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Mengkui Li, Shuangxi Zhang, Chaoyu Zhang, Yu Zhang. Fault slip model of 2013 Lushan Earthquake retrieved based on GPS coseismic displacements. Journal of Earth Science, 2015, 26(4): 537-547. doi: 10.1007/s12583-015-0557-4
Citation: Mengkui Li, Shuangxi Zhang, Chaoyu Zhang, Yu Zhang. Fault slip model of 2013 Lushan Earthquake retrieved based on GPS coseismic displacements. Journal of Earth Science, 2015, 26(4): 537-547. doi: 10.1007/s12583-015-0557-4

Fault slip model of 2013 Lushan Earthquake retrieved based on GPS coseismic displacements

doi: 10.1007/s12583-015-0557-4
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  • Corresponding author: Shuangxi Zhang, shxzhang@sgg.whu.edu.cn
  • Received Date: 13 Aug 2014
  • Accepted Date: 26 Dec 2014
  • Publish Date: 12 Aug 2015
  • Lushan Earthquake (~Mw 6.6) occurred in Sichuan Province of China on 20 April 2013, was the largest earthquake in Longmenshan fault belt since 2008 Wenchuan Earthquake. To better understand its rupture pattern, we focused on the influences of fault parameters on fault slips and performed fault slip inversion using Akaike's Bayesian Information Criterion (ABIC) method. Based on GPS coseismic data, our inverted results showed that the fault slip was mainly confined at depths. The maximum slip amplitude is about 0.7 m, and the scalar seismic moment is about 9.47×1018 N·m. Slip pattern reveals that the earthquake occurred on the thrust fault with large dip-slip and small strike-slip, such a simple fault slip represents no second sub-event occurred. The Coulomb stress changes (ΔCFF) matched the most aftershocks with negative anomalies. The inverted results demonstrated that the source parameters have significant impacts on fault slip distribution, especially on the slip direction and maximum displacement.

     

  • The 2013 Mw 6.6 Lushan Earthquake occurred in Sichuan Province of China. It is the largest earthquake event along the Longmenshan fault belt since 2008 Wenchuan Earthquake. According to the measurement of China Earthquake Networks Center (CENC), the hypocenter of this earthquake is located at (30.3ºN, 103.0ºE) and at 13 km in depth (Fig. 1). It occurred in the southwest part of Longmenshan fault zone, located at about 80 km to the southwest of the epicenter of 2008 Wenchuan Earthquake. Hundreds of aftershocks occurred after the mainshock, and the largest aftershock is about Mw 5.5 (Feng et al., 2013). The white circles in Fig. 1 represent the aftershocks of Lushan Earthquake. The source parameters, fault rupture process were soon studied after the occurrence based on teleseismic waveforms (Liu et al., 2013; Zeng et al., 2013), jointed inversion of teleseismic and near-field seismograms (Han et al., 2014; Zhang et al., 2014; Hao et al., 2013; Zeng et al., 2013), as well as geological survey (Xu et al., 2013). All the results of the focal mechanisms and slip models retrieved the similarities that Lushan Earthquake occurred on a thrust fault with a large dip-slip component and small strike-slip component. Global Centroid Moment Tensor (GCMT) solution (http://www.globalcmt.org) reveals a nearly pure thrust motion of the focal mechanism. While, some differences are obvious in the inverted results of hypocenter, centroid depth, fault dip angle, and rake angle (Chen et al., 2013). These distinctions are mainly caused by different observed data, errors in earth structure, and inversion methods adopted (Jiang et al., 2014; Chen et al., 2013).

    Figure  1.  Location of the 2013 Lushan Earthquake with focal mechanism derived from GPS coseismic displacements (Jiang et al., 2014). The yellow star indicates the epicenter determined by CENC. The black triangles represent the GPS sites with site names nearby (a). White circles represent the aftershocks relocated by Feng et al. (2013). The green lines AA', BB' and CC' are three cross-section profiles for the calculations of Coulomb stress changes (b).

    There are increasing observation data available to invert focal mechanisms and fault slip distributions. Teleseismic waveforms are traditional data source to invert the focal mechanism and fault slip distribution for far distance, but their resolution is limited (Xu and Wang, 2010). Geodetic data, such as GPS and InSAR, can provide independent near-source constraints on focal parameters and fault rupture models (Feng et al., 2013; Weston et al., 2012; Xu et al., 2010; Funning et al., 2007; Funning, 2005). Slip models retrieved from teleseismic data alone (Liu et al., 2013; Zhang et al., 2013) and joint inversion of teleseismic and strong motion data (Hao et al., 2013) were soon proposed after the occurrence of this event. Recently, Jiang et al. (2014) published their slip model based on 3D GPS coseismic displacements. Though all of these models revealed the thrust-motion characteristic of this earthquake, they still have differences in slip pattern and maximum slip displacements. Except the different datasets they used, focal mechanisms may also contribute a lot to the differences.

    The authors tried to evaluate the influences of fault parameters on the fault slips, and the aftershocks' triggering by calculating the Coulomb stress changes caused by the main event. The same dataset as Jiang et al. (2014) was used in the inversions. The authors first invert the fault slip distribution based on 3D GPS coseismic displacements. The combination of the Akaike's Bayesian Information Criterion (ABIC; Funning et al., 2014; Fukahata, 2003; Yabuki and Matsu'ura, 1992) and a fast non-negative least-squares algorithm (FNNLS; Bro and De Jong, 1997) are adopted. The smoothing weight factor of the spatial smoothing constraint is obtained by minimizing the ABIC values. This method is more objective than "L-curve" method, which determines an optimal smoothing parameter by balancing data fitness and model roughness (Wright et al., 2004; Jónsson et al., 2002). Then, four fault slip models corresponding to four different focal mechanisms are compared to evaluate the influence of source parameters on the fault slips. Finally, based on our preferred inverted slip model, the Coulomb stress changes (△CFF) at different depths are calculated to evaluate its influence on the occurrence and patterns of aftershocks.

    The GPS coseismic displacements were collected from 33 GPS stations, which fully covering the epicenter of Lushan Earthquake and provide good azimuthal coverage for fault slip inversion. As shown in Fig. 1, black triangle indicates the location of the stations. These stations belong to three networks: the Tectonic and Environmental Observation Network of China, a regional network operated by Sichuan Earthquake Administration and a local network operated by the Institute of Earthquake Science, China Earthquake Administration. All the GPS data were processed using the GAMIT/GLOBK software package within the reference frame ITRF2008. The horizontal and vertical displacements are shown in Fig. 2 (blue arrows). Small error ellipse corresponds to good quality of measurement data. Obviously, near-field GPS stations have better data quality than far-field GPS stations. The horizontal coseismic displacements have better data quality than the vertical components. The full coverage data provide perfect constraints for the slip model inversion. GPS data processing refers to the works of Jiang et al. (2014).

    Figure  2.  Comparison of observed (blue arrows) with model-based synthetic (red arrows) coseismic displacements. (a) Horizontal component; (b) vertical component. The error-ellipses and gray error-bars represent the uncertainties of horizontal and vertical GPS-observed displacements with 95% confidence levels. Black arrows in (a) and (b) are length scales of displacement, both observed and synthetic displacements having the same length scale.

    Given source parameters and fault plane size, fault slip can be obtained by linear inversion based on geodetic deformation data (Funning, 2005; Jónsson et al., 2002). The fault plane is divided into a number of small patches; each of them is treated as a uniformed cell. The total slip on each patch is projected into two orthogonal components. The next goal is to obtain the slip displacement (amplitude) of each patch. Assuming that there are I patches along strike direction and J patches along dip direction, and then there are a total of I×J mosaic patches covering the fault plane. Then, the coseismic displacement caused by an earthquake is the summation of the responses of all the individual patches. Let d be an N-dimensional vector of observed coseismic displacement, and a denotes the M-dimensional unknown parameter vector, where M=2IJ. The observed coseismic displacement can be related to the fault slip by following stochastic model

    d=Ga+e (1)

    where G is an N×M kernel matrix or Green's function matrix that relates the slip of each individual patch to the predicted displacements. There are many methods that can be used to calculate the Green's function G under 1-D earth model, for example, the infinite homogeneous half space and layered earth model (Wang et al., 2003; Okada, 1985), the spherically layered and self-gravitational model (Sun et al., 1996) and spherically layered model (Pollitz, 1996). a is a vector containing the estimated slips in the two orthogonal directions of each patch. e is the error vector consisting of observation errors and modeling errors due to the simplified earth structure and inelasticity property etc. (Duputel et al., 2014, 2012; Yagi and Fukahata, 2008). Since the actual total error is unknown, we assume the error term e to be Gaussian distributed with zero mean and covariance σ2E, e~N(0, σ2E). Here σ2 is an unknown scale factor accounting for the modeling errors due to the imperfect earth structure, and E is the covariance matrix of observation constructed by the formal uncertainties of the observed coseismic displacements. Thus, the mathematical relation between the observed data d and the unknown model parameters a can be expressed by probability density

    p(da,σ2)=(2πσ2)N/2|E|1/2×exp[12σ2(dGa)TE1(dGa)] (2)

    where |E| represents the determinant of the matrix E.

    It is noted that a spatial smoothing constraint is needed to handle realistic fault slip inversion (Funning, 2005; Yabuki and Matsu'ura, 1992). If there is no constraint, the derived slip model may oscillate in spatial space, causing extreme large local stresses gradients (Funning et al., 2014). In the present study, we apply a second-order Laplacian smoothing constraint to minimize the slip gradients between the adjacent patches, following the strategy of Jónsson et al. (2002). The spatial smoothing constraint can be expressed as a linear stochastic model

    Sa+es=0 (3)

    where S is an M×M matrix represents the approximation of the Laplacian operator. es is the error vector which follows a Gaussian distribution with zero mean and covariance α2I, es~N(0, α2I), where I is a unit matrix. The prior information can be rewrite as the following probability density function (PDF) (Yagi and Fukahata, 2008; Yabuki and Matsu'ura, 1992)

    p(a;α2)=(2πα2)M/2|GS|12exp(12α2aTGSa) (4)

    where GS=STS, |GS| is the determinant of matrix GS. α2 is a hyper-parameter controlling the smoothness of the model. According to Bayes' theorem, the posterior probability can be expressed by

    p(a;σ2,β2|d)=c(2πσ2)(N+M)2|E|1/2|β2GS|1/2exp(12σ2s(a)) (5)

    where β2=σ2/α2 is the relative weight of spatial smoothing constraint respect to the data, s(a) represents the data misfit and can be expressed as

    s(a)=(dGa)TE1(dGa)+β2aTGSa (6)

    Based on Eq. (6), the hyper-parameters β2 is a very important hyper-parameter for getting the optimal final slip model, which can be obtained by minimizing the ABIC value (Akaike, 1980), defined as

    ABIC=2logL(σ2,β2|d) (7)

    where L(σ2, β2|d) is marginal likelihood for hyper-parameters and can be given as

    L(σ2,β2|d)=p(a;σ2,β2|d)da (8)

    Equations (7) and (8) are the basic forms of ABIC (Funning et al., 2014; Fukahata, 2003; Yabuki and Matsu'ura, 1992). By further derivation, Eq. (7) can be reformed as

    ABIC(β2)=Nlogs(a)log|β2GS|+log|GTE1G+β2GS|+log|E|+C (9)

    where C is a constant that has no relation to the hyper- parameters. For simplification, the value of C is set to be zero. The data covariance matrix E can be constructed by the formal uncertainties of observed data and is unchanged during inversion process; the term log|E| can also be ignored. So the remaining task is to determine the optimal value of β2 by minimizing ABIC. The best-fitting model can be given by

    a=(GTE1G+β2GS)1GTE1d (10)

    And the estimation of σ2 is in the term of σ2= s(a*)/N. The corresponding posterior covariance of the model parameters is determined by

    C=σ2(GTE1G+β2GS)1 (11)

    The uncertainty of the slip distribution can be measured by the square roots of the diagonal elements of posterior covariance C. This method was recently extended for joint inversion of rupture process using both seismic and geodetic data (Funning et al., 2014).

    To obtain the fault slip model, we assume that the rupture occurs on a single rectangular fault plane with strike 208º, dip angle 43º and centroid depth 13.5 km (Jiang et al., 2014). The location of the centroid is located at (102.938ºE, 30.295ºN). Slip angles on each patch are inverted independently. We consider a large enough fault plane size, 48×39 km2, and the top edge reaches to the ground surface. We then divide the fault plane into 16×13 sub-fault patches with dimensions of 3×3 km2. For each patch, according to the rake angle of the point source model (~81º), its slip is divided into two orthogonal slip directions, one is 45º and the other is 135º. The slip amplitudes are independently inverted in the two slip directions, respectively. The total number of unknown model parameters is doubled as 2×16×13. Based on the layered structural model (Table 1) by Hao et al. (2013), the EDGRN/EDCMP software package (Wang et al., 2003) is adopted to calculate the Green's functions. In order to prevent reversals in slip, we use FNNLS method (Bro and De Jong, 1997) to obtain the best-fitting model. Then the slip direction of the fault slip is effectively bounded between 45º and 135º, which are consistent with the point-source focal mechanism.

    Table  1.  Crustal velocity model from Hao et al. (2013), which was modified from Zhao et al. (1997)
    VP (km/s) VS (km/s) ρ (g/cm3) Depth (km)
    4.88 2.86 2.55 3
    5.80 3.40 2.70 5
    6.04 3.55 2.75 14
    6.82 3.98 2.90 21
    7.61 4.45 3.10 25
    8.08 4.47 3.38 100
    VP, VS, ρ and depth represent velocity of P-Wave, velocity of S-Wave, density and thickness of each layer, respectively.
     | Show Table
    DownLoad: CSV

    As shown in Eq. (9), the ABIC is the only function of the hyper-parameter β2. For the convenience of following discussions, logarithmic coordinate system of ABIC-β2 is preferred. We search β2 in a large range with a coarse spacing in initial stage and then reduce the searching range with a finer spacing. The curves of ABIC versus β2 are shown in Fig. 3. It reaches to the minimum at β2=42.35, which is the optimal value to be chosen. In the case of β2 smaller than the optimal value, ABIC value is near-linearly reversely proportional to β2, which is very similar to the InSAR-only inversion (Funning et al., 2014). While when the value of β2 is larger than the optimal value, the ABIC increases sharply with the increment of β2. Once the optimal β2 is determined, the best fitting-model is then obtained accordingly.

    Figure  3.  ABIC curves for GPS data inversion. (a) Log-linear plot of ABIC in a wider range and coarser search spacing; (b) the same with (a) but in a smaller range and fine search spacing.

    Figure 4 shows the best-fitting slip model corresponding to the optimal β2 values. It showed that this earthquake occurred on a thrust fault plane with large dip-slip component and small strike-slip component. The slip pattern of the fault motion is pretty simple, only one slip concentration occurs around the hypocenter. This earthquake has no predominant rupture direction, which is different from Wenchuan Earthquake that has a clear northeast rupture direction. On the other hand, our result confirms the absence of the subsequent sub-event, as proposed by Zhang et al. (2013) with teleseismic waveform inversion. The maximum slip is about 0.7 m, a little smaller than that retrieved from seismic data and a little larger than that of Jiang et al. (2014). This difference may be caused by different inversion methods, fault parameterization strategies and earth structures. The seismic moment is about 9.47×1018 N·m, corresponding to a moment magnitude about Mw 6.6. The seismic moment is smaller than that obtained from seismic data. The formal uncertainties correspond to the slips in two orthogonal directions are shown in Fig. 5. Both are quite small comparing to the slip magnitude, ensuring the reliability of our inversion results. Slips in the concentration area almost have uniform uncertainties. Figure 2 shows the data fitness of the observed (blue arrows) and synthetic coseismic displacements (red arrows) from the inverted slip model. The synthetic displacements match the observed displacements very well, especially for the horizontal component. All synthetic displacements are within the 95% confidence interval of observed data, justifying the validation of the inverted slip model. The synthetic and observed vertical displacements are not exactly matched, since the uncertainties of vertical displacements are much larger than that of horizontal components (Fig. 2). It is reasonable to pay less attention to the vertical displacements.

    Figure  4.  Slip distribution on the fault plane. The arrows represent the slip directions of each sub-fault. White star denotes the location of the centroid.
    Figure  5.  The uncertainties of the slip in two orthogonal slip direction. (a) Uncertainties of the slip at the slip direction 45º; (b) uncertainties of the slip at the slip direction 135º.

    To further check the reliability of the inversion, we adopt a resolution test. The input slip is shown in Fig. 6a. We then synthetic 3-components of coseismic displacements based on this input model with the same station configuration, layered earth structure and parameterization strategy as in the real case. Considering the fact that vertical displacements have larger uncertainties than horizontal components, we add Gaussian noises with zero mean and standard deviation 1-mm into horizontal component, and Gaussian noises with zero mean and standard deviation 2-mm into vertical component. ABIC method is also conducted to invert the slip on the fault. The inverted slip model is shown in Fig. 6b. Due to smoothing constraints and limited stations, the slip amplitude of each individual patch cannot be determined independently. But our station configuration provides enough constraints, prone to solving the local average slip. Once the slip distribution is inverted, the Coulomb stress changes can be calculated accordingly.

    Figure  6.  Resolving ability test of the inversion. (a) Input slip model; (b) inverted slip model.

    For inversion problem, the final uncertainties of model parameters are mainly caused by two sources of errors. One is the observation error induced by imperfect measurement, which is represented by the data covariance matrix Cd. The other is the modeling error induced by simplified earth structure and uncertainties in focal mechanism, which is represented by Cp (Duputel et al., 2014, 2012; Minson et al., 2013; Yagi and Fukahata, 2011). The total data covariance is CD=Cd+Cp. The matrix Cd indicates the formal uncertainties of the observations, characterized by diagonal components for GPS observations and non-diagonal for InSAR measurement (Fukahata and Wright, 2008). Since the real uncertainties of earth structure and source parameters are not known, it is hard to construct the covariance matrix Cp. The oversimplification on earth structure and physical parameters may cause modeling errors (Duputel et al., 2014; Minson et al., 2013; Yagi and Fukahata, 2011). The evaluation of focal mechanism influencing on fault slip is non-practical since changing source parameters must require the recalculation the Green's functions. It brings a computation challenge for complicated inversion problems (Duputel et al., 2014). For layered earth structure, as an example, there is no analytical solution at all. An alternative way to explore the influences of focal mechanism is to perform inversions with the same earth structure models and different focal mechanisms and then compare the inverted slip models (Zhang et al., 2014).

    For Lushan Earthquake, fortunately, the source parameters were soon studied after the occurrence by a group of researchers and institutions. Based on different datasets, they obtained similar results of thrust motions of the earthquake, but there are still significant differences remained (Han et al., 2014). In this study, we compared four typical focal mechanisms listed in Table 2. Model Ⅰ was obtained by Jiang et al. (2014) using GPS coseismic displacements. It is the only geodetic-data sourced model. Han et al. (2014) obtained the focal mechanism based on regional seismogram, which is the Model Ⅱ. Referred to Zeng et al. (2013), Model Ⅲ was obtained by teleseismic body-wave inversion. The hypocenter location and depth are determined by CENC, the hypocenter is relocated using near-field strong motion data and W-phase focal mechanism solution, Zhang et al. (2014) proposed Model Ⅳ.

    Table  2.  Various source parameters for Lushan Earthquake
    Location Strike
    (º)
    Dip
    (º)
    Rake
    (º)
    Depth
    (km)
    Longitude (ºE) Latitude (ºN)
    Model Ⅰ 102.938 30.295 208 43 81 13.5 (C)
    Model Ⅱ 102.964 30.299 210 47 97 13.0 (H)
    Model Ⅲ 102.990 30.300 212 44 92 12.0 (H)
    Model Ⅳ 102.889 30.261 218 39 103 16.0 (H)
    Models Ⅰ, Ⅱ, Ⅲ and Ⅳ are point source models obtained by Jiang et al. (2014), Han et al. (2014), Zeng et al. (2013) and the USGS W-phase solution with depth relocated by Zhang et al. (2014). Models Ⅰ, Ⅱ, Ⅲ and Ⅳ are obtained using GPS coseismic data, regional seismograms, teleseismic body wave and strong motion data (relocation), respectively. (H) and (C) denote that the location and depths are for hypocenter and centroid, respectively. Focal mechanism for Model Ⅲ was obtained by USGS with W-phase waveforms. Location and depth of Model Ⅳ are determined by CENC.
     | Show Table
    DownLoad: CSV

    The slip model corresponding to Model Ⅰ is the preferred model that we obtained in Section 3. Slip models corresponding to other three models are inverted based on the same earth structure, fault plane size, and fault parameters. All the best-fitting slip models are shown in Fig. 7. Figures 7a-7d correspond to Model Ⅰ, Model Ⅱ, Model Ⅲ and Model Ⅳ, respectively. Similarly all the four slip models have large slip concentrations around the hypocenters. While, there are still non-neglected differences in slip rake, maximum amplitude and slip area. Slip differences shown in Fig. 7 have similar characteristics as that obtained by Zhang et al. (2014) using different hypocenters released by GFZ, CENC and USGS, respectively. For instance, Model Ⅰ and Model Ⅲ have similar slip areas and slip directions, but different peak slip displacements. Model Ⅲ has larger peak amplitude than Model Ⅰ. Neglecting the elongation slip along the reverse-strike direction, slip Model Ⅱ has similar slips to Model Ⅲ and Ⅰ. It has the same peak amplitude as that of model Ⅲ, and smaller slip concentration area around the hypocenter. For Model Ⅳ, however, slip features show significant differences from that of the other three models. This slip model shows two slip areas, one is around the hypocenter and similar to that of other three models; the other is much shallower and reaches the top edge. The existence of second sub-event (the shallower slip area) is somewhat consistent with the rupture model based on teleseismic waveforms (Zhang et al., 2013). However, the distribution of the second slip area reaches to the earth surface, much shallower than that by Zhang et al. (2013), which is significantly conflict with the geology survey (Xu et al., 2013).

    Figure  7.  Fault slip models with different focal mechanisms. (a), (b), (c) and (d) are slip models corresponding to Model Ⅰ, Model Ⅱ, Model Ⅲ and Model Ⅳ, respectively.

    It is noted that the four slip models have almost the same fitting level to the observed data although their inverted results are pretty different. At this point, data fitness is not enough to constrain the final inverted result. The variations in focal mechanisms can cause significant influences on fault slip distribution. Furthermore, they will affect the subsequent results such as the Coulomb stress change (He et al., 2013).

    Coulomb stress change is often used to study the triggering of the subsequent aftershocks (Görgün, 2014; He et al., 2013; Toda et al., 2011, 2008). Calculation of the static Coulomb stress change on a specific receiver fault requires a slip model of mainshock and the geometrical parameters of the receiver fault (Görgün, 2014; Toda et al., 2011). The static Coulomb stress change can be expressed as (King et al., 1994)

    ΔCFF=Δτ+μΔσ (12)

    where τ and ∆τ are the shear stress and shear stress change over the target fault plane respectively; σ and ∆σare the normal stress and normal stress change (positive if the fault is unclamped) over the target fault plane respectively. μ is the effective coefficient of friction. Based on the preferred slip model, the Coulomb stress changes △CFF is calculated with μ=0.4 (Toda et al., 2011, 2008) and Coulomb 3.3 software package (Toda, 2005; Lin and Stein, 2004). The receiving fault has the same parameters as the source fault. Figure 8 shows the spatial distribution of Coulomb stress change caused by Lushan Earthquake. The Coulomb stress changes △CFF at different depths are calculated and displayed spatially. The black box and green line are the projections of the fault plane and the upper boundary on the ground surface. Obviously, △CFF distributes with three zones. The center is a negative zone, circled by positive doughnuts, and out zone likes negative wings beyond the fault plane projection area. Three zones have the same symmetric axle at the center of the fault plane extending from northeastern to the southwestern. Comparing the aftershocks with the distributions of △CFF, only a small portion of aftershocks locate in the areas of positive △CFF at deeper part (i.e., depths of 19, 17, and 15 km), except a little more shallow aftershocks locate in the positive areas of △CFF (i.e., depths of 11 and 9 km). The inconsistent of aftershocks' distribution and the positive areas of △CFF is also realized by Miao and Zhu (2013). To further check the relation of the △CFF and aftershocks, three cross-sections along the routes of AA', BB' and CC' (Fig. 1) are presented in Fig. 9. They show similar pattern of Coulomb stress changes. The shallow and deep portions of the fault plane show positive △CFF, though the areas vary with each other. Another two positive areas are located aside the fault plane. Aftershocks along the three routes are also projected to the cross-sections. Similar to the aftershocks' distribution at different depths, most of the aftershocks lie in the areas with negative △CFF values. The reason why most aftershocks occurred at the negative △CFF zone is still a puzzle (Miao and Zhu, 2013).

    Figure  8.  Spatial distributions of the Coulomb stress change at depths of 19, 17, 15, 13, 11, and 9 km. White circles are aftershocks at corresponding depth, black box represents the surface projection of the adopted fault plane, green line is the upper edge of the fault plane on the earth surface.
    Figure  9.  Three cross-sections of the Coulomb stress changes. Black line represents the fault geometry. Green circles in each sub-figure represent aftershocks along (near) the corresponding cross-section profile.

    We preferred the focal mechanism of Jiang et al. (2014) and then invert the fault slip distribution of Lushan Earthquake using ABIC method. The rupture of this earthquake is relative simple with only one large concentration around the initial break point, with maximum amplitude about 0.7 m and a scalar seismic moment about 9.47×1018 N·m, corresponding to moment magnitude Mw 6.6. The seismic moment is slight larger than that of Jiang et al. (2014). Since the databases are the same, this misfit is purely caused by the inversion methods, and the adopted parameterization strategies. Our slip model shows no clear surface rupture, agreed with the results of geology survey.

    The spatial distribution of the static Coulomb stress change varies with depth. The northeastern and southwestern ends show positive Coulomb stress change. Most of the aftershocks occurred in the areas of negative Coulomb stress changes. Referring to the influences of the focal mechanisms on the fault slip models, four types of focal mechanisms obtained using different datasets are considered. The inversion results show that focal mechanisms may produce significant influence on fault slip models, especially on maximum slip amplitude and slip direction. Slip model based on Model Ⅳ show a shallower slip area which rupture to the ground surface. It is inconsistent to other inversion results and geology survey (Xu et al., 2013). The location and focal mechasnism of the fault control the inverted slip pattern. An alternative way to generally consider the influences of focal mechasnim is taking the variable source parameters into consideration, i.e., variable dip and strike angles. According to ABIC method, source parameters can also be taken as hyper-parameters and then using a grid search approach to find the minimum ABIC value theoretically (Funning et al., 2014). However, due to heavy burden of recalculating Green's functions, it is sometimes impractical to consider the influence of source parameters using a perturbation theory (Duputel et al., 2014). Geodetic data (e.g., GPS and InSAR) can provide good constraints on source geometry. Joint inversion of geodetic and seismic data for obtaining source parameters is a good way to get accurate source parameters (Weston et al., 2012).

    ACKNOWLEDGMENTS: We thank Gareth J. Funning for his help on the application of ABIC method. We benefited from discussions with Lei Yi. Thanks to Lihua Fang and Jianping Wu for providing us the relocated aftershock sequence. We are grateful to Dr. Xin Zhou and anonymous reviewers for their suggestions, which helped to improve the quality of the manuscript. This study was supported by the 973 Project of China (No. 2013CB733303), the National Natural Science Foundation of China (No. 41474093), and the Open Research Fund Program of the Key Laboratory of Geospace Environment and Geodesy of Ministry of Education, China (No. 12-02-08). Most of the figures were drawn using GMT software (Wessel and Smith, 1998).
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