Mechanism for generating stagnant slabs in 3-D spherical mantle convection models at Earth-like conditions

Seismic tomography reveals the natural mode of convection in the Earth is whole mantle with subducted slabs clearly seen as continuous features into the lower mantle. However, simultaneously existing alongside these deep slabs are stagnant slabs which are, if only temporarily, trapped in the upper mantle. Previous numerical models of mantle convection have observed a range of behavior for slabs in the transition zone depending on viscosity stratification and mineral phase transitions, but typically only exhibit flat-lying slabs when mantle convection is layered or trench migration is imposed. We use 3-D spherical models of mantle convection which range up to Earth-like conditions in Rayleigh number to systematically investigate three effects on mantle dynamics: (1) the mineral phase transitions, (2) a strongly temperature-dependent viscosity with plastic yielding at shallow depth, and (3) a viscosity increase in the lower mantle. First a regime diagram is constructed for isoviscous models over a wide range of Rayleigh number and Clapeyron slope for which the convective mode is determined. It agrees very well with previous results from 2-D simulations by Christensen and Yuen (1985), suggesting present-day Earth is in the intermittent convection mode rather than layered or strictly whole mantle. Two calculations at Earth-like conditions (Ra and RaH = 2 × 107 and 5 × 108, respectively) which include effects (2) and (3) are produced with and without the effect of the mineral phase transitions. The first calculation (without the phase transition) successfully produces plate-like behavior with a long wavelength structure and surface heat flow similar to Earthʹs value. While the observed convective flow pattern in the lower mantle is broader compared to isoviscous models, it basically shows the behavior of whole mantle convection, and does not exhibit any slab flattening at the viscosity increase at 660 km depth. The second calculation which includes the phase transitions successfully exhibits the coexisting state of stagnant and penetrating slabs within the transition zone. These results indicate the importance of both a viscosity increase and mineral phase transitions for generating the structure of stagnant slabs observed by seismic tomography.