Introduction

The 2500 km Himalayan arc from west to east consists of major thrust faults from south to north: Main Frontal Thrust (MFT), Main Boundary Thrust (MBT), Main Central Thrust (MCT), STDS (South Tibet Detachment System) and Indus Suture Zone (ISZ)/Indus Yalu Suture Zone (Figs. 1, 2). The tectonic units bounded by these thrust faults from south to north are Sub Himalaya, Lesser Himalaya, Higher Himalaya, Tethyan Himalaya and Trans Himalaya. These thrust faults sole in to the basal decollement termed as Main Himalayan Thrust (MHT), which marks the upper boundary of under-thrusting Indian plate. Kashmir valley is located to the extreme west of Himalayan arc bounded by Pir Panjal range to the south and Zanskar range to the north (Figs. 1, 2, 4) and it extends about 140 km with a width of ~ 40 km at an altitude of ~ 1600 m. Kashmir Himalaya is tectonically different from the rest of Himalaya with very narrow lesser Himalaya (bounded by MBT and MCT) below the Pir Panjal and wider sub Himalaya. Major known tectonic structures of the study region are Balapora fault (BF), a NW–SE trending thrust structure, in southern region of the basin and Riasi fault (RF) further south of Pir Panjal range, bounding SW side of the valley.

Figure 1
figure 1

Map of Kashmir valley and adjoining regions (boxed area in the inset map of India) along with major fault/ thrust lines mapped using41,42,43,44 and seismo-tectonic atlas of India45: MFT—Main Frontal Thrust, MBT—Main Boundary Thrust, MCT—Main Central Thrust, STDS—South Tibet Detachment System, ISZ—Indus Suture zone, MMT—Main Mantle Thrust. IKSZ—Indus Kohistan Seismic Zone. Regional fault lines are BBF—Bagh-Balakot fault, RTF—Riasi Thrust fault, BF—Balapora fault and KF—Kishtwar fault. India-fixed velocities of cGPS sites are plotted as arrows: Black (Present study), Red14 and Brown25. Black dashed line is the apparent northern edge of locked decollement estimated from location of microseismicity using data from collocated broadband seismic network (Supplementary section A1). Solid circles denote seismic events: Blue (M ≥ 3; source: https://www.isc.ac.uk/iscbulletin/search/catalogue/), Red (M ≥ 1 located from collocated broadband network) and Yellow5. Focal mechanisms of seismic events of magnitude ≥ 5.0 are plotted from (https://www.globalcmt.org/CMTsearch.html) Global CMT catalogue. Figure was created using GMT (Generic mapping tool) software version 5.2.1 (ftp://ftp.soest.hawaii.edu/gmt/legacy/)46.

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Figure 2
figure 2

GPS derived surface convergence rates in 2500 km Himalayan arc along with major fault lines mapped using41,42,43,44,45: MFT—Main Frontal Thrust, MBT—Main Boundary Thrust, MCT—Main Central Thrust, STDS—South Tibet Detachment System, ISZ—Indus Suture Zone, IYSZ—Indus-Yalu Suture Zone, WFNS—Western Nepal Fault System. Red ellipses represent rupture of 2005 instrumental era event and historical events of 1555 (in Pir Panjal; apparently last major event in the Kashmir seismic gap), 1885 (with epicenter near Pattan, SE of station BARM) and 1905 Kangra earthquake1,2,3,7,8,14,42,43,47,48. GPS site locations are denoted by solid triangles. Black (present study); Magenta14; Brown25; Red15; Blue19; dark Brown20; Green21. Figure was created using GMT (Generic mapping tool) software version 5.2.1 (ftp://ftp.soest.hawaii.edu/gmt/legacy/)46.

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Historical seismicity of Kashmir valley and the adjoining region indicates about ~ 14 damaging earthquakes occurred since year 1123, though the accurate magnitude of these earthquakes could not be determined due to lack of data1. Few of these earthquakes with well documented data on intensity of ground shaking suggest magnitude, Mw of 6–8 (Figs. 1, 2, 4). The most recent and first documented historical earthquake in this region occurred on 30 May 18852,3 with an assigned magnitude of Mw 6.2. The 1555 earthquake is the only earthquake between 1123 and 1885 with tentative magnitude of Mw ~ 7.64. Figure 1 shows the earthquakes that occurred in the region from 1964 to 2019. Seismic events are plotted from three sources i.e. M ≥ 3 events with epicentral error of ~ 5 km from 1964 to 2019 from International Seismological Centre (ISC) revised catalogue, local events of M ≥ 1 (for two epochs: June to September 2013; January 2015 to March 2018) with epicentral error of < 5 km from our collocated broadband seismic network and events of M ≥ 1 with epicentral error of ~ 1 km to southeast of the Kashmir valley from5. Together these events indicate seismicity cluster to the northwest in IKSZ (Indus Kohistan Seismic Zone) related to post seismic activity of October 2005 Muzaffarabad earthquake, scattered micro-seismicity in Kashmir valley and a cluster related to Mw 5.7 Kishtwar earthquake of 2013 to south east in Kashmir Himachal (or Kishtwar region). Crustal structure beneath the Kashmir valley6 delineates the Moho beneath Pir Panjal at depths of ~ 58 ± 2 to 60 ± 2 km and shows crustal thinning of ~ 4 km along the valley axis. Absence of seismicity and duplex nature of topographic height makes it difficult to demarcate the extent of locked MHT in the valley.

The Muzaffarabad earthquake of October 8, 2005 (Mw 7.6) to the northwest of Kashmir valley (Figs. 1, 2, 4) is the first earthquake in Himalaya7,8 with well documented surface rupture. This event occurred in IKSZ along the Balakot-Bagh thrust (Figs. 1, 4) and hence termed as an out of sequence event7,8 as large Himalayan earthquakes are mostly located along the MHT. Post-seismic deformation of this earthquake9,10,11 was estimated using GPS measurements for a period of 5 years (2005–2010) within 100 km of the rupture and several post seismic relaxation models were suggested. Afterslip rectangular dislocation models10 of this earthquake based on Okada dislocation theory12 that best fit the GPS displacements cover extreme northwest edge of the Kashmir valley. The ~ 250 km long segment of Kashmir Himalaya (Fig. 1) between rupture zones of the 1905 Kangra earthquake and 2005 Kashmir earthquake has not experienced any major earthquake for past ~ 500 years i.e. since 1555 earthquake and hence termed as Kashmir seismic gap13. In 2013, earthquake of Mw 5.7 occurred to the south east of Kashmir valley where micro-seismicity cluster with magnitude of 1–5 were recorded by a recent broadband seismic network5. On September 24, 2019, a shallow (depth ~ 10 km), thrust mechanism earthquake of Mw 5.4 occurred in Mirpur, Pakistan bordering south-west of the Pir Panjal range.

Previous GPS studies in Kashmir Himalaya14 from 2006 to 2012 indicate ~ 12 mm/year shortening in the 250 km southern most cross section of Kashmir Himalayas. They suggested that earthquake of Mw 6.5–7.6 is long due in this region, depending on the assumption of three failing segments. A decade of GPS measurements in Kashmir-Himachal Himalaya (Figs. 1, 2, 3a) and Ladakh15 gave arc normal convergence of ~ 14 mm/year for this transect partitioned to 5 mm/year in lesser Himalaya and 3 mm/year in Higher Himalaya. GPS data from 2008 to 201116 at 7 continuous Global Positioning System (cGPS) and four episodic (eGPS) sites in Kashmir (out of which 3 cGPS and 3 eGPS sites are located in Valley) gave oblique convergence rate of ~ 14 mm/year along the MHT with a locking line located beneath Zanskar range with width ~ 175 km at a depth of 38 km. These studies are inconclusive due to limited data duration from sparse network of GPS sites in Kashmir. We present results from total of 16 cGPS sites data (Table 1) out of which 10 cGPS sites are spatially spread across the length and breadth of Kashmir valley, 4 cGPS located northeast of the valley in Zanskar ranges and 2 cGPS sites further northeast at Leh and Hanle during 2008 to 2019. Our study gives well constrained, precise estimates of crustal deformation and strain rate in Kashmir Himalayan transect with more data and dense network of stations.

Figure 3
figure 3

(a) Arc-normal rates of GPS sites in northwest Himalaya (boxed region of Fig. 2) with error bars determined by rotating the site velocities on to the direction locally orthogonal to the arc using arc geometry defined by18. Figure was created using qtiplot software version 0.9.8.9 (https://sourceforge.net/projects/qtiplot.berlios/files/qtiplot-0.9.8.9.tar.bz2/download)49. (b) Arc-parallel rates of GPS sites in northwest Himalaya (boxed region of Fig. 2) with error bars determined by rotating the site velocities onto the direction locally parallel to the arc using arc geometry defined by18. Figure was created using qtiplot software version 0.9.8.9 (https://sourceforge.net/projects/qtiplot.berlios/files/qtiplot-0.9.8.9.tar.bz2/download)49.

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Table 1 ITRF and India Fixed rates of GPS sites used in the analysis with the location description and the data span.
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Results and discussions

GPS displacements

Velocities of all the cGPS sites of the present study are estimated using the methodology detailed in Data and Methods section. ITRF14 and Indian plate frame of reference17 velocities and the associated uncertainties are given in Table 1. India fixed velocities of cGPS sites in Kashmir valley and adjoining regions are plotted in Fig. 1. Arc normal and parallel deformation rates for sites located in Kashmir valley and the adjoining regions are computed and plotted in Fig. 3a,b. These rates are determined by rotating the site velocities, perpendicular and parallel to the local arc geometry as defined by18. In addition, we have plotted in Fig. 3a,b arc normal and arc parallel rates from the published14,16 velocities of four GPS sites (ARJA, DHUL, URII, RAUJ) located to south of valley and five sites (RANK, KULG, NISH, SUMB, NARA) located in the valley (Figs. 1, 2, 4). For the rest of northwest Himalaya, we plotted arc-normal and arc-parallel rates from the published GPS velocities of continuous and campaign sites15,19. All the published GPS velocities are transformed to ITRF14 reference frame and converted to India fixed reference frame using the angular velocity of Indian plate given by17. Arc normal rates indicate total convergence of about 14 mm/year partitioned as 5 mm/year in the Kashmir valley, 5 mm/year south of the valley and 4 mm/year in the Zanskar range north of valley. GPS derived surface convergence rates along the arc normal transects of rest of Himalaya (Fig. 2) from west to east are ~ 16 mm/year in Ladakh, ~ 13 mm/year in Gharwal, ~ 18 mm/year in Kumaon, ~ 13 mm/year in Nepal Himalaya, ~ 10 mm/year in Sikkim, ~ 12 mm/year in Bhutan and ~ 15 mm/year in Arunachal Himalaya15,19,20,21,22. Kashmir valley recorded arc-parallel extension rate of about 7 mm/year from our cGPS sites (Fig. 3b) spatially spread across the valley indicating that the present day active regional deformation in Kashmir valley is oblique in nature. About 9 mm/year arc parallel rate in Ladakh Himalaya is a result of east–west extension of Tibetan plateau. Rest of the Himalaya records low arc parallel extension rate of ~ 3 mm/year, which is due to curvature of locked decollement15,19,23,24.

Figure 4
figure 4

Topographic Map of Kashmir valley and adjoining regions along with surface projection of dislocation plane (dashed box) with residual velocities of the cGPS sites: Black (present study), Red14 and Brown25. Solid red circles denote seismic events of M ≥ 1 from collocated broadband network. India fixed velocity (bold Pink) is plotted at KUPW GPS site to the extreme northwest of Kashmir valley. Blue velocity vectors at Pakistan GPS sites PS01, PS03, PS05, PS13, PS19, PS21 from10 denote post seismic displacements of October 2005 Muzaffarabad earthquake during March 2007 to August 2009 and Indian GPS site KERN11 soon after the earthquake. Published post seismic displacements were transformed to ITRF14 reference frame and converted to India fixed reference frame using the angular velocity of Indian plate given by17. Fault lines and ruptures are same as Fig. 1, 2. Figure was created using GMT (Generic mapping tool) software version 5.2.1 (ftp://ftp.soest.hawaii.edu/gmt/legacy/)46.

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Kupwara site (KUPW) located to the extreme northwest of Kashmir Valley recorded significantly high westward velocity of 14 mm/year i.e. ~ 8 mm/year relative to rest of the valley sites (Table 1, Fig. 4). Post seismic after slip dislocation models of 2005 Muzaffarabad earthquake in IKSZ zone7 suggest post seismic displacements in this region. Afterslip of this earthquake released 56 ± 19% of the seismic moment of main event. GPS measurements10,11,16,25 soon after the earthquake at KERN site, located to the west of KUPW (Fig. 4) recorded post seismic displacement of 2005 earthquake. Coordinate time series of KUPW cGPS site in India fixed reference frame from 2015 to 2019 (~ 4.5 years) is given in Figure S5. Though these measurements were made almost a decade after the 2005 Muzaffarabad earthquake, the orientation of India fixed velocity of KUPW site (located ~ 75 km from the epicenter of 2005 event) is similar to the azimuth of post seismic displacement (Fig. 4) recorded at six GPS sites in Pakistan during 2007 to 200910. Further the temporal distribution of seismicity within 100 km radius of the rupture of October 2005 earthquake (Figure S6) for a period of 5000 days (~ 13.7 years) after the earthquake indicated active post seismic deformation in ISKZ, coinciding with period of GPS measurements at Kupwara (2015–2019). This indicates that ~ 8 mm/year westward motion of Kupwara relative to Kashmir valley sites has a component of post-seismic displacement associated with October 2005 Muzaffarabad earthquake.

There is no consensus regarding the geological structure beneath Kashmir valley from previous studies in this region. Deep Seismic sounding recordings in Kashmir Himalaya26,27 indicate a complex Moho structure beneath the NW edge of the basin. For example28, reported Moho depth of 45 km beneath the Sopore (~ 37 km SSE of Kupwara; ~ 15 km NNE of BARM) and few km to the north Moho dips to a depth of 54 km near BAND cGPS site. Further27, reports that Moho dips to ~ 65 km beneath the Kanzalwan (North of Bandipora town), and further up-warping to the depth of ~ 60 km beneath the Nanga Parbat. The Moho offsets beneath the Sopore and Kanzalwan are ascribed to 2 deep rooted faults beneath the region, apparently oriented in NW–SE direction. The processed broadband data from our network (Supplementary section A1) could not find any evidence of the Moho dip between Sopore and Bandipora. However, increase in Moho depth from ~ 54 ± 2 km beneath the Sopore to ~ 64 ± 2 km north of Kanzalwan is clearly observed, indicating ~ 11° dip of the Moho along with a similar dip of the decollement underneath (Supplementary section A2). This step in decollement and Moho may represent one of the deep rooted faults described by27 which may have contributed to the ~ 8 mm/year westward velocity of KUPW in addition to the post seismic component of 2005 Muzaffarabad earthquake which can be only be confirmed by establishing additional cGPS sites in this region.

Three cGPS sites (PAND, BHIM, and KARG) located in the Indus Suture Zone (ISZ) (Fig. 1, Table 1) record relative motion of ~ 3 mm/year indicating active regional deformation in this region. Collocated broadband seismic data (Supplementary section A3) indicates upwarping of the Moho from the depth of 66–68 km beneath Pandrass (PAND) to 60 km beneath Kargil (KARG). This undulation of about 6 km of the Moho in arc normal direction requires further corroboration in terms of the subsurface structures in this region. Present day regional deformation rate of ~ 3 mm/year recorded in ISZ may be due to the presence of active unmapped subsurface structures in this region. Confirmation or rejection of this hypothesis would require further cGPS and broadband seismic data from the region. Further, a similar Moho depth of ~ 68 ± 2 km is obtained beneath surface expression of ISZ at different points from Kashmir broadband data. A similar depth of the Moho (~ 70 km) was also observed beneath the ISZ in Nepal Himalaya29. However, seismic data points towards more complex crustal structure beneath the Zanskar as compared to the Kashmir valley (Supplementary section A3).

Surface projection of Balapora fault (Fig. 1) in Kashmir valley coincides with southwest end of Kashmir valley seismic line defined by26,27,30. Balapora fault is northeast dipping reverse fault with 40 km surface length31 where as it is also been interpreted as surface expression of SW dipping back thrust32. Aharbal cGPS site is located to the south of Balapora fault (~ 12 km) and Batpal site is located to the north (~ 27 km). Baseline between these two sites indicates convergence rate of about 3.5 ± 1 mm/year. Given that, cGPS sites (UOKA, RANK, GULM, BARM) located in Kashmir valley to west of Balapora fault do not record significant convergence across the valley suggesting that the fault may be active and is accommodating about 3.5 mm/year convergence in the Kashmir valley. Earlier study14 reported that the entire long-term convergence in this region is absorbed by Balapora, Riasi and MFT faults.

Broadband seismic network in the valley recorded Mw 5.4, 24 September 2019 earthquake in Mirpur, Pakistan to the south of Jammu and Kashmir. For example, maximum absolute peak velocity of 0.688 mm/s was recorded at the nearest station AHAR on N–S component and slightly less on both E–W (0.559 mm/s) and vertical (0.517 mm/s) components for this event. This is also evident from earthquake intensity map which reported higher intensity in NW–SE direction of the event, more towards SE direction (https://earthquake.usgs.gov/earthquakes/eventpage/us60005mqp/map). However, both 30 s and 1 s interval cGPS data of Kashmir valley did not record any co-seismic offset of Mw 5.4 2019 earthquake with epicenter at about 100 km southwest of the valley.

Dislocation models

Inverse modeling using Okada dislocation theory and weighted least square inversion12 of India fixed velocities of Kashmir valley and the adjoining regions (Table 1) provide buried dislocation parameters and the associated slip. Assuming that the surface deformation is caused due to slip along the single planar dislocation (MHT) of finite length and width in elastic half space, the equation for slip, say m following12 is given as m = (GT·We·G)−1 GT·We·d, Where G is a function of dislocation parameters, We is weight matrix, d are GPS velocities. The slip m consists of two orthogonal components, dip-slip and strike-slip. The weight matrix is taken as the inverse of covariance matrix of the observed GPS velocities. Input to the inverse program are the range of a-priori dislocation parameters (starting point, dip, strike, depth, length, width), and GPS velocities. The output is the slip estimated using inversion technique for all possible combination of dislocation parameters. Best fit is the solution for which the residual between the observed and modelled displacements is minimum (Fig. 4). Complete detail of the dislocation modeling theory is given in15.

We used the GPS velocities from our study along with the published velocities14,25 of 9 cGPS sites in this region (Fig. 4). The best-fit dislocation model for Kashmir valley gives a dip-slip of ~ 15.5 mm/year and strike-slip of ~ 4 mm/year along the single buried dislocation with a depth of ~ 15 km, length and width of ~ 145 km. Dip and strike angle of the buried dislocation is 7° and 142° respectively (Fig. 4). Micro-seismic events recorded by collocated broadband network in Kashmir valley and adjoining regions are plotted in Figs. 1 and 4 along with seismic events from ISC catalogue (Fig. 1) and one year local events from5. Micro-seismicity in Kashmir valley from collocated broadband data (Supplementary Section A1) points towards probable location of the northern edge of locked decollement plotted by dashed black line in the Fig. 1. In addition, results from Kashmir broadband network (Supplementary Section A1) found a low velocity layer at a depth of 12–16 km representing the locked decollement6. Our dislocation model is consistent with the northern edge of locked decollement, as highlighted by location of micro-seismicity, and the depth of decollement reported from Kashmir broadband network data.

Previous studies with limited spatial spread and duration of GPS data16,25 and using33 elastic dislocation theory, reported oblique slip of ~ 13.6 mm/year with dip slip component of 11.8 mm/year and strike slip component of 6.7 mm/year in Kashmir valley along locked decollement of 175 ± 20 km width, (38 km depth) and dip of 12.5°. Boundary element method was used14 to identify subsurface geometry and slip distribution that best fits the GPS velocities from the limited GPS data. Their GPS data gave good constraints on the slip rate of 11 mm/year along a single planar dislocation with a dip of 7°. They could not constrain the depth of dislocation and it varies between 15 and 23 km. They also gave an alternative model with double ramp geometry with tapered slip with a width of 35 km terminating beneath the north edge of Kashmir valley at 25 km depth that fits the surface GPS velocities with a slip of 11 mm/year14. Our GPS measurements with good spatial spread and long duration data give well constrained depth of dislocation as 15 km and oblique slip of ~ 16 mm/year which is consistent with the presence of low velocity layer of 12–16 km depth interpreted as shear zone associated with locked decollement6. Diffused seismicity at shallower depths is observed to the southeastward of the valley at longitude 75.75° E.

Strain rates

Our surface GPS velocities along with published GPS velocities at 9 additional sites14,16,25 were used to determine the crustal strain rates in Kashmir valley and adjoining region. Displacements (Un) and position (Xn) of n GPS sites are used to determine the strain tensor (I) using least square approach expressed as U = AI + e in matrix form, where matrix A is given by the position of GPS points and e is the residual vector34. Modified least square method35 is used in which adjustment based on the effect of nearest sites is made on the least square covariance matrix using a scale factor. This gives the choice to use different scales of analysis and evaluate the scale-dependent behavior of the observed system and select a scale factor that best fits the observed system. Grid-Strain program34 enables to include or exclude a GPS point to estimate the effect of the specific point and is advantageous to compute strain rates using unevenly distributed cluster of GPS points. The inputs to the program are GPS velocities and positions and the output is the strain tensor.

We used two dimensional grid strain program in which computations are performed at each node of XY grid (Fig. 5) and the output given as strain field tensors consisting of eigen vectors, eigen values and the normalized shear. Strain at a point is considered highly significant if the distance between the reference point and at least one GPS point in that sector is less than the scale factor chosen for the observed system. High significant strain for Kashmir valley along with associated rigid rotations are plotted in Fig. 5, which indicates high compression (red) with a mean rate of 4.5e−08 year−1 approximately normal to the arc in Kashmir valley and adjoining regions. Maximum compression of 7e−08 year−1 occurs along the northern edge of decollement. High extension (blue) rate of 7.4e−08 year−1 is observed to the northwest of the valley which is due to the anomalous westward motion recorded at KUPW GPS site. In Zanskar range and ISZ the strain rates are higher compared to the valley. Demarcation of strain rates to the south of Zanskar and north of valley indicates high strain accumulation in this region that coincides with the northern boundary of locked decollement. Our results are broadly consistent with that of16 indicating high strain concentration in southern Zanskar Himalayan region with the limited data.

Figure 5
figure 5

High significant strains at each grid point (resolution: 10 × 10 km). Red: Compression, Blue: Extension, Yellow: Rotation. cGPS site velocities used for determining the strain rates are denoted by solid triangles. Black dashed line is the northern edge of locked decollement estimated from dislocation model. Figure was created using GMT (Generic mapping tool) software version 5.2.1 (ftp://ftp.soest.hawaii.edu/gmt/legacy/)46.

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Conclusions

cGPS measurements in Kashmir Himalaya and adjoining region give well constrained oblique surface deformation rate of ~ 15.6 mm/year in this transect of Himalaya. This region records total arc normal GPS convergence rate of 14 mm/year and arc-parallel extension rate of 7 mm/year. Elsewhere in the Himalaya, from Ladakh in the west to Arunachal in the east record ~ 10 to 20 mm/year arc-normal convergence with lowest rate of ~ 10 to 12 mm/year in Sikkim and Bhutan Himalayas. Additional cGPS measurements are required (1) to precisely quantify the contribution of post seismic component of 2005 Muzaffarabad earthquake to the high westward velocity recorded to the extreme northwest of Kashmir valley, (2) to estimate the slip rate along Balapora fault and (3) to better constrain the crustal deformation in ISZ.

Inverse modeling of GPS velocities in Kashmir valley and adjoining regions give oblique slip of ~ 16 mm/year along the 145 km wide decollement at a depth of 15 km. Our study using good spatial spread and long duration cGPS data gave reliable constraints on the depth of decollement which is consistent with the recorded seismic activity and low velocity structure6 mapped around same depth (12–16 km). Strain rates estimated using the GPS velocities indicate high strain accumulation (7e−08, compression) to the north of the valley and south of Zanskar consistent with the northern edge of the locked decollement mapped using the seismic activity and inverse models. Strain rates (extension) to the SE of Kupwara are due to the anomalous westward GPS velocity of KUPW cGPS site which needs further investigation.

Historical earthquake record suggests about 14 damaging earthquakes occurred during 1123 to 1885, with only one earthquake of Mw ~ 7.6 in 1555 with poorly estimated rupture parameters. Kashmir seismic gap of ~ 250 km length between the rupture zones of 2005 Muzaffarabad and 1905 Kangra earthquakes did not record any major seismic slip during the intervening ~ 465 years. Considering that all the accumulated strain is fully released during the 1555 earthquake and fresh strain accumulation started since then, high strain rates recorded in this region give a scalar geodetic moment accumulation rate36 of ~ 8.91e24 dyne-cm/year (~ 4.14e27 dyne-cm for 465 years) which is capable of generating Mw 7.7 earthquake. Accumulated slip deficit since 1555 event is ~ 7.4 m (16 mm/year for 465 years) and assuming rupture of the probable earthquake to be similar to 2005 Muzaffarabad earthquake, seismic moment37 is ~ 5.3e27 dyne-cm suggesting Mw 7.8 earthquake is long due in this region. If the seismic moment released due to the after slip of the 1555 event is assumed to be similar to the 2005 earthquake10, the reduction in the Mw for a single event would be ~ 0.14. Micro-seismicity recorded in Kashmir valley further corroborate that a high magnitude earthquake is long due in this region. Our hypothesis is broadly consistent with the conclusions drawn by6,14 that large magnitude earthquake is anticipated in this region, may be with low probability of occurrence.

Methodology

GPS data and analysis

Complete details of cGPS sites and data span used for the study is given in Table 1. In addition to 16 cGPS sites in Kashmir we have used cGPS data of 9 sites in the rest of Himalaya and 10 plate interior sites (Fig. 1). All the cGPS sites are located on hard rock exposures (except the Kashmir University (UOKA) cGPS site) with 3–10 years of data. cGPS data spanning 12 years (2008–2019) is analysed using GAMIT/GLOBK software38 along with 22 IGS sites (Table 1) after performing quality check on the data using TEQC software39. Loosely constrained daily solutions were obtained using sampling interval of 30 s and elevation cut off angle of 15° after eliminating data with short duration (< 20 h), multipath and several cycle slips. Errors related to satellite clock, receiver clock, phase ambiguities, atmosphere, phase center and multipath are minimized in the daily solutions as detailed in19. Final daily solutions are combined using GLORG to determine the positions and velocities of the cGPS sites in ITRF2014 reference frame40 by stabilizing the IGS sites to their ITRF2014 positions and velocities. ITRF2014 velocities and the associated uncertainties are given in Table 1 for all the cGPS sites used in the present study. India fixed velocities (Table 1) and associated uncertainties of the cGPS sites are determined using the angular velocity of India-ITRF14 as given by17.