Estimation and Propagation of Uncertainties Associated with Paleomagnetic Direction

Abstract:

Principal component analysis is a well-established technique in paleomagnetism, and provides a means to estimate magnetic remanence directions from stepwise demagnetization data. Derived directions constrain past geomagnetic field behavior and form the foundation of chronological reconstructions. Principal component analysis does not, however, lend itself to the quantification of uncertainties associated with estimated directions. Thus, inferences drawn from paleomagnetic reconstructions suffer from an inability to propagate uncertainties from individual specimens to higher levels, such as mean directions and pole positions. Additionally, the relatively small number of demagnetization data points used to quantify remanence directions for an individual specimen can result in unstable or distorted principal component solutions. We will show how a probabilistic reformulation of principal component analysis can be used to rigorously quantify uncertainties associated with remanence directions estimated from demagnetization data. These uncertainties can be propagated readily through each step of a paleomagnetic reconstruction to provide rigorous quantification of uncertainties for all stages of the data interpretation sequence. Proper uncertainty determination helps to protect against spurious inferences being drawn from uncertain data.