Bayesian Paleomagnetic Euler Pole Inversion for Paleogeographic Reconstruction and Analysis

Abstract

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.

Quantifying Inclination Shallowing and Representing Flattening Uncertainty in Sedimentary Paleomagnetic Poles

“…Additionally, the Kent distribution can be incorporated into frameworks such that probabilistic inversion (e.g. Rose et al., 2022) or parametric Monte Carlo resampling can enable development of future apparent polar wander paths that incorporate uncertainty.…”

“…Additionally, the Kent distribution can be incorporated into frameworks such that probabilistic inversion (e.g. Rose et al, 2022)…”

A global apparent polar wander path for the last 320 Ma calculated from site-level paleomagnetic data

“…It is important to note that there have been many previous efforts to propagate or weight uncertainties in the computation of apparent polar wander, for instance using a weighted running mean or spherical spline (e.g., Thompson and Clark, 1981;Harrison and Lindh, 1982;Torsvik et al, 1996;Schettino and Scotese, 2005;Swanson-Hysell et al, 2019;Wu et al, 2021;Gallo et al, 2021;Rose et al, 2022). However, the majority of the APWPs computed in these studies were still derived from paleopole-level data, and these weighting methods did not account for the subjectivity in the choice of the number of data underpinning each paleopole.…”

“…Quantifying the age uncertainty by a uniform distribution is intuitive for sediment-derived datasets, whose age uncertainty range is often determined by bio-and/or magnetostratigraphy, and a uniform distribution may straightforwardly be defined by the upper and lower age limit of the geological time period or interpreted magnetozones. The age of igneous rocks, on the other hand, is often based on radiometric dating, for which the uncertainty on individual age determinations is often reported as one or two standard deviation(s), and a Gaussian distribution could thus be used to quantify the uncertainty in age (see e.g., Swanson-Hysell et al, 2019;Wu et al, 2021, Gallo et al, 2021Rose et al, 2022). However, because the age of sampled igneous rocks is typically determined by multiple radiometric ages, either from multiple dated samples or determined for the regional magmatic activity (e.g., for a large igneous province (LIP)), it is difficult to use a Gaussian distribution for the age uncertainty for all igneous datasets.…”

Embracing Uncertainty to Resolve Polar Wander: A Case Study of Cenozoic North America

“…Our workflow has only mild assumptions: directional errors are assumed to be Fisher‐distributed around the site‐mean directions (e.g., Lanos et al., 2005) prior to their transformation into VGPs. Additionally, site‐level ages are considered to have normally or uniformly distributed uncertainties, depending on whether they are directly radiometrically dated or stratigraphically constrained, respectively (e.g., Rose et al., 2022; Thébault & Gallet, 2010).…”