The behaviour of the Earth's magnetic field, at the timescale of a polarity interval, can be represented with the help of "Giant Gaussian Process" statistical models that describe the value of the mean field and the variability of the field about this mean value (or paleosecular variation). The magnetic field produced by numerical geodynamo simulations has first been used to test the validity of this approach. The study of the morphology of the mean field and the paleosecular variation in these simulations shows that "GGP" models can give information on the way the geodynamo works and on the influence of the core mantle boundary conditions. We next developed a new method to test "GGP" models against paleomagnetic directional data, taking measurement errors into account. Finally, the numerous sea-surface magnetic profiles available in databases have been used to show the existence of numerous coherent short wavelength anomalies (or "tiny wiggles") which are, for most of them, associated to temporal variations of the intensity of the Earth's magnetic field. The temporal distribution of these tiny wiggles within chrons and throughout the investigated period (83-41 Ma, chrons 33r à 19r) is homogenous and suggests that they simply correspond to a filtered record of a constant secular variation regime, contrasting with the evolution of the reversal frequency that characterises the investigated period.
