Stress regime analysis for the transition to a stagnant-lid convection regime in the terrestrial mantle

A series of numerical simulations of terrestrial mantle convection with temperature-dependent viscosity in a three-dimensional spherical geometry was performed to investigate the thermal structure of the mantle interior and the mechanical condition of the lithosphere. The common “sluggish-lid” convection regime has the thermal structure of the mantle interior with a slowly mobile lid under a moderately temperature-dependent viscosity of mantle rocks, whereas the “stagnant-lid” convection regime has a convection pattern in which the entire surface is covered by a highly viscous lid due to the strongly temperature-dependent viscosity. This study focused not only on the thermal structure of the mantle but also on the mechanical conditions in the lithosphere on an intermediate, transitional convection regime between these end-member convections both under the standard- and the extended-Boussinesq approximations. In this “quasi-stagnant-lid” convection regime, the entire surface of the planet is covered by a highly viscous stagnant-lid that moves slowly, whereas the mantle interior is dominated by a long-wavelength (i.e., degree-one) thermal structure. The stress regime analyses revealed that the strike-slip regime is highly restricted spatially in the lid. If the constitutive laws allow the formation of faults in the future numerical model, the time-dependent formation of weak faults that can initiate plate tectonics may differ among the three convection regimes (i.e., degree-one, quasi-stagnant-lid, and stagnant-lid convection regimes). The range of viscosity contrast of the lid required to realize the “quasi-stagnant-lid” convection regime in the model under the extended-Boussinesq approximation was wider than under the standard Boussinesq approximation, because the adiabatic heating of the mantle increased the mantle temperature with the depth and enhanced the formation of stagnant-lid owing to the strong mechanical decoupling between the cold lid and the underlying hot mantle.