Trends in Cretaceous and Tertiary geomagnetic reversals

The statistical theory of modulated renewal processes is used to analyze the polarity reversal scales of Larson & Hilde (1975) and LaBreque, Kent & Cande (1977). The results suggest that the trending effect in these data may be modelled by a rate parameter with an exponential quadratic trend. Short times in one polarity state tend to be followed by short times in the other state. The graphical analysis points to the possibility of an undulating pattern in reversal rates. The empirical distributions of the normal and reversed polarities show slight differences in comparison with each other in most of the statistical tests, but a moving-window analysis indicates possible serial effects for the normal times. As a rough approximation, a statistical two-state model for reversals might be realistic, for example, an alternating renewal process under relaxed assumptions. There has been a gradual stepping-up of the minimum reversal rate from the Oligocene to the present, but little change in the observed range of the reversal rates. With the long quiet (Mercanton) interval removed from the data, the average time spent in the reversed polarity state is slightly greater than for the normal state. A change in statistical properties for the entire set of data considered as a single sample occurs around the Eocene-Oligocene transition (Middle Eocene on earlier time scales). The analyses of the statistical second-order properties of the entire sequence of 271 observations, and the subsets of normal and reversed between-times, reject a renewal hypothesis if theoretical statistical considerations are strictly applied to the results (although this hypothesis is not rejected for the Oligocene to Recent observations); this result is at variance with some geophysical models. A short appendix on the theory of point processes is provided to aid the general reader in following the arguments used in this paper.