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.

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.

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 fundamental problem, however, that the amount of paleomagnetic data 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.

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 accuracy and precision 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 contain demonstrably unreliable datapoints. We show that data filters based on within-site scatter (a k-cutoff, a minimum number of samples per site, and eliminating the farthest outliers per site) cannot objectively 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 eliminate datapoints even have an adverse effect: the accuracy as well as the precision of paleopoles decreases with the decreasing number of data. Between-site scatter far 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.