Variations in the geomagnetic dipole 2: Statistical analysis of VDMs for the past 5 million years.

Abstract

Virtual Dipole Moments (VDMs) are analysed to determine the distribution of True Dipole Moments (TDMs) from which they were derived. The data set used is all the available VDMs for the past 5 million years which have associated Virtual Geomagnetic Poles (VGPs) with latitudes greater than 45°. These data do not support a model which predicts a cyclic variation of the dipole moment during stable polarity periods. Neither do they support a model in which the field strength of the non-dipole components is a constant ratio of the mean dipole field strength. Instead they support a model in which the TDMs have a truncated Gaussian distribution and the field strength of the non-dipole components is linearly proportional to the TDM. These components introduce a Gaussian distributed scatter to the observed VDMs with standard deviation about 18.6% of the dipole moment, and the palaeointensity determinations themselves introduce a further Gaussian distributed scatter with standard deviation about 10%. The data give no reason to reject the hypothesis of a common mean and variance for the (untruncated) Gaussian distribution of the normal and reverse polarity TDMs but the hypothesis of a common truncation point can be rejected. This indicates a difference in the overall properties of the two polarity states.The term Palaeomagnetic Dipole Moment (PDM) is introduced for the value at which the truncated Gaussian distribution of TDMs peaks. As determined from the present data the PDM for the past 5 million years is 8.67±0.65×1022Am2 with 95% confidence. The estimated standard deviation of the untruncated distribution is 3.63±0.75×1022Am2 with 95% confidence, this variation (41.9%) relating solely to variation in the dipole moment itself. This reinforces the view that fluctuations in the dipole moment are much greater than are observed in data for the past 104 years, suggesting that they must occur over time scales of 105 or 106 years.