Abstract
Understanding why Earth's lithosphere is divided into several plates while other terrestrial bodies have unbroken lids is a long-standing challenge, often addressed with the help of numerical modelling. A key mechanism defining the transition between these two convective regimes is the formation of shear zones that cut through the entire lithosphere in regions with high stresses.
Here we present a modelling study in which lithospheric stresses resulting from small-scale convection in the upper mantle are analysed. We perform model simulations that include elasticity and a free surface and evaluate how these physical complexities affect stress distribution inside the lithosphere, which in turn controls the depths of yielding and the possible initiation of subduction.
We show that the spatial distribution of stress is significantly altered by the presence of elastic deformation only when the model lithosphere acts as a thick plate capable of bending. Whether or not this is the case depends on the viscosity model.
For an Arrhenius viscosity limited by a cut-off value that produces an essentially rigid lid, flexure dominates the observed lithospheric stress pattern in simulations with a free surface. The amplitudes of the stress are, when a free surface is assumed but elasticity is neglected, largely overestimated.
Including both a free surface and elasticity results in stresses with maximum amplitudes close to those observed in the traditional models with a viscous rheology and a free-slip upper boundary, suggesting that having no additional complexity is, in a way, better than employing just a free surface. We also demonstrate how the use of impermeable free-slip side boundaries can result in the formation of unnatural, laterally locked convection cells, and bias the results of a parametric study.
For each point in the parameter space, we perform several simulations with slightly different initial temperature fields in order to statistically eliminate the occurrence of locked states.