Self-consistent generation of tectonic plates in three-dimensional mantle convection

Despite the fundamental importance of plates in the Earth's mantle convection, plates have not generally been included in numerical convection models or analog laboratory experiments, mainly because the physical properties which lead to plate tectonic behavior are not well understood. Strongly temperature-dependent viscosity results in an immobile rigid lid, so that plates, where included at all in 3-D models, have always been imposed by hand. An important challenge is thus to develop a physically reasonable material description which allows plates to develop self-consistently; this paper focuses on the role of ductile shear localization. Tn two-dimensional geometry, it is well-established that strain-rate softening, non-Newtonian rheologies (e.g. power-law, visco-plastic) cause weak zones and strain-rate localization above up- and down-wellings, resulting in a rudimentary approximation of plates. Three-dimensional geometry, however, is fundamentally different due to the presence of transform plate boundaries with associated toroidal motion. Since power-law and visco-plastic rheologies do not have the property of producing shear localization, it is not surprising that they do not produce good plate-like behavior in three-dimensional calculations. Here, it is argued that a strain-rate-weakening rheology, previously shown to produce plate-like behavior in a two-dimensional sheet representing the lithosphere, is a reasonable generic description of various weakening processes observed in nature. One-and two-dimensional models are used to show how this leads to shear localization and the formation of 'faults'. This rheology is then applied to the high-viscosity lithosphere of 3-D mantle convection calculations, and the velocity-pressure/viscosity solution for the entire 3-D domain (lid and underlying mantle) is solved self-consistently, It is found that the lithosphere divides into a number of very high-viscosity plates, separated by narrow, sharply defined weak zones with a viscosity many orders of magnitude less than the plate interiors. Broad weak zones with dominant convergent/divergent motion above up- and down-wellings are interconnected by a network of narrow weak zones with dominant strike-slip motion. Passive spreading centers are formed in internally heated cases. While the resulting plates are not fully realistic, these results show that self-consistent plate generation is a realizable goal in three-dimensional mantle convection, and provide a promising avenue for future research. (C) 1998 Elsevier Science B.V. All rights reserved.