On modelling the lithosphere in mantle convection with non-linear rheology

Numerical convection experiments were carried out with the aim of simulating the lithosphere as a strong mechanical boundary layer participating in the circulation, and to study its dynamical role and the governing parameters. The rheological model parameters were successively refined, effective viscosity depending on (1) depth, (2) temperature and pressure, and (3) temperature, pressure, and stress. In all cases a high-viscosity plate rested on a low-viscosity asthenosphere; in the two latter cases it could in principle subduct, but did so only if zones of weakness were built into it. It was possible to model active or inactive plates (moving faster or slower than the asthenosphere below). Because of a lack of numerical resolution it was however, not possible to simulate a narrow sinking slab; rather a broad zone of cooled and highly viscous material developed, often limiting the rate of descent and leading to non-steady convection. The circulation, including subduction, was stabilized by introduction of stress-dependence of viscosity (non-linearity), dissipation, and adiabatic heating. The parameter chiefly responsible for deciding the (active or passive) role of the plate is its decoupling from its neighbours, achieved in the models by assuming weakness zones. Another important result seems to be that the assumption of plausible mantle rheologies and heat input leads to equally plausible effective viscosities, plate velocities, and to upper-mantle temperatures which are relatively low by current ideas, but conforming to earlier estimates based on convection theory. Viscosity distribution and flow pattern are also in reasonable agreement with more detailed boundary layer computations. The main obstacles to our modelling are the numerical limitations, forcing upon us such artificialities as two-dimensionality, rectangular model boxes, coarse grids, and generalized weakness zones.