Lithosphere structure and upper mantle characteristics below the Bay of Bengal

analysis as well as the ﬂexural modelling along these ridges led to the conclusions: (i) 85 ◦ E Ridge was emplaced in off-ridge environment ( T e = 10–15 km); (ii) the higher T e values of ∼ 25 km over the Afanasy Nikitin Seamount (ANS) reﬂect the secondary emplacement of the seamount peaks in off-ridge environment, (iii) that the emplacement of the Ninetyeast Ridge north of 2 ◦ N occurred in an off-ridge environment as indicated by higher T e values (25–30 km). Furthermore, the admittance analysis of geoid and bathymetry revealed that the admittance signatures at wavelengths > 800 km are compensated by processes related to upper mantle convection.


I N T RO D U C T I O N
Combined analyses and modelling of gravity/geoid anomalies together with bathymetry data provide key information on thermal structure, mass distributions and evolution of the oceanic lithosphere and upper mantle (Parsons & Daly 1983;Black & McAdoo 1988;Sandwell & McKenzie 1989). While gravity anomalies are more sensitive to crustal variations, the geoid can better detect deeper mantle density variations (Zeyen & Fernandez 1994;Zeyen et al. 2005;Afonso et al. 2008) and our combined approach permits simultaneous modelling of crustal structure and the lithosphereasthenosphere boundary (LAB). The LAB is of fundamental importance in understanding the mantle dynamic processes as it separates the cold, rigid, conducting lithosphere from the underlying weaker, hot, convective asthenosphere. Seismological studies have revealed that the LAB is sharp and identifiable in the case of younger continental lithosphere, whereas, below stable continents it is too diffused and/or heterogeneous to identify as a single coherent boundary (James 2011). However, below the ocean basins, the LAB is generally related to an isotherm as its thickness is mainly controlled by thermal cooling with respect to oceanic lithosphere age (Parsons & Sclater 1977), except in the regions affected by plumes or major tectonism. The spectral domain analysis of topography with gravity/geoid data provides valuable information for comparing thermomechanical models of the lithosphere and sublithosphere in the oceanic areas (McKenzie & Bowin 1976;Black & McAdoo 1988;Watts 2001). Further, the spatial domain analysis of geoid and topography data is also found to be useful for determining the deep structure beneath oceanic aseismic ridges and their mode of compensation (Sandwell & McKenzie 1989 Figure 1. Topographic map of the Bay of Bengal (BOB) and the contiguous regions. This study area is outlined in red. Black rectangles (named blocks 1-3) are three overlapping areas of 13 • × 13 • size selected for the long wavelength admittance analysis. The N-S oriented fracture zones (dotted lines) and the magnetic anomaly identifications (E-W trending short lines and the corresponding numbers) in the central Indian Ocean basin are adopted from Royer et al. (1989). Folded thrust front at the Burmese arc is adopted from Steckler et al. (2008). ASC, Abandoned Spreading Centre, ANS, Afanasy Nikitin Seamount. Inset, shows location of the BOB.
Oceanic lithosphere in the Bay of Bengal 677 may all have significantly impacted the lithosphere structure below the BOB. Previous investigations have been limited to deriving crustal structure based on seismic reflection and refraction data or through the integrated interpretation of gravity and magnetic data (Curray et al. 1982;Mukhopadhyay & Krishna 1991;Gopala Rao et al. 1997;Ramana et al. 1997;Subrahmanyam et al. 1999;Krishna 2003;Krishna et al. 2009;Radhakrishna et al. 2010Radhakrishna et al. , 2012; and have not provided constraints on structure, mechanical properties of lithosphere and sublithospheric processes, hence making our understanding of the evolution of the BOB lithosphere incomplete. Here, we focus on determining variability in LAB depth along and across the BOB, sublithospheric upper mantle characteristics, the compensation mechanism and mode of emplacement of the aseismic ridges on the oceanic lithosphere, through spatial and spectral domain analysis of the correlation between geoid/gravity and bathymetry, and by combined gravity-geoid modelling.

R E G I O N A L G E O L O G I C A L S E T T I N G A N D E V O L U T I O N
The lithosphere in the northeast Indian Ocean resulted from the breakup of eastern Gondwanaland in the early Cretaceous and evolved through three major phases of seafloor spreading; (i) in a NW-SE direction until mid-Cretaceous, (ii) N-S until the early Tertiary and (iii) subsequently in a NE-SW direction continuing until the present (Royer et al. 1989;Müller et al. 2000). While the N-S spreading regime can be easily recognized in the distal Bengal Fan (south of 6 • N) as evidenced by well-developed E-W trending magnetic anomaly identifications offset by N-S oriented fracture zones (Fig. 1); the presence of thick sediments and lack of identifiable magnetic anomalies in the northern part of BOB prevents the recognition of NW-SE spreading regime identified elsewhere (e.g. Krishna et al. 2009). Recently, based on basement trends observed from large number of multichannel reflection profiles, Radhakrishna et al. (2012) have mapped several NW-SE trending fracture zones in the northern part of the BOB. The BOB is also characterized by the presence of one of the largest submarine fans of the world which extends from 20 • N to 7 • 40 S over a length of 3000 km (Krishna et al. 2001a;Curray et al. 2003). The BOB has received sediments from different sources since the breakup of eastern Gondwanaland (∼130 Ma): initially from the Indian peninsular rivers including the Mahanadi, Krishna-Godavari and Cauvery rivers until Oligocene time (Bastia et al. 2010). After the continental collision between India and Eurasia, the Ganges and Brahmaputra rivers have discharged a huge volume of sediments from the Himalayan mountain range. Seismic stratigraphic studies of the BOB sediments (Gopala Rao et al. 1997;Michael & Krishna 2011) have recognized the unconformity separating the pre-collision sediments from the postcollision sediments and it has been ascribed an Eocene age, but the age of sediments at the base of the Bengal Fan is still uncertain. The sediment thickness estimated as over 22 km in offshore Bangladesh (Curray 1991), decreases towards the south with a significant decrease in sediments thickness between 8 • and 10 • N, with also relative thinning over the 85 • E and Ninetyeast ridges. These two linear longitudinal features divide the BOB into three major subbasins: Western, Central and Nicobar basins (Fig. 1). While, emplacement of the Ninetyeast Ridge is known to be the result of the Kerguelen hotspot related volcanism (Frey & Weis 1995); in the case of 85 • E Ridge, the nature and source of plume as well as mode of its emplacement is not yet clear.

DATA S E T S U S E D
In this study, we carried out an integrated analysis of bathymetry, gravity, geoid, multichannel seismic reflection and refraction data to understand the lithospheric structure beneath the BOB. The bathymetry data from the ETOPO1 (Amante & Eakins 2009) and free-air gravity data from the 1 min grid DNSC08 global gravity database (Andersen & Knudsen 2008) were used to prepare the bathymetry map (Fig. 2a) and free-air gravity anomaly map (Fig. 2b) of the BOB region. Sediment thickness data in the region (Curray 1991;Divins 2003;Radhakrishna et al. 2010) were integrated with the bathymetry to generate the basement depth map (Fig. 2c). The geoid grid for the BOB region was extracted from geoid data generated for the northern Indian Ocean by . The regional multichannel seismic reflection profiles (Curray et al. 1982;Curray 1991;Gopala Rao et al. 1997;Krishna et al. 2001a;Michael & Krishna 2011) and sonobuoy refraction data (Naini & Layden 1973;Curray et al. 1982) within the study region are utilized for gravity-geoid modelling. Additionally, for the purpose of 2-D flexural analysis over the aseismic ridges, we used several short E-W seismic reflection profiles across the 85 • E Ridge (Bastia et al. 2010;Radhakrishna et al. 2012;Krishna et al. 2014;Rao & Radhakrishna 2014) and across the Ninetyeast Ridge (Curray et al. 1982;Gopala Rao et al. 1997;Subrahmanyam et al. 2008;Maurin & Rangin 2009).

Spectral analysis of the geoid
As the geoid data include the effects of all distributed masses within the Earth, the contribution of deeper mantle density sources must be removed from the observed geoid data using a reference geoid model in order to separate the anomalies contributed by lithospheric and sublithospheric mass variations (Bowin 1983;Sandwell & Renkin 1988). We, therefore, generated three residual geoid anomaly maps from the full spectrum geoid (Fig. 3a) by subtracting different geoid contributions corresponding to the spherical harmonic coefficients of degree and order less than or equal to 10, 30 and 50 using the EGM2008 reference geoid. This procedure removes the contribution of the geoid of wavelengths >4000, >1334 and >800 km, respectively and give rise to different residual geoid anomalies. As suggested by Sandwell & Renkin (1988), while subtracting these different geoid contributions, the model coefficients are smoothly rolled over by applying a cosine taper at that particular degree and order to avoid sharp truncation effects. However, in order to check the reliability of the EGM2008 data, we made a spectral comparison with the latest DTU10 model (Andersen 2010) and observed that the difference between the EGM2008 and DTU10 models is found mainly at shorter wavelengths (<30 km, Fig. 3b).
In general, long wavelength components of geoid data (>4000 km) are sensitive to the density variations in the lower mantle (Bowin 1983), whereas, shorter wavelength components (<330 km) reflect the crustal thickness variations and lithosphere flexural effects (Marks & Sandwell 1991). Three residual geoid anomalies were generated (Figs 3c-e) for the BOB region in order to approximately understand geoid contributions from different depth regions. While, n = 10 (λ < 4000 km) and n = 30 (λ < 1333 km) degree residual geoid anomaly maps mostly reflect the sublithospheric mass variations, the n = 50 (λ < 800 km) corresponds to sources within the lithosphere (Featherstone 1997  prepared the bandpass filtered residual geoid anomaly map ( Fig. 3f) for degree (10 < n < 50) for the eastern Indian Ocean region as it reflects the mass variations within the upper mantle.

Geoid-topography ratio (GTR)
The geoid data are known to relate linearly to the topography between wavelengths 400 and 4000 km (Sandwell & Renkin 1988), therefore, the GTR analysis for these wavelengths can be used to understand the mode of compensation of topographic features such as swells, plateaus and aseismic ridges (Haxby & Turcotte 1978;Sandwell & McKenzie 1989;Coblentz et al. 2011). In general, low GTR values (0-2 m km −1 ) indicate shallow level of compensation, whereas, the intermediate GTR values (2-6 m km −1 ) suggest that the compensation takes place at deeper level by lithosphere thinning (Crough 1978). Conversely, higher GTR values (>6 m km −1 ) indicate compensation below the lithosphere supported by convective stresses (McKenzie et al. 1980). In this study, we carried out GTR analysis along the 85 • E and the Ninetyeast ridges at two wavelength scales. First, the bandpass filtered (330-4000 km) maps of the bathymetry and geoid data were prepared (Figs 4a and b) by considering the spherical harmonic coefficients for degrees between n = 10 (<4000 km) and n = 120 (>330 km). The scatter plots of these bandpass filtered geoid and the bathymetry (corrected for sediment load using the method of Sykes 1996) have been prepared for twenty-two 4 • × 2 • overlapping (1 • overlap) blocks along these two ridges (see Fig. 4b for location of blocks). For each block, least-square regression lines are fitted and the correlation coefficient is estimated. While, the correlation coefficient for each block reveals goodness of fit, the slope of the regression line gives the GTR value for each block. Similarly, we analysed the bandpass filtered geoid and bathymetry data between 330 and 800 km wavelengths corresponding to degrees n = 50 (<800 km) and n = 120 (>330 km). The computed GTR values for each block are plotted longitudinally (centred at particular latitude) along both the 85 • E and Ninetyeast ridges (Figs 5a and b) are presented.

Admittance/coherence analysis
Though the aforementioned GTR analysis provides valuable information on the nature of isostatic compensation, it would not be able to discriminate between different isostatic compensation models along the aseismic ridges. For this purpose, the relationship between geoid/ gravity and the topography in the spectral domain (admittance/coherence) is utilized for better understanding the isostatic response of the topographic loads, and for studies related to thermomechanical characterization of the oceanic lithosphere and/or sublithospheric upper mantle. Several researchers have effectively used this approach (i) for evaluating isostatic response of the oceanic lithospheric using free-air gravity/geoid and bathymetry admittance function (e.g., McKenzie & Bowin 1976;Watts 1978;Black & McAdoo 1988); (ii) for estimation of flexural rigidity of continental lithosphere through Bouguer gravity and topography coherence function (Forsyth 1985;Lowry & Smith 1994;McKenzie & Fairhead 1997;Simons et al. 2000;Swain & Kirby 2003). In this  , (b) the power spectral density and coherence between the EGM2008 and DTU10 geoid models for spectral comparison, (c-f) the residual geoid maps of the BOB obtained after subtracting different long wavelength geoid contributions using smoothly truncated EGM2008 spherical harmonic coefficients from the full spectrum geoid (after . (c) degree-10 residual geoid anomaly map, (d) degree-30 residual geoid anomaly map, (e) degree-50 residual geoid anomaly map, (f) Bandpass filtered residual geoid map between wavelengths corresponding to spherical harmonic coefficients of degree and order >10 and <50. Dashed lines in (c) represent location of the modelled lithospheric profiles. Trace of both 85 • E and Ninetyeast ridges is shown on the residual geoid maps. Blocks 1 to 11 shown in (e) are selected for the admittance and coherence analysis along these ridges, and profiles marked (S1-S5) across 85 • E Ridge and (P1-P5) across the Ninetyeast Ridge are seismic lines used for the study of 2-D flexure modelling.  study, we analysed the admittance between bathymetry and residual geoid on two wavelength scales, one using degree-10 residual geoid for modelling upper mantle convection processes, and other using degree-50 residual geoid for understanding mode of isostatic compensation along the 85 • E and Ninetyeast ridges. Further, as these two linear ridges in BOB are buried below thick sediments, we computed the Mantle Bouguer Anomalies (MBA) to further analyse the mode of isostatic compensation of these ridges. The MBA were computed by removing the gravity contributions of water, sediment and a 6 km uniformly thick oceanic crust from the free-air gravity anomalies using a normal oceanic crustal density of 2900 kg m −3 . We then carried out MBA-bathymetry coherence analysis along these two ridges. Further details on the methodology are described below

Long wavelength (>800 km) geoid-bathymetry admittance
We computed the admittance of bathymetry and residual geoid for three overlapping blocks of size 13 • × 13 • with a grid sampling of around 3 × 3 covering the BOB region (Fig. 1). The large block size and the degree-10 residual geoid is purposely chosen in order to incorporate the wavelengths greater than 800 km in the spectral estimates that are attributable to upper mantle convection processes. The blocks were limited to 17 • N latitude in the BOB region to avoid the effect of continental mantle signatures on the admittance computation. The method used for the calculation was adopted from Black & McAdoo (1988). For each block, 256 E-W and N-S profiles of bathymetry and the residual geoid (degree-10) data were extracted from the grid, and these profiles were stacked to obtain average E-W and N-S bathymetry and geoid profile data sets. For these averaged profiles, admittance was computed using power spectrum of the bathymetry and cross spectra of the bathymetry and geoid data using the formula (after McKenzie & Bowin 1976) where k is the wave number, Z(k) admittance between geoid and bathymetry; C(k) is cross spectrum of the geoid and bathymetry, E b (k) is power spectrum of the bathymetry. We compare the observed admittance values with the theoretical admittance curves computed for a simplified mantle convection model assuming Newtonian convection in a uniformly viscous mantle layer, and neglecting the effect of inertia, self-gravitation and sphericity (Parsons & Daly 1983). It is known that the observed geoid can be defined as a function of the deformation of the upper and lower surfaces of the convective layer and density structure imposed by the temperature distribution (T) within the convective layer (Black & McAdoo 1988). The admittance values were computed assuming free slipping upper boundary and non-slipping rigid lower boundary conditions for two different temperature distribution models 1 and 2. While, model-1 (eq. 2) imposes temperature  variations at the top boundary of the convecting layer, model-2 (eq. 3) imposes temperature variation at the bottom boundary.
Here, k | and z | represent non-dimensional wavenumber and depth of the convecting layer, respectively. It is notable that model-2 produces higher amplitudes for theoretical admittance, and according to Parsons & Daly (1983) as the largest temperature variation occurs closer to the bottom boundary, the amplitude of transfer increases. The analytical expressions for the calculation of theoretical admit-tance curves for the above temperature distributions (after Parsons & Daly 1983) and for different convective layer thicknesses (640 and 400 km) were presented in detail in earlier publication (Black & McAdoo 1988), and we do not reproduce here.
The computed E-W and N-S admittances were plotted along with the theoretical admittance curves as shown in Fig. 6. While, the E-W admittances show comparable amplitudes with the theoretical admittance curves derived for the mantle convection model (after Parsons & Daly 1983;Black & McAdoo 1988), the N-S admittances are significantly low, particularly at longer wavelengths. According to Black & McAdoo (1988), such low admittances ( Fig. 6) are observed for the profiles oriented in the direction of plate motion (N-S in the case of BOB) due to weaker signal of convective rolls in the upper mantle along the plate motion.  Fig. 4) along the 85 • E Ridge (left-hand panel). Both degree 10-120 (red) and degree 50-120 (blue) wavelength scales of residual geoid and bathymetry are used for this analysis. Representative scatter plots for two selected blocks are also presented. Further the along ridge variation of GTR values are also shown in plan view (right-hand panel) for better perception.

Isostatic response study of the aseismic ridges
In order to estimate the effective elastic thickness (T e ) variation along the aseismic ridges in the BOB region (85 • E and the Ninetyeast ridges), we computed the admittance of bathymetry and the degree-50 residual geoid for eleven 4 • × 4 • blocks (see Fig. 3e for location), with 2 • overlap, along each of these ridges. For each block, we selected 88 E-W lines of bathymetry and residual geoid anomalies, and averaged them to define a profile representing the centre of that block. For this averaged profile, admittance is computed using the formula given in (eq. 1). The computed admittance values for each block in the flexural waveband (0.01 < k < 0.04) were compared with the theoretical admittance curves for different T e values derived based on the flexural model of isostasy (Sandwell & Renkin 1988) as shown in Fig. 7(a). Additionally, in order to incorporate subsurface loads in the flexural response estimation (Forsyth 1985), we carried out coherence analysis for the same blocks along both the ridges.
In the case of small-scale tectonic features, the admittance/coherence functions based on the periodogram method do not possess sufficient spectral resolution for robust estimation of T e (Lowry & Smith 1994). In order to overcome this problem, Lowry & Smith (1994) suggested the maximum entropy method (MEM) in which the spectrum of signal is estimated by extrapolating the signal's autocorrelation function (the inverse Fourier transform of the power spectrum) under the condition of it having maximum en-tropy. Here, for each block along these ridges, the observed coherence between MBA (see Section 4.3) and bathymetry is computed using MEM and these were compared with the theoretical coherence curves (Fig. 7b) calculated for subsurface to surface loading ratio f equal to 0.5 using the formula given by Forsyth (1985).
The best-fitting T e was chosen based on the least residual error of L 2 norm of observed minus theoretical coherence (Fig. 7b) within the flexural waveband (0.01 < k < 0.04). The choice of f equal to 0.5 is based on the earlier studies over the Ninetyeast Ridge in the southern part of this study area (Grevemeyer & Flueh 2000;Grevemeyer et al. 2001;. The T e values obtained from the admittance and coherence analysis along the 85 • E and Ninetyeast ridges are given in Table 1.

2-D flexural modelling
T e values obtained from the admittance/coherence analysis (Table 1) indicate the strength of the lithosphere due to all geological processes since the emplacement of the aseismic ridges/seamounts (Calmant et al. 1990;Watts 2001). In order to analyse the T e at the time of emplacement of the loads, we further carried out flexural modelling along five multichannel seismic profiles crossing over both the 85 • E (S1-S5 in Fig. 3e) and Ninetyeast (P1-P5 in Fig. 3e) ridges. In order to reconstruct the topography of both the ridges at the time of emplacement, the overlying sediment layer was backstripped by assuming that the strength of the lithosphere remained constant since the emplacement. Accordingly, we considered a constant T e value for flexurally backstripping the sediment layer. In the case of Ninetyeast Ridge, we further removed the subduction related forebulge from the reconstructed topography. Here the maximum forebulge (w b ) has been estimated based on the method of Harris & Chapman (1994) by assuming a T e of 35 km for the subducted portion of the Indian plate (after Subrahmanyam et al. 2008) and it varies between 190 and 250 m at a distance of 100 km from the trench axis. Further, the ridge emplacement is modelled as a load on thin elastic plate to estimate the flexural Moho configuration. For the flexural calculation, we used a density of 2300 kg m −3 for the sediments (1.6-4.4 km s −1 ) and 2650 kg m −3 for the ridge material (4.2-4.6 km s −1 ) based on the seismic velocity data available for the 85 • E Ridge (Rao & Radhakrishna 2014) and Ninetyeast Ridge (Curray et al. 1982;Maurin & Rangin 2009). A simpli-fied density configuration of 2900 kg m −3 for the oceanic crust (6.0-7.5 km s −1 ) and 3300 kg m −3 for the upper mantle (7.9-8.1 km s −1 ) were used from the available seismic refraction velocities in the BOB region (Curray et al. 1982). Finally, the backstripped sediment layer was added to the restored section to construct the present-day configuration of the ridge, and for the resultant crustal structure, the gravity and geoid response was calculated through forward modelling (Figs 8a and b). The modelling was iteratively carried out for a range of T e values, and the best-fitting T e was obtained based on the minimum RMS error between the observed and calculated by matching both amplitude and wavelength of anomalies.

Geoid-gravity modelling
The lithospheric structure was modelled along three regional transects AA to CC (two E-W, one N-S) in the BOB region (see Fig. 3c for profile locations). For this purpose, the gravity and geoid anomalies were extracted along these transects from the freeair gravity (Fig. 2b) and residual geoid anomaly (Fig. 3c)

#BLOCK-3
Combined flexure & Convection model Figure 6. Comparison of the observed (black dots indicate E-W admittances; red dots represents N-S admittances) and theoretical (green and blue lines) admittance between the geoid and bathymetry for three 13 • × 13 • blocks ( Fig. 1 for location) in the BOB region. (a) Here, the theoretical admittance curves are computed for the mantle convection model involving different convective layer thicknesses (640 and 400 km) and for two different temperature distributions within the convecting layer; model-1 (in eq. 2) imposes temperature variation at the top boundary (blue curves) and model-2 (in eq. 3) imposes temperature variation at the bottom boundary (green curves) (after Black & McAdoo 1988). The observed admittance values falling within the diagnostic waveband (0.004 < k < 0.008) are compared with the theoretical curves derived for mantle convection model. The theoretical admittance curves (thick black lines) for pure flexure model (after Sandwell & Renkin 1988) also presented in the figure. (b) Here, the theoretical admittance curves are computed for the combined convection and flexure model by incorporating combination of convective loading and flexural loading of the lithosphere for different values of 'f ', which is ratio of convective load on the bottom to the flexural load on the top of the lithosphere (after Black & McAdoo 1988). In this model, we considered thickness of the convecting layer 640 km with temperature structure defined by model-2, and effective elastic thickness (T e ) of 10 km for the BOB region. Details are discussed in the text.
longitudinal transect AA , constructed from the results of Curray (1991) and Krishna et al. (2001a), gradually decreases from >9 km in the north to about 2 km in the south. Curray (1991)  In the initial model, the geometry of the Moho was constructed either by utilizing the crustal velocity information (for the N-S transect AA ) available from the published seismic refraction data (Curray et al. 1982) or adding 6-km-thick normal oceanic crust to the basement (in the case of transects BB and CC ). The Base of the lithosphere (LAB) was initially chosen based on the plate cooling model for the lithospheric ages in the region (Parsons & Sclater 1977). Available seismic velocities along transects allowed us to consider the densities 2300 kg m −3 for the upper sediment layer from present to upper Miocene 2400 kg m −3 for the middle layer from middle Miocene to upper Oligocene base and 2550 kg m −3 for the pre-collision sediment layer. A two-layer oceanic crustal density configuration having 2700 kg m −3 for the upper crust and 2900 kg m −3 for the lower crust was considered (after Mukhopadhyay & Krishna 1991). A generalized density configuration for both lithospheric mantle and underlying asthenosphere were chosen as 3300 and 3250 kg m −3 , respectively. As the sediment and oceanic crustal densities are reasonably constrained by the seismic velocity data, we computed the gravity/geoid responses for different models by adjusting the geometry of Moho and LAB interface adopted for the initial model, and these responses were compared with the observed anomalies. The final Moho and LAB geometries were obtained by minimizing the discrepancies between the computed response and the observed anomalies through several iterations until a good fit was achieved. The gravity response of the model was calculated using the algorithm of Talwani et al. (1959) and the geoid response of the model was computed based on the algorithm of Chapman (1979) and Ayala et al. (1996). These algorithms are useful to compute the gravity/geoid response for any arbitrary 686 G.S. Rao et al.   shaped 2-D body by approximating the body to a 'n' sided polygon. The polygons are defined with the vertices in coordinate system and the respective responses (gravity/geoid) are calculated using the line integral method. Hence, these forward modelling methods are highly useful to compute the gravity/geoid responses in the case of complex geological structures. Using the above methodology, we computed the best-fitting lithospheric structure along the three regional transects AA -CC in the BOB region (Figs 9a-c). Additionally, as the N-S profile (AA ) lies across oceanic lithosphere of age ranging from 65 to 110 Ma, we incorporated the temperature-dependent lithospheric mantle density structure defined by the global plate cooling models (Parsons & Sclater 1977;Stein & Stein 1992) while deriving the lithospheric structure.

R E S U LT S A N D D I S C U S S I O N
The wavelength filtering analysis of geoid anomalies in the BOB region (Figs 3c-f) revealed that the amplitude of the degree-10 residual geoid varies from −10 m to +12 m with a prominent high parallel to the Andaman subduction zone close to the Ninetyeast Ridge between 10 • N to 5 • S and a low corresponding to the rifted basins (Fig. 3c) offshore Eastern Continental Margin of India (ECMI). The degree-30 residual geoid map (Fig. 3d) reveals a distinct geoid high corresponding to the Ninetyeast Ridge between 2 • N to 16 • N. However, to the north of 4 • N, where the Ninetyeast Ridge intersects with the Andaman subduction zone, the geoid anomalies of the ridge merge with the arc parallel anomalies and become indistinguishable. The signature of the Ninetyeast Ridge can be clearly identified in degree-50 residual geoid anomaly map (Fig. 3e), and is seen to extend up to 17 • N as series of localized highs. Overlapping of long wavelength arc parallel geoid anomalies and short wavelength anomalies of the ridge at places indicate the interaction of the Ninetyeast Ridge compensation with the subduction process. The 85 • E Ridge is weakly identifiable in the degree-30 residual geoid anomaly map (Fig. 3d), whereas, on the degree-50 residual geoid anomaly map (Fig. 3e), the ridge distinctly appear as a belt of geoid lows in the north, and as geoid highs in the region south of 5 • N to the Afanasy-Nikitin Seamount (ANS) location. It is to be noted that morphologically, the northern part of the ridge (north 688 G.S. Rao et al. of 5 • N) is buried below the thick Bengal Fan sediments, whereas; towards south the ridge is intermittently exposed on the seafloor with a thin sediment veneer. Further, the ridge is also wider having double peaked morphology in the north (Rao & Radhakrishna 2014). These characteristic structural/geometrical variation and the differences in sediment thickness along the ridge between north and south is reflected on the gravity/geoid anomalies in north and south. West of the 85 • E Ridge in the northern BOB, a localized high at 13 • N is also observed in the degree-50 residual geoid anomaly map (Fig. 3e).
The bandpass filtered residual geoid anomaly map (10 < n < 50) reveals strong bi-polar signature of the geoid field with a belt of positive anomalies in the Andaman-Sumatra arc region and a negative field parallel to the ECMI with a transition zone in the central part of BOB (Fig. 3f). Subduction zones in general are characterized by long-wavelength (n = 4-9) positive geoid anomalies due to the cold upper mantle slabs, particularly in the case of subduction zones that are associated with the deeper penetration of subducted slabs to the lower mantle, and an effective mantle viscosity change (Hager 1984;King 2002). The Andaman-Sumatra arc forms part of the Sunda subduction zone in the eastern Indian Ocean, along which the Indian and Australian plates together subduct below the Eurasian plate. Seismicity and other geophysical data along this subduction zone demonstrates that maximum depth of the down going lithospheric slab varies from 600 to 800 km below Java, 250-350 km below Sumatra and ca. 200 km beneath the Andaman arc region (Hayes et al. 2012). The long-wavelength residual geoid anomalies in the eastern Indian Ocean region did not reveal significant geoid signature associated with the Sunda subduction zone. However, in the bandpass filtered (10 < n < 50) residual geoid anomaly map (Fig. 3f), a geoid high zone is observed between the Ninetyeast Ridge and the Sumatra trench, which could be related to mass heterogeneities within the upper mantle below the region. Elsewhere, the low geoid anomalies observed in the northern BOB and along the ECMI (Fig. 3f) are attributed to gradual transition of oceanic lithospheric mantle of BOB to more continental affinity beneath the eastern Indian shield.

Upper mantle characteristics
As described in Section 4.3.1, the geoid-bathymetry admittance at wavelengths >800 km provides some insights on thermal structure of the upper mantle beneath the BOB. The theoretical admittance curves derived for two convective layer thicknesses (400 and 640 km) defined by different temperature distribution models (1 and 2 described in Section 4.3.1) are compared with the observed admittance values (Fig. 6a) at wavelengths greater than 800 km (k < 0.008). As the spatial extent of study area in the BOB is confined to 13 • × 13 • region, the observed admittance is available at only one wavenumber that falls within the wavelength band of the mantle convection model. The peak value of the observed admittance at this wavenumber (k ∼ 0.004) is very high (>8 m km −1 ) and closely matches with the theoretical admittance curve computed for a 640-km-thick convective layer with the temperature distribution defined by model-2, which means that maximum temperature variation lies at the bottom of the convecting layer. However, for higher wavenumbers k > 0.01, the observed admittance values are not related to the mantle convection processes, therefore they are not comparable with the theoretical curves derived for convection model. The admittance values at these higher wavenumbers could be ascribed to the compensations related to flexure of the BOB lithosphere. It is evident from Fig. 6(a) that observed admittance values fall within the pure flexure curves at the higher wavenumbers. In order to bring these two processes into a single unified model, Black & McAdoo (1988) presented theoretical admittance due to a combination of convective loading and flexural loading of the lithosphere following the relations developed by Forsyth (1985). Accordingly, we computed theoretical admittance curves for combined flexure and convection model for different values of f, which is the ratio of convective load to the flexural load. For this purpose, we consider a 640-km-thick convecting layer with temperature distribution defined by model-2 and an effective elastic thickness T e of 10 km for the BOB lithosphere. The resultant curves along with observed admittance values are presented in Fig. 6(b). While, the admittance value at the lowest wavenumber (Fig. 6b) supports mantle convection, the admittance values at higher wavenumbers (k > 0.01) agree well with flexural compensation. are observed showing >2 m km −1 and negative values. For the 85 • E Ridge, the GTR values are higher ∼3-6 m km −1 between the equator and 6 • N, >4 m km −1 at 17 • N in the 10-120 degree data set, and negative GTR values of −2 to −3 m km −1 between 9 • N and 12 • N in the 50-120 degree data set (Fig. 5a). The blocks in the north at around 18 • N show higher GTR values in 10-120 degree data set as this part of the ridge is under the influence of continental edge effect of the adjoining Indian lithosphere. A correlation of degree-10 and degree-50 residual geoid anomalies of the ridge further reveals that the blocks between equator and 6 • N falls in the region of stronger gradients in the degree-10 map. While, the GTR values for 50-120 • data set indicate compensation of the ridge at shallow level, the higher GTR values observed over these blocks in the 10-120 • data set could be due to the influence of deeper mass variations. On the other hand, between 9 • and 12 • N, the negative GTR values of −2 to −3 m km −1 observed in the 50-120 • data set changes to 0-2 m km −1 in the 10-120 • data set (Fig. 5a) and the scatter plots do not seem to indicate any data artefacts at this location. A close look at the image enhanced gravity maps ( fig. 2 of Bastia et al. 2010) and the degree-50 residual geoid anomaly map ( Fig. 3e present study) of the 85 • E Ridge reveal minor breaks in the trend of the ridge and presence of localized body west of the ridge around 12-13 • N. It is not clear whether the negative GTR values in 50-120 data set could be ascribed to these shallow structural heterogeneities. For the Ninetyeast Ridge, the 10-120 • data set gave rise to slightly higher GTR values of 3 m km −1 between 6 • N and 8 • N and negative GTR values between 9 • and 13 • N with the lowest value of −2 m km −1 at 11 • N (Fig. 5b). The higher GTR values between 6 • N to 8 • N correlate with the prominent geoid high zone observed in the degree-10 residual geoid map and could be due to deeper mass heterogeneities. The negative GTR values observed between 9 • and 13 • N in the 10-120 • data set become close to 0 m km −1 in the 50-120 • data set. As the Ninetyeast Ridge between 9 • and 13 • N is closer to the Andaman trench, we believe that the negative GTR values observed in the longer wavelengths could be due to complex interaction of ridge subduction below the Andaman-Sumatra arc.

Mode of compensation below 85
The residual geoid-bathymetry admittance analysis and MBAbathymetry coherence analysis carried out along the 85 • E and Ninetyeast ridges provide further insights with regard to the nature of compensation as well as mode of emplacement (on ridge/off ridge). The T e values obtained from both the methods, in general, show similar variations along both the ridges and over the ANS (Table 1). In selective blocks, the observed admittance values (in the diagnostic waveband) show large scatter and do not match with the theoretical curves (e.g. Block-9 on 85 • E Ridge and Block-6 on Ninenyeast Ridge, see Fig. 7a), hence, the T e value becomes less reliable for these blocks. This could be due to lack of ridge expression yielding low coherence between bathymetry and geoid/gravity in the case of 85 • E Ridge, or due to close proximity of the trench around 8 • N in the case of Ninetyeast Ridge (see Figs 2 and 3e). However, the T e was considered from the coherence analysis (Fig. 7b) in these blocks. As stated earlier, for the coherence analysis, we considered a value of 0.5 for the loading ratio f as the modelled f values elsewhere along the Ninetyeast Ridge range from 0.5 to 0.7 (Grevemeyer & Flueh 2000;Grevemeyer et al. 2001) and 0.3-0.6 ).
Further, T e values at the time of emplacement of these ridges were obtained through flexural modelling along five seismic profiles crossing the ridges. The study reveals T e values of 10-15 km for the 85 • E Ridge, 20 km for the ANS and 25-30 km for the Ninetyeast Ridge. The crustal structure modelled along these profiles (as described in section 4.4) for the best-fitting T e values are presented in Figs 8(a) and (b). In order to check the sensitivity of T e on the choice of upper mantle density, we computed flexural response for a range of upper mantle densities from 3200 to 3400 kg m −3 and found that variation in T e is not significant (<2 km). While, the admittance/coherence analysis as well as the flexural modelling give rise to similar T e values for the 85 • E Ridge; for the Ninetyeast Ridge (north of 10 • N), the T e values obtained through flexural modelling are relatively higher than from the admittance/coherence analysis. This difference in T e values is ascribed to subsequent modification of the ridge topography by subduction related forebulge effect of the Andaman-Sumatra arc system in this region.
The present T e values obtained from both 85 • E and Ninetyeast ridges are combined with the T e estimates published for the 85 • E Ridge (Sreejith et al. 2011) and for the Ninetyeast Ridge  to provide a comprehensive picture on the T e variation along the ridges (see Figs 8a and b). It is notable that for the 85 • E Ridge the estimated T e values range from 10 to 15 km except in the area of ANS, where comparatively higher T e values of 20 km is observed. However, along the Ninetyeast Ridge, the T e values are about 20-30 km for the ridge north of 2 • N latitude.
The T e values extracted from the global T e estimates presented by Watts et al. (2006) for the Ninetyeast Ridge in the study area in general show higher T e values (>25 km) for the ridge north of 2 • N and around 7-18 km between equator and 6 • S. We observed that T e values obtained in this study are in general agreement with the global T e values (Watts et al. 2006), however, our estimates are better constrained due to the availability of regional seismic data for the ridge north of 10 • N which is progressively buried below the Bengal Fan sediments.

Lithospheric structure
LAB depths derived from combined modelling of gravity and residual geoid anomalies along profile AA (Fig. 9a) range from 122 km in the north to 73 km in the south. Further, the degree-10 residual geoid anomalies (Fig. 3c) along this profile reveal that the regional geoid high observed in the southern BOB turns into a regional low towards northern BOB. This change in both residual geoid and gravity anomalies is explained by the deepening of LAB towards north on profile AA and the geometry of upper crustal layers in the model further indicates the extent of sediment depocentre of the Bengal Fan.
In order to understand the effect of temperature-dependent mantle densities at LAB depths, we further modelled the lithosphere geometry along profile AA taking into consideration of two different thermal structures, the GDH1 (Stein & Stein 1992) and the PSM (Parsons & Sclater 1977) for the BOB lithosphere. The isotherms defined by these two thermal models were utilized to constrain the initial density layering for the lithospheric upper mantle and this geometry was changed iteratively to fit with the observed geoid and gravity anomalies along the profile. The final modelled geometry (see Fig. 9a) reveals that depth to the LAB varies from 77 to 127 km for the GDH1, while the LAB depths derived from the PSM model are systematically deeper by 15-20 km than GDH1. We observed that the modelled LAB geometry for the PSM matches well with the LAB values retrieved from the global grid of upper mantle structure PM v2 2012 (Priestley & McKenzie 2013) except for the difference in lateral placement of their deepening. On the other hand, the modelled LAB values from the GDH1 agree well with the estimates of LAB based on the available seismological data in the BOB (Singh 1990;Mitra et al. 2011;Bhattacharya et al. 2013). Hence, we consider the modelled LAB along profile AA based on GDH1 as a representative one for the BOB. It is interesting to note that the modelled LAB depths (127-77 km) below BOB are significantly deeper than the LAB values derived in the Pacific Ocean lithosphere (Rychert & Shearer 2011;Rychert et al. 2012 and references there in) of similar age (65-110 Ma). This observation would be consistent with the presence of colder upper mantle below the BOB, as earlier suggested by Brune et al. (1992), causing the deepening of isotherms at the LAB level. Alternatively, the deeper LAB below the northernmost BOB may indicate a greater continental affinity of the BOB lithosphere. The modelled LAB geometry along two E-W profiles, profile BB (Fig. 9b) and profile CC (Fig. 9c), which reveal that LAB is almost flat below the 85 • E Ridge, whereas minor localized thinning is observed below the Ninetyeast Ridge. This eastward thinning of the lithosphere observed in both the profiles could be ascribed either to the plume related thinning below the Ninetyeast Ridge (Davies 1994) or due to the interaction of the ridge with the Andaman-Sumatra subduction zone in this region. However, resolving these two competing processes needs further detailed investigation.

G E O DY N A M I C I M P L I C AT I O N S
Generally, in plume-affected basins such as the northern Atlantic, high amplitude geoid anomalies are associated with shallow basement depths (Jung & Rabinowitz 1986). In contrast, presence of deeper basement depths and low amplitude geoid anomalies in the BOB region suggest that the mantle rheology is not significantly affected by mantle plume activities, despite the presence of two major hotspot traces on the seafloor-the 85 • E Ridge and the Ninetyeast Ridge. Ito & Keken (2007) noticed that the rise of swells formed by the hotspot volcanism decreases with time and becomes undetectable beyond 80 Ma. As the volcanism leading to the emplacement of the 85 • E and Ninetyeast ridges in the BOB are older (>80 Ma), the swells associated with the initial volcanism will have subsided. Earlier derived crustal models show the presence of thicker crust with and without underplating below these ridges (Detrick & Watts 1979;Mukhopadhyay & Krishna 1995;Subrahmanyam et al. 1999Subrahmanyam et al. , 2008Grevemeyer et al. 2001;Krishna et al. 2001b;Krishna 2003;Radhakrishna et al. 2010). The present analysis revealed that both ridges, in general, are compensated at shallow depths. The T e values of 10-15 km estimated for the 85 • E Ridge further confirms its emplacement in off-ridge environment. The consistently higher T e value of 20 km over the ANS is not in agreement with the low T e values reported by Paul et al. (1990), however, match very well with the T e values obtained by Watts et al. (2006) in this region. Recent geophysical studies and 40 Ar/ 39 Ar dates of the ANS (Krishna et al. 2014) suggested that the ANS was emplaced in two phases with the construction of main plateau in the initial phase around 80-73 Ma close to the spreading centre, and emplacement of seamount highs in later stage at about 67 Ma. Hence, the higher T e values obtained over the ANS could be related to the later emplacement over a relatively stronger lithosphere. The Ninetyeast Ridge is also characterized by higher T e values of 20-30 km for the ridge segment at Indian Institute of Geomagnetism on June 13, 2016 http://gji.oxfordjournals.org/ Downloaded from north of 2 • N, suggesting its emplacement in the intraplate setting. On the other hand, the scattered T e values observed by earlier investigators for the ridge south of 2 • N revealed that this part of the ridge had evolved due to frequent ridge jumps in the vicinity of the Kerguelen hotspot during the rapid northward migration of the Wharton spreading ridge (Royer et al. 1991;Krishna et al. 1999Krishna et al. , 2012Sager et al. 2010). The modelled lithosphere structure across these ridges suggests a lack of plume impact at the LAB, although there is minor eastward thinning beneath the Ninetyeast Ridge.

C O N C L U S I O N S
Forward as well as flexural modelling of geoid-gravity anomalies of the BOB have provided a new understanding on lithospheric structure and nature of emplacement of the 85 • E Ridge, ANS and Ninetyeast Ridge. The major conclusions of this study are described below: (1) The seismically constrained geoid-gravity modelling defined by the temperature-dependent mantle densities based on the GDH1 model has revealed that depth of LAB is about 127 km for the 110 Ma age oceanic lithosphere in the northern BOB region, while it is about 77 km for the 65 Ma age lithosphere in the south BOB. The deepening of LAB towards the north, and the geometry of upper crustal layers constrain the extent of sediment depocentre of the Bengal Fan. Comparison of LAB depths for the lithosphere of similar age in the Pacific Ocean suggested the presence of anomalously thick lithosphere beneath BOB.
(2) Spatial variations in GTR values as well as T e estimates along the 85 • E Ridge, ANS and the Ninetyeast Ridge suggests variable isostatic mechanism beneath the ridges. While, the Ninetyeast Ridge could have been emplaced during the interaction of Kerguelen hotspot with the Wharton spreading ridge, present study reveals that the ridge north of 2 • N was emplaced on a stronger lithosphere in an intraplate setting. The modelled lithospheric structure across these two ridges in the BOB suggests that they are dominantly crustalscale features regionally compensated through flexure at shallow depths.
(3) Further, the admittance analysis between geoid and bathymetry had revealed that the admittance signatures at wavelengths >800 km are compensated by an upper mantle convective layer below the BOB region.

A C K N O W L E D G E M E N T S
This research was funded by the ISRO as a part of MOP II and III-Marine Lithospheric Studies program between IITB, NIO and SAC. JMB was supported by UKIERI funding. Critical comments from the reviewers and the Editor Prof Randy Keller helped to greatly improve the manuscript. The research work presented in this paper is part of the Ph.D. thesis of the first author.