Testing the relationship between timing of geomagnetic reversals/excursions and phase of orbital cycles using circular statistics and Monte Carlo simulations

Fuller (Fuller, M., Geomagnetic field intensity, excursions, reversals and the 41,000-yr obliquity signal, Earth Planet. Sci. Lett. 245 (2006) 605–615.) pointed out that, for 9 reversals over the last 3 Myr, reversal age has a non-random relationship to the phase of orbital obliquity. Our analysis, based on Rayleigh tests, indicates that reversals have no preferred phase distribution in the obliquity cycle at the 5% significance level over the last 3 Myr. There is, however, a statistically significant relationship (at the 5% level) between reversal age and the phase of orbital eccentricity for the last 3 Myr, although this relationship breaks down on adding just a few reversals beyond 3 Ma. Over the last 5 Myr, reversals preferentially occurred during decrease of the maximum obliquity envelope although, yet again, the relationship does not hold as additional reversals are added to the analysis, no matter which timescale is tested. The Rayleigh tests are all based on the assumption of no uncertainty in reversal/excursion age, or in orbital solutions. Monte Carlo simulations indicate that reversal/excursion ages would have to be known within 5–10 kyr to resolve a preferred phase in obliquity similar to that advocated by Fuller (Fuller, M., Geomagnetic field intensity, excursions, reversals and the 41,000-yr obliquity signal, Earth Planet. Sci. Lett. 245 (2006) 605–615.) over the last 3 Myr. Reversal/excursion ages would have to be known within ~15 kyr to resolve a preferred phase in orbital eccentricity for reversals over the last 3 Myr, and within ~40 kyr for the last 25 Myr. Comparison of astrochronological reversal timescales indicates that reversal age uncertainties exceed these limits, making it unlikely that a relationship of reversal/excursion age to the phase of obliquity or eccentricity would be resolvable. In the case of the obliquity envelope, the critical levels of reversal age uncertainty (~50 kyr for 0–3 Ma, ~200 kyr for 0–5 Ma, and ~400 kyr for 0–25 Ma) are less stringent. The presence of a significant relationship between reversal age and phase of the obliquity envelope for the last 5 Myr, but not further back in time, implies either larger than expected reversal age uncertainties in pre-Pliocene polarity timescales and a link between reversal age and the obliquity envelope, or, more probably, the fortuitous occurrence of a low probability relationship over the last 5 Ma that has no mechanistic implication.