Contribution of gravitational potential energy differences to the global stress field

Modelling the lithospheric stress field has proved to be an efficient means of determining the role of lithospheric versus sublithospheric buoyancies and also of constraining the driving forces behind plate tectonics. Both these sources of buoyancies are important in generating the lithospheric stress field. However, these sources and the contribution that they make are dependent on a number of variables, such as the role of lateral strength variation in the lithosphere, the reference level for computing the gravitational potential energy per unit area (GPE) of the lithosphere, and even the definition of deviatoric stress. For the mantle contribution, much depends on the mantle convection model, including the role of lateral and radial viscosity variations, the spatial distribution of density buoyancies, and the resolution of the convection model. GPE differences are influenced by both lithosphere density buoyancies and by radial basal tractions that produce dynamic topography. The global lithospheric stress field can thus be divided into (1) stresses associated with GPE differences (including the contribution from radial basal tractions) and (2) stresses associated with the contribution of horizontal basal tractions. In this paper, we investigate only the contribution of GPE differences, both with and without the inferred contribution of radial basal tractions. We use the Crust 2.0 model to compute GPE values and show that these GPE differences are not sufficient alone to match all the directions and relative magnitudes of principal strain rate axes, as inferred from the comparison of our depth integrated deviatoric stress tensor field with the velocity gradient tensor field within the Earth\u27s plate boundary zones. We argue that GPE differences calibrate the absolute magnitudes of depth integrated deviatoric stresses within the lithosphere; shortcomings of this contribution in matching the stress indicators within the plate boundary zones can be corrected by considering the contribution from horizontal tractions associated with density buoyancy driven mantle convection. Deviatoric stress magnitudes arising from GPE differences are in the range of 1–4 TN m−1, a part of which is contributed by dynamic topography. The EGM96 geoid data set is also used as a rough proxy for GPE values in the lithosphere. However, GPE differences from the geoid fail to yield depth integrated deviatoric stresses that can provide a good match to the deformation indicators. GPE values inferred from the geoid have significant shortcomings when used on a global scale due to the role of dynamically support of topography. Another important factor in estimating the depth integrated deviatoric stresses is the use of the correct level of reference in calculating GPE. We also elucidate the importance of understanding the reference pressure for calculating deviatoric stress and show that overestimates of deviatoric stress may result from either simplified 2-D approximations of the thin sheet equations or the assumption that the mean stress is equal to the vertical stress