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Article

Assessing Slip Rates on the Xianshuihe Fault Using InSAR with Emphasis on Phase Unwrapping Error and Atmospheric Delay Corrections

by
Peiyan Xi
1,
Xing Li
2,
Chuang Song
3,
Bin Wang
1,
Zhi Yin
4 and
Shuai Wang
1,*
1
School of Geomatics Science and Technology, Nanjing Tech University, Nanjing 211816, China
2
Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia
3
College of Geological Engineering and Geomatics, Chang’an University, Xi’an 710054, China
4
School of Marine Technology and Geomatics, Jiangsu Ocean University, Lianyungang 222005, China
*
Author to whom correspondence should be addressed.
Remote Sens. 2024, 16(11), 1872; https://doi.org/10.3390/rs16111872
Submission received: 21 April 2024 / Revised: 16 May 2024 / Accepted: 21 May 2024 / Published: 24 May 2024
(This article belongs to the Section Remote Sensing in Geology, Geomorphology and Hydrology)
Browse Figures
Versions Notes

Abstract

:
Located on the southeastern periphery of the Tibetan Plateau, the Xianshuihe fault (XSHF) is an active left-lateral strike-slip fault renowned for its frequent and intensive seismic activities. This highlights the necessity of employing advanced geodetic methodologies to precisely evaluate the fault kinematics and seismic hazard potential along this fault. Among these techniques, interferometric synthetic aperture radar (InSAR) stands out for its high spatial resolution and regular revisit intervals, enabling accurate mapping of interseismic deformation associated with fault motion. However, the precision of InSAR in measuring deformation encounters several challenges, particularly artifacts stemming from phase unwrapping errors and atmospheric phase delays. In this study, we utilize ascending and descending Sentinel-1 InSAR images spanning from January 2017 to January 2023 to drive the line-of-sight (LOS) mean crustal velocities associated with the XSHF with emphasis on phase unwrapping errors and atmospheric delay corrections. Then, the reliability of the derived LOS velocities is assessed using independent observations from the Global Navigation Satellite System (GNSS). The inferred fault slip rate along the XSHF shows significant along-strike variations, gradually decreasing from ~11.1 mm/yr at the Luhuo section to ~6.6 mm/yr at the Kangding section and then sharply increasing to ~13.0 mm/yr towards its eastern terminus at the Moxi section. The fault locking depth shows similar along-strike variations, decreasing from ~19.5 km in the northwestern part to ~4.8 km at the Kangding section, before increasing to 19.6 km at the Moxi segment. Notably, apparent surface fault creeping, characterized by a slip rate of ~2.7 mm/yr, is observed at the Kangding segment, likely resulting from postseismic slip following the 2014 Mw 6.3 Kangding earthquake.

1. Introduction

The XSHF, spanning ~400 km along the southeastern edge of the Tibetan Plateau, plays a vital role in accommodating the converging deformation between the Indian and Eurasian plates [1]. As one of the most dynamically active left-lateral strike-slip faults, the XSHF has facilitated the lateral extrusion of the lithosphere and the eastward flow of middle-to-lower crustal materials on the Tibetan Plateau. Since 1900, the XSHF has experienced more than ten Mw ≥ 6.0 earthquakes, including the 2014 Mw 6.3 Kangding earthquake and the 2022 Mw 6.8 Luding earthquake (Figure 1) [2,3]. Intersecting and displacing various geomorphic features such as moraines, gullies, and debris flow [4], the XSHF can be segmented into two parts: a northwestern section composed of the linear and contiguous Luhuo, Daofu, and Qianning segments and a southeastern section composed of the Kangding and Moxi segments. Particularly, the Kangding segment bifurcates into three right-stepping, en echelon branches, namely, the Yalahe, Selaha, and Zheduotang faults (Figure 1) [2,4,5]. Both geological and geodetic observations reveal significant variations in the fault slip rate along the XSHF, gradually increasing from ~7 mm/yr in its northwest portion to ~15 mm/yr in its southeast section [2,6]. Moreover, distinct shallow creeping has been observed at the Daofu and Kangding segments [7,8,9]. The frequent and intense seismic activities, combined with the high average slip rate, underscore the crucial role of the XSHF in the southeastward extrusion escape of the Tibetan Plateau [10,11]. Consequently, accurately determining the slip rate variation and creeping behavior of the XSHF is of utmost importance for assessing seismic hazards in the region.
Geological investigations, including the late Quaternary studies, reveal that the XSHF exhibits an obvious segmented deformation pattern [14]. The Holocene slip rate in the northwest section, comprising the Luhuo, Daofu, and Qianning segments, ranges from 10 to 18 mm/yr, surpassing that of the southeast section, i.e., the Kangding and Moxi segments, where the rate varies from 3 to 8 mm/yr [1,15,16,17,18,19,20,21]. Notably, the Kangding segment shows lower slip rates ranging from 1 to 5 mm/yr on each of its three branches [1,15,18,20], suggesting a relatively distributed crustal deformation pattern. Geodetic investigations using GNSS observations reveal slip rates of approximately 7 to 12 mm/yr of the XSHF [5,9,22,23,24,25,26]. However, both geological and GNSS methods have their limitations. Geological approaches are unable to determine current fault slip rates as they measure across multiple seismic cycles, while the number of GNSS stations is often limited. InSAR technology can effectively address these limitations and is widely utilized for analyzing surface deformation and assessing geological hazards [27,28,29]. By using InSAR observations, Qiao et al. [12] reported slip rates of 9.4 mm/yr for the Luhuo segment, 8.8 to 9.4 mm/yr for the Daofu segment, ~10.2 mm/yr for the Qianning segment, 9.9 to 14.3 mm/yr for the Kangding segment, and 17.9 mm/yr for the Moxi segment. Another InSAR study by Zhang et al. [30] revealed slips rate of ~8.5 mm/yr for the Luhuo segment, ~8.0 mm/yr for the Daofu segment, ~9 mm/yr for the Qianning segment, ~9.5 mm/yr for the Kangding segment, and ~12 mm/yr for the Moxi segment. Furthermore, Li et al. [31] concluded that the overall slip rate for the XSHF is ~12 mm/yr.
The noticeable inconsistency among the aforementioned InSAR studies can be partially attributed to the primary error sources in InSAR analysis including phase unwrapping errors (PUEs) and atmospheric disturbances. For instance, to address unwrapping errors during InSAR processing, Qiao et al. [12] manually selected interferograms featuring good coherence and insignificant topography-correlated phases. Zhang et al. [30], on the other hand, employed a spatial filtering strategy to identify pixels with significant phase deviations, which were labeled as poorly unwrapped pixels, where the phase values were adjusted iteratively by introducing/subtracting 2π phase ambiguities. Li et al. [31] calculated the average coherence of the selected interferograms designated for stacking and subsequently masked out any pixels with coherence values below 0.09. In terms of atmospheric phase corrections, Qiao et al. [12] and Zhang et al. [30] relied on the Generic Atmospheric Correction Online Service (GACOS) [32], while Li et al. [31] implemented a linear correction directly related to topography from the original unwrapped interferograms to mitigate the effects of tropospheric delays.
The precision of InSAR in measuring deformation faces several challenges, particularly the presence of artifacts arising from phase unwrapping errors and atmospheric phase delays. These two types of errors have the potential to significantly obscure the true tectonic deformation, lending to an inaccurate estimation of the fault slip rate. Therefore, correcting these errors is essential for accurately mapping fault movements and assessing earthquake hazards. Otherwise, they could contribute to the observed disparities described above. In this study, we utilize ascending and descending Sentinel-1 InSAR images spanning from January 2017 to January 2023 to calculate the mean LOS velocities associated with the XSHF, focusing on correcting phase unwrapping errors and atmospheric delays. Furthermore, we evaluate the reliability of the derived LOS velocities using independent observations from GNSS. Subsequently, by integrating InSAR and GNSS observations, we compute a high-resolution 3D deformation field for the XSHF and invert for fault slip rates based on an elastic interseismic fault model. Finally, we discuss the significance of correcting phase unwrapping errors and atmospheric phase delays in an InSAR time series analysis and provide insights into the slip characteristics and seismic hazard of the XSHF.

2. Data and Method

2.1. Data

In this study, we use SAR images from the Sentinel-1 ascending (T026A) and descending (T135D) tracks to map the surface deformation due to the fault motion of the XSHF. The InSAR interferograms are obtained from the COMET-LiCS web portal with the products processed using the LiCSAR system [33]. To achieve full coverage of the XSHF, interferograms from two frames of descending track 135 are used (Figure 1 and Figure 2).
Within the LiCSAR processing pipeline, newly acquired data are aligned to a single primary image. Subsequently, each acquisition is used to generate interferograms with three forward and three backward acquisitions by default, aimed at addressing low coherence resulting from vegetation during summer months and snow cover during winter months. Additional interferograms with a temporal baseline spanning more than one year are also generated. The generated interferograms are then multilooked by a factor of 20 × 4 and are subject to spatial filtering to reduce noise using an adaptive power spectrum filter [34]. Phase unwrapping is conducted using a statistical cost approach with the SNAPHU software (v1.4.2) [35], and then pixels with coherence lower than 0.5 are masked out.
For the investigation of interseismic tectonic deformation, the detailed resolution of ~100 m in InSAR data is deemed excessive. Therefore, we employ the LiCSBAS software (v1.5.11) [36] to preliminarily downsample the data to a resolution of ~1 km. This resolution does not alter the shape of the displacement profile or the inversion parameters, as validated by previous studies [30,37], thus enhancing computational efficiency.

2.2. Method

2.2.1. Phase Unwrapping Error (PUE) Correction

Theoretically, movements on Earth’s surface can result in phase changes in the radar waves emitted by SAR satellites. However, due to the periodic nature of radar signals, displacements exceeding half the radar wavelength wrap back into the range of 0 to 2π. Consequently, directly measuring actual displacements from the original interferogram becomes unfeasible. Phase unwrapping is crucial to recover unambiguous phase values from the original phase information, which are measured at modulo 2π rad. PUE occurs when the number of phase wraps is inaccurately estimated. Such errors are particularly prevalent in regions with low coherence and/or large contrast in topography relief, which can lead to incorrect displacement calculations and interpretations [38].
Despite advancements in phase unwrapping algorithms, PUE may persist. Consequently, various methods have been proposed to detect and correct these errors based on loop closure phase information calculated from sets of three interferograms. However, PUEs where the absolute phase difference exceeds π between two adjacent points can break the consistency of interferometric phase triplets, resulting in a nonzero closure phase [39]. One method to correct PUEs involves visually inspecting each interferogram with the aid of loop closure phase information and manually adding an integer-cycle phase offset to incorrectly unwrapped pixel regions. Nonetheless, this process can be time-consuming and labor-intensive, particularly when PUEs occur across multiple interferograms within the same region. In such scenarios, manually correcting these errors can prove challenging, often leading to the common practice of detecting/selecting interferograms or relevant pixels with PUE and discarding them directly. However, this practice can disrupt the connectivity of the interferogram network, thereby reducing its spatiotemporal resolution. To address this issue, automatic correction algorithms have been proposed [40]. Nevertheless, as pointed out by Wang et al. [39], automatic approaches are more suitable for highly redundant networks of interferograms with rare unwrapping errors, and this becomes particularly challenging in the context of interseismic studies, where such conditions are often not met.
In order to effectively address PUEs and enhance the accuracy of InSAR-derived displacement along the XSHF, in this study, we employ a hybrid approach combining manual and automatic correction methods for PUEs, as outlined in [39]. Initially, PUEs are manually corrected in interferograms, followed by using the least absolute shrinkage and selection operator (LASSO) to automatically correct any remaining PUEs [40] (Figure 3a–e). The initial manual correction can establish favorable conditions for the subsequent automatic method, ensuring a unique solution to the greatest extent possible. Further details on the combined PUE correction method are available in [39]. It is worth noting that before PUE correction, interferograms with an average coherence of lower than 0.05 and valid pixels representing fewer than 80% are pre-screened and discarded. Consequently, we obtain 720 interferograms with temporal baselines ranging from 12 to 408 days for ascending track 26 and 417 and 425 interferograms with temporal baselines ranging from 12 to 468 days for the two frames of descending track 135, respectively (Figure 2).

2.2.2. Atmospheric Phase Correction

Variations in pressure, temperature, and humidity across space and time can lead to tropospheric phases, which can introduce discrepancies of up to tens of centimeters in a single interferogram, posing a critical challenge in monitoring millimetric-level crustal deformation. For example, a mere 20% change in relative humidity could lead to errors ranging from 0.10 to 0.14 m in land surface deformation monitoring [41]. Atmospheric errors primarily comprise stratified and turbulent components [42], with the stratified portion often correlating with regional elevation, while the turbulent component exhibits short wavelengths and lacks temporal correlation. Such errors significantly hamper the accuracy of InSAR in monitoring crustal deformation and seismic activities.
To correct tropospheric delays in interferograms, we combine the GACOS model with the APS_Phase method as described in [39]. APS_Phase is a novel phase-based approach for mapping interseismic deformation utilizing short-period interferograms. This method formulates the InSAR phase after topographic-related delay correction as the sum of three components: (1) spatiotemporally varied turbulent tropospheric phase; (2) topography-correlated stratified tropospheric phase; and (3) interseismic-related deformation assumed to accumulate at a constant rate. The atmospheric phase delays estimated by APS_Phase can be spatially and temporally synchronized with the SAR images, thereby resulting in an effective correction of atmospheric phase delays. As suggested by Wang et al. [39], for regions with strong stratified tropospheric noises, a preliminary tropospheric correction in combination with the APS_Phase method may be useful in improving the corrections of tropospheric delays. In this study, we initially apply GACOS corrections to both ascending and descending track interferograms to primarily mitigate the tropospheric phase delays, particularly the stratified component, followed by the implementation of the APS_Phase method with the threshold of the temporal baseline at 60 days as suggested by Wang et al. [39] (Figure 3e–i).

2.2.3. Long-Wavelength Artifact Removal

Following Ou et al. [37], a planar ramp was removed from each interferogram by solving for a correction term for each epoch through a network approach [43]. This procedure aims at reducing any residual long-wavelength signals, which could be attributed to unmodelled tropospheric delays, ionospheric phases [44], orbital inaccuracies [45], and solid Earth tides [46]. Long-wavelength artifacts in an individual interferogram may mimic tectonic deformation signals. Attempting to estimate such errors using all pixels in a single interferogram can lead to overfitting, thereby resulting in an underestimated tectonic deformation signal. In this study, we estimate these long-wavelength artifacts using pixels from one side of the XSHF, as outlined by the dashed rectangle in Figure 3i.

2.2.4. InSAR Time Series Analysis and Frame Mosaicking

In this study, we utilize the LiCSBAS software (v1.5.11) [36], which is built upon the NSBSA method [47], for conducting time series analysis. NSBAS calculates the increments of phase changes per pixel and applies a smoothed temporal constraint to regularize the problem when there are existing gaps in the interferogram network. The mean displacement velocity is derived from the cumulative displacements using least squares.
When integrating two or more velocity frames into a unified regional map, noticeable discontinuities emerge in the overlapping regions along track frames and across track boundaries. This phenomenon is attributed to several factors: (1) local referencing causing constant offsets between frames; (2) variations in incidence angles resulting in offsets at track overlaps; and (3) the removal of ramps from the interferograms. In this study, we employ the method developed by Ou et al. [37] to mosaic the frames. Unlike previous approaches [48], this method minimizes the LOS differences between frame overlaps without relying on interpolated GNSS velocities from frame tying. In our study, we simply invert for a planar ramp per frame to minimize alterations to the InSAR data. This choice is informed by the lack of compelling evidence in the interferograms necessitating higher-order adjustments and the consideration that higher-order ramps could potentially remove tectonic signals.

2.2.5. Calculation of the Three-Dimensional Velocity Field

Accurate determination of the present-day slip rate of the XSHF derived from horizontal interseismic surface deformation is crucial for regional seismic hazard analysis. However, InSAR observations can only provide one-dimensional LOS deformation. Consequently, relying solely on ascending and descending InSAR observations is insufficient for inferring the three-dimensional deformation. To achieve this, a third constraint is required. Weiss et al. [48] used the interpolated north velocities from GNSS data to solve for the east and vertical velocity components. Xu et al. [49] decomposed the LOS velocities into a vertical component and a horizontal component aligned with the local direction determined by interpolated east and north GNSS velocity fields. As pointed out by [49], the three-dimensional deformation fields drove by these two methods do not show significant differences, as the decomposed north–south component largely derives its information from the GNSS observations. Thus, in this study, we simply follow the strategy outlined by Weiss et al. [48] to decompose the InSAR observations from different viewing geometries into east–west and vertical components.

3. Results

3.1. Mean LOS Velocities

Figure 4a,b show the derived mean LOS velocities from ascending and descending track InSAR observations, which cover the entire XSHF. SAR pixels with an average residual root-mean-square (RMS) exceeding 5 mm/yr are masked out for both tracks. After mosaicking the InSAR LOS frames using the method described in Section 2.2.4, we can see that phase inconsistencies over the frame overlap regions have been diminished (Figure 4c,d). The STD of the resulting overlapping residuals along the track frames ranges from 0.3 to 0.8 mm/yr, with a mean value of 0.54 mm/yr, which is generally less than 1 mm/yr. Positive values denote motion toward the satellite, while negative values motion away from it. This, along with the pronounced gradient of the LOS rate change, aligns well with the mapped XSHF (Figure 4c,d), indicating the significant left-lateral strike-slip motion of the XSHF (Figure 4). We observe that the rate map from descending track 135 reveals a prominent coseismic deformation field corresponding to the 2022 Mw 5.7 Maerkang earthquake (Figure 4b,d).

3.2. Decomposed Three-Dimensional Velocities

Figure 5 represents the decomposed three-dimensional velocities derived from the ascending and descending track mean velocities, with the north–south velocities constrained by the GNSS interpolations. Notably, the east–west velocity gradient across the XSHF (Figure 5c) appears sharper compared to that observed in the GNSS observations (Figure 5a), which can be attributed to the incorporation of high-resolution InSAR mean velocities. Additionally, signals correlated with fault creeping are observed, which will be thoroughly discussed in Section 4.3. As documented in Figure 5d, the decomposed vertical deformation is minimal, indicating that motion within the XSHF zone is predominantly horizontal, consistent with the lateral extrusion of the Tibetan Plateau. Examination of Figure 5e,f reveals that the uncertainties associated with the interpolated velocity fields solely derived from GNSS observations are closely linked to the distribution of GNSS stations, increasing in areas with sparser stations. However, with the integration of InSAR LOS mean velocities, the accuracy of the decomposed velocity fields is substantially enhanced, with relatively large uncertainties of ~1 mm/yr mainly situated in the frame overlapping regions (Figure 5g,h).

4. Discussion

4.1. Significance of PUE Correction on InSAR Time Series Analysis

Given the substantial data volume offered by recent InSAR satellites such as Sentinele-1, many studies adopt conservative strategies to ensure high-quality datasets [30,50,51] that involve simply discarding interferograms or pixels containing PUE, rather than correcting them. This practice can significantly reduce the spatial and temporal resolutions of InSAR observations. As shown in Figure 6e, the conservative strategies can remove 301 out of 720 interferograms from the network, indicating that nearly half of the interferograms are discarded. In contrast, our approach retains all 720 interferograms and effectively increases the number of valid pixels, preserving 91% of them, which is a 45% enhancement over conservative strategies (Figure 6c,d). Consequently, correcting PUE not only enhances the quality of the interferogram network but also substantially increases the number of effective pixels. This augmentation ensures our ability to acquire a high spatial resolution and precise crustal deformation field.

4.2. Effectiveness of Atmospheric Correction on InSAR Time Series Analysis

In this section, we compare interferograms corrected by three different atmospheric phase correction strategies to highlight the impact of atmospheric correction on InSAR time series analysis. Figure 7 illustrates the outcomes of an example interferogram; we can see that the GACOS method reduces the STD from 2.28 rad in the original interferogram to 2.20 rad, and the APS_Phase method achieves a further reduction to 0.13 rad. These findings indicate that the APS_Phase method achieves a better correction compared to the GACOS method. Additionally, as highlighted by Wang et al. [39], in regions with strong stratified tropospheric noise, employing a preliminary troposphere in conjunction with APS_Phase may help improve the tropospheric correction (the atmospheric correction method utilized in this study). We can see from Figure 7 that the STD of the interferogram after correction by GACOS + APS_Phase is further reduced, with a value of only 0.11 rad. We further calculate the slope and correlation between the estimated tropospheric phases and the observed phases of the original interferogram. The results indicate correlation values of 0.4, 1.0, and 1.0 for the GACOS, APS_Phase, and GACOS + APS_Phase methods, respectively, with corresponding slopes of 0.57, 1.04, and 1.02. To comprehensively assess the efficiency of the aforementioned three atmospheric correction methods, we conduct statistical analyses on the STD for all interferograms. Here, we exclusively present results from descending track 135, as the ascending track yields comparable results. The GACOS + APS_Phase method achieves satisfactory correction, with ~99% of the interferograms experiencing a positive STD reduction (Figure 8). These results prove that the GACOS + APS_Phase method is the most effective method at mitigating atmospheric turbulence.
Figure 9 illustrates the mean LOS velocities derived from the three atmospheric phase correction methods for descending track 135. One can see that the LOS velocities derived from the GACOS + APS_Phase method exhibit more uniform spatial patterns, particularly within regions outlined by dashed ellipses when compared to the other two methods (Figure 9(a1–c1)). We conduct a comparative analysis between the InSAR LOS velocities and GNSS LOS velocities derived from GNSS horizontal velocities through the calculation of the RMS, the slope, and the correlation between them. The RMS values for the GACOS, APS_Phase, and GACOS + APS_Phase methods are 2.03, 1.99, and 1.97 mm/yr, respectively (Figure 9(a2–c2)). Correspondingly, the slope values are 0.53, 0.56, and 0.57, and the correlation values are 0.69, 0.70, and 0.71. In summary, the collective evidence strongly supports that the GACOS + APS_Phase method outperforms the other two methods in mitigating atmospheric phase delays within the study region.

4.3. Modeling Long-Term Fault Slip Rate and Shallow Surface Creeping

To invert for the long-term fault slip and shallow creeping rates of the XSHF, we first project the three-dimensional velocities calculated in Section 2.2.5 onto fault-parallel and vertical directions (Figure 10a,b). Then, we extract a series of across-fault velocity profiles (100 km in length and 20 km in width) from the fault-parallel velocity map (Figure 10a). Based on these displacement profiles, the kinematic inversion is conducted by using a simple elastic dislocation model [52]. For a strike-slip fault, the surface fault-parallel velocities at a specific location due to fault motion can be expressed as:
v ( x ) = s π arctan ( x − x 0 d ) + v o
where v represents the surface fault-parallel velocities at distance x from the fault, and x 0 indicates the offset of the location of the fault relative to the mapped fault trace. s and d are the long-term slip rate and locking depth, respectively, and v o defines a static offset in fault-parallel velocities.
In this study, we employ a Bayesian geodetic inversion method to estimate the optimal values for each model parameter [53]. This method involves employing semi-random walks with a specified number of walkers to explore the posterior probability distribution of the model, considering known prior constraints. The solutions are evaluated based on the weighted misfit between observed and model velocities. Figure 10c shows the observed and modeled across-fault profile displacements, along with the optimally inverted slip rate and locking depth. We can see that the XSHF exhibits apparent along-strike variations in fault slip rate, decreasing from 11.1 mm/yr in the eastern part of the Luhuo section to ~9.5 mm/yr in the Daofu section and ~8.0 mm/yr in the Qianning section, then rapidly increasing in the Moxi section to approximately 13.0 mm/yr. The locking depth exhibits similar along-strike variations, decreasing from 16.9 km in the eastern part of the Luhuo section to 10.9 km in the Daofu section and ~5.0 km in the Qianning section, then rapidly increasing in the Moxi section to approximately 19.5 km.
We thoroughly compare our findings with other geodetic and geological results (Figure 11). We can see that for the Luhuo, Daofu, and Qianning segments, slip rates derived from geological studies exceed those from geodetic results, including our InSAR studies. This difference could be attributed to geological rates spanning multiple seismic cycles, whereas geodetic observations cover only a few years, mainly reflecting the present-day fault slip behavior [54]. We note that the geological slip rates on the Kangding segment are considerably lower than those obtained from geodetic studies. This could be because the Kangding section comprises three parallel branches: Yalahe, Selaha, and Zheduotang. The geodetic results represent the total slip rates of all three branches, while the geological findings solely represent slip rates for a single-branch fault. Importantly, our results are in closer agreement with geological findings from [14], which provide the total slip rates of all three branches along the Kangding segment. When comparing the slip rates derived from InSAR studies, Figure 11 illustrates that our findings are more consistent with those inferred from GNSS observations. For instance, our observed gradual decline in slip rate from the Luhuo to Qiangning segments closely corresponds to the GNSS finding by [5], whereas InSAR studies by [12] indicated an increasing trend, and those by [30] showed relatively constant rates. As highlighted by [12], potential overestimation in their results may stem from unwrapping errors and local atmospheric disturbances. This underscores the reliability of our tectonic deformation and associated modeling results obtained after meticulous handling of unwrapping errors and atmospheric phase corrections.
We note that the displacement profiles across the Kangding segment exhibit a sharp discontinuity, indicating the possibility of surface creeping along this fault segment (Figure 12). This offset is not observed on other fault segments of the XSHF, contrasting with the findings of Li et al. [28] and Qiao et al. [12]. In the case of a strike-slip fault, the surface fault-parallel velocity at a given location due to long-term fault motion and shallow surface creeping can be expressed as [55]:
v ( x ) = s π arctan ( x − x 0 d 1 ) + c π arctan ( d 2 x − x 0 ) + v o
where c is the shallow creeping rate, and d 1 and d 2 are the depth extents of long-term slip rate and shallow creep rate, respectively. Other parameters in Equation (2) are the same as those in Equation (1).
Figure 12b shows the modeled displacements across the Kangding segment, revealing an apparent fault creeping behavior. The modeled result suggests a fault creep rate of ~2.8 mm/yr, notably lower than the range of 5–12 mm/yr obtained in previous studies [8]. Previous studies propose that fault creeping on the Kanding segment could be linked to postseismic slip following the 2014 Mw 6.3 Kangding earthquake [8]. This may explain the comparatively lower creeping rate of our study, as the postseismic slip decays over time, and our study utilizes a recent dataset (much closer to the later stages of post-seismic deformation).
The Luhuo segment exhibits a notable slip rate of ~9.5 mm/yr and a relatively large locking depth of 16.9 km, suggesting a rapid accumulation of strain and a heightened potential for significant seismic events in the future. The slip rate gradually decreases towards the Qiangning segment, where it measures 6.6 mm/yr at its eastern end. Given the absence of major earthquakes for over 120 years (Figure 1) [1], historical earthquake studies suggest that the Qianning segment could represent a seismic gap. This implies that the segment might be in the latter stages of an earthquake cycle, thus explaining its comparatively lower present-day slip rate. Considering the historical seismic activity in the Moxi segment, alongside its high slip rate of ~13.0 mm/yr and considerable locking depth of ~19.5 km, it is evident that the rate of elastic strain energy accumulation within this fault zone is substantial, raising the likelihood of a significant earthquake in the future. Apart from the Kanding segment, there are no apparent indications of fault creeping on other segments, which could be attributed to the transient nature of shallow aseismic slip along faults.

5. Conclusions

In this study, we utilize both ascending and descending Sentinel-1 SAR data spanning from 2017 to 2023 to derive a high-resolution LOS velocity field of the XSHF. To achieve this, we process the InSAR time series data carefully with a series of corrections. Initially, we apply a combined PUE correction method to the interferogram network, significantly improving the spatiotemporal resolution of InSAR data by increasing the number of effective pixels and interferograms. Then, we use the GACOS + APS_Phase method to mitigate atmospheric phase delays, effectively improving the correction of turbulent and stratified tropospheric components. The inferred slip rates along the XSHF exhibit notable along-strike variations, decreasing from ~11.1 mm/yr at the Luhuo section to ~6.6 mm/yr at the Kangding section, before sharply increasing to ~13.0 mm/yr at the Moxi section. Similarly, the locking depth decreases from 16.9 km in the northwestern part to 4.8 km at the Kangding section and then increases again to 19.6 km at the Moxi segment. Of particular interest is the evident surface fault creeping observed at the Kangding segment, with a slip rate of ~2.7 mm/yr. This finding is likely attributed to the postseismic slip following the 2014 Mw 6.3 Kangding earthquake.

Author Contributions

Conceptualization, S.W.; methodology, P.X. and S.W.; software, P.X. and S.W.; validation, S.W.; formal analysis, P.X., X.L., C.S., B.W., Z.Y. and S.W.; investigation, S.W.; resources, P.X. and S.W.; data curation, P.X., X.L., C.S., B.W., Z.Y. and S.W.; writing—original draft preparation, P.X. and S.W.; writing—review and editing, P.X., X.L., C.S., B.W., Z.Y. and S.W.; visualization, P.X., X.L., C.S., B.W., Z.Y. and S.W.; supervision, S.W.; project administration, S.W.; funding acquisition, S.W. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the National Natural Science Foundation of China under Grant 42204001 and by the Natural Science Foundation of Jiangsu Province under Grant BK20200712.

Data Availability Statement

The InSAR data used in this study is publicly available at https://comet.nerc.ac.uk/COMET-LiCS-portal (accessed on 30 February 2023). The GACOS product can be freely accessed from http://www.gacos.net (accessed on 20 January 2024). The APS_Phase software is open-source and can be freely obtained from https://doi.org/10.5281/zenodo.7847743 (accessed on 16 February 2024).

Acknowledgments

We thank the two anonymous reviewers for their valuable comments. The figures in this study were generated by adopting the Generic Mapping Tools (GMT) [56].

Conflicts of Interest

The authors declare no conflicts of interest.

References

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Figure 1. Tectonic settings of the study area. Red lines show the surface expressions of the XSHF [12]. Yellow circles denote the historical Mw ≥ 6.0 earthquakes from the National Earthquake Data Center (NEDC) of China since 1900, with yellow pentagrams representing those that occurred on the XSHF. Green and blue polygons outline the footprints of Sentinel-1 SAR images used to measure the interseismic surface deformation in this study. Blue arrows indicate the horizontal GNSS velocities with respect to the Eurasian plate [13].
Figure 1. Tectonic settings of the study area. Red lines show the surface expressions of the XSHF [12]. Yellow circles denote the historical Mw ≥ 6.0 earthquakes from the National Earthquake Data Center (NEDC) of China since 1900, with yellow pentagrams representing those that occurred on the XSHF. Green and blue polygons outline the footprints of Sentinel-1 SAR images used to measure the interseismic surface deformation in this study. Blue arrows indicate the horizontal GNSS velocities with respect to the Eurasian plate [13].
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Figure 2. Plots of spatial and temporal baselines for interferograms from (a) ascending track 26 and (b,c) descending track 135 with two different frames. Red dots indicate SAR image acquisitions, with the blue lines indicating the selected interferograms. The vertical gray line indicates the break in the connected interferogram network resulting from the removal of poor-quality interferograms containing significant unwrapping errors.
Figure 2. Plots of spatial and temporal baselines for interferograms from (a) ascending track 26 and (b,c) descending track 135 with two different frames. Red dots indicate SAR image acquisitions, with the blue lines indicating the selected interferograms. The vertical gray line indicates the break in the connected interferogram network resulting from the removal of poor-quality interferograms containing significant unwrapping errors.
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Figure 3. Flowchart of InSAR data processing in this study. UE and APS stand for unwrapping error and atmospheric phase screen, respectively.
Figure 3. Flowchart of InSAR data processing in this study. UE and APS stand for unwrapping error and atmospheric phase screen, respectively.
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Figure 4. Interseismic InSAR observations. (a,b) are the mean LOS velocities derived from ascending track 26 and descending track 135, respectively. (c,d) are the same as (a,b), but the velocities have been tied to the GNSS coordinated system. Red lines indicate the XSHF, and the black dashed circle outlines the coseismic region of the 2022/06/10 Mw 5.7 Maerkang earthquake.
Figure 4. Interseismic InSAR observations. (a,b) are the mean LOS velocities derived from ascending track 26 and descending track 135, respectively. (c,d) are the same as (a,b), but the velocities have been tied to the GNSS coordinated system. Red lines indicate the XSHF, and the black dashed circle outlines the coseismic region of the 2022/06/10 Mw 5.7 Maerkang earthquake.
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Figure 5. Decomposed three-dimensional velocities. (a,b) are the east and north velocities interpolated from horizontal GNSS velocities [13], respectively. (c,d) are the same as (a,b) but from the decomposition of ascending and descending track mean LOS velocities with the north velocities constrained by the GNSS observations. (e–h) are the associated uncertainties of (a–d), respectively. Red lines denote the surface traces of the XSHF, and the black triangles in panel e mark the locations of the GNSS sites.
Figure 5. Decomposed three-dimensional velocities. (a,b) are the east and north velocities interpolated from horizontal GNSS velocities [13], respectively. (c,d) are the same as (a,b) but from the decomposition of ascending and descending track mean LOS velocities with the north velocities constrained by the GNSS observations. (e–h) are the associated uncertainties of (a–d), respectively. Red lines denote the surface traces of the XSHF, and the black triangles in panel e mark the locations of the GNSS sites.
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Figure 6. Significance of PUE correction for InSAR time series analysis. (a) One example interferogram (20180413-20180531) with apparent PUEs from ascending track 26. (b) PUEs detected for (a) based on loop closure phase information. (c) is the same as (a), but with the PUEs detected in (b) masked out. (d) is the same as (a), but with PUEs corrected instead of being masked out. (e) shows the interferogram network with the PUEs corrected, with the red lines showing the interferograms that would be removed from the network if PUE solely masked out, leading to several gaps between interferograms.
Figure 6. Significance of PUE correction for InSAR time series analysis. (a) One example interferogram (20180413-20180531) with apparent PUEs from ascending track 26. (b) PUEs detected for (a) based on loop closure phase information. (c) is the same as (a), but with the PUEs detected in (b) masked out. (d) is the same as (a), but with PUEs corrected instead of being masked out. (e) shows the interferogram network with the PUEs corrected, with the red lines showing the interferograms that would be removed from the network if PUE solely masked out, leading to several gaps between interferograms.
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Figure 7. One example interferogram to assess the quality of tropospheric correction. (a) shows an interferogram (20181110-20181122) from descending track 135. (b) exhibits the regional elevation. (c1–e1) are the atmospheric phase delays estimated from GACOS, APS_Phase, and a combination of GACOS and APS_Phase, respectively, with (c2–e2) being the results of (a) with the tropospheric delays mitigated by (c1–e1). (c3–e3) are scatter plots of the estimated atmospheric phases (c1–e1) and phases of the original interferogram (a), with the red line showing the fitted regression result between estimated atmospheric delays and the original interferogram phase.
Figure 7. One example interferogram to assess the quality of tropospheric correction. (a) shows an interferogram (20181110-20181122) from descending track 135. (b) exhibits the regional elevation. (c1–e1) are the atmospheric phase delays estimated from GACOS, APS_Phase, and a combination of GACOS and APS_Phase, respectively, with (c2–e2) being the results of (a) with the tropospheric delays mitigated by (c1–e1). (c3–e3) are scatter plots of the estimated atmospheric phases (c1–e1) and phases of the original interferogram (a), with the red line showing the fitted regression result between estimated atmospheric delays and the original interferogram phase.
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Figure 8. Quality assessments of atmospheric correction on interferograms from descending track 135. (a) Scatter plots of the STD of the interferograms corrected by GACOS, APS_Phase, and the combined method, with their statistical distributions shown in (c). (b,d) are the same as (a,c), but for STD reduction.
Figure 8. Quality assessments of atmospheric correction on interferograms from descending track 135. (a) Scatter plots of the STD of the interferograms corrected by GACOS, APS_Phase, and the combined method, with their statistical distributions shown in (c). (b,d) are the same as (a,c), but for STD reduction.
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Figure 9. Comparison between the GNSS LOS rates and InSAR LOS rates for descending track 135. (a1) Average InSAR LOS rates estimated from the GACOS method. Color-coded points are the GNSS horizontal velocities projected onto the LOS direction. (a2) Comparison between InSAR LOS and GNSS LOS rates. Horizontal error bars represent the uncertainties of the InSAR LOS rates, while vertical error bars are the uncertainties of GNSS LOS rates. The red line shows the fitted regression result between GNSS LOS and InSAR LOS, with the gray line the one-to-one line for reference. (b1,b2) and (c1,c2) are the same as (a1,a2) but for the results from the APS_Phase and GACOS + APS_Phase methods, respectively.
Figure 9. Comparison between the GNSS LOS rates and InSAR LOS rates for descending track 135. (a1) Average InSAR LOS rates estimated from the GACOS method. Color-coded points are the GNSS horizontal velocities projected onto the LOS direction. (a2) Comparison between InSAR LOS and GNSS LOS rates. Horizontal error bars represent the uncertainties of the InSAR LOS rates, while vertical error bars are the uncertainties of GNSS LOS rates. The red line shows the fitted regression result between GNSS LOS and InSAR LOS, with the gray line the one-to-one line for reference. (b1,b2) and (c1,c2) are the same as (a1,a2) but for the results from the APS_Phase and GACOS + APS_Phase methods, respectively.
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Figure 10. Estimated long-term fault slip rate and locking depth of the XSHF. (a) Fault-parallel velocities and (b) vertical velocities inferred in this study. (c) Blue dots and red lines are the observed and modeled fault-parallel velocities along the across-fault profiles shown in (a). SR: slip rate, LD: locking depth.
Figure 10. Estimated long-term fault slip rate and locking depth of the XSHF. (a) Fault-parallel velocities and (b) vertical velocities inferred in this study. (c) Blue dots and red lines are the observed and modeled fault-parallel velocities along the across-fault profiles shown in (a). SR: slip rate, LD: locking depth.
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Figure 11. Fault slip rate variations along the XSHF. 1: Jiang et al. (2015) [5], 2: Guo et al. (2018) [9], 3: Wang et al. (2008) [22], 4: Rui et al. (2016) [23], 5: Zheng et al. (2017) [24], 6: Tang et al. (2005) [25], 7: Shen et al. (2005) [26], 8: Allen et al. (1991) [1], 9: Qian et al (1988) [15], 10: Zhao et al. (1990) [16], 11: Tang et al. (1993) [17], 12: Li et al. (1997) [18], 13: Xu et al. (2003) [19], 14: Chen et al. (2008) [20], 15: Zhang et al. (2013) [21], 16: Bai et al. (2021) [14], 17: Qiao et al. (2021) [12], 18: Zhang et al. (2022) [30].
Figure 11. Fault slip rate variations along the XSHF. 1: Jiang et al. (2015) [5], 2: Guo et al. (2018) [9], 3: Wang et al. (2008) [22], 4: Rui et al. (2016) [23], 5: Zheng et al. (2017) [24], 6: Tang et al. (2005) [25], 7: Shen et al. (2005) [26], 8: Allen et al. (1991) [1], 9: Qian et al (1988) [15], 10: Zhao et al. (1990) [16], 11: Tang et al. (1993) [17], 12: Li et al. (1997) [18], 13: Xu et al. (2003) [19], 14: Chen et al. (2008) [20], 15: Zhang et al. (2013) [21], 16: Bai et al. (2021) [14], 17: Qiao et al. (2021) [12], 18: Zhang et al. (2022) [30].
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Figure 12. Surface creeping rate of the Kangding segment. (a) Fault-parallel displacements across the Kangding segment. (b) Blue dots and red lines are the observed and modeled fault-parallel velocities along the profiles shown in (a). SR: slip rate, CR: creep rate, LD: locking depth, CD: creep depth.
Figure 12. Surface creeping rate of the Kangding segment. (a) Fault-parallel displacements across the Kangding segment. (b) Blue dots and red lines are the observed and modeled fault-parallel velocities along the profiles shown in (a). SR: slip rate, CR: creep rate, LD: locking depth, CD: creep depth.
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Xi, P.; Li, X.; Song, C.; Wang, B.; Yin, Z.; Wang, S. Assessing Slip Rates on the Xianshuihe Fault Using InSAR with Emphasis on Phase Unwrapping Error and Atmospheric Delay Corrections. Remote Sens. 2024, 16, 1872. https://doi.org/10.3390/rs16111872

AMA Style

Xi P, Li X, Song C, Wang B, Yin Z, Wang S. Assessing Slip Rates on the Xianshuihe Fault Using InSAR with Emphasis on Phase Unwrapping Error and Atmospheric Delay Corrections. Remote Sensing. 2024; 16(11):1872. https://doi.org/10.3390/rs16111872

Chicago/Turabian Style

Xi, Peiyan, Xing Li, Chuang Song, Bin Wang, Zhi Yin, and Shuai Wang. 2024. "Assessing Slip Rates on the Xianshuihe Fault Using InSAR with Emphasis on Phase Unwrapping Error and Atmospheric Delay Corrections" Remote Sensing 16, no. 11: 1872. https://doi.org/10.3390/rs16111872

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