There has been an increased effort to study non-Newtonian, or power-law, rheologies in thermal convection calculations. Weinstein and Olson [1992] demonstrate that a thin layer with a power-law rheology on top of a uniform viscosity fluid can produce reasonably plate-like surface velocities. Their model consists of a thin, non-Newtonian layer with constant thickness situated atop a thick Newtonian viscous layer. Convection in the Newtonian layer causes deformation in the non-Newtonian layer by generating shear stresses on the base of the non-Newtonian layer. For a large enough power-law exponent, the deformation in the non-Newtonian layer is concentrated in narrow regions. This method is compared with several Newtonian methods where plates are generated by geometrical constraints; one using prescribed strong and weak regions and one using a balance of tractions on a predefined plate geometry. On a simple test problem, these three methods produce very similar results [ King et al. , 1992].
Bercovici [1993] shows that a stick-slip rheology produces more uniform, plate-like surface velocities than a power-law rheology. Unlike the power-law rheologies described previously, a stick-slip rheology can model the rapid build-up in stress with little change in deformation rate, followed by the release of stress once a cut-off deformation-rate is reached. As the power-law exponent (n in Equation (1)) increases, the power-law rheology appears to reach an asymptotic limit in its ability to generate plate-like behavior. The stick-slip rheology produces sharper changes in plate velocity.
Following the prediction of Karato and Li [1992], van den Berg et al. [1991] consider a model with a non-Newtonian upper mantle and a Newtonian lower mantle. They find that this composite rheology can produce plate-like surface velocities. They also find that a low-viscosity upper mantle improves the plate-like distribution of the surface velocities. It is interesting to note that independent of the calculations of mantle rheology from geoid and plate velocities, thermal convection calculations suggest a preference for a low viscosity region in the upper mantle.
Power-law rheologies are also being explored in postglacial rebound [ Gasperini et al. , 1992; Wu, 1993] and global geoid and plate velocity models [ Cadek et al. , 1993].