Principal component analysis in paleomagnetism

When studying the mean and variance of paleomagnetic data it is a common practice to employ principal component analysis (Jolliffe, 2002). The theory of this method is related to the mathematics quantifying the moment of inertia of a set of particles of mass about some reference point of interest. For the purposes of data analysis, principal component analysis was first promoted by Pearson (1901) and Hotelling (1933), and it also often associated with Karhunen (1947) and Loéve (1977). Principal component analysis is widely applied in crystallography (e.g., Schomaker et al., 1959). In paleomagnetism (e.g., Mardia, 1972; Kirschvink, 1980), it finds application in studies of the average paleofield, paleosecular variation, demagnetization, and magnetic susceptibility. Here we discuss and demonstrate principal component analysis in application to full paleomagnetic vectorial data and, separately, to paleomagnetic directional data.