A source-sink model of the generation of plate tectonics from non-Newtonian mantle flow

A model of mantle convection which generates plate tectonics requires strain rate- or stress-dependent rheology in order to produce strong platelike flows with weak margins as well as strike-slip deformation and plate spin (i.e., toroidal motion). Here, we employ a simple model of source-sink driven surface flow to determine the form of such a rheology that is appropriate for Earth's present-day plate motions. In this model, lithospheric motion is treated as shallow layer flow driven by sources and sinks which correspond to spreading centers and subduction zones, respectively. The source-sink field is derived from the horizontal divergence of plate velocities and thus directly prescribes poloidal motion. The toroidal flow field is solved through the non-Newtonian Stokes equation for shallow layer tangential flow on the surface of a sphere. Two plate motion models are used to derive the source-sink field. The first is an idealized “square” plate which is used to explore the basic aspects of the model. The second is an analytically continuous model of Earth's present-day plates (Bercovici and Wessel, 1994). As originally implied in the simpler Cartesian version of this model (Bercovici, 1993), the classical power law rheologies do not generate platelike flows as well as the hypothetical Whitehead-Gans stick-slip rheology (which incorporates a simple self-lubrication mechanism). For the idealized plate geometry, the power law rheologies yield much more diffuse strike-slip shear (i.e., radial vorticity) than the stick-slip rheology. For the present-day plate geometry, the power law rheologies fail to reproduce the original proportion of left- and right-lateral strike-slip shear, whereas the stick-slip rheology gives almost exactly the right proportion. None of the fluid rheologies examined, however, produce more than approximately 60% of the original maximum shear. For either plate model, the viscosity fields produced by the power law rheologies are diffuse, and the viscosity lows over strike-slip shear zones or pseudo-margins are not as small as over the prescribed convergent-divergent margins. In contrast, the stick-slip rheology generates very platelike viscosity fields, with sharp gradients at the plate boundaries, and margins with almost uniformly low viscosity. Quantitative comparisons with the toroidal-poloidal kinetic energy partitioning and vorticity fields of the original plate model are also examined, and the stick-slip rheology is generally found to yield the most favorable comparisons. Power law rheologies with high viscosity contrasts, however, lead to almost equally favorable comparisons, though these also yield the least platelike viscosity fields. This implies that the magnitude of toroidal flow and platelike strength distributions are not necessarily related arid thus may present independent constraints on the determination of a self-consistent plate-mantle rheology. The results of this study, however, predict that if such a rheology can indeed be uniquely determined, it is likely to be in the class of stick-slip, self-lubricating rheologies.