Multi Phase Flows and Computational Aspects of Plate Tectonics

A Lagrangian Particle Finite Element scheme is presented which is suited to problems in which material composition and history must be tracked through very large deformations associated with creeping fluid flow. The method is applied to large-scale geodynamic modeling in which some parts of the system are actively convecting which others remain nearly stagnant. Introduction Geology records the slow movements of the continents with respect to one another; the theory of plate tectonics describes the manner in which this happens. Plate tectonics is regarded as the surface manifestation of solid-state convection in underlying rocky mantle which is responsible for releasing the EarthÕs inner heat. In the past it has proved to be very difficult to reproduce plate-like behaviour selfconsistently at the surface of a convection experiment. The intimate connection between plate boundaries and earthquakes suggests that this is because such experiments lack a description of the brittle nature of the cool lithosphere. History-dependent, visco-elastic-plastic rheologies have been used in modelling crustal deformation for some time, and there has been considerable work recently to incorporate some of these ideas into mantle convection / plate tectonics models. Two serious difficulties arise, one is that it is necessary to track history parameters despite the existence of enormous strains within the convecting fluid. The second is the difference in scale between the brittle plate boundary zones (km's) and the plates themselves and their associated convection cells (thousands of km's). Recent modeling has mainly ignored the first of these difficulties, concentrating on the influence of highly non-linear rheological laws on the surface motions of convecting systems [e.g. References 1,2,3] Figure 1 is a numerical simulation which illustrates the components of the system which must be modeled accurately if the surface motions and stresses are to be predicted accurately. Temperature dependent viscosity results in a very low strain rate within the cold boundary layer (lithosphere) relative to the strain rate in the convecting interior. Chemically buoyant continental crust stabilizes some parts of the cold Stiff Lithosphere Buoyant Crust