Analysis of the Hypothesis of a Giant Gaussian Process as a Means for Describing Secular Variations of the Geomagnetic Field Vector

Abstract

The consistency of the empirical data on the paleointensity and paleoinclinations contained in the BOROKPINT paleointensity world database with the Geocentric Axial Dipole (GAD) hypothesis and the Giant Gaussian Process (GGP) model describing the geomagnetic field variations in the Brunhes epoch is tested. The calculation procedure is based on the representation of the geomagnetic field potential by the sum of the spherical functions of a spatial coordinate with random coefficients, which enables the computer simulation of the data that correspond to the given statistical characteristics of the coefficients. The estimation shows that according to the Kolmogorov–Smirnov and Anderson–Darling tests, the GAD hypothesis in its canonical form should be rejected. The extension of GAD to GGD with nonzero time-average quadrupole and octupole terms brings the paleointensity and paleoinclination data into agreement with the GGP model realizations; however, these models turn out to be mutually exclusive because their parameters are inconsistent with each other. Testing the paleoinclination data against GDP model demonstrates the necessity of introducing a small correction to the purely dipole component of the geomagnetic field. At the same time, the analysis of the paleointensity data shows that these data with a very high probability agree with the GGP models with a high quadrupole contribution making up 1/3 of the dipole coefficient, which is strongly at odds with the parameters of the model corresponding to the paleoinclination data. This inconsistency is most probably caused by the artifacts due to the incorrect determinations of paleointensity; however, this interpretation leaves unsolved the question about the causes of such a strong latitudinal dependence of the intensity of the Virtual Axial Dipole Moment (VADM) what follows from the empirical data.