniseed star) of the 2008 great Wenchuan (GCMT) solution, but with a slight difference[9]. earthquake and spatial distribution of long period seismic stations (trian- gles) used in this study. The striking and dipping directions of the inverted nodal plane I (strike 220°/dip 32°/rake 118°) are con- Only P waveforms on vertical components were used sistent with the overall trend of Longmenshan fault zone, in the inversion since horizontal components are con- also with the NE-SW orientation of aftershock distribu- taminated by noise, and a 3-order bandpass Butterworth tion; thus this plane is preferred as the causative fault. In filter of 0.002 to 0.2 Hz was applied to the observed the following inversion for rupture process, we will take

Table1 Seismic moment, moment magnitude, fault parameters and principal stress axes parameters of the great Wenchuan earthquakea)

M0 Nodal plane I Nodal plane II T axis B axis P axis Source 21 Ｍw (10 Nm) Strike (°) Dip (°) Rake (°) Strike (°) Dip (°) Rake (°) Az (°) Pl (°) Az (°) Pl (°) Az (°) Pl (°) Harvard 0.94 7.9 229 33 141 352 70 63 227 57 2 25 114 9 USGS 0.75 7.9 238 59 128 2 47 45 202 57 36 31 110 16 [9] Liu et al. 2.0 8.1 220 32 118 8 63 74 245 69 16 14 302 6 This study 0.94 7.9 225 39 120 8 57 68 230 69 21 18 103 20 a) Az, azimuth; Pl, plunge.

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this plane as the initial fault model. in NE direction and 205 km in SW direction of epicenter) in strike direction and a width of 50 km in down-dip 3 Equations and inversion parameters direction was used as initial fault plane. The fault plane of 510 km×50 km was divided into 51×5=255 sub-faults Study on inversion for source rupture process started in with length of 10 km and width of 10 km. Initial rupture the 1980s. In the past 20 years, a number of inversion point was set at the 31st sub-fault in strike direction and methods were developed, such as the waveform inver- the 3rd sub-fault in dip direction in accordance with the sion methods proposed by Kikuchi and Kanamori[10] and hypocentral location (31.0°N, 103.4°E, focal depth: 15 Hartzell and Heaton[11]. In all these methods time-histo- km). Rupture duration time of sub-fault was allowed to ries of the sub-faults were assumed a priori, which, to be 25 s at most and the rupture velocity was allowed to some extent, affects the objectivity in rupture mode be 4.5 km/s at most. Besides, no constraints on the and/or rupture propagation velocity. In this study, we source time function of sub-fault, and no initial rupture take advantage of the method used in the study of the [13] time of sub-faults were imposed in the inversion . In 2007 Ning’er earthquake[5]. In this method, time-histo- order to fit or interpret all the observed data, the same ries of the sub-fault are not given a priori, and the weights were imposed on all the station data by adjust- inversion scheme is formulated with data equation, ing λ for the maximum amplitude of each seismogram spatially smoothing equation, temporally smoothing 0 to be around 1. Based on this, other weights can be set equation, and scalar seismic moment minimizing equa- referring to λ . After a number of tests, λ =30, λ =80, tion as following: 0 1 2 and λ3=0.4 were adopted in the inversion. ⎡⎤λ0U ⎡⎤λ0G ⎢⎥ Following the method described in the preceding sec- ⎢⎥0 λ D ⎢⎥= ⎢⎥1 [],s (1) tion, we performed the inversion for spatio-temporal ⎢⎥0 ⎢⎥λ2T rupture process by trial-and-error technique using dif- ⎢⎥⎢⎥ ⎣⎦0 ⎣⎦λ3Z ferent focal mechanisms started from the initial model where U is vector of observed data; G, matrix of Green’s (fault plane strike 220°/dip 32°/rake 118°), as mentioned functions; s, vector of unknowns, which consists of the before, and the best-fit fault-plane solution was found to source time functions of sub-faults; D, spatially be strike 225°/dip 39°/rake 120° (the 4th line in Table 1 smoothing matrix; T, temporally smoothing matrix; Z, and the beach-ball in Figure 2). matrix of minimizing scalar moment. λ0, λ1, λ2 and λ3 4 Static slip distribution denote the weights. λ0 is usually a sparse matrix while λ1, λ2 and λ3 are scalar constants. The non-negative As shown in Figure 4, the Wenchuan earthquake pro- [12] conjugate gradient method was used to solve eq. duced highly heterogeneous slip distribution on the fault (1). plane. There are four slip patches on the fault plane. The A rectangular area with a length of 510 km (305 km first one lies underneath the Wenchuan-Yingxiu area,

Figure 4 Static (final) slip distribution on the fault of the 2008 great Wenchuan earthquake. White aniseed star denotes location of hypocenter (rupture initiation point). White lines and white numbers are contours of the slip and slip values (m), respectively. Arrows on the top show the projected location of cities and counties on the fault trace (intersection of fault plane and ground surface). Different scales are used for abscissa and ordinate in this figure.

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with a length of 180 km in strike direction and a width model[14,15]. The results indicate that the maximum and of 50 km in down-dip direction, and the maximum slip average values over the fault plane are 53 MPa and 18 is 7.3 m appearing near the hypocenter (rupture initia- MPa, respectively. The average value is of the same or- tion point); the second slip patch lies underneath der as the average stress drop for intraplate earthquakes Beichuan County and extends to underneath Pingwu (about 10 MPa), but about twice the stress drops of this [16] County, with a size of 60 km in strike direction and 35 value . There is no distinct difference between Wen- km in down-dip direction, and the maximum slip is 5.6 chuan earthquake and other intraplate earthquakes in the m; the third slip patch lies underneath the zone between stress drop. 120 km and 170 km in southeast to the epicenter, with a maximum slip of 1.8 m; and the fourth, and the smallest, 5 Spatio-temporal variation of rupture is at northeast of Qingchuan County, with the maximum process slip of 0.7 m. The average slip over the whole fault is Figure 5 shows the slip variation with space and time on about 2.4 m. the fault. In the period of the first 12 s after the rupture Based on the static (final) slip distribution (Figure 4), initiation, rupture propagation appeared to be bilateral the stress drop on the fault was calculated using Brune toward NE and SW directions, and moment released

Figure 5 Snapshots of slip variation with time on the fault of the 2008 great Wenchaun earthquake. White aniseed star denotes location of the hypocenter (rupture initiation point). Each rectangle denotes the slip distribution at the time as indicated at its lower left corner on the fault plane. The last rectangle at lower right corner is the static (final) slip distribution at 90 s. Red lines represent the evolution of rupture fronts with time. The figures beside the red lines are the corresponding rupture velocity values (unit: km/s).

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fastest at the 5th s. After this time interval there was a function indicates that the scalar seismic moment re- short pause of about 4 s. In the period of 16 to 30 s, a leased in the whole earthquake rupture process was new rupture started 80 km away in the northeast to the about 9.4×1020 Nm, corresponding to a moment magni- epicenter and propagated quickly toward SW direction. tude Mw7.9. The whole time history of the Wenchuan In this time interval, the rupture occurred in a larger ex- earthquake is divided into five stages, that is, consists of tent, which was a main stage of the Wenchuan earth- five sub-events. The first event occurred in the first 14 s quake. In the period of 30 s to 42 s, there were some after the rupture initiation, releasing 14% of the total weak ruptures distributed in a sparse way in both NE scalar seismic moment. The second event, the main and SW directions. In the following 6 s, rupturing event, was from 14 s to 34 s, releasing 60% of the total seemed to stop. But, in the time interval of 48 s to 58 s, scalar seismic moment. The third one started at 34 s and rupturing occurred successively near zones underneath ended at 43 s, releasing 8% of the total scalar seismic Beichuan 140 km away in northeast of epicenter and moment. The fourth occurred in the time period of 43 s Kangding 150 km away in southwest of epicenter. In the to 58 s, releasing 17% of the total scalar seismic moment. time interval of 60 s to 66 s, only a small patch of rup- And the last one started at 58 s, and ruptured weakly turing occurred 200 km away in the northeast of epicen- until the end of the whole rupture process (90 s), releas- ter. Later, the rupturing in southwest direction almost ing only 6% of the total scalar seismic moment. ceased while there existed patches of weak rupturing 280 km in northeast of epicenter. 7 Displacement field on the ground sur- As described above, the source process of the Wen- face and mechanism causing serious chuan earthquake is highly complicated and the slip dis- disaster in the nearfault areas tribution is very inhomogeneous. Red thin lines in Fig- ure 5 emphasize the temporal progression of the rupture Displacement in homogeneous and isotropic elastic half fronts. Figure 5 also shows that the speed at which the space produced by a rectangular dislocation fault can be [17―19] rupture front is propagating (rupture velocity) was vary- expressed in analytic form , thus it is possible to ing with space and time during the whole earthquake calculate the co-seismic displacement field produced by rupture process. We estimated the rupture velocities for a finite fault model. The co-seismic displacement field several typical time intervals and marked the values be- on the ground surface in the epicentral area was calcu- side the red lines in red color in Figure 5. From the fea- lated (Figure 7) by summing the displacement fields tures of the rupture propagating along strike direction of produced by the 255 sub-faults of 10 km×10 km, which the fault, the average rupture velocities were estimated were obtained from the inversion of the earthquake rup- to be 3.4 km/s in the NE direction and 2.2 km/s in the ture process. Figure 7 compares the spatial distribution SW direction, respectively. of the co-seismic displacement field with the isoseis- mals[20]. Right-lateral movement can be clearly observed 6 Source time function in horizontal component of the displacement field (Fig- ure 7(a)), with the NW block moving toward NE direc- The moment-rate function (source time function) shown tion while the SE block moving toward SW direction. in Figure 6 can be obtained based on the spatio-temporal Also, the hanging wall (NW to the fault strike trace) up- [5] rupture images as shown in Figure 5 . The source time lifting and the foot wall (SE to the fault strike trace) de- ducing can be clearly observed in vertical component of the displacement field (Figure 7(b)). The features of both the horizontal and vertical components of the co-seismic displacement field are in good agreement with those of the isoseismals in the meizoseimal area, with two areas of the maximum displacement just being around Wenchuan County and Beichuan County where there are also two areas of the maximum intensity XI (Figure 7). In Wenchuan County, the maximum hori- Figure 6 Source time function of the 2008 great Wenchuan earthquake. zontal and vertical displacements are 3.2 m and 2.8 m,

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Figure 7 Comparison of the co-seismic displacement field and the isoseismals of the 2008 great Wenchuan earthquake. (a) Horizontal displacement; (b) vertical displacement. Black full thin lines represent the isoseismals[20]. respectively, and in Beichuan County, the maximum and 0.8. It means that the inverted model of dynamic horizontal and vertical displacements are 2.9 m and 2.6 rupture process well interprets most features of the ob- m, respectively. The maximum displacements all ap- served waveforms. peared where the fault broke the ground surface. The The comparison of the feature of the co-seismic dis- calculated relative displacement or dislocation is about placement field calculated from the inverted static slip 6.1 m where the maximum displacement appeared (at distribution with the feature of the spatial distribution of the 50 km northeast of epicenter), which is also in good disastrous areas from the field investigation indicates agreement with the result of field investigation. All these that they are very similar: the two areas with the larger results suggest that the surface-broken thrusting disloca- displacement values are just where the two meizoseis- tion is the main cause for the serious disaster in the mal areas are, reflecting close correlation between the near-fault areas in the great Wenchuan earthquake. meizoseismal areas and the surface-broken thrusting dislocation of the causative fault. 8 Discussion and conclusions However, some details in the inverted results require further study. For example, the inverted results clearly We selected 21 teleseismic stations with evenly azi- show that in northeast of Kangding occurred a slip patch muthal coverage of the vertical long period recordings with the maximum slip of about 1.8 m, no surface from the GSN, and inverted for the spatio-temporal rup- breakage features have been found yet in field investiga- ture process of the Wenchuan Ms8.0 earthquake on 12 tion; and the fitness of the synthetic waveforms with the May 2008. Reliability of the inverted results can be re- observed waveforms at some stations remains unsatis- flected, to some extent, by fitness between observed factory even though the dynamic model inverted for the waveforms and synthetic waveforms. Therefore, we great Wenchuan earthquake has well interpreted most calculated synthetic waveforms for 21 stations based on features of the observed waveforms. the inverted model of the spatio-temporal rupture proc- In this paper, focal mechanism, source time function ess and compared the synthetic waveforms with ob- and spatio-temporal variation of the slip on the fault are served waveforms. As Figure 8 shows, the fitness of the obtained, and the co-seismic displacement field in the synthetic waveforms with the observed waveforms is epicentral area is calculated based on the inverted model good, with most of them (13 stations) having correlation of static slip dislocation. The inverted focal mechanism coefficients of above 0.8 and other 3 being between 0.7 and rupture process indicate that the Wenchuan earth-

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Figure 8 Comparison of the observed seismograms of the Global Seismic Network (GSN) and the synthetic seismograms. In each panel, the upper trace denotes the observed waveform and the lower trace denotes the synthetic waveform. On the left are the maximum amplitude of observed waveform, the correlation coefficients and the maximum amplitudes of the synthetic waveform, respectively. On the right from top to bottom are the station codes, com- ponents names and phase names, respectively. quake was mainly a thrust event, and the rupture propa- epicentral area indicates that the large-scale, high-am- gated mainly toward northeast direction in asymmetri- plitude and surface-broken thrusting dislocation resulted cally bilateral mode, with the maximum slip of about 7.3 from the earthquake source is the main cause for the m, and large-scale slip-patches strongly breaking the serious disaster in the near-fault areas. ground surfaces. The striking coincidence of the features of the co-seismic displacement field calculated based on The authors would like to express their sincere thanks to the anonymous the static slip model with those of the isoseismals in the revewers for valuable suggestions.

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