Uncertainty Propagation in Hierarchical Paleomagnetic Reconstructions

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.