Introduction

The Himalayan range is a diffused plate boundary evolved through continental collision between the Indian land mass and the Asia, and began at some 50 Ma before (Besse et al. 1984; Molnar 1984; Patriat and Achache 1984; Gaetani and Garzanti 1991). The convergence rates of Indian plate against the southern margin of the Tibetan plateau vary significantly between ~4.2 and 5.4 cm/years (DeMets et al. 1990). The convergence led to the tectonic stacking of upper and mid-crustal slabs on the northern margin along the foreland of the Indian plate originating from the basal decollement called the Main Himalayan Thrust (MHT). The compression due to convergence and stacking of crustal slabs over the leading edge of the Indian plate results its flexure and progressive thickening of the crust toward the north (Lyon-Caen and Molnar 1985). The weight of the mountains is supported in part by the strength of the plate, and the plate distributes the load by flexing down in front of the range to form a basin (e.g., Lyon-Caen and Molnar 1983). The Moho configuration of the lithosphere beneath the Greater Himalaya toward north accounts for decrease in flexural rigidity (Jin et al. 1996; Cattin et al. 2001; Jordan and Watts 2005; Hetényi et al. 2006; Tiwari et al. 2006, 2010). Gravity data show an increase in gravity gradient from ~1 mgal km−1 over the Indo-Gangetic plain to 2 mgal km−1 over the Greater Himalaya, which accounts for more steepening of the Moho beneath the Greater Himalaya (i.e., ~10°–15°) than beneath the Lesser Himalaya (i.e., ~2°–3°) (Molnar 1983; Ni and Barazangi 1984). The seismic experiments conducted in southern Tibet indicate a crustal thickness of the order of 70–80 km (e.g., Hirn et al. 1984; Zhao et al. 1993; Nelson et al. 1996), consistent with isostatic adjustment of the plateau (Lyon-Caen and Molnar 1985; Jin et al. 1996; Hetényi et al. 2006; Tiwari et al. 2006, 2010). Tectonic crustal thickening associated with deformation in the Himalaya is in part compensated by denudation (Cattin and Avouac 2000); however, the denudation rates vary laterally along the stretch of the Himalayan arc (Cattin and Avouac 2000). Lavé and Avouac (2000) have shown that the localized thrust faulting on the Main Frontal Thrust (MFT) is continued along the MHT and absorbs ~22 mm/years, an amount that accounts for all shortening rate across the range. This is in agreement for thrusting of the Himalaya over the MHT with little internal deformation (Cattin and Avouac 2000). Li et al. (2008) advocated a significant lateral variations in subduction-related mantle structure beneath the Himalayan collision zone and inferred that the horizontal distance over which the Indian lithosphere slides northward beneath the plateau decreases from west to east.

Our study area is focused over two important tectonic domains of the Himalayas: (1) the Nepal and (2) the Sikkim–Darjeeling sector (Fig. 1a). Along with north-south variations of tectonic processes all through the ~ 2500 km long Himalayan belt (Ni and Barazangi 1984; Hodges 2000), there is significant west-east variations of topography (Duncan et al. 2003; Yin 2006; Khan et al. 2014), a reduction in crustal shortening (McQuarrie et al. 2008; Long et al. 2011), decrease in flexural wavelength (Hammer et al. 2013) and patterns of focal mechanisms (Hazarika et al. 2010). Besides, the Indian plate obliquity increases both toward west and east of Kathmandu, Nepal, and reaches to highest values at the termini of the Himalayan orogen (McCaffery 1996). Northward penetrating evenly spaced basement ridges (e.g., Monghyr-Saharsa, Faizabad, and Delhi–Hardwar) in the central sector of the Himalayan foothill (Sastri et al. 1971; Rao 1973; Valdiya 1976; Dasgupta et al. 1987; Gahalaut and Kundu 2012), uneven along-strike distribution of seismicity (Ni and Barazangi 1984; Khattri 1987; Verma and Kumar 1987; Bilham and Gaur 2000; Rajendran and Rajendran 2005), counterclockwise rotational underthrusting, oroclinal bending and the consequent southward non-uniform migration of overriding land mass toward the Himalayan margin (Klootwijk et al. 1985; Willet and Beaumont 1994), and the confinement of earthquakes in the deeper part of the converging Indian lithosphere (Nábelek et al. 2009; Ansari and Khan 2013) clearly envisage a lateral change in dynamics/kinematics of the Himalaya. In line with these evidences, we examine the gravity data through modelling of Nepal and Sikkim–Darjeeling sectors of this intercontinental diffuse boundary. We note an apparent change in dip of the Moho between these regions. We further testify our observations through finite-element stress modelling and earthquake’s source processes in these areas. Two trench-orthogonal vertical models for the oppositely converging Indian lithosphere and the Asian land mass for Nepal as well as Sikkim–Darjeeling Himalayas have been proposed through improving model parameters for geometry and density of each prism by linear inversion (Webring 1985). To minimize the non-uniqueness of the modeling, the initial geometries of different layers and crustal boundaries within the converging Indian lithosphere and the overriding Asian land mass (Fig. 1b) have been initially constrained by the works of Owens and Zandt (1997), Johnson (2002), Thiede et al. (2004), Bollinger et al. (2006), Robert et al. (2009), Zhang and Klemperer (2010), and Hammer et al. (2013).

Fig. 1
figure 1

a Simplified tectonic map with overview of topography of Nepal and Sikkim–Darjeeling Himalayas reconstructed after Gansser (1964), Valdiya (1980), Verma and Kumar (1987), Gahalaut and Kundu (2012). The shaded areas in the inset map on top right represent the study area. The topographic elevation is shown by the colored scale on left bottom corner. Solid arrows represent the convergence velocity direction of the Indian plate with respect to the Asian plate (after DeMets et al. 1994). Barbed solid triangle represents the thrusting. Various profiles (1 after Thiede et al. 2004; 2 after Bollinger et al. 2006; 3 after Schulte-Pelkum et al. 2005; 4 after Tiwari et al. 2006; 5 and 6 after INDEPTH; 7, 8, and 9 after Hammer et al. 2013) used for constraining the initial lithosphere geometries are also shown by solid green-colored lines. Profiles AA′ and BB′ are considered for the present study. b Simplified section across the Himalaya illustrating the subduction of Indian lithosphere beneath southern Tibet (after Owens and Zandt 1997; Johnson 2002; Thiede et al. 2004; Bollinger et al. 2006; Robert et al. 2009; Zhang and Klemperer 2010; Hammer et al. 2013). MFT Main Frontal Thrust, MBT Main Boundary Thrust, MCT Main Central Thrust, MHT Main Himalayan Thrust, STD South Tibetan Detachment, ITS Indus-Tsangpo Suture, SH Siwalik Himalaya, LH Lesser Himalaya, GH Greater Himalaya, THS Tethys Himalaya, ST Southern Tibet, IUC Indian Upper Crust, ILC Indian Lower Crust

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During the last two decades, numerical modeling has been widely used to explore the stress field and mechanics of lithospheric deformation in different tectonic regimes of the world (Makel and Walters 1993; Willett et al. 1993; Beaumont et al. 1994; Sassi and Faure 1997; Vanbrabant et al. 1999; Mikhailov and Marin 2001) and also in the Himalayan arcuate belt (Wang and Shi 1982; Singh et al. 1990; Vergne et al. 2001; Sanker et al. 2002; Berger et al. 2004). We also do the finite-element modeling on the converging lithosphere, delineated through gravity modeling, for understanding the local deformation in the crust and mantle, and also along crustal discontinuities. We further analyze 114 earthquake events (magnitude ≥4.0) occurring during the period 1902 to 2012 in these sectors of the Himalayan arcuate belt (Fig. 2). The earthquake data were taken from the catalogues of Indian Society of Earthquake Technology (Bapat et al. 1983), International Seismological Centre, and US Geological Survey. A total of 13 focal mechanisms of earthquakes of magnitude M w ≥ 4.7 are also compiled from the Harvard Centroid Moment Tensor Catalogue, Chandra (1978), Molnar and Tapponnier (1978), Tandon (1972) for better understanding the deformation processes.

Fig. 2
figure 2

Contour map illustrates the variations in Bouguer gravity anomalies across the Nepal and Sikkim–Darjeeling Himalayas reconstructed based on EGM2008 gravity model. Profiles AA′ and BB′ were chosen through Nepal and Sikkim–Darjeeling Himalayas for gravity modeling of the converging Indian lithosphere. A comparison of dip-angle variations in Moho boundaries is made between profiles AA′ and BB′ (present study) and XX′ (after Schulte-Pelkum et al. 2005) and YY′ (after Tiwari et al. 2006). Black stars represent the distribution of earthquake’s epicenters with magnitude 4.0 and above. Note the higher concentration of seismicity in Sikkim–Darjeeling Himalayas. Solid blue rectangle represents the epicenter of 2011 Mw 6.9 Sikkim earthquake. Abbreviations are explained in the caption of Fig. 1

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Tectonic framework

The Himalaya marking the southern edge of the Tibetan Plateau was built through southward transportation of thrust packages along the numbers of east–west-oriented crustal-scale discontinuities, viz., Main Central Thrust fault (MCT), Main Boundary Thrust fault (MBT), and the MFT (Le Fort 1986). Deformation of the overriding Asian land mass has been migrated southward and the MFT being the most recently activated one in the sequence (Lavé and Avouac 2000). This fault is delineated to the top of the Indian basement at a depth of about 5 km and extends sub-horizontally beneath the Lesser Himalaya (Schelling and Arita 1991; Lavé and Avouac 2000). The MFT places the sub-Himalayan molasse belt over undeformed foreland sediments of the Indo-Gangetic plain. The basement of the active Himalayan foreland basin is irregular, with several subsurface ridges extending from the Peninsula Highlands northwards to the Himalayan front. These structural highs generally trend at high angles to the Himalayan range and have structural relief locally exceeding ~2.0 km along east–west direction parallel to the Himalayan thrust front (Raiverman 2000). The sub-Himalayan belt, consisting of Miocene to Quaternary molasse exposed in the Himalayan foothills (Acharya and Ray 1977), has an average elevation of about 0.9–1.5 km (Valdiya 1988). The ruggedly youthful Siwalik domain is characterized by steep slopes, swift-flowing consequent streams, and deep valleys of antecedent rivers (Valdiya 1988). The south-vergent MBT, which appears to have been active some ~10 Ma before (Meigs et al. 1995; Burbank et al. 1996), placed the Lesser Himalayan meta-sedimentary belt over the sub-Himalayan molasse belt. The Lesser Himalayan belt consists of ~12-km-thick section of phyllites, schists, slates, and marbles (Schelling 1992). The average elevation of rising Lesser Himalaya is 1.5–2.5 km, and its sub-province shows a mild and mature topography with gentle slope toward the north (Valdiya 1988; Yin 2006). The region is characterized by several nappes of metamorphic rocks brought southward over long distances by imbricate thrusting (e.g., Le Fort 1975; Valdiya 1976, 1989; Gansser 1981). The south-vergent MCT places the Greater Himalayan crystalline belt over the Lesser Himalayan belt, resulting in upward increasing metamorphic grade within both (Hubbard and Harrison 1989). The Main Himalayan Seismic belt is mostly confined within the MBT and MCT zones (Ni and Barazangi 1984). The Greater Himalayan belt is interpreted as a thrust sheet of Indian continental basement displaced southward along the MCT (Argand 1924; Heim and Gansser 1939; Le Fort 1975; Schelling and Arita 1991). The Great Himalaya rises to a height over 6.5–7.0 km (Valdiya 1988) over which lies the perennial snows (Yin 2006). The Greater Himalayan zone consists of 15- to 20-km-thick slab of crystalline rocks, which has been thrusted southwards along the MCT, overriding the Lesser Himalayan formations (Yin 2006). Structural relations, together with the INDEPTH profiling (Hauck et al. 1998), imply that MFT, MBT, and MCT merge at depth to a single northward dipping decollement, the MHT (Schelling and Arita 1991; Zhao et al. 1993; Makovsky et al. 1996; Hauck et al. 1998; Bollinger et al. 2006). The Greater Himalayan belt is succeeded northward by the Tethyan sedimentary belt. The Tethyan belt strata were deposited on the northern passive continental margin of India (Burg and Chen 1984; Searle et al. 1987). The Greater Himalayan belt is generally considered basement of the Tethyan belt cover (Gansser 1964; Burg and Chen 1984). The Tethyan belt is succeeded northward by the Indus-Tsangpo Suture zone, which is characterized by dismembered ophiolites, radiolarian cherts, forearc flysch deposits, and tectonic mélange-containing blocks of Tethyan strata (Burg and Chen 1984). The composite Gangdese batholiths of Cretaceous to Eocene age (Schärer et al. 1984; Debon et al. 1986; Copeland et al. 1995) lies immediately north of the suture.

Gravity modeling

Several new global gravity models (EIGENGL04C, Forste et al. 2008; EGM2008, Pavlis et al. 2008) are developed based on the data from GRACE/CHAMP satellite mission for long wavelengths (low degree and order of spherical harmonics) and terrestrial data for short wavelengths. Gravity field of the EIGENGL04C model is computed for spherical harmonics of degree and order 360. It combines GRACE data for spherical harmonic coefficients up to degree and order 70, amalgamation of satellite and terrestrial data at intermediate wavelength, and terrestrial data at short wavelength (higher spherical harmonics of 115–360). The EGM2008 gravity model is complete to the spherical harmonics of degree and order 2,159, and also combines primarily the satellite and surface measurements (Pavlis et al. 2008). The EGM2008 model is computed for higher spherical harmonics, and thus, its spatial resolution is relatively more than the EIGENGL04C model. The present Bouguer gravity anomaly (BGA) map (Fig. 2) is constructed from EGM2008 gravity model after incorporating Bouguer correction and all terrain corrections and compared with ground gravity data. The Bouguer anomalies are consistent with terrestrial data; however, short-wavelength anomalies are filtered for consistency. Thus, such map has potential in studying large-scale geologic features across the Himalaya, where little or no terrestrial data are available (e.g., Tiwari et al. 2010). The 2D modeling is undertaken by choosing long profile that cuts all through the main geological features of the collision zone, to understand the long-wavelength gravity anomalies. Both the profiles AA′ and BB′ are taken nearly orthogonal to the strike of the India–Eurasia collision zone.

One of the most common problems encountered in geophysical studies is the determination of the geometry of geological contacts at depth. Bouguer gravity anomalies reflect lateral variations in density at depth. The largest subsurface density discontinuity near the surface of earth occurs at the Moho, a chemical boundary between crust and mantle rocks. Seismic velocities also have a significant jump across the Moho. The deformation of the Moho can be used to gauge the deformation of the upper mantle of the lithosphere. The Bouguer gravity anomalies caused by heterogeneities in the distributions of masses and therefore density contrast between them can be used for delineating structures in the subsurface (Molnar 1988). Models based on gravity and seismic data suggest that the long-wavelength gravity anomalies arise due to Moho-depth variations caused by flexing of the Indian lithosphere (Tiwari et al. 2006). Flexural model (e.g., Hetényi et al. 2006) explains the base of the foreland Indo-Gangetic basin and crustal thickness variations that corroborate with the results of receiver function analysis. Considering that long-wavelength gravity anomalies are explained with flexural Moho and basement, we have first defined Moho depth and basement based on average effective elastic thickness (EET) of ~40 km with Moho depth of 36 km in the south of Ganga Basin (Krishna and Rao 2005). The initial densities of different layers are assigned based on the previous studies (Gansser 1981; Cattin et al. 2001; Tiwari et al. 2006; Hetényi et al. 2007). Our initial model geometry is similar in the depth range inferred from seismic, seomological studies (DMG 1990; Hauck et al. 1998; Schulte-Pelkum et al. 2005). We consider the densities of 2,300 kg/m3 for the Indo-Gangetic sediment (Gansser 1981); 2,450 kg/m3 for the Siwalik sediment; 2,670 kg/m3 for the Indian Basement rock, Lesser, and Greater Himalaya formations; 2,900 and 3,270 kg/m3 for the Indian Lower Crust and Upper Mantle (Cattin et al. 2001), respectively. Besides, the initial densities of Tethys sediment, Asian Crust, part of the Indian Upper Crust toward north below the Asian Crust, and part of the Indian Lower Crust toward north below the Asian Crust are taken as 2,650 and 2,870 kg/m3 (Tiwari et al. 2010), 2,740 kg/m3 (Hetényi et al. 2007), and 2,980 kg/m3. We consider a single-fault geometry system (i.e., MHT, a major shear zone) where all the MFT, MBT, and MCT terminate at depth (cf. Makovsky et al. 1996; Hauck et al. 1998; Bollinger et al. 2006). We find the best fit between the observed and computed gravity field for the effective elastic thickness of ~40–50 km of the northward converging lithosphere. The present procedure (Fig. 3) is based on an interactive forward modeling (Webring 1985), which calculates the gravity responses of the modeled geometries. The initial geometries and initial densities of different layers provide the initial rms errors of 33 mgal for modeling along the profile AA′ and 30 mgal along BB′, respectively. The fit between observed and calculated gravity is compared through successive iterations, and the best fit is selected for the improved model. Finally, the rms error values reduce to 5.59 mgal and 7.41 mgal for profiles AA′ and BB′ for the optimum models (Figs. 4, 5). It is well known that Bouguer anomalies are combined effect of lateral density heterogeneities beneath reference level (in the present study, mean sea level, MSL) and anomalies due to departure of lithological densities from the reduction density (2.67 gm/cc) above reference level. The second component is small particularly over low-lying flat region; however, it is considerable in the regions like Himalaya. To overcome this problem, we have used density contrast with respect to 2,670 kg/m3 for the layers above MSL.

Fig. 3
figure 3

Flowchart illustrating the path followed for gravity modeling

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Fig. 4
figure 4

Plot showing the 2D gravity modeling with topography along profile AA′ for Nepal Himalaya. Plot at the top illustrates the topography of the area along AA′ compiled from GTOPO 30, a global digital elevation model with a horizontal grid-spacing of 30 arc s (a). Plot at the mid illustrates a comparison between observed and computed Bouguer gravity anomalies along the profile (b). Lower plot (c) represents the 2D gravity density model. Hypocenter of 28 earthquake events and 2 focal mechanisms are also shown in the section of the model

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Fig. 5
figure 5

Plot showing the 2D gravity modeling with topography along profile BB′ for Sikkim–Darjeeling Himalaya. Plot at the top illustrates the topography of the area along AA′ compiled from GTOPO 30, a global digital elevation model with a horizontal grid-spacing of 30 arc seconds (a). Plot at the mid illustrates a comparison between observed and computed Bouguer gravity anomalies along the profile (b). Lower plot (c) represents the 2D gravity density model. Hypocenter of 86 earthquake events and 11 focal mechanisms are also shown in the section of the model

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Finite-element modeling

Finite-element modeling for quantitative estimates of regional and local tectonic stress fields within the lithosphere is an important tool for analyzing the lithospheric deformation (Artyushkov et al. 1996). In view of this, several workers (Willett et al. 1993; Beaumont et al. 1994; Sassi and Faure 1997; Mikhailov et al. 2002; Chamlagain and Hayashi 2004) have applied numerical modeling for understanding faulting and resulting geodynamics. Singh et al. (1990) modeled a cross section extending from the Ganga Plain to the Tibetan Plateau, aiming to simulate earthquake activity using force rather than displacement boundary conditions. Vergne et al. (2001) preferred 2D finite-element model consisting of different rheological layering of the continental lithosphere. Using the distinct-element method (Cundall 1990) or the finite-element method (Zienkiewicz and Taylor 1989, 1991), Sassi and Faure (1997) computed stress pattern, which depends on the boundary conditions, the presence of large-scale discontinuities, and/or contrasting mechanical properties of the constitutive rocks. Wang and Shi (1982) proposed through 2D finite-element modeling that the Himalaya is dynamically supported. Berger et al. (2004) used the ADELI 2D finite-element code (Hassani 1994; Hassani et al. 1997) to simulate the interseismic deformation in the three distinct western, central, and eastern Nepal blocks. They considered three geological domains along each profile, Indian crust, Tibetan crust, and upper mantle. The rheologies of these three blocks were assumed to be homogeneous along the models and similar for eastern, central, and western Nepal.

In the present study, we perform finite-element modeling on two 2D vertical sections of the underthrusted Indian and overthrusted Asian lithospheres, along the profiles AA′ (~520 km long) and BB′ (~515 km long) in the Nepal Himalaya and Sikkim–Darjeeling Himalaya. The vertical section is divided into 11 different layers following the works of Owens and Zandt (1997), Cattin et al. (2001), Tiwari et al. (2006), Hetényi et al. (2007), and Hammer et al. (2013). Meshing is done through reconstruction of 1,039 nodes and 1,774 triangular elements along profile AA′ for the Nepal Himalaya, and 993 nodes and 1,746 triangular elements along the profile BB′ for the Sikkim–Darjeeling Himalaya. To understand the localized deformation vis-à-vis displacements, one should have the knowledge of rheology of the constituent rocks. The rock rheology has a significant influence on the occurrences of earthquakes as well as the source dynamics/kinematics (Watts and Burov 2003; Khan and Chakraborty 2009). The rock rheologies involving density, Poisson’s ratio, Young’s modulus, angle of friction, and cohesive strength of the rock are used for elastic modelling. The other parameters like cohesion coefficient (c) and frictional angle (φ) have been taken from the studies of Cattin et al. (2001), Hetényi et al. (2006), and Clark (1966). The improved density parameters of the different rock layers, achieved through the present gravity modeling (Figs. 4, 5, Table 1), are used for the finite-element modeling. The rock properties vary laterally as well as vertically. For the simplicity of computation, the whole models are divided into 11 layers and each layer has been assigned with distinct rock properties. The other parameters such as Poisson’s ratio (v) and Young’s modulus (E) have been computed using the following equations (Timosenko and Goodier 1970; Shearer 1999).

$$ v = \frac{{\left( {V_{\text{p}}^{2} {-} \, 2V_{\text{s}}^{2} } \right)}}{{2\left( {V_{\text{p}}^{2} {-} V_{\text{s}}^{2} } \right)}} $$
(1)

where seismic wave velocities, V P (P-wave) and V S (S-wave), were taken from the studies of Cotton et al. (1996) and Khattri et al. (1995).

$$ {\rm E} = \rho V_{\text{p}}^{2} \frac{(1 + v)(1 - 2v)}{(1 - v)} $$
(2)

where ρ is the density. The values of densities for different layers are taken from Table 1.

Table 1 Physical parameters for different crustal units used for the gravity and finite-element modeling
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Boundary conditions play important role in simulating the tectonic processes. In order to get the real situation, we apply the reasonable boundary conditions to represent the present-day kinematics in the Himalayan fold-and-thrust belt. The boundary conditions are illustrated in Fig. 6a, b under the present finite-element modeling. In both the models, the upper surface is free to move in all directions. The lower section of the northern boundary below the MHT is fixed horizontally (cf. open circles, Fig. 6) for understanding the deformation caused by resistive forces along the Himalaya (Richardson 1992; Copley et al. 2010). The force balance calculations for the pre- and post-collision configurations under application of forces on the edges of the plate and the tractions on the base of the plate (Copley et al. 2010) showed that the resistive force induced by mountain building in the Himalaya–Tibet area is ~5–6 × 1012 N/m. We therefore impart an amount of 6 × 1012 N/m force, instead of displacement, on the frontal vertical part of the section (cf. arrows in Fig. 6), which is equivalent to the resistive force caused by the Himalayan–Tibet system to the Indian plate (Copley et al. 2010).

Fig. 6
figure 6

Plot showing the simplified geometries (after present gravity models) with boundary conditions for the 2D finite-element modeling for Nepal (a) as well as Sikkim–Darjeeling (b) Himalayas

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Results and discussion

The varying degrees of tectonic loading and flexure are imaged by earthquake receiver function analysis (Hetényi et al. 2006; Rai et al. 2006), seismicity studies (Seeber and Armbruster 1981; Ni and Barazangi 1984), magnetotelluric (MT) experiments (Chen et al. 1996; Lemonnier et al. 1999; Unsworth et al. 2005; Arora et al. 2007), seismic profiling (DMG 1990), INDEPTH (Zhao et al. 1993; Nelson et al. 1996; Hauck et al. 1998; Alsdorf et al. 1998), HIMNT experiment (Schulte-Pelkum et al. 2005), and gravity modeling (Lyon-Caen and Molnar 1985; Cattin et al. 2001; Banerjee and Prakash 2003; Jordan and Watts 2005; Tiwari et al. 2006) in different parts of the Himalaya. Invariably, different studies are in agreement with the three interfaces, the Moho, lower–upper crustal interface (Conrad discontinuity), and mid-crustal decollement (Hetényi et al. 2006). We summarize the gravity modeling results in Table 2 for depth distributions of these three different interfaces beneath the different crustal provinces along the south–north transects AA′ and BB′ for the Nepal and Sikkim–Darjeeling Himalayas. We note that the northward continuity of the MHT, Conrad (boundary between IUC and ILC), and Moho is more or less gentle and similar beneath the Indo-Gangetic plain, Siwalik Himalaya, and Lesser Himalaya. However, a sharp change in dips of all these crustal features is quite apparent further north beyond the Lesser Himalaya. Dip changes are reduced significantly from the Tethys Himalaya toward southern Tibet. We also critically examine the distribution of seismicity below different tectonic provinces and note a clear distinction of seismicity concentration. Greater Himalaya in both Nepal and Sikkim–Darjeeling records maximum concentration of seismic events. Another important feature is the shallower Moho of 40–44 km in Nepal and 38–43 km in Sikkim–Darjeeling beneath the Gangetic alluvium increases beyond the Lesser Himalaya and attains ~69 km in Nepal and ~75 km in Sikkim–Darjeeling beneath the southern Tibet (Figs. 4, 5), suggesting a locus of flexural loading on the Indian crust beneath the Greater Himalaya. A relative assessment clearly demonstrates a higher concentration of seismicity (i.e., 48 events) beneath the Greater Himalaya of Sikkim–Darjeeling than the Nepal Himalaya (i.e., 19 events). We thus find an excellent correlation between the zone of sharp bending of the descending Indian lithosphere and the maximum concentration of seismicity. This is possibly indicating the highest degree of deformation within the sharp flexing zone of the converging lithosphere.

Table 2 Showing the depth variations in different crustal interfaces along profiles AA′ and BB′ below different crustal provinces in the Nepal and Sikkim–Darjeeling Himalayas
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During finite-element modeling, a series of model calculations have been carried out, but only representative models are illustrated here. The computed stress fields and related faulting processes have been assessed through contouring of maximum compressive stress (σ 1) (Fig. 7a, b) and minimum compressive stress (σ3) (Fig. 8a, b). We invariably note a zone of maximum compression (~1013 Pa) all along the northern part of the MHT (Fig. 7a, b). This higher compressive zone of one order more is abruptly terminated to the south of the Greater Himalaya. It was also noted that the compressive stress fields are more dominated within the different layers, and the relatively less compressive stress fields are distributed laterally in different layers of the Nepal Himalaya, while the bending zone of the converging lithosphere in Sikkim–Darjeeling Himalaya documents southwesterly distributed compressive stress field. The distribution of moderate (~3.3 × 1012 Pa) compressive stress field is also found at the shallower part near the Indo-Gangetic plain. Figure 8a, b shows the distribution of minimum compressive stress field within the converging lithosphere. Although the minimum compressive stress fields are mainly confined near the upper surface of different layers around the bending portion of the descending Indian lithosphere, the minimum compressive stress is distributed laterally in Nepal Himalaya (Fig. 8a). Here, another important observation is that the magnitude of minimum compressive stress is nearly half of the maximum compressive stress.

Fig. 7
figure 7

Contour plot illustrates the variations in the maximum compressive stress fields (σ 1) for Nepal (a) and Sikkim–Darjeeling (b) Himalayas. Note the confinement of σ 1 right within the layers

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Fig. 8
figure 8

Contour plot illustrates the variations in the minimum compressive stress fields (σ 3) for Nepal (a) and Sikkim–Darjeeling (b) Himalayas. Note the distribution of σ 3 along the upper surfaces of different layers

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Microseismicity survey in Nepal Himalaya shows that the seismic belt follows approximately the front of the Greater Himalaya and especially more concentrated in eastern and far western Nepal. The earthquakes are generally shallower, clustered at a depth range of 10–20 km (Pandey et al. 1999; Kayal 2001). Based on the microseismicity survey in Sikkim–Darjeeling Himalaya, De (2000), Kayal (2001), Monsalve et al. (2006), and Hazarika et al. (2010) reported that the higher concentration of earthquakes is noted to the north of the MBT without following any particular trend. In addition, Kayal (2001) observed the earthquakes occurring predominantly below the plane of detachment and proposed that the MBT is seismogenic up to the mantle in the Sikkim Himalaya. While the present study reveals that the seismic activity is more concentrated right within the converging Indian lithosphere beneath the Greater Himalaya (Figs. 4, 5) with a significant distribution in the uppermost part of the Indian mantle lithosphere. Kayal (2001) and Nábelek et al. (2009) also identified active deformation within the upper mantle in the Sikkim Himalaya. Besides, the occurrence frequency or the incidences of numbers of earthquakes in Sikkim–Darjeeling section are quite unusual, whereas the Nepal Himalaya documents less seismic activity. Figure 9 illustrates the variation in dip-angle of the Moho boundary of the penetrating Indian lithosphere. A noteworthy change in dip-angles (e.g., ~6°–8°) of the Moho boundary beyond MCT, particularly, beneath the Greater Himalaya is identified from Nepal to Sikkim–Darjeeling sectors. We thus may anticipate that the higher seismicity concentration might be caused by the increasing bending of the Indian lithosphere below the Sikkim–Darjeeling Himalaya. This was also appreciated in the literature (Conrad and Hager 1999) that ~60 % of energy dissipation occurs through the bending portion (flexing zone) of the subducting slab. It was noted that the hypocenters of the mega-earthquake events coincide with the zone of flexing (cf. Khan and Chakraborty 2005, 2009; Khan 2011; Khan et al. 2012) where the descending lithosphere takes a sharp change in inclination to reach into the deeper level. It was estimated that the maximum bending stress in the descending oceanic lithosphere at the subduction margins is about an order of magnitude larger than the maximum strength of the oceanic lithosphere (Kohlstedt et al. 1996; Conrad and Hager 1999); only 10 % of the elastic bending stress is supported without deformation, and the remaining stress is relieved in the form of seismicity by fracturing of rocks (e.g., Turcotte and Schubert 1982). Recent works of Singh et al. (2008), Khan and Chakraborty (2009), Khan (2011), and Khan et al. (2012) on the source dynamics and localization of hypocenter of the 2004 off Sumatra mega event envisage its association with the uppermost part of the mantle and advocate its intraplate origin.

Fig. 9
figure 9

Plot showing the variations in dip-angles of Moho boundaries with depth along profiles AA′, BB′, XX′, and YY′, respectively. All profiles are shown in Fig. 2. Note the change in dip-angles of ~6°–8° between sections of Nepal and Sikkim–Darjeeling Himalayas

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Focal mechanisms of moderate magnitude earthquakes reveal that the sharp bending section of the lithosphere is associated with both strike-slip and thrust-dominated movements, and shear planes of most of these events are more or less parallel with the interfaces of the different crustal layers. Another significant observation is the dominant right-lateral shear movements operative in the crust part of the converging lithosphere, which is possibly controlled by either local or regional changes in plate obliquities (Liu et al. 1995). These typical features might be accounting an accommodation of crustal packages along both orthogonal and parallel with the arc of the Himalaya. We thus propose that the deformation is more dominant within the sharp bending zone than other parts of the converging lithosphere, and the lateral shearing between crustal blocks is presumably constrained by the obliquity of the plate. It was noted that the motions following the occurrences of moderate-to-large earthquake events in an oblique convergent margin are generally partitioned into trench-parallel shear component and trench perpendicular subduction component (Fitch 1972; Ben-Menahem et al. 1974; McCaffrey 1992, 1996; Ishii et al. 2005; Lay et al. 2005; Khan 2005; Khan et al. 2010). McCaffrey and Nabalek (1998) interpreted the right-lateral strike-slip fault motion on the Karakoram-Jiali fault zone and the east–west extension on north-trending normal faults, and the radial vergence slips in the Himalayas are all due to basal shear caused by the obliquely converging Indian plate beneath the Tibet. The fluids at the mid-crustal depths surrounding MHT (Gokarn et al. 2002; Spratt et al. 2005; Unsworth et al. 2005; Patro and Harinarayan 2009) might be facilitating the slips along both orthogonal and parallel to the Himalayan arc.

Conclusions

Although the converging Indian lithosphere takes a sharp downward turn beneath the Greater Himalaya, relatively more steepening Moho boundary is identified through gravity modeling beneath the Sikkim–Darjeeling Himalaya. This is likely correlated with higher seismicity concentration for this region. Further, a significant distribution of seismicity in the upper-most part of the mantle clearly shows its higher degree of deformation. It is also apparent from the finite-element modeling that the maximum compressive stress field is more confined right within the bending zone of the penetrating Indian lithosphere beneath the Greater Himalaya. We thus propose that the sharp bending zone of the converging Indian lithosphere is the nodal area of stress concentration and recording maximum deformation. Amplitude of estimated stresses might change due to uncertainties in the several parameters utilized to compute the stresses; however, the pattern would remain same, and the inferences drawn from our studies remain valid.

We find dominant right-lateral shear motion in the crustal blocks of the Indian lithosphere and thrust-dominated movements orthogonal to the strike of the Himalaya. The strike-parallel components of motions of the converging Indian plate against the southern part of the Asian plate are presumably motivating the shear motion, and the strike-perpendicular components driving the radial vergence slips. The Indian plate obliquity is increasing both toward east and west of the Nepal Himalaya, and might be intrinsically related with the degree of arc-parallel shear motion. We thus may expect maximum lateral shearing of crustal blocks toward the termini of the Himalaya, where the Indian plate obliquity reaches its highest values.