We present analytical derivations and 2-D numerical simulations that quantify magnitudes of deviatoric stress and tectonic overpressure (i.e. difference between the pressure, or mean stress, and the lithostatic pressure) by relating them to lateral variations in the gravitational potential energy (GPE). These predictions of tectonic overpressure and deviatoric stress associated with GPE differences are independent of rock rheology (e.g. viscous or elastic) and rock strength. We consider a simple situation with lowlands and mountains (plateau). We use a numerical two-layer model consisting of a crust with higher Newtonian viscosity than that in the mantle, and also a three-layer model in which the two-layer lithosphere overlies a much less viscous asthenosphere. Our results (1) explain why estimates for the magnitude of stresses in Tibet, previously published by different authors, vary by a factor of two, (2) are applied to test the validity of the thin sheet approximation, (3) show that the magnitude of the depth-integrated tectonic overpressure is equal to the magnitude of the depth-integrated deviatoric stress if depth-integrated shear stresses on vertical and horizontal planes within the lithosphere are negligible (the thin sheet approximation) and (4) show that under thin sheet approximation tectonic overpressure is required to build and support continental plateaus, such as in Tibet or in the Andes, even if the topography and the crustal root are in isostatic equilibrium. Under thin sheet approximation, the magnitude of the depth-integrated tectonic overpressure is equal to the depth-integrated horizontal deviatoric stress, and both are approximately 3.5 × 10 12 N m −1 for Tibet. The horizontal driving force per unit length related to lateral GPE variations around Tibet is composed of the sum of both tectonic overpressure and deviatoric stress, and is approximately 7 × 10 12 N m −1 . This magnitude exceeds previously published estimates for the force per unit length required to fold the Indo-Australian Plate south of India, and hence the uplift of the Tibetan plateau could have folded the Indian Plate. We also discuss the mechanical conditions that are necessary to achieve isostasy, for which the lithostatic pressure is constant at a certain depth. The results show that tectonic overpressure can exist at a certain depth even if all deviatoric stresses are zero at this depth, because this tectonic overpressure is related to horizontal gradients of vertical shear stresses integrated across the entire depth of the lithosphere. The magnitude of the depth-integrated tectonic overpressure of 3.5 × 10 12 N m −1 implies that the pressure estimated from observed mineral assemblages in crustal rocks is likely significantly different from the lithostatic pressure, and pressure recorded by crustal rocks is not directly related to depth. In case of significant weakening of the entire lithosphere by any mechanism our analytical and numerical studies provide a simple estimation of tectonic overpressure via variations in GPE.

Lateral variations along the Himalayan arc are suggested by an increasing number of studies and carry important information about the orogen’s segmentation. Here we compile the hitherto most complete land gravity dataset in the region which enables the currently highest resolution plausible analysis. To study lateral variations in collisional structure we compute arc-parallel gravity anomalies (APaGA) by subtracting the average arc-perpendicular profile from our dataset; we compute likewise for topography (APaTA). We find no direct correlation between APaGA, APaTA and background seismicity, as suggested in oceanic subduction context. In the Himalayas APaTA mainly reflect relief and erosional effects, whereas APaGA reflect the deep structure of the orogen with clear lateral boundaries. Four segments are outlined and have disparate flexural geometry: NE India, Bhutan, Nepal & India until Dehradun, and NW India. The segment boundaries in the India plate are related to inherited structures, and the boundaries of the Shillong block are highlighted by seismic activity. We find that large earthquakes of the past millennium do not propagate across the segment boundaries defined by APaGA, therefore these seem to set limits for potential rupture of megathrust earthquakes.

S U M M A R YVarious models have been proposed to explain tectonic deformations during continent collision. A frequently applied model is the thin viscous sheet model which is however not fully 3-D and assumes a priori diffuse thickening as the dominant deformation style.We compare a fully 3-D multilayer numerical model with a corresponding thin viscous sheet numerical model for the scenario of continent indentation. In our comparison we focus on the three basic viscous deformation styles thickening, buckling (folding) and lateral crustal flow. Both numerical models are based on the finite element method (FEM) and employ either a linear or power-law viscous rheology. The 3-D model consists of four layers representing a simplified continental lithosphere: strong upper crust, weak lower crust, strong upper mantle and weak lower mantle. The effective viscosity depth-profile in the 3-D model is used to calculate the depth-averaged effective viscosity used in the thin-sheet model allowing a direct comparison of both models.We quantify the differences in the strain rate and velocity fields, and investigate the evolution of crustal thickening, buckling and crustal flow resulting from the two models for two different phases of deformation: (1) indentation with a constant velocity and (2) gravitational collapse after a decrease of the indenting velocity by a factor of 5. The results indicate that thin-sheet models approximate well the overall large-scale lithospheric deformation, especially during indentation and for a linear viscous rheology. However, in the 3-D model, additional processes such as multilayer buckling and lower crustal flow emerge, which are ignored in the thin-sheet model but dominate the deformation style in the 3-D model within a range of a few hundreds of kilometres around the collision zone and indenter corner. Differences between the 3-D and thin-sheet model are considerably larger for a power-law viscous than for a linear viscous rheology. Buckling and lower crustal flow are significant in the 3-D model with power-law viscous rheology. For example, fibre strain rates due to buckling can be several hundred per cent different to the depth-averaged strain rate and the lateral mass flow of lower crustal material can be up to six times more than the flow of upper crustal material. Our results also show that the horizontal velocity fields of the upper crust and upper mantle remain nearly identical in the 3-D model during indentation despite their mechanical decoupling due to an intermediate weak lower crust. This result questions the validity of using similarities between velocities from the surface global positioning system (GPS) and mantle shear wave splitting data as evidence for a mechanically coupled lithosphere.3-D multilayer models provide a more complete picture of continental collision than thinsheet models as they enable studying the timing, locality and relative importance of different processes simultaneously which is especially important for the hundreds of kilometre scale around the collisi...

[1] We investigate flexural geometry and rheology of the India plate beneath the eastern Himalaya from a new gravity data set acquired in Bhutan. Compared to the well-studied Nepal Himalaya, the obtained Bouguer anomaly profiles across the range show shorter wavelength flexure of the lithosphere with a narrower and shallower foreland basin. This new data set and seismic Moho constraints are interpreted together in terms of lithospheric flexure using a 2-D thermomechanical model. Our results suggest that the strongest layer of the continental lithosphere beneath Bhutan is the upper mantle, as it is beneath Nepal. The observed west-to-east decrease in flexural wavelength is associated with weakening mantle rheology. The simulations show that this decrease can be related to ductile mantle behavior: either hydrated wet dunite or dry and hot olivine rheology. Both models display decoupled lithospheric layers leading to an eastward decrease of flexural rigidity from 10 24 to 5 10 22 N m in Nepal and Bhutan, respectively.