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.

Inclination is the angle of a magnetization vector from horizontal. Clastic sedimentary rocks often experience inclination shallowing whereby syn- to post-depositional processes result in flattened detrital remanent magnetizations relative to local geomagnetic field inclinations. The deviation of recorded inclinations from the true values presents challenges for reconstructing paleolatitudes. A widespread approach for estimating the flattening factor ($f$) compares the shape of an assemblage of magnetization vectors to that derived from a paleosecular variation model (the elongation/inclination [$E/I$] method). However, few studies exist that compare the results of this statistical approach with empirically determined flattening factors and none in the Proterozoic Eon. In this study, we evaluate inclination shallowing within 1.1 billion-year-old, hematite-bearing, interflow red beds of the Cut Face Creek Sandstone that is bounded by lava flows of known inclination. We found that detrital hematite remanence is flattened with f = 0.65{0.75}_{0.56}$ whereas the pigmentary hematite magnetization shares a common mean with the volcanics. Comparison of detrital and pigmentary hematite directions results in $f = 0.61^{0.67}_{0.55}$. These empirically determined flattening factors are consistent with those estimated through the $E/I$ method ($f = 0.64^{0.85}_{0.51}$) supporting its application in deep time. However, all methods have significant uncertainty associated with determining the flattening factor. This uncertainty can be incorporated into the calculation of paleomagnetic poles with the resulting ellipse approximated with a Kent distribution. Rather than seeking to find “the flattening factor,’ or assuming a single value, the inherent uncertainty in flattening factors should be recognized and incorporated into paleomagnetic syntheses.

Laboratory reanalysis of paleomagnetic samples from two sets of superposed ~ 4.5 m.y. old lava flows (N=64) collected on Kauai (Hawaii) in the 1960s, when combined with more recently published results from two additional flow sequences (N=59) on the island, yields a mean paleomagnetic pole that differs significantly from the spin axis. The new laboratory work was motivated by the fact the 60% of the published flow mean directions on the old collection derived from measurements of natural remanent magnetization without any demagnetization treatment. In our reanalysis, we subjected all specimens to stepwise alternating field (AF) demagnetization (13 steps; 90 mT peak AF) and modern line-fit analysis. As has been found in many restudies of this sort on young, well-behaved basaltic lavas, modern demagnetization technique produced little change in the flow-mean directions (an average change of just over 2° in this case.) To minimize the bias introduced when rapidly erupted flow sequences sample a single geomagnetic field direction, we thinned the combined data by grouping superposed flows with similar paleomagnetic directions. The procedure requires choosing a minimum angle between directions that will be considered independent samples of the ancient geomagnetic field. Previous studies have commonly used a 6° threshold. We found, however, that much larger values (10° to 16°) were needed to eliminate significant serial correlation (measured in several ways) in the thinned directional sequence. Our conclusion is that the 123 lava flows in this study provide only 33 independent estimate of the ancient field direction. The mean normal polarity paleomagnetic pole resulting from the analysis (Lon=076.8, Lat=82.2, N=13) is almost perfectly antiparallel (179°) to the mean reverse polarity pole (Lon=258.4, Lat=-83.2, N=20). The grand mean of 33 normal and reverse polarity data is Lon=077.3 Lat=82.8 k=31.8 α95=4.5°. The VGP dispersion (without correction for within-site dispersion, of order 0.5° for these very well-behaved paleomagnetic recorders) is 14.3° about the mean pole and 15.9° about the spin axis, comparable to that found in other analyses of Hawaiian paleomagnetic data.

Anorthosites are attractive paleomagnetic recorders as silicate-hosted magnetite inclusions can be single-domain and be shielded from alteration. However, petrofabrics within anorthosites may result in magnetic remanence anisotropy that is potentially detrimental to recovering paleomagnetic direction and intensity. The Beaver River diabase of the North American Midcontinent Rift contains abundant nearly 100 percent plagioclase anorthosite xenoliths that are hypothesized to have been liberated from the lower crust by the magma enroute to becoming embedded in shallow crustal sills. In this study, we compare the remanent paleomagnetic directions recorded by anorthosite xenoliths to those of the Beaver River diabase host rocks. Given that both lithologies should record the same thermal remanent magnetization, this comparison provides a means to assess the effects of remanence anisotropy on the paleodirection recorded by the anorthosites. Thermal and anhysteretic remanence (TRM and ARM) anisotropy experiments, which are typically used to assess for anisotropy, can be compared to the natural remanence of the diabase and anorthosite in this geologic experiment that was conducted 1.1 billion years ago. Paleodirection data from the interior of the largest (>300 m) anorthosite xenoliths also have the potential to test their hypothetical lower crustal origin. An origin below the Curie depth would result in a full thermal remanence from the time of diabase emplacement, while a shallower origin from above the Curie depth could have resulted in a distinct remanence direction in the xenolith interior that predates the intrusion (with samples from the exterior having acquired a Beaver River diabase coeval thermal remanence in either scenario). Overall, this novel geological association between diabase and anorthosite provides a means to assess the effects of remanence anisotropy providing valuable context for efforts to use anorthosites to understand the ancient geomagnetic field.