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The consistency of the empirical data on paleointensity and paleoinclinations contained in the BOROKPINT paleointensity world database with the Geocentric Axial Dipole (GAD) hypothesis and Giant Gaussian Process (GGP) model describing the geomagnetic field variations in the Brunhes epoch is tested. The calculations are based on the geomagnetic field potential representation by the sum of spherical functions of spatial coordinates with random coefficients, enabling computer simulation of the data with the given statistical characteristics of the coefficients. The estimates show that the Kolmogorov–Smirnov and Anderson–Darling tests reject the GAD hypothesis in its canonical form. The extension of GAD to GGD with nonzero time-average quadrupole and octupole terms makes the paleointensity and paleoinclination data to comply with GGP model realizations; however, these models are mutually exclusive because of mutual inconsistency of their parameters. Testing the paleoinclination data against GDP model shows that a small correction to the purely dipole component of the geomagnetic field should be introduced. At the same time, the paleointensity data analysis suggests that these data highly probably agree with 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 paleoinclination data. This inconsistency is most likely to be due to the artifacts associated with incorrect paleointensity determinations; however, this interpretation does not explain the causes of the strong latitudinal dependence of the intensity of the Virtual Axial Dipole Moment (VADM) which follows from the empirical data.