On the age calibration of the geomagnetic polarity timescale

Knowledge of the age of undated events is not null if a time-order relationship can be found among these events. The knowledge of such a time-ordered sequence can be formalized by using non-informative (uniform) prior probability densities for the ages of undated events and Bayes’ theorem to introduce the time-order relationship condition. We show that the conditional probability densities of the ages of events of unknown age are given by various forms of Euler’s beta distribution. These distributions yield an estimate of the probability for an undated event to occur in a given age interval. We use this method to propose appropriate probabilistic representations of our actual knowledge of the dating of the magnetic polarity reversals during the Cenozoic. These representations take into account the uncertainties arising from irregularities in accretion process and from the quality of a few calibration points. Both types of uncertainties generate large ambiguities in the age of magnetic reversals, which should be taken into consideration when the geomagnetic polarity timescale is used for dating purposes. We propose to use the entropy function to quantify these ambiguities.