Source model for the Mw 6.0 earthquake in Jiashi, China on 19 January 2020 from Sentinel-1A InSAR data

On January 19, 2020, an Mw 6.0 earthquake occurred in Jiashi, Xinjiang Uygur Autonomous Region of China. The epicenter was located at the basin-mountain boundary between the southern Tian Shan and the Tarim Basin. Interferometric Synthetic Aperture Radar (InSAR) is used to obtain the coseismic deformation field from both ascending and descending Sentinel-1A satellite images of the European Space Agency. The results showed that the coseismic deformation is distributed between the Kalping fault and the Ozgertaou fault. The earthquake produced significant deformation over an area of approximately 40 km by 30 km. The maximum and minimal displacements along the line of sight (LOS) are 5.3 cm and − 4.2 cm for the ascending interferogram and are 7.2 cm and − 3.0 cm for the descending interferogram, respectively. The fault geometry from the Multi peak Particle Swarm Optimization computation indicates that the seismogenic fault is a shallow low-dipping planar fault that is 4.58 km depth underground. The finite slip model inverted by the Steepest Descent Method implies that the rupture is dominated by a thrust fault. The slips are concentrated in a depth of 5–7 km with a maximum slip of 0.29 m. The estimated total seismic moment is 1.688 × 1018 Nm, corresponding to a magnitude of Mw 6.1. The seismogenic fault is the Kalping fault which has a listric structure. The coseismic deformation only occurred on the décollement layer and did not involve the ramp segment. The coseismic Coulomb stress changes have enhanced the stress on the deep margin of the Jiashi earthquake rupture area, indicating that there is still the possibility of strong earthquakes in this region in the future.


Introduction
An M w 6.0 earthquake struck Jiashi (39.83° N,77.21° E) in Xinjiang, western China on January 19, 2020 (Fig. 1a). The focal mechanism solutions from the United States Geological Survey (USGS) and Global Centroid Moment Tensor (GCMT) indicated that the Jiashi earthquake was caused by a thrust fault with a slight strike-slip (Table 1).
The epicenter of the Jiashi earthquake is located at the southern margin of the Kalpingtag thrust system (Kalping block), which is situated in the basin-mountain junction region between the south Tian Shan and the northwestern margin of the Tarim Basin. The Tian Shan orogen is an intracontinental mountain belt revived from rapid and ongoing convergence in response to the Indo-Eurasian collision. Modern geodetic measurements have been used to study the current characteristics of convergent deformation rates in the Tian Shan area, but the deformation mechanism is still under debate. For example, some researchers suggested that the Tian Shan convergent deformation is formed by concurrent slip across several faults and intermontane basins that span the mountain belt (Abdrakhmatov et al. 1996;Thompson et al. 2002;Zubovich et al. 2010). Most of the convergence is not absorbed by a single predominant fault and the strain field is roughly homogeneous. Other researchers proposed that convergence is not uniformly distributed across the Tian Shan, and the slip on the detachment fault under the Tian Shan dominates the deformation pattern and seismicity of major earthquakes (Yang et al. 2008a, b;Li et al. 2015;Qiao et al. 2017). The existence of large-scale, high slip rate and low-angle detachment fault between the Tian Shan and the foreland basin is the key indicator to distinguish the above two kinematic models. Assuming that there is a main detachment fault, the slip rate and dip angle estimated from geodetic observations are ~ 10 mm/a and < 5°, respectively. It is consistent with the speculation of the leading edge thickening model (Yang et al. 2008a, b;Li et al. 2015), but there is still a lack of direct seismic evidence to confirm the existence of such low-angle detachment fault. Therefore, the use of coseismic geodetic measurements to study the slip distribution of strong earthquakes plays an important role in clarifying the geometric structure of active faults in this area.
The Tian Shan orogen is resurrected by the far-field effect from the collision between the Indian Plate and the Eurasian plate since the Neogene era. The Kalping block thrusts to the Tarim Basin from the north to the south, forming the Kalpingtag thrust system (Wang, 2007) (Fig. 1b), which is the largest present-day crustal deformation region in the south Tian Shan except the Wuqia-Kashi zone (Avouac et al. 1993). There have been 15 earthquakes over magnitude 6 in the Kalping block just since 1990 such as the 1997 Jiashi strong earthquake swarm. Maidan-Karatieke fault is the northern boundary of the Kalping block, where the Tarim Basin subducts northward to the Tian Shan orogen belt (Allen et al. 1999). It is a large lithosphere-scale fault with obvious vertical movement at the end of the Late Pleistocene. The southern boundary of the Kalping block is the Kalping thrust fault. To the south of the fault is the rigid Tarim Basin with a stable basement. The Kalpingtag thrust system consists of many reverse and anticline fractures from north to south. It is divided into two segments by the Piqiang fault (Fig. 1a). The Jiashi earthquake occurred at the southern margin of the Kalpingtag thrust system, west of the Piqiang fault. The epicenter is between the Kalping fault and Ozgertaou fault (Fig. 1b). Studies from geological and deep seismic-reflection profile indicate that the geometry of the Kalping fault is a listric-shaped structure (Qu et al. 2003). The dip of the fault is steep at the top and gentle at the bottom. The fault is inclined to the north at an angle with 30 ~ 70° near the surface. It merges into a detachment surface along the bottom of Cambrian with a depth of about 9 km. The Ozgertaou fault is mostly east-west trending. Its western segment is developed between the Paleogene red sandstone, mudstone and Wuqia group mudstone. Its eastern segment consists of several north inclined thrust faults with a dip of 40-60°. It roots into the same detachment in the deep just like the Kalping fault (Qu et al. 2003;Yang et al. 2008a, b). The balanced geological cross section revealed that the crustal shortening of the Kalpingtag thrust system on the west side of the Piqiang fault is 45 km. If the initial deformation occurs at the starting time of the Xiyu conglomerate deposition since 2.5 Ma, the crustal shortening rate is 17.3 mm/a (Yang et al. 2008a, b). Modern geodetic measurements have shown that the crustal shortening rate in the Jiashi area relative to the Kazakh block in the northern Tian Shan is about 17-19 mm/a Qiao et al. 2000). The characteristics of the Kalping fault and the Ozgertaou fault given by geological investigations is general, which is relatively rough and lack of detailed information such the dip angle with a wide range. Although GPS surveys can provide a fine geometric constraint on the fault, the distribution of stations in the epicenter and adjacent areas is relatively scarce (Fig. 1b). Therefore, the InSAR observations of coseismic deformation are used to highlight the fault geometry and the slip model.
Crustal deformation is the most direct manifestation of an earthquake. Interferometric Synthetic Aperture Radar (InSAR) is a powerful technique, which can quickly obtain large-scale, high-precision, high-resolution surface deformations and has been successfully used for many earthquakes to map the coseismic deformation and study the source model (Wright et al. 2003;Li et al. 2011;Weston et al. 2012;Qiao et al. 2014;Ma et al. 2018;Xiong et al. 2019a, b;Chen et al. 2019). In this study, the coseismic deformation of the 2020 Jiashi earthquake is measured with the InSAR technique using both the ascending and descending interferograms from the Sentinel-1A Fig. 1 a Distribution map of topography, fault, major historical earthquake and InSAR data in the Jiashi areas. The black beach balls are focal mechanism solutions of the historical earthquake from the GCMT catalog. The red star marks the epicenter of the Jiashi earthquake from CENC. The green box is the coverage of Sentinel SAR data. The blue dots represent the major cities. The black lines are faults that are from the display system of active faults in China provided by the Institute of Geology, China Earthquake Administration. (http://www.neote ctoni cs.cn/arcgi s/apps/ webap pview er/index .html?id=3c0d8 234c1 dc43e aa0be c3ea0 3bb00 bc). b Tectonic map of the Kalping thrust system. The red beach balls are focal mechanism solutions of the Jiashi earthquake from USGS and GCMT. The purple circles represent the aftershocks till 17 June 2020 from CENC. The red arrows represent the horizontal velocity field relative to the Eurasian plate (from CMONOC between 1999 and 2019) provided by the GNSS Data, Products and Services Platform (http://www.cgps.ac.cn/) of the China Earthquake Administration satellite. The fault geometry and slip distribution are retrieved based on coseismic interferograms. Finally, the Coulomb stress changes triggered by this event are evaluated and the potential seismic hazards are analyzed in the study area.

InSAR coseismic deformation
The coseismic deformation of the Jiashi earthquake is completely captured and imaged by the Sentinel-1A radar satellite of the Europe Space Agency (ESA). The data are acquired using a very advanced scanning mode called terrain observation with progressive scans (TOPS) in the Interferometric Wide (IW) mode (Table 2), which can effectively reduce the scalloping effect and improve the interference performance. Two pairs of ascending and descending Sentinel-1A images have the shortest temporal interval of 12 days to minimize the effect of afterslip. Meanwhile, the short perpendicular baselines of − 57 m and 12 m can reduce the impact of the digital elevation model (DEM) error (Simons et al. 2002).
The Sentinel-1A SAR data are processed using the Gamma software (Werner et al. 2000). The interferograms are generated from the Single Look Complex (SLC) products. The multi-look ratio between the range and azimuth direction is set to 10:2 to improve the signal-to-noise ratio. The accuracy of the azimuth coregistration better than 0.001 pixel is acquired to avoid the phase jumps between subsequent bursts. The Shuttle Radar Topographic Mission (SRTM) DEM with a 30-m spacing resolution is used to remove the phase related to ground topography (Farr and Kobrick 2000). A weighted power spectrum technique is employed to filter the interferograms to reduce the phase noise and achieve a high signal-to-noise ratio result (Goldstein and Werner 1998). The Generic Atmospheric Correction Online Service (GACOS) products for InSAR is used to correct the atmospheric phase delay (Fig. 2a, 2b) (Yu et al. 2018). The minimum cost flow is adopted to unwrap the filtered phase (Pepe and Lanari 2006). Then, the unwrapped interferograms are geocoded to the WGS84 geographic coordinates and converted to displacements along the line of sight (LOS) (Fig. 2).
The coherence of the ascending and descending results is high in most areas because of a high spatial-temporal correlation between images acquired in a Gobi Desert region with little vegetation. The slight discrepancy between the two interferograms can be attributed to different looking incidence and azimuth. The continuous fringes are visible in both ascending and descending interferograms in the epicentral area (Fig. 2c, d). The maximum and minimum LOS displacements are 5.3 cm and − 4.2 cm for the T129A interferogram and are 7.2 cm and -3 cm for the T34D interferogram, respectively (Fig. 2e, f ). It indicates that the earthquake produced obvious deformation over an area of approximately 40 km by 30 km. The coseismic deformation field is distributed along the Kalping fault and the Ozgertaou fault. The long axis of the deformation field is approximate EW, which is consistent with the strike of the Kalping fault and the Ozgertaou fault. The deformation in the epicentral area between the Kalping fault and the Ozgertaou fault is large and dominated by uplift along LOS. The epicentral area near the Ozgertaou fault and its north side are dominated by subsidence uplift along LOS. The south side of the Kalping fault is deformed slightly. It is uncertain Table 1 Source parameters for the Jan. 19, 2020 M w 6.0 Jiashi earthquake a* represents the planar fault model, b* represents the listric fault model and its dip angle, c* is the dip of the ramp segment, the dip of the flat segment is fixed to be 2°, d* is the mean rake of each patch   . 2 a, b represent the atmospheric delay maps along the LOS direction. c-f represent the coseismic interferograms and LOS deformation fields with atmospheric delay corrected along ascending and descending orbits, respectively which fault is the seismogenic fault from InSAR interferogram.
The InSAR coseismic deformation field consists of millions of points and has a high spatial correlation between adjacent observations. It is inefficient to use all of them to invert for the slip model. The LOS coseismic deformation field is firstly masked with a coherence coefficient 0.5 to obtain high-quality deformation data. Then a quadtree algorithm is used to down-sample the data sets to reduce the point number and improve the computational efficiency (Jónsson et al. 2002). Despite the dramatic reduction in quantity, the major features of the original interferograms are well retained in the down-sampled observations (Additional file 1: Figure S1). The unit vector of each point is also calculated from the individual incidence and azimuth angle.

Fault geometry and slip model
A two-step strategy is used to construct the coseismic source model. Firstly, a nonlinear inversion is applied to obtain the optimized fault geometry by assuming a uniform slip on a rectangular fault. Secondly, the distributed slips are estimated by a linear inversion base on a discretized fault plane.

Fault geometry optimization
Based on an elastic and half-space dislocation model, a Multi peak Particle Swarm Optimization (MPSO) algorithm is used to invert for the nine fault parameters consisting of location, length, width, depth, strike, dip, rake and slip by minimizing the misfits between the observed and the model predictions (Feng 2010). The weighted ratio of the ascending and descending datasets is set by 1:1. On the basis of the focal mechanism solutions from different agencies and distribution of aftershocks, we set the strike and dip as 270° and 15° for the initial fault parameters. An optimized plane fault of 22.7 km × 4.7 km with uniform slip of 0.37 m is derived from MPSO inversion. The strike, dip and rake angle are 274.8°, 8.8° and 105.6°, respectively. The Monte Carlo method is used to estimate the uncertainties of the fault parameters (Table 1, Additional file 1: Figure S2) (Funning et al. 2005). The results show that the inversion is stable and robust. The results indicate that the rupture of this earthquake is dominated by a thrust fault.

Slip model inversion
Based on a variable-slip distribution model, we used the constrained least-squares principle and the Steepest Descent Method (SDM) to invert for rakes and coseismic slips on discretized subfault . SDM is an iterative optimization algorithm that usually does not require a good initial approximation to achieve computation converge. The step proportional to negative of the gradient is chosen to achieve the maximum amount of decrease of the objective function at each step.
The dimension of the fault plane is expanded to 50 km along the strike and 20 km along the down-dip direction to avoid edge effects. It is divided into 25 × 10 subfaults by 2 km × 2 km for each patch. The position, strike and dip of each subfault are fixed at the optimized values derived from MPSO. We set the rake to a range from 45° to 135° account for the focal mechanisms from GCMT and USGS as well as the result of the nonlinear inversion from MPSO. The depth of the fault top position is 4.58 km. The constrained least squares method is used to solve the following objection function  where G is the Green function relating unit model slip to the predicted displacement, s is the slip on each patch, d is the observed LOS displacement of InSAR, α is the smoothing factor, H is the finite difference approximation of the Laplacian operator, and τ is the shear stress drop. L-curve method is used to determine the optimal smoothing factor, which can balance the roughness of the fault slip and the model misfit (Additional file 1: Figure  S3). Finally, the slip model of the Jiashi earthquake is calculated (Fig. 3). The significant slip area is distributed in 8 ~ 42 km along the strike and 4 ~ 16 km along the downdip direction. The maximum slip is 0.29 m and located at 39.91° N, 77.30° E in a depth of 6.30 km beneath the earth's surface (Fig. 3). The total seismic moment estimated from the optimal slip model is 1.688 × 10 18 Nm, corresponding to a magnitude of M w 6.1. The correlation coefficient between the observations and simulations is 95.62%. The Okada dislocation model is used for forward modeling (Okada, 1985). The root-mean-square (RMS) residual between observations and simulations is 5 mm for ascending datasets and 5 mm for descending datasets, respectively (Fig. 4).

Static Coulomb stress changes
The seismogenic fault usually generates considerable static coseismic deformations and cause static coseismic stress changes in the near and far-field after a strong earthquake occurred (Xiong et al. 2019a, b). Computing and analyzing the coseismic Coulomb stress changes is an important means to evaluate the seismic effect on the surrounding faults.
The PSCMP/PSGRN software is used to calculate the coseismic stress changes caused by the Jiashi earthquake (Wang et al. 2006). The effective friction coefficient is set at a common value of 0.4 (King et al. 1994).
The shear modulus is assumed to be 30 GPa. The plane fault inverted above is used as the receiver fault in the calculation of Coulomb stress. The Coulomb stress changes along a profile across the southern edge of the Kalpingtag nappe show that the area below the rupture of the Jiashi earthquake is a stress-enhancing zone (Fig. 5).

Planar fault vs. listric fault
The deep seismic-reflection profiles showed that the Kalping fault is a listric structure with flat and ramp segments. The dip of the ramp near the surface is 30-70° (Qu et al. 2003). The dip of the flat segment is 2-3° at a depth of 9 km (Yang et al. 2008a, b;Gao et al. 2013). Therefore, a listric fault geometry is used to invert for the slip model by SDM (Additional file 1: Figure S4). The result showed that the RMS is 7 mm for ascending datasets and 6 mm for descending datasets, respectively. The data-model correlation is 93.45%. The slip models from the planar fault (Fig. 3) and the listric fault (Additional file 1: Figure S5) both demonstrate that the Jiashi earthquake is a shallow rupture and caused by a thrust fault with slight strike slips. Considering that the planar fault model has the minimum RMS and is more concise, we take the planar fault model as our preferred source model. The Kalping fault is the seismogenic fault, since the position of the modeled fault is close to it.
The preferred model in this study implies the seismogenic fault is very flat with a dip angle 8.8°, which is consistent with the geometrical model of Zhou (2013) who proposed a low-dipping fault of 8.2° for the Kalping thrust system. Studies of geology and seismic reflection profile proposed that the Kalping fault has a listric geometry with typical characteristics of the thin-skinned tectonics (Qu et al. 2003). For thin-skinned tectonics, the sedimentary cover of the thrust sheets is detached from its crystalline basement along a décollement layer. The thickness of the detached cover sediments is typically on the order of 1 to 10 km (Pfiffner, 2017). Here, the coseismic slips of the Jiashi event are distributed in a low dip fault 5-7 km deep underground. The InSAR coseismic measurements further determined the exact geometry of the listric structure for Kalping fault in this study. It is suggested that the mainshock occurred on the flat segment of the listric fault, while the ramp segment did not rupture.

A shallow event
Results show that the maximum slip of the Jiashi earthquake occurs at the depth 6.3 km which is very shallow. It is contributed to the fault geometry and regional geological settings. The thin-skinned tectonics with shallow décollement structure is the main cause of shallow earthquakes. On the other hand, shallow earthquakes often occur in ancient craton regions, such as the southwest region of Western Australia (Langston 1987;Dawson et al. 2008) and Lake Ontario region in North America (Ma and Atkinson 2006;Kim et al. 2006), where a large number of shallow earthquakes with a depth of less than 5 km occurred. Due to the strong strength of the cold and hard ancient shield, the rock strength in all parts except near the surface exceeds the surrounding deviatoric stress. Driven by deviatoric stress, the fault rupture is difficult to expand to the deep, so it can only rupture at the shallow part to form shallow earthquakes (Langston 1987;Luo et al. 2011). The Tarim Basin, developed on the crystalline basement, has the property of stable craton, which is conducive to form shallow earthquakes in the area.
In orogenic belts, the normal stress due to the large mountain ranges makes the ramp with higher dip angles tend to have greater frictional resistance than the flat with lower dip angles (Styron and Hetland 2015;Yue et al. 2017;Tan et al. 2018). Thus, most earthquakes tend to nucleate on a flat with a lower dip angle, and then expand to a deeper or shallower region (Hubbard et al.  (Zhou, 2013) 2016). In this context, earthquakes in orogenic belts mostly occur on low-angle detachment faults with a burial depth larger than 10 km, and only a few ruptures of strong earthquakes can expand to ramps near the surface. Therefore, shallow earthquakes larger than M w 6.0 occurring at the transition zone from fault ramp to fault flat independently in orogenic belts are rare.

Regional seismic risk assessment
Being the front edge of the Kalpingtag thrust system, the slip rate of the Kalping fault is only 1-2 mm/a since late Cenozoic, which is just a quarter of the subduction rate of the Tarim Basin in this region (Yang et al. 2008a, b). It indicates that the deformation pattern of the Kalpingtag thrust system is different from that of other orogenic belts. Deformation of most orogenic belts is dominated by front thrust faults and deep detachment faults, while internal faults within orogenic belts are weakly deformed such as the Himalayan orogeny belt (Stevens and Avouac 2015) and the New Guinea Highlands Fold-and-Thrust Belt (Koulali et al. 2015). However, the Kalping fault and the internal faults of the Kalpingtag nappe have been active since late Quaternary, and the tectonic activities have not completely migrated to the frontal fault of the nappe (Wu et al. 2014). This special deformation pattern makes the faults of Kalpingtag nappe have a low slip rate of 1-3 mm/a, but all faults can accumulate stress and trigger earthquakes. The coseismic Coulomb stress of this earthquake increased the stress of adjacent faults, but the magnitude is not large. For example, the Ozgertaou fault located on the north side of the Kalping fault has a stress disturbance of up to 0.7 bar (Fig. 5).
The faults in the Kalpingtag nappe are locked, accumulating elastic strain, but the detachment fault under the south Tian Shan is free to creep due to the weakening of friction under high-temperature conditions, driving the convergent deformation of the Kalping block (Li et al. 2015). Li et al. (2015) suggested that the locked area of the detachment fault extends to the north of Maidan fault based on the interseismic deformation of InSAR and GPS, while Yang et al. 2008a, b andQiao et al. (2017) proposed that the locked point of the detachment fault is at the Totgumbaz-Alpaleh fault. The two views are slightly different, but it indicates that the rupture of the Jiashi earthquake is far from the locked point of the detachment fault. The Jiashi earthquake significantly increased the stress in the locked area of the detachment fault (Fig. 5). The maximum stress disturbance is 10.1 bar, which is located at the deep margin of the rupture area. If the remaining locked area of the deep detachment fault is completely ruptured, the deformation width will exceed 50 km, and the released seismic moment is equivalent to an M w 7.5 earthquake (Wells and Coppersmith 1994).

Conclusion
Based on the coseismic deformation of the 2020 Jiashi M w 6.0 earthquake obtained from ascending and descending InSAR observations of Sentinel-1A, the fault geometry, slip model and coseismic Coulomb stress changes are calculated.
The source model shows that the Jiashi earthquake occurred on the Kalping fault which is a thrust fault with a listric structure. The main shock only ruptured the flat segment of the listric fault and failed to deform the ramp segment. The coseismic slip is mainly concentrated on a patch of 34 km × 12 km in a depth of 5 ~ 7 km. The maximum slip is 0.29 m at a depth of 6.3 km. The released moment is 1.688 × 10 18 Nm, corresponding to a magnitude of M w 6.1.
The coseismic Coulomb stress changes have enhanced the stress on the deep margin of the Jiashi earthquake rupture area, indicating that the seismic risk of this region is increasing. Considering the relatively few aftershocks after the mainshock and strong earthquake swarm records were recorded in Jiashi area, there is still the possibility of another strong earthquake in this region in the future.
Additional file 1: Figure S1. (a) and (c) represent observations of ascending and descending data. (b) and (d) represent the down-sampling results of ascending and descending data. Figure S2. Uncertainties of the fault parameters computed using the Monte Carlo method. X and Y coordinates are in UTM (zone 43). X, Y, and Depth represent the location of the midpoint of the top boundary of the fault plane. Figure S3. Trade-off curve of relative fitting and roughness for the planar fault. Figure S4. (a) The geometry of the planar fault and the listric fault. The green line represents the planar fault. The blue line represents the listric fault. The dashed red lines represent the rupture of the Jiashi earthquake on the two faults, respectively. For the listric fault, the dip of the ramp segment is set to 52° determined by a grid search (c). Based on the results of deep seismicreflection profiles, the dip of the flat segment is set to 2°, and the depth of the top boundaries of the flat segment is set to 9 km. The width of the flat segment is set to 20 km. The elevation difference is magnified 10 times to represent the topography. (b) The surface rupture (the blue line) of the listric fault, which is fixed based on the fault datasets from the Institute of Geology, CEA. Its strike is fixed at 274.8° based on the nonlinear inversion.