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SUMMARY 3-D SPHERICAL MODELS OF MANTLE CONVECTION WITH FLOATING CONTINENTS One of the major questions within the Earth Sciences is to understand the mechanism behind plate tectonics, which results in the quasi-periodic assembly of the continents into a super continent similar to Pangaea. In addition to understanding the tectonics of the oceanic plates, we are attempting to carry out quantitative analysis to describe the forces behind continental plate motion. The first fully selfcontained 3-D spherical numerical model of mantle convection with eight freely floating continents is presented. The mantle is modeled by a spherical liquid layer, which is heated from below. The viscosity of the liquid depends on temperature and pressure. The continents are modeled by thick, rigid, buoyant plates. Mantle flow velocities, temperature and pressure are determined from the space and time coordinates from the well-known equations of thermal convection (equations of mass, heat and momentum transfer). To find the velocities of the continents, we first use Euler's equations of motion for a solid 3-D body. These two systems of equations assume strong coupling by the boundary conditions on the surfaces of the continental plates (due to heat and momentum exchange). We use an original numerical method for solving these equations. The eight modeled continents are similar in shape and size to the real continents (North and South America, Africa, Eurasia, Australia, Antarctica and two large islands: Madagascar and Kalimantan). As an initial state, we assume a motionless mantle with a 3-D temperature distribution T=T(r, 0, (p, t=0), recalculated from seismic tomography data. The initial positions of the continents are similar to their present state. A numerical solution to the coupled models of mantle convection and floating continents results in a distribution over 3-D space and time of temperature, viscosity, and mantle flow velocities, as well as continental movement. The main results of our numerical model are as follows: 1. We obtained a repeatable model for the assembly and dispersion of the continents into a super continent similar to Pangaea. 2. The distribution of the aforementioned parameters describes the evolution of the asthenosphere and lithosphere because, by definition, the asthenosphere and lithosphere are areas of anomalous low and high viscosity. The appearance of deep continental roots was obtained and is of particular interest. 3. The solution shows the evolution and break-up of subducted slabs, and the splitting and pulsation of giant plumes under the Pacific and Africa. Comparisons of calculated continental velocities with observed data (e.g. GPS data) will give new constraints for the interior structure of the Earth and its dynamics.

3-D spherical models of mantle convection with floating continents