Reconstructing global continental motions through time using data assimilation: a proof of concept.

Kinematic plate tectonic reconstructions are central to our understanding of the dynamics of the solid Earth over hundreds of millions of years. These reconstructions are typically based on a combination of qualitative geological and paleontological observations supplemented with quantitative geophysical data, such as paleomagnetism. As a result, reconstructing plate and continental motion generally involves largely manual processes to integrate regional tectonic histories into a geometrically self-consistent global model. Further, with this methodology it is very difficult to quantify the uncertainties of the resulting time-dependent plate configurations and motions. To overcome these difficulties, ensemble-based data assimilation methods present a promising approach to paleogeographic reconstruction as they provide a formal statistical framework to assimilate time-dependent geoscientific data of variable nature and source within a dynamical model whilst providing quantitative estimates of uncertainties on the proposed trajectory.

To develop this concept, we apply a particle filter to reconstruct the time-dependent motion of continents on Earth. We start with a kinematic-stochastic model of continental drift: the motion of continents is governed by random rigid rotations, where velocity, rate of rotation (around polygon centroid) and rate of motion change are drawn randomly. Each of the probability density functions is chosen using geometrical and geodynamical arguments. This stochastic-kinematic model is then used to compute possible continent motion trajectories. We integrate this forward model into a data assimilation framework to incorporate paleomagnetic data, starting from present day and moving backward through time. From observing system simulation experiments using this technique, results suggest the number of ensemble members needed is of the order of several thousands to obtain accurate reconstructions of continent motions. Leveraging these experiments, we present the results of applying this method to a global paleomagnetic dataset spanning the last 100 Ma.