Analyzing paleomagnetic data: To anchor or not to anchor?

Paleomagnetic directions provide the basis for use of paleomagnetism in chronological and tectonic reconstructions and for constraining past geomagnetic field behavior over a variety of timescales. Crucial to paleomagnetic analysis is the separation and quantification of a characteristic remanent magnetization (ChRM), which relates to a process of interest, from other remanence components. Principal component analysis (PCA) of stepwise demagnetization data is employed routinely in these situations to estimate magnetic remanence directions and their uncertainties. A given ChRM is often assumed to trend toward the origin of a vector demagnetization diagram and prevailing data analysis frameworks allow remanence directions to be estimated based on PCA fits that are forced to pass through the origin of such diagrams, a process referred to as anchoring. While this approach is adopted commonly, little attention has been paid to the effects of anchoring and the influence it has on both estimated remanence directions and their associated uncertainties. In almost all cases, anchoring produces an artificially low uncertainty estimation compared to an unanchored fit. Bayesian model selection demonstrates that the effects of anchoring cannot typically be justified from a statistical standpoint. We present an alternative to anchoring that constrains the best fit remanence direction to pass through the origin of a vector demagnetization diagram without unreasonably distorting the representation of the demagnetization data.