Self-Consistent Generation of Tectonic Plates in Three-Dimensional Mantle Convection

Paul J. Tackley

Department of Earth and Space Sciences

University of California, Los Angeles

Abstract

Despite the fundamental importance of plates in 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. In 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 upwellings and downwellings 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 an promising avenue for future research.

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Figure 1. Relationship between stress and weak zone width W for one-dimensional shear with various values of imposed velocity V (marked on curves). (d) as (b) for visco-plastic rheology, maximum velocity is 550. (e) As (c) for visco-plastic rheology.

Figure 2. Two-dimensional model of lithospheric and asthenospheric shear, with Newtonian rheology (left) and SRW rheology (right). Velocity (top), viscosity (2nd row), strain rate (3rd row) and stress (bottom). A standard blue-green-red colorbar is used, scaled to minimum and maximum values respectively.

Figure 3. Three-dimensional Case 1. (a) Temperature isocontours 0.3 (blue) and 0.7 (red). (b) Lithospheric viscosity and velocity vectors for SRW rheology. Viscosity ranges from 0.1 (violet) to 104 (orange), and the maximum velocity value is 670. (c) Isocontours of horizontal divergence/convergence (±50, light & dark purple) and vertical vorticity (±50, green and blue) for SRW rheology.

Figure 4. Three-dimensional Case 2. (a) Residual temperature isocontours 0.15 (red) and -0.15 (blue). (b) Lithospheric viscosity and velocity vectors for SRW rheology. Maximum velocity in the domain is 780. (c) Isocontours of horizontal divergence (±50, green and blue) and vertical vorticity (±25, yellow and mauve) and for SRW rheology. (d) as (b) for visco-plastic rheology. (e) As (c) for visco-plastic rheology. Horizontal divergence (±40, green and blue) and vertical vorticity (±10, yellow and mauve).

Figure 5. Three-dimensional Case 3. (a) Residual temperature isocontour -0.15. (b) Lithospheric viscosity and velocity vectors (domain maximum velocity is 302). (c) Horizontal divergence (±35, green and blue) and vertical vorticity (±20, yellow and mauve).

Figure 6. Three-dimensional Case 4. As Figure 5 except (a) Residual temperature isocontours 0.15 (red) and -0.15 (green), domain maximum velocity is 2030. (c) Horizontal divergence (±200) and vertical vorticity (±150).