Gravitational Potential Energy of the Tibetan Plateau and the Role of Mantle Circulation in Driving the Indian Plate

We present a study of the vertically integrated deviatoric stress field for the Indian plate and the Tibetan plateau associated with gravitational potential energy (GPE) differences. In previous studies, the driving forces for the Indian plate have been attributed solely to the mid-oceanic ridges that surround the entire southern boundary of the plate. Stress magnitudes at the Tibetan plateau are presumed to provide a lower bound to the ridge-push force magnitude that is transmitted and stored as excess GPE at the Tibetan plateau. However, vertically integrated stress magnitude estimates of ∼6-7×10¹² N/m in Tibet (Molnar and Lyon-Caen, 1988) far exceed those of ∼3×10¹² N/m (Richardson, 1992) associated with GPE at mid-oceanic ridges. This apparent discrepancy calls for an additional force that is required to drive the Indian plate. We use the Crust 2.0 dataset to infer gravitational potential energy differences in the lithosphere. We then apply the thin sheet approach, in which Stokes equations of steady motion, (∂{σ}_ij)/ (∂ {x}_ij) + ρ g ̂ {z}_i =0, are integrated vertically and then solved to infer a global solution of vertically integrated deviatoric stresses associated only with gravitational potential energy differences. The results around Tibet and the Indian ocean dramatically illustrate the inadequacy of ridge-push forces driving the Indian plate into Tibet. For example, we show that deviatoric stresses associated with GPE differences between the elevated ridges, the deeper Indian ocean, and the elevated Tibetan plateau are insufficient to explain the onset of folding and reverse faulting that is now occurring in the Indian Ocean within the Indo-Australian plate boundary zone. In addition, our global deviatoric stress field solution indicates that both the ridge-push forces ( ∼1.5×10¹² N/m) and the forces associated with GPE differences around the Tibetan plateau ( ∼3.5×10¹² N/m) have previously been overestimated by a factor of 2 or more. These overestimates have resulted from either incorrectly simplified 2-D calculations or from defining total stress as σ _ij = τ _ij + σ _{zz}δ {ij}, in which τ _zz= 0, as opposed to the correct 3-D definition σ _ij = τ _ij + 1/3 σ _{kk}δ {ij}, in which τ _zz ≠ 0. Our results of a global deviatoric stress field solution associated with GPE differences alone can be used to calibrate the magnitudes of shear tractions that have to be applied to the base of the lithosphere to give the expected styles of stresses in tectonically active regions. Such tractions where they exist are expected to be associated with buoyancy driven circulation of the sub-lithospheric mantle. For Tibet in particular, N-S deviatoric compressional stresses needed to cancel the large N-S deviatoric tension ( ∼3-3.5× 10¹² N/m) associated with Tibetan plateau GPE can be explained by the coupling of lithospheric dynamics with buoyancy driven mantle flow, most likely associated with the long history of subduction of the Indo-Australian plate, both below Tibet and elsewhere.