Introduction

On November 19, 1996, at 18:44 CST, an earthquake with a surface-wave magnitude of 7.1 (Ms) occurred in the Karakoram Pass region, just southwest of Hetian, ** that uses fast transforms and iterative methods. JOSA A 11(1):107–117" href="/article/10.1186/s40623-019-1089-4#ref-CR3" id="ref-link-section-d222666367e798">2014; Sun et al. 1985). The aim of the present paper is to investigate the causes and mechanisms of shallow earthquakes in the Karakoram fault zone and to broaden our understanding of the impact of the Karakoram Pass earthquake on the pattern of strong seismic activity in the Qinghai-Tibetan Plateau.

Regional tectonic background

The collision between the Indian and Eurasian plates due to their continuous convergence has led to strong intracontinental deformation in Central Asia, giving rise to intense tectonic activity in the Pamir Plateau and the surrounding regions (Pan et al. 1998; Valli et al. 2008; Matte et al. 2013). The Linjitang fault in the basin forms the boundary between the anticlinal fold belt of the South Kunlun Mountains and the Linjitang depression. The Ageledaban fault is a normal crustal fault, which has displayed strong activity in the Late Paleozoic, Mesozoic, and Cenozoic (Luo et al. 2003). The earthquake epicenter was at the location of China’s maximum gravity value. Its measured Bouguer anomaly was approximately − 500 mGal and the measured isostatic gravity was − 180 mGal (Xu et al. 2014). Based on geodetic leveling data acquired from 1955 to 1995, the uplift rate in the epicenter area before the Karakoram Pass earthquake was 4–5 mm/year (Wang et al. 2009).

Fig. 1
figure 1

Location and regional tectonic background of the 1996 Karakoram Pass earthquake. The red dot is the earthquake epicenter, the red lines are traces of faults from Central Asia Fault Database, and the purple arrows show the GPS velocity from Zheng et al. (2017). a is a topographic map, the red box is the range of b, c is a detailed topographic map near the earthquake. WKM West Kunlun Mountains, KM Karakoram Mountains, KXF Kangxiwa fault, KGF Kegang fault, TDF Tianshendaban fault, LF Linjitang fault, AF Ageledaban fault, KF Karakoram fault, LDF Longmu-Dulishi fault

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InSAR co-seismic deformation field acquisition

SAR data acquisition and processing

The number of SAR images available for the Karakoram Pass earthquake is very limited. A total of 4 images were downloaded from the ERS 1/2 data catalog published by the ESA. Table 2 and Fig. 2 show detailed image pairing data.

Table 2 Information for pairing InSAR images(trace number: 334, frame number: 2889)
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Fig. 2
figure 2

InSAR image pair baselines

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Due to the low vegetation coverage in the Qinghai-Tibetan Plateau, the multi-path scattering effect caused by vegetation is minimal in this region. To minimize the loss of coherence due to topographic errors or image distortion, NASA’s 30-m SRTM DEM data and the ERS Precise Orbit data provided by Delft University, Netherlands are used to perform two-pass differential interferometry (Massonnet et al. 1995) using the advanced radar image processing software ENVI/SARscape. Figure 3 shows a data processing flow chart. The robust Goldstein filtering method was used to ensure the clarity of fringes and reduce coherence loss due to noise from the spatial and temporal baselines (Goldstein and Werner. 1994; Liu et al. 2018). Because the spatial and temporal baselines of the interferometric image pairs were relatively long, the obtained interferograms still contained some phase noise caused by residual orbital errors, despite the use of precise ephemeris data. To reduce this effect, polynomial model-based orbital refinement and phase shift correction were applied using multiple ground control points (GCPs) located far from the deformation region in open and flat areas, such as river valleys. Finally, after clip** and geocoding, we obtain the co-seismic surface deformation field produced by the Karakoram Pass earthquake (Fig. 4).

Fig. 3
figure 3

InSAR image processing flowchart

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Fig. 4
figure 4

InSAR results of the 1996 Ms. 7.1 Karakoram Pass earthquake; a–c are wrapped InSAR deformation field, the white arrows represent the azimuth (AZ) and line of sight (LOS) direction, the black arrow shows the north direction, the white dashed lines are the surface trace of zero displacements, and the black solid line is the Ageledaban fault (AF); aʹ –cʹ are the unwrapped InSAR deformation fields after geocoding, the red solid line are the selected sections position; a″–c″ are LOS deformation curves of sections

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The location of the Karakoram Pass earthquake is the Depsang basin, where melting alpine snowpack and long-time intervals between paired images directly affect the coherence of the interferograms. High coherence could only be obtained in flat regions, such as basins and valleys (coherence coefficient above 0.5).

InSAR co-seismic deformation

It is evident from the InSAR interferograms in Fig. 4a–c that the fringes from the three deformation fields are clearly visible. Deformation along the (LOS) direction for each fringe period is 2.8 cm, and most deformation is concentrated within an area measuring 18 × 9 km2. The surface deformation caused by the Karakoram Pass earthquake presents two deformation areas (north and south) centered on an E–W strike fault. The strike angle of this fault is approximately 96°, which is consistent with nodal plane 1 of the focal mechanism solution provided by USGS. In addition, this fault cuts across the Ageledaban fault. However, it is presumed to be a concealed secondary fault (white dashed line in Fig. 4) because its structure is not clearly visible on the surface.

The north and south deformation areas are clearly asymmetric. It is evident from the periodic changes in the deformation fringes shown in Fig. 4 that the fringes on the north side of the concealed fault are tightly spaced without an obvious diversion trend, indicating the earthquake caused large deformation within a very narrow area. In contrast, the fringes on the south side are half-elliptical and diverge along the southeast direction, consistent with sinistral shear trend. Because SAR produces side-looking images, the co-seismic deformation fields were obtained along the LOS direction. In addition, positive LOS deformation value after geocoding with ENVI/SARscape indicates that the surface was approaching the satellite (e.g., uplift), whereas a negative value indicates that the surface was moving away from the satellite (e.g. subsidence). The three deformation profiles in Fig. 4a–c indicate the area north of the fault was moving away from the satellite during the two imaging periods, on the contrary, the area south of the fault was moving toward the satellite. Consequently, one can conclude that the deformation field reflects sinistral strike-slip fault activity, also shown in Wang and Wright (2012).

The maximum LOS displacement in the southern side is approximately 24.6 cm, and the maximum LOS displacement in the northern side is approximately − 18.5 cm. The maximum deformation area is located at the intersection of the concealed fault and the Ageledaban fault.

Fault source modeling

Fault-geometry parameters provide one of the primary bases for understanding co-seismic deformation. Therefore, we invert the InSAR data for estimating the coseismic slip distribution of the Karakoram Pass earthquake in two steps. First, we performed an exhaustive search for the best-fit fault parameters under the assumption of uniform slip on a rectangular fault. Then, we divided the faults into sub-faults and estimated the slip along each fault patch.

To reduce the number of points and consequently improve the computational efficiency, we first attempted to down-sample the InSAR data using the quadtree partitioning method (e.g., Ji et al. 2017). However, this failed to capture the primary deformation pattern with a sufficiently high resolution. We subsequently grid-sampled the near-field area at a dense regular spacing and the far-field area at a sparse regular spacing. The deformation fields (Fig. 4a–c) are downsampled. Finally, we obtained 1315 points for inversion, including 436 from Fig. 4a, 598 from Fig. 4b and 281 from Fig. 4c, and all the three data are combined in one figure (Fig. 5).

Fig. 5
figure 5

1315 observed values for inversion of the co-seismic deformation field

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Inversion of fault parameters

Okada (1985) showed that the causative fault can be interpreted as one rectangular plane with a uniform slip embedded within a homogeneous, isotropic, elastic half-space. Therefore, using the InSAR surface displacements, we can potentially place constraints on the fault parameters through modeling (Kobayashi 2017).

We use the focal mechanism solution published by USGS as the initial input, the parameters of the fault (latitude, longitude, strike, dip, rake, slip, fault depth, length, and width) were solved iteratively using the Levenberg–Marquardt least squares optimization algorithm (Marquardt 2013) to invert the slip distribution on the fault plane.

$$d_{\text{InSAR}} = Gs + \varepsilon$$
(1)

where \(d_{\text{InSAR}}\) is the observed value at the surface, \(G\) is the Green’s function, \(s\) is the slip on the fault plane, and \(\varepsilon\) is the measurement error.

Since the fault plane is usually divided into many small patches, \(s\) represents the slip on each sub-fault plane. In this paper, we set length and width of the fault to be 38 and 24 km, respectively. The fault plane was subsequently discretized into 912 sub-fault elements, each measuring 1 × 1 km2. In addition, to prevent oscillating solutions for the slip distribution, the relationship between slip on the sub-fault element and the InSAR observation must satisfy the following condition:

$${\text{min}}\left[ {\left\| {Gs - d_{{InSAR}} } \right\|^{2} + \alpha ^{2} \left\| {Hs} \right\|^{2} } \right] \to 0$$
(2)

where \(\left\| {} \right\|^{2}\) is the Euclidean norm, \(H\) is the Laplacian constraint that limits fault smoothness, s is the amount of slip in the underground fault plane to be calculated, \(\alpha\) is a factor that defines fault smoothness, and \(Gs - d_{\text{InSAR}}\) is the residual of a fit to the fault dislocation.

During the inversion process, the CRUST 1.0 model was used to determine the regional crust stratification structure and calculate Green’s function. For the sliding amount of adjacent patches, the stress drop smoothing constraint was applied because a constant stress drop is a more realistic approximation from a physical perspective.

The slip distribution obtained by the inversion is shown in Fig. 7. Gaps between the simulated values were filled using the kriging interpolation method, which is commonly used in geology.

According to the surface deformation distribution characteristics and deformation magnitude of the simulated and observed deformation fields in Fig. 6, the two fields show good consistency with a correlation of 90.1%. This proves that the Okada elastic model can well explain the co-seismic deformation field of the Karakoram Pass earthquake. Quantitative analysis needs to be based on residual error distribution. The residual error values are mainly distributed on both sides of the fault and the edge of the deformation zone, with the values being mostly less than 10 cm and the maximum being 12.1 cm. This shows that the residual error mainly might come from simplification of fault model and unwrap** error caused by excessive deformation gradient.

Fig. 6
figure 6

Inversion of the co-seismic deformation field of the 1996 Karakoram Pass earthquake. a simulated values, and b residual distribution, and c geological surface trace

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The co-seismic fault slip distribution shows that the co-seismic displacement is dominated by sinistral strike–slip accompanied by a small normal slip component. The rupture length along the direction of the strike reaches 24 km. The co-seismic slip distribution was concentrated between 0 and 18 km in depth. The maximum slip was 81 cm, which occurred at a depth of 8.5 ± 0.5 km, which shallower than the depth of derived from the uniform slip model (17 km), with projected ground location at lat. 35.36°N and long. 78.03°E. As shown in Fig. 7a, at about 30 km along the fault strike, the eastward displacement of the fault is obviously obstructed by a nearly vertical dip. The co-seismic slip is smaller below 18 km depth, which shows that this was a shallow-focus earthquake. The inverted dislocation model has a corresponding moment magnitude of Mw 6.5 ± 0.11, which is less than the values provided by the three seismological analyses (shown in Table 1). This might be related to the very long temporal baselines in the interferograms and the sparseness of the deformation field.

Fig. 7
figure 7

a Two-dimensional and b three-dimensional views of the co-seismic fault slip distribution of the 1996 Karakoram Pass earthquake

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Discussion

Uncertainty of co-seismic deformation field

InSAR allows the seismology of remote areas with limited seismic networks to be examined. However, the available SAR image data for the Karakoram Pass earthquake are very limited; only 3 sets of interferometric pairs are available that span minimum and maximum time intervals of 841 and 1120 days, respectively. Therefore, the 3 interferometric deformation fields, which were used to invert the co-seismic slip distribution, include post-seismic deformation data for a 2.5 year period after the earthquake. Post-seismic deformation might be caused by residual slip of a seismogenic fault. Therefore, the co-seismic slip distribution should also contain some after-slip. However, because the magnitude of the main shock was not high, after-slip should be relatively small and should not affect the overall distribution of the co-seismic slip. The residual distribution map of the inversion results (Fig. 6b) exhibits fan-shaped over-fitting surrounding the strip-shaped central area in the deformation zone, where the values are mostly less than 10 cm and the maximum being 12.1 cm. The residual error mainly comes from simplification of fault model and unwrap** error caused by excessive deformation gradient. As shown in Fig. 4aʹ–cʹ, incoherence is the most serious in the mountainous region. Although incoherence caused by the long temporal baseline affect the InSAR results, the InSAR deformation field covers the near-field region of the epicenter well, thus the model-predicted InSAR deformation can account well for the observations in both the near- and the far-fields.

Epicenter location

Due to the scarcity of seismic stations in Asia in 1996 and crustal inhomogeneity in the Qinghai-Tibetan Plateau, the location of the Karakoram Pass earthquake epicenter as determined from seismic data was highly uncertain (Table 1). The largest discrepancy between the GCMT results and those from (Gao et al. 2004). Due to the nearly N–S compressional stress, the Karakoram fault zone has dextral strike–slip characteristics, with multiple strike–slip earthquakes occurring in the fault zone (Valli et al. 2004) based on 33 GPS velocity (Fig. 1) values close to the epicenter measured from 1997 to 2015 (Zheng et al. 2017). The results show that this high-strain zone represents post-seismic deformation from the 1996 earthquake, which is consistent with Wang and Wright (2012), and the Karakoram strike-slip fault zone has undergone a complex tectonic deformation process. The continuous northward movement of the Indian plate is causing a continual uplift of the Qinghai-Tibetan Plateau. This is accompanied by coupling deformation and northward migration of the lithospheric upper mantle, causing accumulation of significant residual mass. Meanwhile, due to the constraining role of the rigid Tarim basin, many surface uplifts and depressions have formed in the Karakoram fault zone (Xu et al. 2014). The principal strain rate shows a decreasing trend on both sides of the Karakoram strike-slip fault. In addition, positive and negative surface expansion rates are present. Under the assumption of volume conservation, a negative value indicates vertical expansion or thickening, and a positive value indicates vertical contraction or thinning. It is evident from Fig. 8b that the expansion rate is primarily positive on the north side of the epicenter region and negative on the south side, meaning the north side is experiencing crustal thinning, while the south side is undergoing crustal thickening. This means that the Karakoram Pass earthquake occurred in a strain gradient zone. In addition, as shown in Fig. 8c, the epicenter is located in a region with the largest value of the maximum shear strain rate field, and the shape of the field in this region is consistent with the strike of the seismogenic fault. Although these results reflect the strain conditions after the 1996 earthquake, they also indicate from the side that left-lateral component of the earthquake may have occurred to offset the accumulated strain energy. This indicates that the Kongur system on the north side of the Karakoram fault zone is extensional, but so is the central part, which might explain the formation of a basin in the middle part of the fault zone.

Fig. 8
figure 8

Tectonic strain field in the epicenter region: a principal strain rate field; blue and red bars indicate the principal compressional and extensional strain rates, respectively; b dilatational strain rate field; and c maximum shear strain rate field: the white line is the seismogenic fault

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Conclusion

The Ms7. 1 Karakoram Pass earthquake on November 19, 1996 occurred at the northwest of the Qinghai-Tibet Plateau, in an area with harsh natural conditions and very weak monitoring capability of the seismic network. We obtained the co-seismic deformation field of the earthquake by using the ERS1/2 SAR data and InSAR technology. With the deformation field as a constraint, the geometric parameters of seismogenic fault were inversed nonlinearly based on Okada dislocation model, and the slip distribution on the fault plane was inversed linearly using SDM method. The main conclusions are as follows:

  1. 1.

    Most of the deformation caused by this earthquake is concentrated within an area measuring 18 × 9 km2, with the maximum LOS shortening in the southern side 24.6 cm. The maximum LOS lengthening in the northern side is approximately 18.5 cm. The inversion result shows that the location of the co-seismic rupture centroid is (78.03°E, 35.36°N), and the calculated moment magnitude is Mw6.5, which is slightly smaller than the magnitude released by other methodologies.

  2. 2.

    The seismogenic fault is a concealed secondary fault with 96° strike, 84° dip, and -24° rake, which is located in the movement range of the Ageledaban fault. The co-seismic displacement is dominated by sinistral strike–slip accompanied by a small normal slip component. The slip distribution was concentrated between 0 and 18 km in depth. The maximum slip was 81 cm, which occurred at a depth of 8.5 ± 0.5 km.

  3. 3.

    The Karakoram strike–slip fault zone has undergone a complex tectonic deformation process: the north side of the epicenter region is experiencing crustal thinning, while the south side is undergoing crustal thickening. This indicates that tension also exists in the central part of the Karakoram fault zone.