Models of plate tectonics with the Lattice Boltzmann Method

Modern geodynamics is based on the study of a large set of models, with the variation of many parameters, whose analysis in the future will require Machine Learning to be analyzed. We introduce here for the first time how a formulation of the Lattice Boltzmann Method capable of modeling plate tectonics, with the introduction of plastic non-linear rheology, is able to reproduce the breaking of the upper boundary layer of the convecting mantle in plates. Numerical simulation of the earth's mantle and lithospheric plates is a challenging task for traditional methods of numerical solution to partial differential equations (PDE's) due to the need to model sharp and large viscosity contrasts, temperature dependent viscosity and highly nonlinear rheologies. Nonlinear rheologies such as plastic or dislocation creep are important in giving mantle convection a past history. We present a thermal Lattice Boltzmann Method (LBM) as an alternative to PDE-based solutions for simulating time-dependent mantle dynamics, and demonstrate that the LBM is capable of modeling an extremely nonlinear plastic rheology. This nonlinear rheology leads to the emergence plate tectonic like behavior and history from a two layer viscosity model. These results demonstrate that the LBM offers a means to study the effect of highly nonlinear rheologies on earth and exoplanet dynamics and evolution.