1 Introduction

Several studies have been carried out on the frequency–magnitude relationship of earthquakes as function of time, space, and depth since Ishimoto and Ida (1939) and Gutenberg and Richter (1954), through their seminal works, established the empirical relationship between occurrence-frequency and magnitude of earthquakes in a given region for a finite time-window. Like many other self-organised and self-similar non-equilibrium systems, the earthquake magnitude–frequency relation follows an exponential relation, represented empirically by the equation

$$ {\text{Log }}N\left( M \right) = a - bM $$
(1)

where N(M) is the cumulative number of earthquakes having Richter magnitude larger than M, ‘a’ is a measure of seismic activity that depends on the size of the area, length of the observation period, the largest seismic magnitude and stress level of the area, etc., measured as the logarithm of the annual total of all earthquakes with M > 0 (Allen, 1986). Statistically, the b-value is the slope on the log N ~ M regression line and is a constant parameter that determines the rate of fall in the frequency of occurrence of events with increasing magnitude. High b-values indicate a large number of small earthquakes expected in regions of low strength and large heterogeneity, and low b-values indicate high resistance (asperity) and homogeneity of the constituent rock-mass (Tsapanos, 1990; Udias, 1999; Wason et al., 2002). In natural situations, b-values are found to lie between 0.5 and 1.5, depending on the tectonics of a region. Mogi (1963, 1967) and Scholz (1968) studied the behaviour of b-values during fracturing of rocks in the laboratory. While the study of Mogi (1967) was mainly concerned with the mechanical behaviour of the rocks, Scholz (1968) inferred that the state of stress, rather than the heterogeneity of the material constituting the rocks, plays the most important role in determining the b-value. Later studies (Mori and Abercrombie, 1997; Wiemer and Wyss, 1997) observed a decrease in b-value with increasing depth and related the observation with increasing applied stress at deeper levels (Bhattacharya and Kayal, 2003). The b-values also decrease with increasing effective stress or increasing seismic moment (M O) release (Scholz, 1968; Wyss, 1973; Cao and Gao, 2002). In this paper we re-examine the distribution of b-values with depth for northeast India through a high resolution analysis using seismic data recorded at stations in a local network.

The study area lies between latitude 24.5°N and 27.2°N and longitude 89°E and 96°E, and is known for its strong seismic history. Although detailed investigations involving seismicity for the Shillong plateau as well as the whole of northeast India have been undertaken by several researchers (Verma et al., 1976; Mukhopadhyay, 1984; Kayal, 1987; Kayal and Zhao, 1998; Radha Krishna and Sanu, 2000; Bilham and England, 2001; Bhattacharya et al., 2008; Steckler et al., 2008; Khan et al., 2009), studies pertaining to the strength of the lithosphere and lithospheric-scale buckling are long-awaited for this convergent margin. Seismic b-values were analysed on a localised scale for appreciation of crustal heterogeneity (Kayal, 1987; Bhattacharya et al., 2002, Bhattacharya and Kayal, 2003; Khan and Chakraborty, 2007). Geophysical tools such as seismic tomography and receiver functions were applied by Kayal and Zhao (1998) and Mitra et al. (2005) for identifying heterogeneities in the crust and upper mantle. Analysis of Bouguer and isostatic gravity anomalies (Verma and Mukhopadhyay, 1977; Chen and Molnar, 1990) led to the quantification of ~33–40 km crustal thickness for the Shillong Plateau area. Also, velocity structure and crustal configuration beneath northeast India were estimated on the basis of arrival time of local/teleseismic events (Tandon, 1954; Kayal and De, 1987; De and Kayal, 1990; Mukhopadhyay et al., 1995; Rai et al., 1999; Bhattacharya et al., 2008). Depth-wise qualitative stress assessment beneath the Shillong Plateau area was carried out by Khan (2005a) and Khan and Chakraborty (2007). Despite all these advancements, documentation of b-value distribution in a space–depth framework over the entire area, recognition of anomalous patterns, if any, and identification of causative forcings are still awaited. The present study thus aims towards characterisation of space- and depth-wise b-value distribution over the entirety of northeast India and to understand the possible bearing of rheology/strength of the lithosphere on the b-value distribution pattern. Although we appreciate the limitations in ‘b’ value estimation using available seismic catalogues (discussed later), we feel that the estimated b-values can be efficiently linked with the lithosphere strength profile in a depth domain (Molnar, 1988).

2 Tectonic Setup

Northward convergence, anticlockwise rotation against Eurasia and oblique convergence against the Southeast Asia (Dewey and Bird, 1970; Fitch, 1970; Seeber et al., 1981; Le Dain et al., 1984; Klootwijk et al., 1985; Maung, 1987; Khan, 2005b) characterise the journey of the Indian plate since the Cretaceous period, and have led to the development of complicated tectonics in the northeast part of India. According to Curray (1989), the situation became even more complex near the syntaxis where the three plates viz., Indian, Eurasian and the Burma platelet, joined together and, accordingly, the deformational style changed from dextral shear, between India and Southeast Asia in the east, to a frontal collision at the eastern Himalayas. The entire northeast area has been tectonically active since the Mesozoic. Along with mountain building activities in the Burma and Himalaya regions in the east and north, large scale vertical movements resulted upliftment of the Shan plateau in Burma and the Shillong Plateau in northeast India (Krishnan, 1960). Interference of Shillong Plateau, Mikir Hill, Namcha Barwa Hill, Himalaya, Indo-Burman Ranges, etc., have resulted the development of a number of major crustal discontinuities, viz. Dauki Fault, Naga thrust, Kopili Lineament, and Main thrust-sheets in the northeast part of India (Fig. 1). As detached blocks from the Peninsular India Shillong plateau and Mikir Hills shifted over 200 km towards east through the gap between Rajmahal and Garo Hills (Evans, 1964), eastward motion of the Shillong Plateau along the transcurrent Dauki fault and the vertical tectonics of the entire northeast region of India (Evans, 1964) led to the development of the complex tectonic setting in northeast India. The 1897 Shillong earthquake and 1950 Sadiya earthquake are explained as fallout of the southward movement of the Shillong Plateau at the last phase of Himalayan orogeny and oblique convergence of the Indian plate against the Burmese micro-plate, respectively (Evans, 1964; Ben Menahem et al., 1974).

Fig. 1
figure 1

Map showing the tectonic setup of the northeast part of India (after Krishnan 1960; Evans 1964). Inset map represents the location of the study area. DT Disang thrust; MBT Main Boundary Thrust; MCT Main Central Thrust; NT Naga Thrust; DF Dauki Fault; PF Padma Fault; TF Tista fault; HF Halflong fault; LT Lohit thrust; MT Mishmi Thrust. The permanent seismic stations are shown by solid squares. Solid stars indicate the locations of historical large earthquakes. Solid converging arrows represent the direction of compressive stress field (after Radha Krishna and Sanu, 2000)

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The combined gravitational, aeromagnetic and seismic data indicate that a buried ridge represents the basement below the alluvial cover of Upper Assam and the ridge extended towards the northeast (Verma and Mukhopadhyay, 1977; Kent and Dasgupta, 2004; Mitra et al., 2005). To the northern part of the Shillong Plateau, the basement of the Lower Assam Valley is exposed as low-lying ridges on either side of the Brahmaputra River. Satellite imagery (Nandy and Dasgupta, 1986) shows a number of buried lineaments beneath the alluvium in the Lower Assam Valley. The Shillong plateau is separated from the western part of the Surma valley by a narrow strip of southerly dipping beds associated with an important E–W discontinuity, the Dauki fault. The Disang thrust, southwest of Naga Hills, passes to a narrow but complex fracture belt near Haflong, i.e., the Haflong fault. With change in orientation from NE–SW to due west (Evans, 1964), the fracture belt continues westward up to the Dauki fault.

3 Seismic Data and Methodology

The seismological observatory network in northeast India was constructed jointly by the National Geophysical Research Institute (NGRI), Hyderabad, and the Regional Research Laboratory (RRL), Jorhat, in the 1980s (Bhattacharya et al., 2002; Bhattacharya and Kayal, 2003; Bhattacharya et al., 2008), and has been recording local seismicity for more than two decades. The earthquake data used for the present study were collected from the earthquake catalogues published by the NGRI, Hyderabad, and RRL, Jorhat. These catalogues incorporate the events recorded by the NGRI and RRL networks containing 30 digital stations and also the data recorded by temporary local networks’ digital seismic stations (~47) run by different institutes in different times and places; these stations were not in operation at a single time in the northeast region. The over all timing accuracy for the temporary stations was maintained to ±0.1 s synchronizing radio signal (Kayal, 1987; Kayal and De, 1991). The timing for the digital seismic stations, is however, maintained by GPS. The three component digital seismograms provided high precision P-wave (±0.01 s) and S-wave (±0.05 s) arrival times. The catalogues generally are completed for the most part down to magnitude 2.0. In the present study we have used the network duration magnitude for an earthquake. Under this measure, the magnitude for an earthquake is determined from the arithmetic mean of duration magnitudes over different stations. A total of 3,655 events occurring in the areas between latitude 24.2°N and 27.5°N and longitude 89.3°E and 96.2°E (Fig. 2) during the period between 1986 and 1999 were used. An extended rectangular area surrounding the main study region was considered to include the analysed b-values along the peripheral zone for high-resolution investigation.

Fig. 2
figure 2

Map showing seismicity in Northeast India occurring between 1986 and 1999, and recorded by the local network of National Geophysical Research Institute (NGRI), Hyderabad, and Regional Research Laboratory, Jorhat

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The study area (Fig. 1) was divided into 240 square grids for exploring the spatial variation of b-values over the region. Each grid has a dimension of 0.6° × 0.6° (geographical window) with a moving window (overlapping area) of 0.3° × 0.3°. The moving window was chosen for comprehensive analysis and to maintain the inherent grid-to-grid continuity of the data points. The dimension of the geographic window under the present study was selected to introduce an adequate number of events representing the b-values at each grid. A few squares with poor event records (Table 1 in Electronic Supplementary Material) were excluded from the analysis. Some other squares which lack sufficient events (occasionally <30) are, however, considered for maintaining good correspondence between projection points in adjacent grids. For a defined magnitude range, b-values for each block were computed using Eq. 1.

Figure 3 illustrates the computed b-values from cumulative frequency–magnitude relationships for four grid squares. The plots ubiquitously show deviations from linearity at both higher and lower ends of the data values. While the deviations in the higher end may be accounted for by scarcity of large magnitude (M) events within the considered time-window (1986–1999 i.e. ~15 years), the deviations in the lower data values may be due to incompleteness in the data catalogue. Such heterogeneity in the data catalogue, particularly in the lower data range, may stem from (1) lack of enough stations to record very small events (2) disinterest of network operators in recording events below a certain threshold or (3) non-random aftershock events which may be too small to be detected within the code of larger events. Several workers (Weimer and Wyss, 2000; Woessner and Weimer, 2005) have discussed this limitation and have stressed the requirement of minimum magnitudes for complete recording (M c) in studies related to seismicity. Despite the understanding that M c may change with time in most catalogues for different regions, usually decreasing with increase in the number of seismographs and improvement in the methods of analysis, it is widely and effectively practised in literature for b-value assessment of high seismic areas (Rydelek and Sacks, 1989; Weimer and Wyss, 2000). Since the area under study is seismically very active, we pursued our study with demarcation of M c (i.e. lower bound of MRBE in Table 1 in Electronic Supplementary Material) on the cumulative frequency–magnitude database (Fig. 3) based on the points at which the b-value departs from linearity (cf. Rydelek and Sacks, 1989). The b-values we estimated are restricted to a dataset that shows the self-similar character (cf. Pacheco et al., 1992) without any significant modulation. Further, we have carried out the exercise of estimating the root mean square error (RMSE) in reference to the predicted best fit line over the self-similar dataset, which enhanced the degree of accuracy of the estimated b-values. We agree that the present entire exercise has narrowed down the considered database (Table 1 in Electronic Supplementary Material; Table 1), but at the same time, confining our study to a self-similar dataset where the catalogue is complete (Fig. 3) placed the estimated ‘b’ values on very strong footing.

Fig. 3
figure 3

Diagram showing the variation of cumulative frequency with earthquake magnitude for four seismic blocks (19, 2), (16, 8), (12, 9) and (13, 10), respectively. Selection of best fit lines is explained in the text. Arrows mark the smallest magnitude at which the distribution in the respective grid is complete

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Table 1 Values of the parameter b computed at different depths for seismic zone I, II, III, IV, V
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On the map, the estimated b-value for each square grid was spatially assigned to a point that defined the intersection of two diagonals of the square block; the projected values were then used for b-value mapping over the entire study area (Fig. 4). Based on a comparative analysis of b-value contours, five broad zones (Zones I–V) of nearly uniform b-values were identified, and depth probing of b-values was carried out at different layers with 12 km thickness, starting from surface down to 54 km depth (Table 1 in Electronic Supplementary Material) for understanding the intra- and inter-zone variations in b-values with respect to depth. An overlapping layer of 6 km thickness (moving depth-window) was considered for maintaining inherent continuity of the data points, minimization of depth error and observation at high-resolution. Further, the total seismic moment energy (\( \sum {M_{\text{O}} = 10^{{(1.53m_{\text{b}} + 16.17)}} } \), M O seismic moment energy for each layer, m b body wave magnitude) released in each zone was estimated and a comparative assessment of M O carried out between layers for individual zones.

Fig. 4
figure 4

b-Value contour map for the northeast India. Contour interval is 0.1. Different seismic zones (demarcate by solid lines) were classified based on b-values

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4 Results

Overall, the b-values are widely spreaded (Fig. 4) over the northeast part of India. The minimum and maximum estimated b-values in the study area are 0.23 and 1.78, respectively (Table 1 in Electronic Supplementary Material; Table 1); maximum concentration around 0.6 (Fig. 5). Based on the distribution (Fig. 5), b-values were classified into three categories; viz. low (b ≤ 0.5), moderate (0.5 < b ≤ 0.7) and high (b > 0.7). High resolution observation reveals sectorial preference of values, e.g., low b values (0.4–0.6) in the southwest, eastern part of ~95.2° longitude, and northwest, comparatively higher values (~0.5–1.6) in the central part between latitudes 24.5°N and 26.5°N and longitudes 92.3°E and 94.5°E. For understanding the vertical strength (Molnar, 1988; Watts and Burov, 2003) variation within the lithosphere of the study area, the estimated b-values over a 54 km thickened single-layer were further critically analyzed. Considering the available concentration of earthquake event data and necessity of depth probing, the b-values were assessed for comparatively thinner slices (of 12 km thickness) in each contoured zone (Fig. 4). To understand the role of different deep-seated geomorphic features on earthquake incidences, analysis of seismic moment release was also carried out in each layer of the five specific zones (Fig. 6). Maximum energy release amounts to 1.66×1026 dyne-cm in Zone IV; successively lesser amounts are recorded in other zones viz. 1.30×1025 dyne-cm in Zone I, 1.09×1025 dyne-cm in Zone II, 3.78×1025 dyne-cm in Zone III and 5.64×1025 dyne-cm in Zone V.

Fig. 5
figure 5

Histogram plots showing the variation of frequency of b-values over the entirety of northeast India (a) and over five zones (b)

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Fig. 6
figure 6

Plots showing the depth-wise variation of percentage of seismic moment (M o) released through the five zones

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The five zones (Zones I–V) can now be characterized spatially in terms of seismic b-values (Fig. 7) and moment energy release (Fig. 6). Zone I documents low to moderate b-values, and the highest seismic moment energy was released through a crustal domain (i.e., ~25 and 36 km depths) where the lower b-values were recorded. Zone II documents, overall, a moderate b-value with the lowest b-value noted at a depth of 30 km, and the highest moment energy release at comparatively greater depths (~40 km). Zone III documents moderate to low b-values, and maximum moment energy released through a domain at depths between 30 and 40 km, whereas the lowest b-value was recorded at a depth of 36 km. Although the different layers document low to moderate b-values, distribution is more or less non-uniform. Zone IV records moderate to high b-values, and high seismic moment energy release at >40 km depth, whereas the lowest b-value was recorded at a depth of 36 km. The b-values are moderate to low in Zone V. The b-values were non-uniformly distributed over the entire depth range; the lowest value was recorded at a depth of 36 km, and the maximum moment was released through a thickened layer between ~20 and 36 km in depth. Depths of higher seismic moment release are not uniform in all zones, and, particularly, a depth-domain (i.e., ~25–40 km) in Zones I, II and III registered the maximum amount of seismic moment release. By contrast, Zones IV and V are odd in this category. The b-values are, however, observed to be lowest at depths between ~30 and 36 km in all the zones. A good correspondence between the lowest b-value and the higher seismic moment release was noted invariably in the mid-crustal domain of all the zones, and might be indicative of a sharp change in rheology within the continental lithosphere (Molnar, 1988). The higher b-values recorded at the shallower part of the lithosphere in all the zones might be associated with more heterogeneous crustal domain at the base of the upper crust.

Fig. 7
figure 7

Plots showing the depth-wise variation of b-values for the five zones

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5 Discussion and conclusions

Widely varying stress in space–depth frame, modified by subsurface heterogeneities (structural/rheological), account for uneven distribution of seismicity in northeast India. More variable b-values in Zones III and V (Fig. 7) perhaps suggest the presence of fractures at different depth-levels along the eastern and northern boundaries of northeast India. Possibly, a substantial amount of ambient tectonic stress gets dissipated in form of earthquakes along the Himalaya and Indo-Burman Ranges, and the remaining part is utilised for enhancing the stress field towards the interior of the northeast part of India. It thus may be proposed that deep-seated fracture zones evolved from continued subduction of the Indian lithosphere towards the north and northeast, and concomitant synorogenic movements in the Himalaya and Indo-Burma Ranges exert significant influence on the seismicity of the area (Evans, 1964; Verma and Mukhopadhyay, 1977). Numerous Hills, elevated lands and flat valleys, which evolved through vertical tectonics (Evans, 1964), also partially influence the seismic activities of the area. High seismicity with high b-values is commonly associated with a high degree of crustal heterogeneity (Lowrie, 1997; Wason et al., 2002), and corroborates the above observation. Structural complexity, including thrust sheets in the north and east and criss-crossing high-density faults/lineament systems are very common features of northeast India (Nandy, 1980). Seismic zones with high b-values in some pockets in the western part of the study area can possibly be related to the presence of high density rock-fractures resulting from strong tectonisation between the Himalaya and the Shillong Plateau (cf. Khan and Chakraborty, 2007). The relatively higher b-values in Zone IV may be the result of mutual interaction between the Shillong Plateau, Mikir Hills, Kopili Lineament and the Indo-Burman Ranges.

The lower b-values and relatively high seismic moment release in the mid-crustal domain beneath the southwestern part of the study area (Figs. 2, 6, 7) may be better understood in terms of rheological anomaly, presen, though unambiguous, in parts of northeast India. Modification of the stress field as a result of continuing interaction of northeast India with the Himalaya and Indo-Burman Ranges is also another dominant process, particularly noted along its northern and eastern boundaries. Positive Bouguer anomaly as high as ~+40 mGal (Fig. 8) and isostatic anomaly ~+100 mGal (Fig. 9) recorded in the southwest part of the area were explained by overcompensation of the Shillong Plateau and Mikir Hills (Chen and Molnar, 1990). In contrast, Bouguer gravity as low as ~−260 mGal and isostatic anomaly ~−125 mGal in the northeastern part clearly argue for a state of undercompensation in the foreland of upper Assam area. The resultant isostatic imbalance near the foothills is possibly accommodated through flexural bulging beneath the Shillong Plateau area. This broad sub-surface trend is normally a typical feature observed at convergence margins where collisional orogens with five tectonic components, viz. thrust belts, foreland flexures, plateaux, widespread foreland deformational zones, and zones of orogenic collisional collapse, are ubiquitous worldwide (Condie, 1997; Khan et al., 2010). It is thus inferred that the positive compensation towards the southwestern part is caused by the elevated descending Indian lithosphere (e.g., lithospheric-scale buckling, cf. Rodgers, 1987), whereas low b-value and high seismic moment release can be linked with a higher level of stress. The proposed active deformation of the uprising Shillong–Mikir massif (a fragmented portion of the Indian shield, Mukhopadhyay, 1984) with crustal thickening of ~2.4 mm/year (Radha Krishna and Sanu, 2000) is possibly linked with incidence of the great 1897 Assam earthquake (Bilham and England, 2001).

Fig. 8
figure 8

Bouguer gravity anomaly contour map for northeast India (after Verma and Mukhopadhyay, 1977). Contour interval is 10 mGal. Note the wide variation of Bouguer gravity from ~+40 mGal over Shillong Plateau to ~−260 near Upper Assam

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Fig. 9
figure 9

Isostatic anomaly map of the study area (after Verma and Mukhopadhyay, 1977). Contour interval is 10 mGal. Note the wide variation of isostatic gravity anomaly from ~+100 mGal over Shillong Plateau to ~−125 near Upper Assam

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A quantitative appreciation of the earthquake record over a time window may sometimes offer clues, not only for understanding the long-term lithosphere deformation, but also the constitution of the continental crust at any particular region in terms of different rheological domains (Meissner and Strehlau, 1982; Chen and Molnar, 1983; Kirby and Kronenberg, 1987). Though it has been postulated that the lower crust in continental areas is devoid of any seismic activity because of its higher geothermal condition and lower strength (cf. Chen and Molnar, 1983), the recorded seismicity at greater depth in northeast India can possibly be correlated with lower heat flow (cf. Thussu, 2002), as usually observed in shield areas and platforms. Further, the crustal strength with depth varies with tectonic setting, strain rate, thickness and composition. In settings with lower geothermal energy, brittle fractures may be continued up to the lower crust level or further below into the upper mantle because mafic and ultramafic rocks can behave in a very resistive manner to plastic failure (Rutter and Brodie, 1992). Indeed, mantle deformation is speculated at more than ~40 km depth beneath the northeast India on the basis of observation of seismicity (Chen and Molnar, 1990). Combining the observations, e.g., positive Bouguer gravity and isostatic anomalies, lowest b-value and high seismic moment release in the southwestern part of the study area (i.e., Zone I) we propose down-buckling of the descending Indian lithosphere. The related flexural upbulging is presumably being accommodated beneath the Upper Assam area. This is also supported by the observed Bouguer gravity and isostatic anomalies in those areas (discussed before). The downward lithosphere-scale buckling (Burg and Podladchikov, 1999) is considered coeval with the block uplift of the Naga Hills on the SE, Mishmi Hills and Assam syntaxis on the NE and Mikir Hills and Shillong Plateau on the SSW (Verma and Mukhopadhyay, 1977) of the study area. The contention is also supported by the work of Chen and Molnar (1990), which postulated the existence of a subducting strong lithosphere beneath the Shillong plateau.