The automatic detection of tectonic plates in 3D mantle convection models and plate motion changes

The rigid surface of the Earth is divided into a jigsaw puzzle of about 50 tectonic plates separated by boundaries. Nowadays, three-dimensional spherical mantle modelling manages to produce self-consistently a stiff surface fragmented into several rigid caps that exhibit a plate-like behaviour. It thus becomes possible to analyse the dynamics of these models through the prism of plate tectonics theory and compare it to plate reconstruction models for the Earth. Such an analysis requires a robust method to automatically detect plates and their boundaries from continuous geophysical fields. The method should further recognize diffuse plate boundaries, as observed on Earth and reproduced in mantle convection models. We propose here a method to automatically detect and track plates through time, based on a trans-disciplinary approach combining a geodynamical and kinematic analysis with applied mathematics and computer sciences. This analysis is performed using the free and open-source software Paraview and the open-source software platform TTK (Topology ToolKit) designed for an efficient topological analysis of scalar fields. We apply our method to a three-dimensional spherical mantle convection model generating Earth-like plate tectonics at its surface. Our results show that, as for the Earth, the motion of modelled plates is stable over million-years-long periods separated by abrupt reorganizations occurring in less than 5 Myrs. The full plate-motion analysis over 262 Myrs in the model allows us to discuss the spatial extent of kinematic changes and shows that a plate reorganization can have regional to global effects on the plate network.