Plate tectonics initiation as a random outcome of time-dependent convection

Abstract:

Plate tectonics initiation has been simulated by convection with yield stress, which is a simplification that can be linked to brittle failure or mechanisms that reduce the strength of the lithosphere. Convection with yield stress is usually occurs in one of the three regimes: mobile lid regime, transitional regime with some episodic failure, and stagnant lid regime. These convective regimes can be recognized as the stable and unstable states of convection behavior. Steady-state stagnant lid convection is a stable state, and the yield stress can be considered as a control parameter that alters the stability. Below a critical value, instability will emerge as the lithosphere is sufficiently weakened. This critical value, which is termed the critical yield stress, can be understood as the bifurcation point where the dynamics of convection changes such that it deviates from the stable stagnant lid regime to a new state. For the lithosphere to become unstable, convective stresses will have to overcome the yield stress. Therefore in estimating the critical yield stress, we have to assess the magnitude of convective stresses. The width of convecting cells is a major factor in determining lithospheric stresses. At high Rayleigh numbers, convection is chaotic and the width of the individual subcell fluctuates with time. We observe that for a given set of parameters with the same yield stress but different initial states, the time of failure is different. We inspect these fluctuations and their effects on convective stresses. We find that even if the convective stresses in the lid is not high enough to cause subduction right away, the convective cells may evolve to a configuration in which the lid stresses are sufficiently large to overcome the yield stress. Our results show that it is important to address not only the question of whether plate tectonics can occur on a planet but also the probability that it will occur within a certain time after planetary formation.