Quantifying the Similarity of Paleomagnetic Poles

Abstract

An ability to compare paleomagnetic poles quantitatively is fundamental to paleogeographicreconstruction. The Fisher distribution provides a statistical framework for both constructing and relatingpaleomagnetic poles to enable comparison of estimated pole positions in paleomagnetic reconstructions.However, Fisher distribution-based confidence regions for paleomagnetic poles are often comparedusing empirical rules of thumb rather than by quantitative analysis of their full structure. Here wedemonstrate potential shortcomings of such comparisons and propose continuous metrics for quantitativecomparison of paleomagnetic poles. These metrics are simple to apply for Fisher distributions and can bemodified readily for a broad range of alternative distributions that may be more appropriate forrepresenting some paleomagnetic data sets. We demonstrate how our proposed metrics provide bothquantitative and probabilistic approaches to common tasks in paleomagnetic reconstruction, such ascomparing estimated mean pole positions with apparent polar wander paths.