Hematite-bearing sedimentary rocks at Earth's surface are widespread and serve as an important paleomagnetic recorder. The geocentric axial dipole hypothesis posits that the long-term average of Earth's magnetic field is dipolar and that the time-averaged geomagnetic pole overlaps with the geographic pole. Using this hypothesis, the inclination (I) of a rock's magnetization can be translated into an interpreted paleolatitude (ϕ) of the location where the rock formed using the dipole formula:Unfortunately, the accuracy of paleomagnetic directions recorded by the detrital remanent magnetization (DRM) of sedimentary rocks has long been recognized as problematic due to the issue of inclination shallowing

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 North American Midcontinent Rift (MCR) is a ca. 1.1 Ga large igneous province for which there is excellent exposure of both the intrusive and extrusive components in the Lake Superior region (Figure 1). An exceptional feature within the MCR is the occurrence of large anorthosite xenoliths within a diabase sill and dike network known as the Beaver River diabase that outcrops in northeastern Minnesota, USA, as part of the Beaver Bay Complex (Figure 1). The anorthosite xenoliths range in size from centimeter-scale megacrysts to meter-scale, decimeter-scale and even  E 150-m-scale blocks (Figure 2; Grout & Schwartz, 1939;Morrison et al., 1983). A particularly large anorthosite xenolith is exposed at Carlton Peak in the eastern Beaver Bay Complex with minimum dimensions of 180  E 240 m (Figures 1 and 2; Boerboom et al., 2006). In the southern Beaver Bay Complex, a large anorthosite xenolith near Corundum Point has dimensions of 180  E 230 m while one exposed at Split Rock Point has dimensions of 180  E 260 m (Boerboom , 2004). To be able to accommodate such large xenoliths during magma ascent, the Beaver River diabase conduits must have been of at least the width of the anorthosite short-axis diameters. Such wide conduits in these near-surface intrusions suggest high magma flux rates and make it likely that the magma extruded to the surface-feeding voluminous lava flows. Miller and Chandler (1997) emphasized the composite nature of the Beaver River diabase network and Silver Bay intrusions (Figure 1), which are locally marked by abrupt transitions to progressively more evolved lithologies. Furthermore, Miller and Chandler (1997) documented geochronologic, geochemical, and structural evidence to support the notion that the diabase network may have served as principal feeder conduits to lava flows including parts of the Portage Lake Volcanics (PLV) on the Keweenaw Peninsula and Isle Royale of Michigan (Figure 1). To more directly test this inferred intrusive-extrusive correlation, Doyle (2016) compared the mineralogical, textural, and geochemical attributes and the composite lithologic nature of the Beaver River diabase against those of the Greenstone Flow, the largest lava flow within the MCR and one of the largest lava flows on Earth (Figure 3). Doyle (2016) documented remarkable similarities in petrography, mineral chemistry, whole rock geochemistry, and interpreted lithologic zonation between the Beaver River

Obtaining estimates of Earth’s magnetic field strength in deep time is complicated by nonideal rock magnetic behavior in many igneous rocks. In this study, we target anorthosite xenoliths that cooled and acquired their magnetization within ca. 1,092 Ma shallowly emplaced diabase intrusions of the North American Midcontinent Rift. In contrast to the diabase which fails to provide reliable paleointensity estimates, the anorthosite xenoliths are unusually high-fidelity recorders yielding high-quality, single-slope paleointensity results that are consistent at specimen and site levels. An average value of ∼83 ZAm 2 for the virtual dipole moment from the anorthosite xenoliths, with the highest site-level values up to ∼129 ZAm 2 , is higher than that of the dipole component of Earth’s magnetic field today and rivals the highest values in the paleointensity database. Such high intensities recorded by the anorthosite xenoliths require the existence of a strongly powered geodynamo at the time. Together with previous paleointensity data from other Midcontinent Rift rocks, these results indicate that a dynamo with strong power sources persisted for more than 14 My ca. 1.1 Ga. These data are inconsistent with there being a progressive monotonic decay of Earth’s dynamo strength through the Proterozoic Eon and could challenge the hypothesis of a young inner core. The multiple observed paleointensity transitions from weak to strong in the Paleozoic and the Proterozoic present challenges in identifying the onset of inner core nucleation based on paleointensity records alone.

Hematite-bearing sedimentary rocks at Earth's surface are widespread and serve as an important paleomagnetic recorder. The geocentric axial dipole hypothesis posits that the long-term average of Earth's magnetic field is dipolar and that the time-averaged geomagnetic pole overlaps with the geographic pole. Using this hypothesis, the inclination (I) of a rock's magnetization can be translated into an interpreted paleolatitude (ϕ) of the location where the rock formed using the dipole formula:Unfortunately, the accuracy of paleomagnetic directions recorded by the detrital remanent magnetization (DRM) of sedimentary rocks has long been recognized as problematic due to the issue of inclination shallowing

Tectonic plate motions are integral in shaping many aspects of Earth, including its thermal, geochemical, tectonic, biologic, climatic, and magnetic evolution. Understanding the history of plate motions is therefore directly relevant to a wide variety of research areas. Robust global plate reconstructions have been constructed back to the Jurassic on the basis of marine magnetic anomalies and hotspot tracks (e.g., Seton et al., 2012), but plate model development for earlier times is challenging due to the lack of preserved oceanic lithosphere. Paleomagnetic data offer a key constraint for plate motions, providing the only quantitative tool for plate modeling in pre-Jurassic times.Earth's magnetic field is dominated by a time-averaged dipole aligned with the planetary spin-axis (e.g., Creer et al., 1954), and when a tectonic plate moves with respect to that axis, the directions of the Earth's magnetic field observed locally on that plate change through time. When recorded in rocks, these temporal changes in magnetic direction provide a quantitative archive of a plate's kinematic history. For convenience, a plate can be treated as fixed, and the changing magnetic directions used to determine the apparent motion of the magnetic pole with respect to the plate can be expressed as an apparent polar wander path (APWP, Creer et al., 1954). Construction of an APWP requires a record of paleomagnetic data of various ages from the same rigid plate, which together can

Our understanding of Earth’s paleogeography relies heavily on paleomagnetic apparent polar wander paths (APWPs), which represent the time-dependent position of Earth’s spin axis relative to a given block of lithosphere. However, conventional approaches to APWP construction have significant limitations. First, the paleomagnetic record contains substantial noise that is not integrated into APWPs. Second, parametric assumptions are adopted to represent spatial and temporal uncertainties even where the underlying data do not conform to the assumed distributions. The consequences of these limitations remain largely unknown. Here, we overcome these challenges with a bottom-up Monte Carlo uncertainty propagation scheme that operates on site-level paleomagnetic data. To demonstrate our methodology, we present an extensive compilation of site-level Cenozoic paleomagnetic data from North America, which we use to generate a high-resolution APWP. Our results demonstrate that even in the presence of substantial noise, polar wandering can be assessed with unprecedented temporal and spatial resolution.

Sampling strategies used in paleomagnetic studies play a crucial role in dictating the accuracy of our estimates of properties of the ancient geomagnetic field. However, there has been little quantitative analysis of optimal paleomagnetic sampling strategies and the community has instead defaulted to traditional practices that vary between laboratories. In this paper, we quantitatively evaluate the accuracy of alternative paleomagnetic sampling strategies through numerical experiment and an associated analytical framework. Our findings demonstrate a strong correspondence between the accuracy of an estimated paleopole position and the number of sites or independent readings of the time-varying paleomagnetic field, whereas larger numbers of in-site samples have a dwindling effect. This remains true even when a large proportion of the sample directions are spurious. This approach can be readily achieved in sedimentary sequences by distributing samples stratigraphically, considering each sample as an individual reading. However, where the number of potential independent sites is inherently limited the collection of additional in-site samples can improve the accuracy of the paleopole estimate (although with diminishing returns with increasing samples per site). Where an estimate of the magnitude of paleosecular variation is sought, multiple in-site samples should be taken, but the optimal number is dependent on the expected fraction of outliers. We provide both analytical formulas and a series of interactive Jupyter notebooks allowing optimal sampling strategies to be derived from user-informed expectations.