On pole position: new approaches to quantifying polar wander and relative paleomagnetic displacements

Paleomagnetism provides the only quantitative tool to reconstruct the position and motion of tectonic plates and continents in deep geological time. These reconstructions often rely on apparent polar wander paths (APWPs), which describe the past position and motion of plates relative to the Earth’s spin axis. In addition to providing a paleomagnetic reference frame for paleogeography, these paths serve to quantify relative tectonic displacements with other lithospheric blocks. A long-discussed problem is that conventional approaches to computing polar wander do not propagate key sources of uncertainty in the underlying data, such as data scatter or age uncertainty, but proposed solutions remained mostly qualitative. Recently, this problem became more urgent: Rowley (2019, Tectonics) showed that as much as 50% of the data that underlie the currently most widely used global APWP are statistically significantly displaced relative to that APWP. This implies that the resolution at which a geologically meaningful statistical difference between a paleomagnetic dataset and an APWP may be determined, is strongly limited, which undermines the current tectonic and paleogeographic applications of paleomagnetism. This thesis aims to examine the causes of dispersion of paleomagnetic data behind APWPs and to build a global APWP in which key data uncertainties are propagated, such that it may be used to determine geologically meaningful relative displacements. We show that the uncertainty of APWPs computed from paleomagnetic poles, which is the current standard, is mostly determined by the arbitrary choice of how many datapoints are used per pole. This thesis then develops a novel approach in which apparent polar wander paths are computed from site-level paleomagnetic data instead of paleomagnetic poles. In this approach, larger weight is assigned to larger datasets and temporal and spatial uncertainties in the paleomagnetic data are incorporated. We present a global apparent polar wander path for the last 320 Ma using the new statistical approach proposed in this thesis, as well as using a fully updated paleomagnetic database. We find that the first-order geometry of this path is similar to previous models but with smaller uncertainties. Moreover, we show that correcting for temporal bias in the paleomagnetic data allows improved quantification of polar wander rates, and that previously observed peaks in polar wander likely resulted from such bias. We introduce the open-source web application APWP-online.org that provides user-friendly tools to compute apparent polar wander paths using our new methodology as well as the computation of relative paleomagnetic displacements. The website also hosts a community platform for the continuous improvement of the path in the future through the addition of new high-quality paleomagnetic data. Finally, we provide new quantitative estimates of true polar wander during the last 320 Ma by comparing our new global apparent polar wander path with existing mantle reference frames. The computed true polar wander paths suggest that the true polar wander rotations occurred about two roughly orthogonal axes in the equatorial plane. We discuss the geodynamic implications of these findings and highlight future opportunities for the identification and quantification of true polar wander on geological timescales

Paleomagnetic Rotations in the Northeastern Caribbean Region Reveal Major Intraplate Deformation Since the Eocene

Relative Caribbean-North American plate motion is partitioned over the trench and intra-Caribbean plate faults that bound large scale tectonic blocks. Quantifying the kinematic evolution of this tectonic corridor is challenging because much of the region is submarine. We present an extensive regional paleomagnetic data set (1,330 cores from 136 sampling locations) from Eocene and younger rocks of the northern Lesser Antilles, the Virgin Islands, and Puerto Rico, and use a statistical bootstrapping approach to quantify vertical axis block rotations. Our results show that the Puerto Rico–Virgin Island (PRVI) block and the Northern Lesser Antilles (NoLA) block formed two coherently rotating domains that both underwent at least 45° counterclockwise rotation since the Eocene. The first ∼20° occurred in tandem in late Eocene and Oligocene time, after which the blocks were separated in the Miocene by the opening of the Anegada Passage. The last 25° of rotation of the PRVI block ended in the middle Miocene, whereas the NoLA block rotated slower, until the latest Miocene. The boundary between the NoLA block and a non-rotated Southern Lesser Antilles was likely the Monserrat-Harvers fault zone. These results require hundreds of kilometers of intra-Caribbean motions with oroclinal bending of the trench or forearc sliver motion along the curved plate boundary as endmembers. These data invite a critical re-evaluation of the kinematic reconstruction of Caribbean-North American plate motion. The consequent changes in paleogeography may provide a new view on the enigmatic eastern Caribbean paleo-biogeography and the Paleogene dispersal of South American mammals toward the Greater Antilles

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

Apparent polar wander paths (APWPs) calculated from paleomagnetic data describe the motion of tectonic plates relative to the Earth's rotation axis through geological time, providing a quantitative paleogeographic framework for studying the evolution of Earth's interior, surface, and atmosphere. Previous APWPs were typically calculated from collections of paleomagnetic poles, with each pole computed from collections of paleomagnetic sites, and each site representing a spot reading of the paleomagnetic field. It was recently shown that the choice of how sites are distributed over poles strongly determines the confidence region around APWPs and possibly the APWP itself, and that the number of paleomagnetic data used to compute a single paleomagnetic pole varies widely and is essentially arbitrary. Here, we use a recently proposed method to overcome this problem and provide a new global APWP for the last 320 million years that is calculated from simulated site-level paleomagnetic data instead of from paleopoles, in which spatial and temporal uncertainties of the original datasets are incorporated. We provide an updated global paleomagnetic database scrutinized against quantitative, stringent quality criteria, and use an updated global plate motion model. The new global APWP follows the same trend as the most recent pole-based APWP but has smaller uncertainties. This demonstrates that the first-order geometry of the global APWP is robust and reproducible. Moreover, we find that previously identified peaks in APW rate disappear when calculating the APWP from site-level data and correcting for a temporal bias in the underlying data. Finally, we show that a higher-resolution global APWP frame may be determined for time intervals with high data density, but that this is not yet feasible for the entire 320–0 Ma time span. Calculating polar wander from site-level data provides opportunities to significantly improve the quality and resolution of the global APWP by collecting large and well-dated paleomagnetic datasets from stable plate interiors, which may contribute to solving detailed Earth scientific problems that rely on a paleomagnetic reference frame

Orbit equivalence superrigidity for type III0_0 actions

We prove the first orbit equivalence superrigidity results for actions of type III$_\lambda$ when $\lambda \neq 1$. These actions arise as skew products of actions of dense subgroups of $SL(n,\mathbb{R})$ on the sphere $S^{n-1}$ and they can have any prescribed associated flow

Classification results for nonsingular Bernoulli crossed products

We prove rigidity and classification results for type III factors given by nonsingular Bernoulli actions of the free groups and more general free product groups. This includes a large family of nonisomorphic Bernoulli crossed products of type III$_1$ that cannot be distinguished by Connes $\tau$-invariant. These are the first such classification results beyond the well studied probability measure preserving case

Influence of Data Filters on the Position and Precision of Paleomagnetic Poles: What Is the Optimal Sampling Strategy?

To determine a paleopole, the paleomagnetic community commonly applies a loosely defined set of quantitative data filters that were established for studies of geomagnetic field behavior. These filters require costly and time-consuming sampling procedures, but whether they improve the precision and influence the position of paleopoles has not yet been systematically analyzed. In this study, we performed a series of experiments on four datasets which consist of 73–125 lava sites with 6–7 samples per lava. The datasets are from different regions and ages, and are large enough to represent paleosecular variation, yet include demonstrably unreliable paleomagnetic directions. We show that the systematic application of data filters based on within-site scatter (a maximum angular deviation filter on individual directions, a k-cutoff, a minimum number of samples per site, and eliminating the farthest outliers per site) cannot identify unreliable directions. We find instead that excluding unreliable directions relies on the subjective interpretation of the expert, highlighting the importance of making all data available following the FAIR principles. In addition, data filters that decrease the number of sites even have an adverse effect; they decrease the precision of the paleopole. Between-site scatter often outweighs within-site scatter, and when collecting paleomagnetic poles, the extra efforts put into collecting multiple samples per site are more effectively spent on collecting more single-sample sites

On Pole Position: Causes of Dispersion of the Paleomagnetic Poles Behind Apparent Polar Wander Paths

Paleomagnetic poles used to compute apparent polar wander paths (APWPs) are strongly dispersed, which was recently shown to cause a large fraction (>50%) of these poles to be statistically distinct from the APWP to which they contributed, suggesting that current statistical approaches overestimate paleomagnetic resolution. Here, we analyze why coeval paleopoles are so dispersed, using the paleopoles behind the most recent global APWP and a compilation of paleomagnetic data obtained from <10 Ma volcanic rocks (PSV10). We find that paleopoles derived from sedimentary rocks, or from data sets underrepresenting paleosecular variation (PSV), are more dispersed and more frequently displaced. We show that paleopoles based on a smaller number of paleomagnetic sites are more dispersed than poles based on larger data sets, revealing that the degree to which PSV is averaged is an important contributor to the pole dispersion. We identify as a fundamental problem, however, that the number of sites used to calculate a paleopole, and thus the dispersion of coeval paleopoles, is essentially arbitrary. We therefore explore a different approach in which reference poles of APWPs are calculated from site-level data instead of paleopoles, thereby assigning larger weight to larger data sets. We introduce a bootstrap-based method for comparing a collection of paleomagnetic data with a reference data set on the same hierarchical level, whereby the uncertainty is weighted against the number of paleomagnetic sites. Finally, our study highlights that demonstrating smaller tectonic displacements requires larger paleomagnetic data sets, and that such data sets can strongly improve future APWPs

Reliability of palaeomagnetic poles from sedimentary rocks

Palaeomagnetic poles form the building blocks of apparent polar wander paths and are used as primary input for quantitative palaeogeographic reconstructions. The calculation of such poles requires that the short-term, palaeosecular variation (PSV) of the geomagnetic field is adequately sampled and averaged by a palaeomagnetic data set. Assessing to what extent PSV is recorded is relatively straightforward for rocks that are known to provide spot readings of the geomagnetic field, such as lavas. But it is unknown whether and when palaeomagnetic directions derived from sedimentary rocks represent spot readings of the geomagnetic field and sediments are moreover suffering from inclination shallowing, making it challenging to assess the reliability of poles derived from these rocks. Here, we explore whether a widely used technique to correct for inclination shallowing, known as the elongation–inclination (E/I) method, allows us to formulate a set of quality criteria for (inclination shallowing-corrected) palaeomagnetic poles from sedimentary rocks. The E/I method explicitly assumes that a sediment-derived data set provides, besides flattening, an accurate representation of PSV. We evaluate the effect of perceived pitfalls for this assumption using a recently published data set of 1275 individual palaeomagnetic directions of a >3-km-thick succession of ∼69–41.5 Ma red beds from the Gonjo Basin (eastern Tibet), as well as synthetic data generated with the TK03.GAD field model. The inclinations derived from the uncorrected data set are significantly lower than previous estimates for the basin, obtained using coeval lavas, by correcting inclination shallowing using anisotropy-based techniques, and by predictions from tectonic reconstructions. We find that the E/I correction successfully restores the inclination to values predicted by these independent data sets if the following conditions are met: the number of directions N is at least 100, the A95 cone of confidence falls within a previously defined A95min-max reliability envelope, no negative reversal test is obtained and vertical-axis rotation differences within the data set do not exceed 15°. We propose a classification of three levels (A, B and C) that should be applied after commonly applied quality criteria for palaeomagnetic poles are met. For poles with classification ‘A’, we find no reasons to assume insufficient quality for tectonic interpretation. Poles with classification ‘B’ could be useful, but have to be carefully assessed, and poles with classification ‘C’ provide unreliable palaeolatitudes. We show that application of these criteria for data sets of other sedimentary rock types classifies data sets whose reliability is independently confirmed as ‘A’ or ‘B’, and that demonstrably unreliable data sets are classified as ‘C’, confirming that our criteria are useful, and conservative. The implication of our analysis is that sediment-based data sets of quality ‘A’ may be considered statistically equivalent to data sets of site-mean directions from rapidly cooled igneous rocks like lavas and provide high-quality palaeomagnetic poles