Planetary Scale Boundary Element and Lithospheric Scale Finite Elements Simulations of Geodynamics

Geodynamics at the planetary scale is inherently a multiscale problem exhibiting very large variations in viscosity and spatial scales. In a nearly isoviscous system, convection occurs through finger-like, cylindrically symmetric Rayleigh-Taylor instabilities. In contrast, highly viscous plates do not sink, but drift laterally and sink asymmetrically at zones known as subduction zones. This subduction process is the driving mechanism of plate tectonics. A self-consistent model of plate tectonics involves flows at planetary scales (the Pacific plate is over 10000km wide) coupled to lithospheric scale dynamics, such as trench fault lubrication (intraplate shear-zones are thought to be 100m to 1km thick). Lithosphere dynamics is characterized by a complex elasto-visco-plastic rheology, where at least three mechanisms of creep are in competition (diffusion creep, dislocation climb and dislocation glide). Numerical simulations of the thermal-mechanical system has shown a very broad spectrum of behaviors. Recent works on lithosphere dynamics, based on a Lagrangian Mechanical Finite Element approach, have shown that localization appears at many scales, due to several feed-back mechanisms acting at different scales and P-T conditions. As a consequence the lithosphere strength is mostly controlled by its strong "core", a zone 10 to 30 km thick in its interior. Three independent arguments support the strong core hypothesis: the nature of the bending of the lithosphere (its flexural rigidity), the power law statistics of plate tectonic boundaries and deep earthquakes distributions. A novel computational approach has been recently developed using a fast multipole acceleration of the boundary elements method for modeling global scale dynamics. It is shown that the code scales linearly with the size of the mesh for large problems and that it scales on a Beowulf cluster with up to 64 processors with an efficiency of 90%. In order to model plate tectonics, an innovative setup for the implementation of plate subduction has been put forward and tested against laboratory experiments. So far the code, called bemEarth, has been applied for testing subduction of large plates, interaction between large and small plates and continents in a spherical setting. Further developments will involve the implementation intra-plate shear zones.