Mantle dynamics with induced plate tectonics

Abstract

Mantle circulation and plate tectonics can be described by means of two scalar fields. The poloidal field is related to horizontal divergence, i.e., to the vertical mass flux. The toroidal field expresses the shear deformation or the rotations within spherical shells. For the Earth, the surface kinetic energy is known to be equally distributed between the two fields. In recent years the lateral mantle density variations revealed by seismic tomography have been introduced in dynamic mantle models which have predicted the major features of both the geoid and the surface divergence. These models assumed a spherical symmetry of the rheological properties of the Earth. However, with this assumption, the Navier‐Stokes equation implies that mass heterogeneities cannot drive any toroidal motion. This prompted us to develop a new model which takes into account the existence of rigid and independent plates. These plates break the spherical symmetry assumed in all earlier models. They modify the mantle circulation and hence the predicted surface observables such as displacement and gravity. In this paper, we first explain by means of a very simple twoplate model, how the poloidal flow caused by mantle heterogeneities can be converted to surface toroidal motion. We then apply the model to the real Earth with its major plates and compare our predictions to those deduced from a more classical Earth model having a uniform free slip condition at the surface. Taking the seismic tomography pattern as a picture of the mantle mass heterogeneities, we achieve a highly satisfactory fit to the observed plate velocities. This new theoretical framework also improves the geoid prediction.