Quantifying the Similarity of Paleomagnetic Poles

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