Understanding lithospheric stresses: systematic analysis of controlling mechanisms with applications to the African Plate

Many mechanisms control the state of stress within Earth plates. First-order well-known mechanisms include stresses induced by lateral variations of lithospheric density structure, sublithospheric tractions, ridge push and subduction pull. In this study, we attempt to quantify the influence of these mechanisms to understand the origin of stresses in the lithosphere, choosing the African plate (TAP) as an example. A finite-element based suite, Proshell, was developed to combine several data sets, to estimate the gravitational potential energy (GPE) of the lithosphere and to calculate stresses acting on the real (non-planar) geometry of TAP. We introduce several quantitative parameters to measure the degree of fit between the model and observations. Our modelling strategy involves nine series of numerical experiments. We start with the simplest possible model and then, step by step, build it up to be a more physically realistic model, all the while discussing the influence of each additional component. The starting (oversimplified) model series (1) is based on the CRUST2 data set for the crust and a half-space-cooling approximation of the lithospheric mantle. We then describe models (series 2-5) that account for lithospheric mantle density heterogeneities to build a more reliable GPE model. The consecutive series involve basal traction from the convective mantle (series A, C) and the rheological heterogeneity of the TAP via variations in its effective elastic thickness (series B, C). The model quality reflects the increase in complexity between series with an improving match to observed stress regimes and directions. The most complex model (series D) also accounts for the bending stresses in the elastic lithosphere and achieves a remarkably good fit to observations. All of our experiments were based on the iteration of controlling parameters in order to achieve the best fit between modelled and observed stresses, always considering physically feasible values. This gives us confidence that our methodology appropriately models the stress pattern of Africa, and that it may be further applied to other plates on Earth. Our modelling approach allows us to quantify several important features controlling the lithospheric stress pattern. Even though the initial oversimplified model does not fit the observations satisfactorily, it shows how ridge push may create significant compressive stresses in the lithosphere. More complex models show the importance of the density structure of the lithosphere, specifically in the subcrustal lithosphere. The stress regime within the TAP mainly results from a global balance of masses and mass moments between continental and oceanic parts of the plate. The orientation of stresses, in turn, is influenced more by local features expressed by topographic and crustal density variations, whereas existent subcrustal density variations appear to be smoothed by the crust above. The models show that accounting separately for either basal tractions or rheological heterogeneities brings moderate improvement, but the combination of these two mechanisms results in a substantially better match between model and observations. The bending stresses caused by isostatical readjustment improve the model match, but they have to be analysed with caution because of their depth-dependent nature.