InSAR is widely applied for earthquake crustal deformations (Cakir and Akoqlu, 2008; Massonnet et al., 1993). Because of its centimetric level accuracy with the Sentinel-1A ascending and descending data, deformation analysis is carried out. Sentinel-1A has global coverage of 12 days repetition cycle with high spatial resolution capability. Sentinel-1A satellite acquires wide swath data of 250 km, utilizing terrain observation by progressive scan (TOPS) mode (Torres et al., 2012). Pair of Sentinel-1A TOPS mode ascending track T124 and descending track T0057 with shortest temporal baseline are selected for this study as in Table 1. Acquisition dates for ascending images used are 14th Jan, 2024 and 26th Jan, 2024 respectively with incident angel range of 340 to 420. Descending data with acquisition dates of Jan 20th, 2024 and Feb 25th, 2024 having incident angel range of 360 to 460, are utilized for this coseismic deformation studies as in Table 1.
Table 1
Interferograms utilized for Co-seismic deformation studies 2024 Mw 7 Uqturpan, China earthquake
Acquisitions Master-Slave (yymmdd) | Orbit Direction | Track/Path | B⊥m | Br days | Incidence (degree) |
20240114–20240126 | Ascending | 56 | 21 | 12 | 340 − 420 |
20240120–20240225 | Descending | 136 | 7 | 36 | 360 − 460 |
From InSAR imagery of Sentinel-1A Single Look Complex (SLC), ascending track and descending track interferograms are generated with GMTSAR (Sandwell et al., 2016). In GMTSAR processing, azimuthal coregistration with 0.001 pixel accuracy is carried out to minimize the along-track doppler variations on TOPS mode (Xu et al., 20202). This process includes three steps i.e., geometric alignment with orbit (i.e., orbital geometric files are used to adjust the misalignment between master and slave images), deramping is applied prior to interpolation of SLC data and mis-registration error removal (Miranda et al., 2015; Zan and Gurarnieri, 2006). Additional details of these steps are available in the documentation of GMTSAR. For topographic phase correction and coregistration, digital elevation model (DEM) SRTM 1-arc sec (30m) is applied on SAR interferogram (Farr et al., 2007; Farr and Kobrick, 2000). Interferograms are smoothed with power spectrum filter (Goldstein and Werner, 1998). Interferogram unwrapping is carried out with software SNAPHU (Chen, 2001). From ascending and descending data, the estimated movement noted of the study area, is toward the satellite. It has the maximum displacements of about 150 and 100 mm from both modes of data respectively. For line of-sight (LOS) projection, eastward motion can cancel part of uplift in descending geometry while strengthen in ascending. Therefore, larger ascending displacements indicate westward motion of the hanging wall, corresponding to left-lateral slip for a Northwest-dipping fault plane.
Data are down sampled with total of 81,000 and 78,000 points for ascending and descending interferograms respectively, which retains the major deformation of the original interferograms. We inverted the descending and ascending InSAR observations using a three-stage process for measurement of slip distribution and fault geometry: (1) selecting a nodal plane from two candidate slip sources; (2) inverting parameters for uniform slip source; (3) estimating finite-fault slip distribution (e.g., Atzori et al., 2009; Wen et al., 2016). For the coseismic deformation of Uqturpan, China Mw 7 earthquake, optimal uniform slip model (i.e., nonlinear inversion is applied to estimate the source parameters and measurement of uniform slip distribution) is inverted from both down sampled ascending and descending data, incorporating the fault geometry in homogenous elastic half space model i.e., Okada, 1992. The noted shear modulus is 30 GPa and Poisson ratio is 0.25. We applied the Monte-Carlo analysis to estimate the tradeoffs and uncertainties in model parameters (Liu, 2015; Yu et al., 2018). In this method, we generate 100 sets of spatially correlated random noise, a typical number used in many studies (Elliottetal., 2010; Wrightetal., 1999), based on the1-D covariance function. The observations are then perturbed by adding the simulated noise. We constrain a solution for each of the perturbed data set, and used the 100 solutions to estimate errors and trade-offs between parameters.
In the second step, we perform finite slip distribution inversion by fixing strike, dip, centroid location, and reference offsets based on our best-fit uniform slip source fault models. We extend both fault length and width to 30 km to allow the inversion to constrain the extent of the slip. The fault plane is subdivided into 35×20 sub patches along the strike and dip of the fault, respectively as shown in Fig. 4. The least-square method is used to resolve the slip distribution (Jónssonetal.,2002). We also apply a smoothing Laplacian operator to get more appropriate solutions (Jónssonet al., 2002). The smoothing parameter is selected according to an L-curve between roughness and root mean square (rms) misfit (Fig. 4) and ensure the coherence between individual sub-fault patches.
Many researchers discussed and applied the Coulomb stress changes for the triggering of earthquake and aftershocks due to slightly change in stresses around the rupture area (Anderson et al., 1994; Chan and Stein, 2009; Chan et al., 2016; Cocco and Rice, 2002; Harris and Simpson 1992; Hill et al., 1993; King et al., 1994; King and Cocco, 2001; Ogata 2007; Simpson and Reasenberg, 1994; Stein, 1999, 2003; Toda et al., 1998). This becomes seismic risk for the nearby faults (Tabrez et al., 2008). Static Coulomb stress changes (ΔCFS) are calculated using the inverted slip model of 2024 Uqturpan, China Mw 7 earthquake. Coulomb 3.4 software is used to estimate the Coulomb stress change (ΔCFS) on the nearby faults and discuss the occurrence of aftershocks with positive ΔCFS (King et al., 1994; Lin and Stein, 2004; Toda et al., 1998, 2005, 2011).
This Coulomb stress change (ΔCFS) is defined as
ΔCFS = Δτ - µ (Δ\({\sigma }_{n}\)– p) (1)
Where, Δτ slip direction shear stress, Δ\({\sigma }_{n}\) is defines the normal stress, p represents the pore pressure fluid and effective coefficient of friction is represented with \({{\mu }}^{{\prime }}\) (Jaeger and Cook, 1979; Scholz, 1990). \({{\mu }}^{{\prime }}\) is derived from the equation below
\({{\mu }}^{{\prime }}\) = µ (1-B)
Where Skempton’s coefficient is represented with B and ranges between 0.5 to 0.9 (Roeloffs, 1996). The coefficient of friction µ varies between 0 to 0.75 in coseismic analysis. Coefficient of friction µ depends on time and velocity, also the number of contact points between the two lithology layers of the slip area also matters (Dieterich, 1978; Ruina, 1983). Usually, \({{\mu }}^{{\prime }}\) value is taken as 0.4. For this calculation preexisting stresses due to any other event in the region and regionals stresses are not incorporated. The pore pressure of fluid is incorporated as proportional to stress change in normal condition (Cocco and Rice, 2002). Therefore, the Static Coulomb failure stress is expressed as
ΔCFS = Δτ – µʹΔσ (2)
Where Δσ is the normal stress.