Stress evolution and fault interactions before and after the 2008 Great Wenchuan earthquake

Tectonophysics 491 (2010) 127–140

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Tectonophysics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / t e c t o

Stress evolution and fault interactions before and after the 2008 Great Wenchuan earthquake Gang Luo a,b,⁎, Mian Liu a a b

Department of Geological Sciences, University of Missouri, Columbia, Missouri 65211, USA Bureau of Economic Geology, Jackson School of Geosciences, The University of Texas at Austin, Austin, Texas 78713, USA

a r t i c l e

i n f o

Article history: Received 17 February 2009 Received in revised form 12 December 2009 Accepted 29 December 2009 Available online 6 January 2010 Keywords: Wenchuan earthquake Coulomb stress Fault interaction Viscoelastoplastic Finite element modeling

a b s t r a c t The 12 May 2008 Wenchuan earthquake (Mw 7.9) ruptured ∼ 300 km of the Longmen Shan fault, claiming ∼ 90,000 lives and devastating many cities in the Sichuan province, China. The coseismic stress changes due to the Wenchuan earthquake have been studied in kinematic models using the inferred coseismic fault slips, but the cause of the fault slips, the impact of other large earthquakes, and the mechanical interactions between the faults in eastern Tibet are uncertain. Here we explore these issues using a three-dimensional viscoelastoplastic dynamic model that calculates the regional stresses from tectonic and topographic loading, and simulates earthquakes and their stress perturbations. Our calculated coseismic changes of the Coulomb stress associated with the Great Wenchuan earthquake are similar to those in previous models. However, we show that the cumulative Coulomb stress changes, hence the implied earthquake risks, are significantly different when previous large earthquakes in the region are included in the model. Particularly, we show that in spite of stress increase from the Wenchuan earthquake, the southeastern segments of the Xianshuihe fault stay in a stress shadow because of the stress release by six M ≥ 6.9 events in this part of the Xianshuihe fault since 1893. We also found that interseismic locking on the Xianshuihe fault can increase the loading rate on the Longmen Shan fault by up to ∼ 50 Pa/year. © 2010 Elsevier B.V. All rights reserved.

1. Introduction The 12 May 2008 Great Wenchuan earthquake (Mw 7.9, Table 1) caused much damage in Sichuan and neighboring provinces in western China, killing ∼ 90,000 people and destroying many cities and towns. This earthquake ruptured nearly 300 km of the Longmen Shan fault in the eastern Tibetan Plateau (Fig. 1a) (Zhang et al., 2008; Lin et al., 2009), as the crust moves to accommodate the Indo–Asian collision (Burchfiel et al., 2008). A big earthquake can perturb the regional stress field and may trigger earthquakes in neighboring regions and faults (e.g., King et al., 1994; Stein et al., 1997; Stein, 1999; Lin and Stein, 2004). Shortly after the Wenchuan earthquake, Parsons et al. (2008) and Toda et al. (2008) applied elastic dislocation models, using coseismic slip inverted from seismic data (e.g., Nishimura and Yagi, 2008; Ji and Hayes, 2008), to calculate the coseismic Coulomb stress change and assess future seismic risks in the region. Such calculations are useful to provide a quick glimpse of the stress impact of the Great Wenchuan earthquake; however, coseismic Coulomb stress changes are only a small part of an evolving stress field. Many of the triggered earthquakes occur in years to decades after the triggering earthquake, ⁎ Corresponding author. Bureau of Economic Geology, Jackson School of Geosciences, The University of Texas at Austin, Austin, Texas 78713, USA. E-mail address: [email protected] (G. Luo). 0040-1951/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.tecto.2009.12.019

because of stress changes from postseismic viscous relaxation (e.g., Freed and Lin, 2001; Freed, 2005) and perturbations by other earthquakes. Around the Longmen Shan fault is a complex system of faults that collectively accommodate crustal motion in the eastern Tibetan Plateau caused by the Indo–Asian collision, and numerous major earthquakes (M ≥ 7.0) have frequently ruptured the neighboring faults in the recent history (Fig. 1a). If the Great Wenchuan earthquake can affect earthquakes on these neighboring faults, one needs to ask whether or not these large earthquakes contributed to trigger the 2008 Wenchuan earthquake. In particular, the Xianshuihe fault has had six large earthquakes (M ≥ 6.9) between 1893 and 1981 (Fig. 1a) (Allen et al., 1991; Papadimitriou et al., 2004; Wen et al., 2008). Did these quakes have any link to the 2008 Wenchuan earthquake? Since 1981, the Xianshuihe fault has been seismically quiescent. Given the high slip rates on the Xianshuihe fault, could interseismic locking of the Xianshuihe fault affect the loading rate on the Longmen Shan fault? To address these questions, we developed a three-dimensional viscoelastoplastic model for eastern Tibet. We first use this model to simulate the Great Wenchuan earthquake and the associated changes of the Coulomb stresses. We then simulate the previous large earthquakes in the region and show that the cumulative Coulomb stress changes after the Wenchuan earthquake differ significantly from that caused by the Wenchuan earthquake alone. Finally we discuss fault interactions by simulating how the loading rate on the

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Table 1 Epicenter, hypocenter and magnitude of the 2008 Great Wenchuan earthquake. Epicenter Lon. E (°)

Lat. N (°)

103.364 103.4 104.10

30.986 31.0 31.44

Hypocenter depth (km)

Seismic magnitude

Reference

19 14 12.8

Mw 7.9 Ms 8.0 Mw 7.9/Ms 8.1

USGS (2008) CENC (2008) GCMTC (2008)

Longman Shan fault may be affected by seismic cycles on the Xianshuihe fault. 2. Tectonic background In the eastern Tibetan Plateau, the Indo–Asian collision is collectively accommodated by slip on a network of fault systems (Fig. 1a). To study mechanical interactions between earthquakes and

between faults in this region, we have included the major faults in our geodynamic model. The following is a brief description of these faults and their seismicity. 2.1. The Longmen Shan fault and the 2008 Great Wenchuan earthquake The Longmen Shan fault zone is the boundary between the Tibetan Plateau and the rigid South China Block (Fig. 1a), where the elevation changes from N4000 m to ∼ 500 m within a distance of ∼50 km. Associated with the steep topographic changes are sharp variations of crustal thickness and seismic velocities in the lithosphere (e.g., Burchfiel et al., 2008). The Longmen Shan fault zone consists of three major faults (e.g., Zhang et al., 2008; Lu et al., 2008): the Wenchuan–Maowen fault, the Yingxiu–Beichuan fault, and the Guanxian–Anxian fault (Fig. 1b). These faults are northwest-dipping thrusts with right-lateral motion (Densmore et al., 2007; Zhang et al., 2008; Lu et al., 2008; Burchfiel

Fig. 1. (a) Faults, seismicity and topographic relief in eastern Tibet and the neighboring regions. Gray circles show earthquakes from 2300 B.C. to A.D. 2000 (Lee et al., 2003). Red star indicates the epicenter of the 2008 Great Wenchuan earthquake. The focal mechanism solution is from USGS (2008). Yellow circles are aftershocks of the Wenchuan earthquake ending on 8/22/2008 (CENC, 2008). Green circles are the additional earthquakes modeled in this study. Brown circles are other major earthquakes in eastern Tibet in the recent history. Magenta arrows show crustal block motions relative to stable Eurasia (Zhang et al., 2004). TP: Tibetan Plateau; SCB: South China Block; OP: Ordos Plateau; AM: Alashan– Mongolia shield; QM: Qinling Mountain; LSF: Longmen Shan fault; MJF: Min Jiang fault; KF: Kunlun fault; HF: Haiyuan fault; XF: Xianshuihe fault; AF: Anninghe fault; ZF: Zemuhe fault; and XJF: Xiaojiang fault. The red dashed rectangular area shows the model domain. (b) A sketch profile across the Longmen Shan fault zone. The red circle shows the possible hypocenter for the 2008 Wenchuan earthquake (Zhang et al., 2008; Burchfiel et al., 2008).

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et al., 2008), but detailed geometry is unclear (e.g., Burchfiel et al., 2008). Their dipping angles range from ∼ 45° to nearly vertical near the surface but gradually decrease with depth (Fig. 1b) (Densmore et al., 2007; Lu et al., 2008; Zhang et al., 2008; Burchfiel et al., 2008; Lin et al., 2009). The epicenter and magnitude of the 2008 Wenchuan earthquake vary slightly among different reports (Table 1), and the seismogenic fault for the Wenchuan earthquake is debatable. Zhang et al. (2008) suggested that the Yingxiu–Beichuan fault is the seismogenic fault, whereas Lu et al. (2008) argued that it is the Guanxian–Anxian fault. Ji et al. (2008) used seismic and interferometric data to show that the initial rupture occurred on the Guanxian–Anxian fault, and slip on the Yingxiu–Beichuan fault was triggered about 10 s later. Burchfiel et al. (2008) suggested that northeast rupture and southwest rupture probably occurred on different faults, which broke simultaneously in the earthquake. During the Great Wenchuan earthquake, the Longmen Shan fault ruptured from the epicenter to the northeast (Nishimura and Yagi, 2008; Ji and Hayes, 2008); the maximum oblique thrust-dextral slips are ∼ 6–9 m, with two separate slip peaks near the Yingxiu and Beichuan counties (Nishimura and Yagi, 2008; Ji and Hayes, 2008). Shen et al. (2009) found a similar coseismic slip distribution from inverting the GPS (Global Positioning System) and InSAR (Interferometric Synthetic Aperture Radar) data. Although eastern Tibet has been abundant in large earthquakes (Fig. 1a), the Great Wenchuan earthquake came as a surprise, because the Longmen Shan fault has been relatively quiescent in seismicity. This is consistent with its low fault slip rates, which are less than ∼ 3 mm/year (e.g., Chen et al., 2000; Meade, 2007; Densmore et al., 2007; Zhang et al., 2008; Burchfiel et al., 2008), one order of magnitude lower than slip rates on the Xianshuihe fault and other major faults in eastern Tibet (e.g., Meade, 2007). 2.2. The Min Jiang fault The Min Jiang fault (Fig. 1a) is north striking and west dipping (45°–65°), with a strike-slip component (Kirby et al., 2000). The low geological slip rate (b1 mm/year) on the Min Jiang fault during late Cenozoic (e.g., Kirby et al., 2000; Deng et al., 2003) is consistent with the GPS measurements (e.g., Zhang et al., 2008; Burchfiel et al., 2008) and the lack of large earthquakes (M N 7.0) (Fig. 1a). The only recorded major earthquake on the Min Jiang fault is the 1933 M 7.5 Diexi earthquake (Chen et al., 1994). In the Songpan region east of the Min Jiang fault, a cluster of three large earthquakes (M 7.2, 6.7, 7.2) occurred in 1976 (Fig. 1a) (Chen et al., 1994). 2.3. The Kunlun fault The Kunlun fault is a major east–west striking fault that strides through the central and eastern Tibetan Plateau (Wang et al., 2001; Lin et al., 2002; Zhang et al., 2004; Lin et al., 2006). The slip rates are high (∼8–16 mm/year) along the central Kunlun fault (Woerd et al., 2002; Zhang et al., 2004; Li et al., 2005; Lin et al., 2006), and low (b2 mm/year) along the eastern Kunlun fault (Kirby et al., 2007). This is consistent with numerous large earthquakes on the central Kunlun fault and low seismicity along the eastern Kunlun fault (Fig. 1a). The 1937 M 7.5 Tuosuo Hu earthquake (Fig. 1a) ruptured a ∼300-km long segment (96°E–99°E) of the central Kunlun fault with up to 8 m coseismic slip (e.g., Li et al., 2006). Recent large earthquakes include the 1997 Mw 7.6 Manyi earthquake, and the 2001 Mw 7.8 Kokoxili earthquake, both on the central Kunlun fault and more than 1000 km from the Longmen Shan fault, so they are not included in our model (Fig. 1a). 2.4. The Haiyuan fault The Haiyuan fault is an active left-lateral strike-slip fault around the northeastern edge of the Tibetan Plateau (Fig. 1a). The estimated

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slip rates vary from ∼ 10–25 mm/year based on geological data (e.g., Tapponnier et al., 2001; Lasserre et al., 2002) to b5 mm/year from GPS measurements (e.g., Zhang et al., 2004). The most recent large earthquakes along the Haiyuan fault include the 1920 M 8.5 Haiyuan earthquake, the 1927 M 8.0 Gulang earthquake, and the 1932 M 7.6 Changma earthquake (Fig. 1a) (e.g., Fu et al., 2001). 2.5. The Xianshuihe fault The Xianshuihe fault is an active left-lateral strike-slip fault in the southeastern Tibetan Plateau (Fig. 1a). Both geological and GPS measurements indicate ∼ 10–20 mm/year slip on the northwestern segments and ∼5–9 mm/year on the southeastern segments of the Xianshuihe fault (e.g., Allen et al., 1991; King et al., 1997; Shen et al., 2005; Thatcher, 2007; Meade, 2007). Since 1700, clusters of large earthquakes have ruptured various segments of the Xianshuihe fault (Allen et al., 1991; Papadimitriou et al., 2004; Wen et al., 2008), including six M ≥ 6.9 events between 1893 and 1981 (Fig. 1a). However, no M ≥ 5 events have occurred on the fault since 1981. Seismicity along the Xianshuihe fault has been the subject of intensive study in recent years because of the past seismic activity and the dense population around the southeastern Xianshuihe fault (Allen et al., 1991; Zhang et al., 2003b; Papadimitriou et al., 2004; Wang et al., 2008; Wen et al., 2008). 2.6. The Anninghe–Zemuhe–Xiaojiang fault system The Anninghe–Zemuhe–Xiaojiang fault system, also called the Xiaojiang fault system, is the southward continuation of the Xianshuihe fault (Fig. 1a). Geological and GPS slip rates are ∼5– 10 mm/year along the northern segments and ∼ 4 mm/year along the southern segments (e.g., Deng et al., 2003; Shen et al., 2005). More than ten M N 6 earthquakes occurred along the Xiaojiang fault system in the past ∼ 500 years; the largest one was the 1833 M 8.0 Songming earthquake on the central segment of the Xiaojiang fault (Fig. 1a) (Shen et al., 2003; Wen et al., 2008). After the 1850 M 7.5 Xichang earthquake (Fig. 1a), three M 6.5–6.8 earthquakes occurred on this fault system in 1909, 1952, and 1966 (e.g., Wen et al., 2008). 3. Model setup We have developed a three-dimensional viscoelastoplastic finite element model (Fig. 2) to explore coseismic and postseismic Coulomb stress changes by the 2008 Great Wenchuan earthquake and numerous previous large earthquakes (Table 2) on the neighboring faults. We also use this model to investigate fault interactions in the eastern Tibetan Plateau. 3.1. Model domain and boundary conditions To simulate regional stress evolution, stress perturbations by earthquakes, and possible fault interactions, we included the Longmen Shan fault and other major faults in the eastern Tibetan Plateau in the model (Fig. 2) and calculated the background stress field from tectonic and topographic loading. The model consists of two rheological layers: a brittle top layer (the schizosphere) representing the seismogenic upper crust, and a viscoelastic lower layer (the plastosphere) representing the ductile lower crust and upper mantle. Because the viscosity of the lower crust and upper mantle is not well constrained, we use this simplified plastospheric layer to approximate the total effects of viscous relaxation in the lower crust and upper mantle without explicitly implementing their rheological stratification. In most cases both the schizosphere and the plastosphere are 20km thick, and in some cases a thicker (80 km) plastosphere is used. The fault zones are 2-km thick in the model with simplified geometry, simulated by elastoplastic fault elements (Fig. 2b). The model domain

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2009a,b). Stuart (1979, 1981) derived a strain-softening instability model to fit vertical displacement before and after the 1971 M 6.4 San Fernando earthquake. Yin and Zhang (1982, 1984) derived the elastoplastic constitutive relation of strain softening of fault rocks by decreasing their internal frictional angle and cohesion to model earthquakes. As illustrated in Fig. 3a, when stress reaches the yield value σy0, an earthquake occurs, and strain softening causes plastic strain (coseismic slip) and stress drop. When the earthquake-released stress Δσ or strain Δε reaches the preset values, the earthquake ends and the model switches from coseismic deformation (strain softening) to interseismic locking (elastic loading) towards the next earthquake. Such processes could repeat in seismic cycles (Fig. 3b). We model earthquakes by strain softening within the predefined 2-km thick fault elements. To avoid the influence of arbitrary initial conditions (zero initial stress), we let the model domain be loaded to a quasi-steady state until the regional stress patterns have stabilized and the stress fluctuates around the background stress field as the results of earthquakes. The predicted background stress is validated by its consistency with the regional stress field indicated by earthquake focal mechanisms. Based on the background stress field, we calculate earthquakeinduced stress changes. When modeling specific earthquakes, we use the known seismic moment magnitude to constrain coseismic slip or earthquake-released strain Δε. When modeling synthetic earthquake cycles, we use the Drucker–Prager yield criterion for the initiation of earthquakes, and assume a 4-MPa coseismic stress release (Δσ) for each synthetic event (e.g., Kanamori and Anderson, 1975; Mohammadioun and Serva, 2001). 3.3. Governing equations Fig. 2. (a) Finite element mesh and boundary conditions. The model includes two layers: the brittle upper layer (the schizosphere) and the viscoelastic lower layer (the plastosphere). (b) The simplified fault systems in the model. Dipping angles are 35° for the Longmen Shan fault, 50° for the Min Jiang fault, and 90° for the other faults (see Table 2). Labels are explained in Fig. 1.

The model simulates crustal deformation by solving the equation of force balance: ∂σij

is loaded by relative crustal motion on its lateral boundaries interpolated from GPS velocities (He et al., 2003; Zhang et al., 2004) and by the topographic changes on its surface (Fig. 2a). The bottom of the model domain is free horizontally but fixed vertically. The effects of these boundary conditions are discussed later. 3.2. Simulating earthquakes and seismic cycles In geodynamic models, earthquake can be simulated as the result of strain softening when rocks in the fault zone are loaded to their yield stress (e.g., Pande et al., 1990; Jaeger et al., 2007; Luo and Liu,

∂xj

+ ρgi = 0

ð1Þ

where σij is the stress tensor (i, j = 1, 2, 3), ρ is the density, and g is the gravitational acceleration. Because deformation is mainly caused by non-lithostatic tectonic force, the lithostatic stress is ignored in the model except for the calculations of plastic strain. Following Li et al. (2009), the model calculates over each time step the incremental strain, which may include viscous, elastic, and plastic components: v

e

p

fdεg = fdε g + fdε g + fdε g

ð2Þ

Table 2 Parameters of the earthquake sequence modeled in this study. Event number

1 2 3 4 5 6 7 8 9

Date

1893/08/29 1904/08/30 1920/12/16 1923/03/24 1933/08/25 1955/04/14 1973/02/06 1981/01/24 2008/05/12

Earthquake center/epicenter (°) Lon. E

Lat. N

101.37 101.00 104.90 100.90 103.70 101.84 100.52 101.15 103.364

30.70 31.06 36.70 31.17 32.00 30.03 31.50 30.95 30.986

Magnitude

Host fault

Rupture length (km)

Fault segment dipping angle (°)

Referencea

M 7.2 M 7.0 M 8.5 M 7.2 M 7.5 M 7.5 M 7.6 M 6.9 Mw 7.9

Xianshuihe fault Xianshuihe fault Haiyuan fault Xianshuihe fault Min Jiang fault Xianshuihe fault Xianshuihe fault Xianshuihe fault Longmen Shan fault

70 55 230 60 85b 35 90–105 45 N300

90 90 60–88 90 45–65 75 90 90 30–45

(1–3) (1,2) (4–7) (1,2) (8,9) (1,2) (1–3) (1,2) (10–14)

a (1) Wen et al. (2008); (2) Papadimitriou et al. (2004); (3) Allen et al. (1991); (4) Lee et al. (2003); (5) Zhang et al. (2003a); (6) Fan et al. (2004); (7) Fu et al. (2001); (8) Kirby et al. (2000); (9) Chen et al. (1994); (10) USGS (2008); (11) Zhang et al. (2008); (12) Ji and Hayes (2008); (13) Burchfiel et al. (2008); and (14) Lin et al. (2009). b Estimated from empirical relationships between rupture length and seismic magnitude (Wells and Coppersmith, 1994).

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The plastic strain increments are given as:   ∂G p fdε g = dλ ∂σ

ð8Þ

where dλ is the plastic multiplier, which is related to the Drucker– Prager yield function, plastic potential function, and hardening modulus (e.g., Zienkiewicz and Taylor, 2005; Li et al., 2009). We developed the finite element codes based on the commercial package FEPG (http://www.fegensoft.com). The codes are parallelized; all cases were run on a 16-node dual-processor PC cluster. 3.4. The Coulomb stress change The change of the Coulomb stress on a fault plane, Δσcsc, is given by: Δσcsc = μ′Δσn + Δτ

ð9Þ

where Δσn and Δτ are increments of the normal and shear stresses on the plane; μ′ is the effective frictional coefficient. Positive Δσcsc moves the plane towards failure, and vice versa. Outside the fault, the Coulomb stress change is calculated on optimal planes as described by King et al. (1994). We determine the optimal plane of every node by its total stress field (background stress plus stress perturbations by earthquakes), and then resolve the Coulomb stress change on the optimal plane following Eq. (9). 4. Model results Fig. 3. (a) The elastoplastic constitutive relation. (b) A sketch for stress accumulation and release during seismic cycles. E: the elastic modulus; H: the hardening modulus. See text for details.

where {} represents a vector. For the viscoelastic lower layer, the constitutive relation can be written as: −1

v

t

fdε g = ½Q fσ gdt e −1 fdε g = ½D fdσg

ð3Þ

where [Q] and [D] are material matrices related to viscous and elastic deformation, respectively, {σt} is stress vector at time t; {dσ} is incremental stress vector; dt is time increment (Li et al., 2009; Luo and Liu, 2009a). The strain softening of fault elements associated with coseismic slips is simulated with the Drucker–Prager yield criterion: Fðσ; κÞ =

pffiffiffiffi J2 + αI1 −βðκÞ

2 sinϕ α = pffiffiffi 3ð3 + sinϕÞ  1 6C cosϕ 2 p p 2 + Hκ = pffiffiffi + H ðεi εi Þ βðκÞ = pffiffiffi 3 3ð3 + sinϕÞ 3ð3 + sinϕÞ 6C cosϕ

ð4Þ ð5Þ

pffiffiffiffi J2

4.1. The Great Wenchuan earthquake The coseismic slip of the Great Wenchuan earthquake has been inferred from inversions of seismic waves (e.g., Nishimura and Yagi, 2008; Ji and Hayes, 2008) and geodetic data (e.g., Shen et al., 2009), and used in elastic dislocation models to calculate the coseismic changes of the Coulomb stress (Toda et al., 2008; Parsons et al., 2008). Here we provide a geodynamic simulation of the Great Wenchuan earthquake and the associated Coulomb stress changes. Although in this case the geodynamic model is not better than the kinematic models constrained by the observed coseismic slip, it nonetheless provides some insight into the cause of the rupture and the controls on the coseismic slip. In our model the coseismic deformation is constrained by the seismic moment release: n

ð6Þ

where I1 is the first invariant of stress tensor, J2 is the second invariant of deviatoric stress tensor, α and β(κ) are parameters of the Drucker– Prager yield criterion, related to cohesion (C), internal frictional angle (Φ) and effective plastic strain (κ), and H is the hardening modulus. Here we assume linear strain softening. The term ɛpi ɛpi (i = 1, 2, …, 6) in Eq. (6) submits to the Einstein summation convention. Using the plastic potential function (non-associated plastic flow rule):

G=

Using this viscoelastoplastic geodynamic model, we have explored (1) the coseismic and postseismic Coulomb stress changes associated with the Great Wenchuan earthquake, (2) additional stress perturbations from some of the large earthquakes in the region since 1893, and (3) fault interactions between the Xianshuihe fault and the Longmen Shan fault.

ð7Þ

M0 = ∑ Gs Ai Si

ð10Þ

i=1

where M0 is seismic moment; n is the number of predefined fault elements in the model; Gs is shear modulus for fault elements; Ai and Si are area and average coseismic slip for this fault element. The predicted coseismic slip shows both thrust and right-lateral components (Fig. 4a). These results are determined by the background stress field, which is controlled by the tectonic and topographic loading. The general pattern is comparable to those inverted from seismic (e.g., Nishimura and Yagi, 2008; Ji and Hayes, 2008) and geodetic data (e.g., Shen et al., 2009). The northeastward coseismic slip pattern inferred from the seismological and geodetic inversions and predicted in our model, is the consequence of the

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significantly impact slip distribution, as suggested in previous studies (e.g., Chester and Chester, 2000; Li and Liu, 2006; Marshall et al., 2008). To better illustrate the impact of fault geometry, we replaced the Longmen Shan fault with a straight fault plane, and found relatively uniform coseismic slip (Fig. 5a) and stress distribution (Fig. 5b). The small variations of the coseismic slip and shear stress in Fig. 5 may be attributed to non-uniform lateral tectonic and topographic loading. Thus the three-dimensional fault geometry can have an important impact on coseismic displacement, hence earthquake damage. Fig. 6 shows our calculated coseismic Coulomb stress changes due to the Great Wenchuan earthquake. The Coulomb stress increased by ∼0.01–0.05 MPa on the southeastern segments of the Xianshuihe fault, ∼ 0.02–0.05 MPa on the eastern Kunlun fault and the northern Min Jiang fault, ∼ 0.1–1 MPa near the two tips of the ruptured Longmen Shan fault, and ∼ 0.01–0.02 MPa on the eastern Haiyuan fault. The pattern remains similar for a range of effective friction coefficients and at different depths (Fig. 7). Our results are similar to those from elastic dislocation models (Toda et al., 2008; Parsons et al., 2008), except that the lobes of stress increases are broader in our model. Our results also show decrease of coseismic Coulomb stress by

Fig. 4. Predicted coseismic slip (a) and background shear stress (b) on the Longmen Shan fault for the Great Wenchuan earthquake. Viscosity for the plastosphere is 1 × 1019 Pa s under the Tibetan Plateau and the Qinling Mountain, and 1 × 1023 Pa s under other regions.

oblique convergence between the eastern Tibetan Plateau and the Sichuan Basin along the Longmen Shan fault (Fig. 1a). Note that the predicted coseismic slip has two maxima, similar to those from seismological and geodetic inversions (e.g., Ji and Hayes, 2008; Shen et al., 2009). In our model the uneven distribution of coseismic slip is mainly due to the bend of the simplified Longmen Shan fault in the model (Fig. 2b). The bend in the fault causes localized stresses (Fig. 4b). These results show that fault geometry can

Fig. 5. Predicted coseismic slip (a) and background shear stress (b) for the Great Wenchuan earthquake, assuming a flat fault plane for the Longmen Shan fault. Viscosity structure is the same as Fig. 4.

Fig. 6. Predicted coseismic Coulomb stress change on the optimal planes at 10-km depth (a) and on the actual fault planes (b). Heavy white line shows the ruptured segment of the Longmen Shan fault during the 2008 Wenchuan earthquake. Labels are explained in Fig. 1. Effective frictional coefficient is 0.4. This case is the same as Fig. 4. Coulomb stress change is capped at ± 0.1 MPa on the scale bar.

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Fig. 7. Predicted coseismic Coulomb stress change with variable effective frictional coefficients (μ′) on the optimal planes at different depths (a–d) and on the actual fault planes (e and f). Heavy white lines show coseismic rupture of the 2008 Wenchuan earthquake. Labels are explained in Fig. 1. This case is the same as Figs. 4 and 6. Coulomb stress change is capped at ± 0.1 MPa on the scale bar.

∼ 0.01–0.06 MPa on the Anninghe fault, contrasting to negligible stress changes there in the previous models (Toda et al., 2008; Parsons et al., 2008). Some of the differences may be attributed to how background stress and optimal planes are treated in these models. Outside the faults in the model, the change of Coulomb stress is calculated for the

“optimal plane” (e.g., King et al., 1994). Elastic dislocation models do not include the background stress, and the optimal planes are determined from an assumed regional stress field (e.g., King et al., 1994) and by interpolating the observed and known fault geometry and rakes (Toda et al., 2008). In our model the background stress are determined by the combined topographic and the tectonic loading,

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and the optimal planes are determined jointly by the background stress field and the coseismic stress changes, as described in Section 3.4. Postseismic stress changes due to viscous relaxation following a large earthquake may trigger other earthquakes (e.g., Freed and Lin, 2001; Freed, 2005). Hence we predicted the change of Coulomb stress in the near future. The results in Fig. 8 are the total Coulomb stress changes from postseismic viscous relaxation and interseismic loading, in addition to the coseismic stress changes. The results indicate that, in the next 100 years, the Coulomb stress will be restored on the northwestern Xianshuihe fault and the Anninghe fault where coseismic Coulomb stress decreased (Fig. 8), but the ruptured Longmen Shan fault will stay in stress deficiency. Fig. 8b and d show postseismic stress relaxation in the plastosphere and gradual stress recovering in the schizosphere on the Longmen Shan fault. As stated in Section 3.1, postseismic viscous relaxation likely occurs in both the lower crust and the upper mantle, which are collectively represented by a single layer of the plastosphere due to the lack of details of the rheological structure. We varied the thickness of this viscous layer and

the boundary conditions at the bottom, and the results are similar over the timescale considered here. 4.2. Impacts of previous earthquakes Because large earthquakes can perturb the regional stress field and trigger earthquakes in the neighboring region (e.g., King et al., 1994; Stein et al., 1997; Stein, 1999; Lin and Stein, 2004), it is proper to examine the 2008 Wenchuan earthquake and the associated Coulomb stress changes in the context of earthquake history in eastern Tibet, where large earthquakes were numerous in the recent history (Fig. 1a). Here we explore the potential impact of previous large earthquakes on the Great Wenchuan earthquake. Eight large earthquakes since 1893 are selected for their proximity to the Longmen Shan fault; six of them occurred on the Xianshuihe fault (Fig. 1a and Table 2). The sequence of these eight earthquakes and the 2008 Wenchuan event (Table 2) was simulated. We used seismic moment of these earthquakes to constrain the amount of strain softening and stress

Fig. 8. Predicted Coulomb stress changes on the optimal planes at 10-km depth (a) and on the actual fault planes (b) 20 years after the 2008 Wenchuan earthquake. c and d same as a and b, but 100 years after the Wenchuan earthquake. Labels are explained in Fig. 1. Effective frictional coefficient is 0.4. Viscosity structure is the same as Fig. 4. Note the non-linear scale bar. Coulomb stress change is capped at ± 1.0 MPa on the scale bar.

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release for each event, as described in Section 4.1. Interseismic loading and postseismic viscous relaxation are also included. Fig. 9 shows the cumulative Coulomb stress changes immediately before and after the 1933 M 7.5 Diexi earthquake. The results before the Diexi earthquake include four earthquakes since 1893. The biggest one was the 1920 M 8.5 Haiyuan earthquake. Their impact on the Longmen Shan fault, however, was insignificant (Fig. 9a and b). In contrast, the 1933 M 7.5 Diexi earthquake, which occurred on the nearby Min Jiang fault, had more impact on the Longmen Shan fault (Fig. 9c and d). Between 1955 and 1981, three large earthquakes occurred on the Xianshuihe fault (Fig. 1a). Whereas these events had a major impact on the Xianshuihe fault, their influence on the Longmen Shan fault was limited (Fig. 10a and b). The impact of the 2008 Wenchuan earthquake on the neighboring faults, when calculated in the context of the sequence of regional earthquakes since 1893 (Fig. 10c and d), namely the cumulative Coulomb stress change, differs from the coseismic Coulomb stress changes due to the Great Wenchuan earthquake as shown in Fig. 6 and

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in previous studies (Toda et al., 2008; Parsons et al., 2008). While the 2008 Wenchuan earthquake increased the Coulomb stress on southeastern segments of the Xianshuihe fault (Fig. 6), the stress increase was small relative to stress released on these fault segments from the six large earthquakes since 1893, so the southeastern Xianshuihe fault stays in stress deficiency (Fig. 10c and d) after the 2008 Wenchuan earthquake. Consequently, earthquake risk on the southeastern Xianshuihe fault is lower than that estimated from the stress changes due to the 2008 Wenchuan earthquake alone. Other noticeable differences from the results in Fig. 6 include less impact of the 2008 Wenchuan earthquake on the Anninghe fault. The higher Coulomb stress changes in Figs. 9 and 10 result from continued tectonic loading since 1893; the stress variations along the western side of the model domain are due to the uneven boundary velocities, simplified from the GPS velocity field. The impact of each earthquake may be better appreciated from Fig. 11, which shows how the sequence of earthquakes changed the Coulomb stress on selected segments of the Xianshuihe and the

Fig. 9. Predicted Coulomb stress evolution from 1893 to 1933. a and b: Coulomb stress evolution on the optimal planes at 10-km depth and on the actual fault planes before the 1933 Diexi earthquake. c and d: Coulomb stresses after the 1933 Diexi earthquake. Heavy white and gray lines show coseismic ruptures of associated earthquakes. Labels are explained in Fig. 1. Effective frictional coefficient is 0.4. Viscosity for the plastosphere is 2 × 1020 Pa s under the Tibetan Plateau and the Qinling Mountain, and 1 × 1023 Pa s under other regions. Coulomb stress change is capped at ±0.5 MPa on the scale bar.

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Fig. 10. Predicted Coulomb stress evolution from 1893 to 2008. a and b: Coulomb stress evolution on the optimal planes and the fault planes before the 2008 Wenchuan earthquake. c and d: Coulomb stresses after the 2008 Wenchuan earthquake. Black points in d are selected locations to show continuous stress evolution in Figs. 11 and 13. Heavy white and gray lines show coseismic ruptures of associated earthquakes. Labels are explained in Fig. 1. Effective frictional coefficient is 0.4. Viscosity structure is the same as Fig. 9. Coulomb stress change is capped at ± 0.5 MPa on the scale bar.

Longmen Shan faults (see points A, B and C in Fig. 10d). The results show that, whereas large earthquakes may affect the neighboring faults, the dominant impact is on the host fault. For the Xianshuihe fault, the stress increase by the 2008 Wenchuan earthquake is much less than that released by previous earthquakes on the Xianshuihe fault. These earthquakes on the Xianshuihe fault, conversely, had little impact on the Longmen Shan fault. Because of its proximity to the Longmen Shan fault, the 1933 M 7.5 Diexi earthquake increased the Coulomb stress by ∼0.02–0.03 MPa on the segment of Longmen Shan fault ruptured during the 2008 earthquake (Fig. 11b). The major impact of the 2008 Wenchuan earthquake is on the Longmen Shan fault: more than 2 MPa decrease on the ruptured segment (Fig. 11b) and more than 0.1 MPa increase on the southern unruptured segment (Fig. 11c). 4.3. Fault interactions in Eastern Tibet We have shown that the impact of the 2008 Wenchuan earthquake on the neighboring Xianshuihe fault is small relative to the stress

perturbations by the recent earthquakes on the Xianshuihe fault. Does this mean that seismicity on one of the faults in eastern Tibet has nothing to do with the neighboring faults? To address this question, we investigated how seismicity on the Xianshuihe fault may affect the loading rates on the Longmen Shan fault. As shown in Fig. 1a, the Xianshuihe fault is a major strike-slip fault accommodating the east-southeast extrusion of the Tibetan lithosphere; the slip rate on the Xianshuihe fault is one order of magnitude higher than that on the Longmen Shan fault. When the Xianshuihe fault is locked, the crust north of the fault presumably would be dragged eastward by the faster moving crust south of the Xianshuihe fault, hence increasing the loading on the Longmen Shan fault. We simulated a synthetic history of stress evolution and earthquakes on the Xianshuihe fault to see how the loading rates on the Longmen Shan fault may be affected. We divided the Xianshuihe fault into 7 segments, roughly following its recent rupture history (Allen et al., 1991; Wells and Coppersmith, 1994; Papadimitriou et al., 2004; Wen et al., 2008), and simulated seismic cycles of these segments.

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When the Xianshuihe fault is locked, accumulation of the Coulomb stress on the Longmen Shan fault is up to ∼ 50 Pa/year faster than the long-term average (Fig. 14a and b); during the periods of clustered earthquakes on the Xianshuihe fault, the loading on the Longmen Shan fault is lower than the long-term average (Fig. 14c and d). The Xianshuihe fault has been locked since 1981, which could have caused ∼0.001 MPa additional Coulomb stress to the Longmen Shan fault when the 2008 Wenchuan earthquake occurred. This amount of stress change is likely too low to be a meaningful contribution to the Great Wenchuan earthquake. On the other hand, because the long-term loading rate on the Longman Shan fault is low (∼250 Pa/year, see Fig. 13), seismic activity on the Xiashuihe fault causes up to ∼20% fluctuation of the loading rate on the Longmen Shan fault, hence indicating significant mechanical coupling between these two faults. These values are dependent on the assumed effective frictional coefficient of the faults in the model. Because locking on the Xianshuihe fault increases both shear and normal stresses on the Longmen Shan and the Min Jiang faults, a higher frictional coefficient causes larger contribution from compressive normal stress, hence lowering the Coulomb stress on the Longmen Shan fault (Eq. (9)), and even leading to negative Coulomb stress change on the Min Jiang fault (Fig. 14b). On the western Haiyuan fault and the eastern Kunlun fault, the accumulation rates of the Coulomb stress increase when the effective frictional coefficient is higher (Fig. 14a and b), because locking on the Xianshuihe fault can induce extensional normal stress on these faults; the opposite is true during the periods of clustered earthquakes on the Xianshuihe fault (Fig. 14c and d). 5. Discussion

Fig. 11. Predicted Coulomb stress evolution since 1893 for selected points on (a) the Xianshuihe fault, (b) the central Longmen Shan fault, and (c) the southern Longmen Shan fault. The locations of these points are shown in Fig. 10d. Labels are explained in Fig. 1. Effective frictional coefficient is 0.4. This case is the same as Figs. 9 and 10.

Each synthetic earthquake is simulated with a 4-MPa stress drop (e.g., Kanamori and Anderson, 1975; Mohammadioun and Serva, 2001); the modeling processes are described in Sections 3.2 and 3.3. The synthetic seismicity on the Xianshuihe fault shows irregular temporal distribution, with clusters over ∼ 100 years separated by relatively quiescent periods of ∼100–500 years (Fig. 12). During the periods of seismic quiescence, the Xianshuihe fault is locked, and the loading rates on the Longmen Shan fault and other neighboring faults are the highest (Figs. 13 and 14). Conversely, during the periods of clustered earthquakes on the Xianshuihe fault, the loading rates on the Longmen Shan and other neighboring faults are the lowest. Fig. 13 shows the predicted accumulation of the Coulomb stress at a selected point (point D in Fig. 10d, near the earthquake source region of the 2008 Wenchuan earthquake) on the Longmen Shan fault during three different periods of seismicity on the Xianshuihe fault. During the periods of interseismic locking on the Xianshuihe fault, the loading rate on the Longmen Shan fault is ∼20 Pa/year higher than the longterm average and ∼ 40 Pa/year higher than that during the periods of clustered earthquakes. Fig. 14 shows how loading rates on the Longmen Shan fault and other faults fluctuate from the long-term average when the Xianshuihe fault is locked or in the periods of clustered earthquakes.

Shortly after the Great Wenchuan earthquake, its effects on the regional Coulomb stress were calculated using elastic dislocation models with coseismic slip inferred from seismic and geodetic data (e.g., Toda et al., 2008; Parsons et al., 2008). The geodynamic model presented here is not better than these previous models in calculating the coseismic stress changes due to the Wenchuan earthquake, but it allows the impact of the Wenchuan earthquake to be studied in the context of stress perturbations of all major earthquakes in the region. It also provides useful insights into the cause of the rupture of the Wenchuan earthquake. For example, the northeastward coseismic slip of the Great Wenchuan earthquake may have spared Chengdu, the provincial capital located less than 100 km from the epicenter (Fig. 1a), from catastrophic damage. In our model the northeastward coseismic slip can be explained by the oblique convergence between the Tibetan Plateau and the Sichuan Basin (Fig. 1a). The background stress dictates that, when the Longmen Shan fault ruptures, the Tibetan crust would move up and northeastward along the fault. Our predicted coseismic slip of the Great Wenchuan earthquake is comparable with that inverted from seismic and geodetic data (e.g., Nishimura and Yagi, 2008; Ji and Hayes, 2008; Shen et al., 2009). The predicted two areas of peak displacement (Fig. 4), similar to those in the inferred coseismic slip, are where the Longmen Shan fault bends. These results suggest that fault geometry can affect coseismic slip pattern (e.g., Chester and Chester, 2000; Marshall et al., 2008). On the other hand, the three-dimensional geometry of the Longmen Shan has not been clearly mapped in detail (e.g., Burchfiel et al., 2008), and the Longmen Shan fault in our model is necessarily simplified. Including the sequences of recent large earthquakes in eastern Tibet allows a better assessment of the stress impact of the Great Wenchuan earthquake and the associated earthquake risks in eastern Tibet. Particularly noteworthy is the Xianshuihe fault, where six M ≥ 6.9 earthquakes occurred since 1893, but has been quiescent since 1981. Because of its high slip rates and frequent earthquakes, the Xianshuihe fault has been the focus of attentions of the seismological communities (Allen et al., 1991; Zhang et al., 2003b; Papadimitriou et al., 2004; Wang et al., 2008; Wen et al., 2008). The Great Wenchuan

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Fig. 12. Synthetic seismicity on the Xianshuihe fault. Inset is a selected series of the synthetic seismicity showing the periods of clustered earthquakes and seismic quiescence. Viscosity for the plastosphere is 1 × 1022 Pa s under the Tibetan Plateau and the Qinling Mountain, and 1 × 1023 Pa s under other regions. Cohesion and internal frictional angle are 40 MPa and 5°, respectively.

earthquake may have brought the southeastern Xianshuihe fault closer to failure, as shown in Fig. 6 and by previous studies (Toda et al., 2008; Parsons et al., 2008). However, stress increase from the Great Wenchuan earthquake is insufficient to compensate for the stress released from the previous earthquakes on the Xianshuihe fault (Figs. 10 and 11a), hence the earthquake risk on the southeastern Xianshuihe fault is lower than that estimated from the impact of the Wenchuan earthquake alone (Toda et al., 2008; Parsons et al., 2008). In the model we assumed that the six earthquakes completely ruptured these segments of the Xianshuihe fault. Some recent studies (e.g., Wen et al., 2008) suggested that a ∼20–30 km long segment of the Xianshuihe fault between the 1893 and 1981 ruptured segments has never been ruptured since 1893, if so this part of the Xianshuihe fault would be most likely to rupture in the near future, but the

Fig. 13. Predicted Coulomb stress accumulation at a selected point on the Longmen Shan fault (location shown in Fig. 10d) during the periods of interseismic locking (heavy black line), long-term average (gray line), and clustered earthquakes (dashed black line) on the Xianshuihe fault. Effective frictional coefficient is 0.4. This case is the same as Fig. 12.

resulting earthquake would be limited by the length of this fault segment. In addition to static Coulomb stress changes associated with stress release on the ruptured fault segment, a large earthquake may affect other faults or fault segments in many other ways. Dynamic Coulomb stress change, caused by the passage of transient seismic waves, may directly lead to fault rupture in both near-fault and remote regions or induce other mechanisms, such as changing fluid pressure (Hill et al., 1993; Kilb et al., 2000, 2002; Prejean et al., 2004; Freed, 2005). The transient dynamic Coulomb stress change can be one order of magnitude larger than static Coulomb stress change (e.g., Kilb et al., 2002). Time-dependent processes following a large earthquake, such as afterslip, poroelastic stresses, viscous relaxation, and rate-state frictional property changes, may all lead to delayed earthquake triggering (Toda et al., 1998; Peltzer et al., 1998; Zeng, 2001; Freed and Lin, 2001; Toda and Stein, 2003; Freed, 2005; Piombo et al., 2005; Ge et al., 2009). In this study, we considered only static Coulomb stress change and postseismic viscous relaxation. In eastern Tibet, the Indo–Asian collision is accommodated collectively by slip on a network of faults, including the Longmen Shan fault. Hence we have reason to speculate that these faults are kinematically and mechanically coupled. The mechanical interactions between these neighboring faults, however, are poorly understood and probably vary for different timescales. What we explored in this work is mechanical fault interaction that varies over multiple seismic cycles, assuming constant slip rates on each fault, hence no kinematic coupling between faults. Over longer timescales, faults are likely kinematically coupled as well, with secular variations of slip rates on one fault affecting the others. Within the timescale of seismic cycles, or thousands of years, we found that interseismic locking of the Xianshuihe fault can cause additional stress to the Longmen Shan fault and other major faults in eastern Tibet by up to ∼50 Pa/year. This is roughly 20% of the long-term averaged loading rates on the Longmen

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Fig. 14. Fluctuations of loading rates on the regional faults when the Xianshuihe fault is locked (a and b) or in a period of clustered earthquakes (c and d) relative to the long-term average loading rates. The results also show the effects of effective frictional coefficient. Labels are explained in Fig. 1. This case is the same as Figs. 12 and 13. The rates of Coulomb stress accumulation are capped at ± 50 Pa/year on the scale bar.

Shan fault, indicating significant mechanical coupling between these faults during seismic cycles. 6. Conclusions We have developed a three-dimensional viscoelastoplastic geodynamic model to explore Coulomb stress changes before and after the 2008 Great Wenchuan earthquake. Our major conclusions include the following: 1) The 2008 Wenchuan earthquake may have brought most major faults in the eastern Tibet closer to failure: ∼ 0.01–0.05 MPa on the southeastern Xianshuihe fault, ∼ 0.02–0.05 MPa on the eastern Kunlun fault and the northern Min Jiang fault, and ∼0.1–1 MPa on the two tips of the ruptured Longmen Shan fault. Coulomb stress will continue to increase on these fault segments by postseismic viscous relaxation and continued tectonic loading. 2) The full impact of the Great Wenchuan earthquake needs to be examined together with other large earthquakes in the region. The 1933 M 7.5 Diexi earthquake, because of its proximity to the segment of the Longmen Shan fault ruptured in 2008, may have contributed to the Great Wenchuan earthquake, but contribution from other large earthquakes in eastern Tibet during the past century is negligible. Conversely, the stress increase on the southeastern Xianshuihe fault from the Great Wenchuan earthquake is minor in comparison to stress decreases from six large earthquakes on this fault since 1893. Consequently, the southeastern segments on the Xianshuihe fault stay in stress deficiency, and the seismic risk is lower than that based on the impact of the Great Wenchuan earthquake alone. 3) Seismicity on the Xianshuihe fault and other major faults in eastern Tibet may affect the loading rates on the Longmen Shan fault and other faults. When the Xianshuihe fault is locked, the

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