Numerical simulation of the subducting lithosphere: Snapshot and time-dependent models

To simulate the convection in the Earth mantle, two complementary approaches are possible. On the one hand one can solve self consistently the full set of equations of thermal convection employing parameters and relationships derived from mineral physics.
Although such models are presently still unable to predict the actual convection pattern in the Earth, they are extremely useful tools to investigate general characteristics of given physical systems. On the other hand, to permit comparison with specific geophysical observables associated with flow, one can consider a more restricted problem. Instead of focusing on the time evolution of mantle flow, assuming to know a priori the temperature anomalies that drive the convection, we can build a snapshot of the present-day flow pattern that successfully predicts the observables and that, in turn, puts important constraints on unknown parameters.
Examples from both such approaches will be presented. In particular, we will focus on numerical models of the evolution of a subducting lithosphere with complex non-linear rheology and on the prediction of the non-hydrostatic geoid associated with the instantaneous flow due to a subducted slab.