Apparent polar wander paths (APWPs) synthesized from paleomagnetic poles provide the most direct data for reconstructing past paleogeography and plate motions for times earlier than ca. 200 Ma. In this contribution, we describe a new method for APWP synthesis that extends the paleomagnetic Euler pole analysis of Gordon et al. (1984, https://doi.org/10.1029/TC003i005p00499) by placing it within the framework of a Bayesian inverse problem. This approach incorporates uncertainties in pole positions and age that are often ignored in standard treatments. The paleomagnetic Euler poles resulting from the inversions provide estimates for full-vector plate motion (both latitude and longitude) and associated uncertainty. The method allows for inverting for one or more Euler poles with the timing of changepoints being solved as part of the inversion. In addition, the method allows the incorporation of true polar wander rotations, thus providing an avenue for probabilistic partitioning of plate tectonic motion and true polar wander based on paleomagnetic poles. We show example inversions on synthetic data to demonstrate the method's capabilities. We illustrate application of the method to Cenozoic Australia paleomagnetic poles which can be compared to independent plate reconstructions. A two-Euler pole inversion for the Australian record recovers northward acceleration of Australia in the Eocene with rates that are consistent with plate reconstructions. We also apply the method to constrain rapid rates of motion for cratonic North America associated with the Keweenawan Track of late Mesoproterozoic paleomagnetic poles. The application of Markov chain Monte Carlo methods to estimate paleomagnetic Euler poles can open new directions in quantitative paleogeography.

The late Mesoproterozoic was a time of large-scale tectonic activity both in the interior and on the margins of Laurentia-most notably the development of the Midcontinent Rift and the Grenvillian orogeny. Volcanism within the North American Midcontinent Rift between ca. 1109 and 1083 Ma, as well as other contemporaneous volcanism within Laurentia, has provided an opportunity to develop extensive paleomagnetic data sets spanning this time period. These data result in an apparent polar wander path (APWP) for Laurentia that goes from a high-latitude apex known as the Logan Loop into a swath known as the Keweenawan Track. A longstanding challenge of these data was the appearance of asymmetry between relatively steep reversed polarity directions from older rift rocks and relatively shallow normal polarity directions from younger rift rocks. This asymmetry was used to support an interpretation that there were large non-dipolar components to the geomagnetic field at the time. Recent data sets support the interpretation that this directional change was progressive and therefore a result of very rapid motion of Laurentia from high to low latitudes rather than a stepwise change across non-dipolar reversals. We present high-precision U-Pb dates from Midcontinent Rift volcanics that result in an improved chronostratigraphic framework for rift volcanics and unconformities that improves correlations as well as constraints on rift development. We use these dates in volcanostratigraphic context to temporally constrain a new compilation of Midcontinent Rift paleomagnetic poles. These paleomagnetic poles include new data from the North Shore Volcanic Group, Minnesota, USA and the Osler Volcanic Group, Ontario, Canada. The U-Pb dates constrain the rate of implied plate motion more precisely than has previously been possible. We apply a novel Bayesian approach to assess the rate of implied plate motion through inverting for paleomagnetic Euler poles. If the path is to be explained by a single Euler pole these inversions reveal that motion of the continent exceeded 27 cm/yr. The path is particularly well-explained by a model wherein there is continuous true polar wander in addition to rapid plate motion that changes direction and slows ca. 1096 Ma. Laurentia's movement from high to low latitudes resulted in collisional tectonics on its leading margin which could be associated with such a change in plate motion. We propose that upwelling of the Keweenawan mantle plume was associated with an avalanche of subducted slab material and associated downwelling that drove fast plate motion. This fast plate motion was followed by the Grenvillian orogeny from ca. 1090 to 980 Ma. Prolonged collisional orogenesis could have been sustained due to this strong convective cell that therefore played an integral role in the assembly of the supercontinent Rodinia.