Principal component analysis of palaeomagnetic directions: Converting a Maximum Angular Deviation (MAD) into an α95 angle

Abstract

Directions recovered from palaeomagnetic samples are usually archived with some quantitative information about their precision, most often in the form of a so-called α95 angle. Such angles are classically co-estimated with the recovered palaeomagnetic direction from a collection of samples providing individual estimates of this direction. In some instances, however, palaeomagnetic directions have to be inferred from a single sample in which case no α95 angle can be recovered in this way. Fortunately, the progressive demagnetization techniques and principal component analysis universally used to recover directional information from single samples provide alternative measures of the error affecting the recovered direction, known as Maximum Angular Deviation (MAD) angles. These have so far only been considered as rough quality indicators. Here, however,we showthat directions recovered in thisway can be assumed to satisfy a Fisher distribution, and that the corresponding MAD angles can be rescaled into α95 estimates by multiplying it by an appropriate factor, which only depends on the number of demagnetization steps used in the principal component analysis and on whether one relies on a standard or a so-called 'anchored' principal component analysis. These coefficients have been tabulated and practical recommendations for taking advantage of them outlined in the final section of the text. They provide simple means for users to produce much needed error bars on declination and inclination time series recovered from sedimentary long sequences.