Uncertainty Propagation in Hierarchical Paleomagnetic Reconstructions

Abstract

Estimation of paleomagnetic directions plays a crucial role in magnetostratigaphy, paleogeographic reconstruction, and constraining past geomagnetic field behavior. While analysis and aggregation of paleomagnetic directional data are performed in a hierarchical fashion, the standard statistical framework employed by paleomagnetists does not consider uncertainty propagation through each level of the hierarchy. With this limitation, inferences drawn from paleomagnetic data will be affected by underestimated uncertainties. We provide here an approximate directional uncertainty propagation scheme that applies to Fisher distributions and, thus, to a number of paleomagnetic data processing tasks. The scheme is a straightforward addition to the existing paleomagnetic statistical framework and is demonstrated using case studies to show how uncertainties can be propagated through different stages of the paleomagnetic data processing chain. Furthermore, we discuss situations, such as the transformation into virtual geomagnetic poles, where this simple form of uncertainty propagation cannot be employed because the data are not Fisher distributed. where is a unit vector (i.e., a direction) corresponding to the distribution mean, is the concentration parameter, and is a given unit vector. Given a collection of N paleomagnetic directions in a Cartesian

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

“…whereby the A 95,ref and the A 95,PP are the radius of the 95% confidence circle around the reference pole and the independent paleopole, respectively. It is important to note that the uncertainty in the position of the underlying paleopoles (their A 95,PP ) is typically not propagated in the calculation of the A 95,ref , which may thus be an underestimate of the uncertainty in the reference pole position (Heslop & Roberts, 2020). Rowley (2019) showed that, with the above equation, >50% of the paleopoles used in the global APWP of Torsvik et al (2012) are statistically displaced relative to the APWP itself.…”

“…In the classical approach, a paleopole is considered statistically displaced if its angular distance to the reference pole exceeds the combined uncertainty of the paleopole and the reference pole, calculated using: $$$\begin{array}{l}\sqrt{{A}_{95,ref}^{2}\,+\,{A}_{95,PP}^{2}}\,\hfill \end{array}$$$ whereby the A 95,ref and the A 95,PP are the radius of the 95% confidence circle around the reference pole and the independent paleopole, respectively. It is important to note that the uncertainty in the position of the underlying paleopoles (their A 95,PP ) is typically not propagated in the calculation of the A 95,ref , which may thus be an underestimate of the uncertainty in the reference pole position (Heslop & Roberts, 2020).…”

Holocene Paleosecular Variations Recorded by Relict Magnetic Minerals in the Anoxic Black Sea Sediments

“…Characteristic remanent magnetization (ChRM) directions were determined by using principal component analysis (PCA) following Kirschvink (1980). Directional maximum angular dispersions (MAD) of individual samples are converted to α 95 uncertainties following Heslop and Roberts (2020). The ARM was imparted along the samples' z ‐axes with a static field of 0.05 mT and an AF field of 100 mT.…”

Chronological Assessment of the Balta Alba Kurgan Loess-Paleosol Section (Romania) – A Comparative Study on Different Dating Methods for a Robust and Precise Age Model

“…The uncertainties of magnetic and luminescence ages may be over-or underestimated, which may influence the age-depth models. Especially for magnetic dating, uncertainties are not easy to calculate, since they include uncertainties that are associated with each stage of paleomagnetic analysis (Tauxe et al, 2010;Heslop and Roberts, 2020). In case of the magnetic data set of the BAK site, we only estimate uncertainty, i.e., we have a component of random uncertainty (e.g., through proxy data) and also systematic effects from correlation with a possibly biased reference chronology.…”