Mantle Convection with a Brittle Lithosphere: Thoughts on the Global Tectonic Styles of the Earth and Venus

Plates are an integral part of the convection system in the fluid mantle, but plate boundaries are the product of brittle faulting and plate motions are strongly influenced by the existence of such faults. The conditions for plate tectonics are studied by considering brittle behaviour, using Byerlee’s law to limit the maximum stress in the lithosphere, in a mantle convection model with temperature dependent viscosity. When the yield stress is high, convection is confined below a thick, stagnant lithosphere. At low yield stress, brittle deformation mobilizes the lithosphere which becomes a part of the overall circulation; surface deformation occurs in localized regions close to upwelling and downwellings in the system. At intermediate levels of the yield stress, there is a cycling between these two states: thick lithosphere episodically mobilizes and collapses into the interior before reforming. The mobile-lid regime resembles convection of a fluid with temperature dependent viscosity and the boundary layer scalings are found to be analogous. This regime has a well defined Nusselt number Rayleigh number relationship which is in good agreement with scaling theory. The surface velocity is nearly independent of the yield stress, indicating that the ‘plate’ motion is resisted by viscous stresses in the mantle. Analysis suggests that mobilization of the Earth’s lithosphere can occur if the friction coefficient in the lithosphere is less than 0.03-0.13 — lower than laboratory values but consistent with seismic field studies. On Venus, the friction coefficient may be high as a result of the dry conditions and brittle mobilization of the lithosphere would then be episodic and catastrophic.