On the interpretation of virtual geomagnetic pole (VGP) scatter curves

Abstract

The present paper aims at assessing the information contained in the so-called virtual geomagnetic pole (VGP) scatter curves which are commonly used in palaeosecular variation studies. As the corresponding curve derived for the last 5 Myr has been compared to a very similar “equivalent” VGP scatter curve derived from the present geomagnetic field (McFadden et al., 1988), we also address the meaning of these “equivalent” curves. We especially investigate the way the two types of curve are related to each other within the statistical formalism first introduced by Constable and Parker (1988). A number of simple and useful (but approximate) properties are derived for that purpose. In particular, a close formal link is established between the two quantities. This allows us to first study the behaviour of the equivalent VGP scatter curve (this curve is shown to be highly time dependent and mainly controlled by the degree and order (1, 1), (2, 1), (3, 1) and (4, 1) terms) and then proceed with some suggestions regarding the interpretation of palaeomagnetic scatter curves. These curves are shown to be (albeit approximately) the quadratic sum of a mean field contribution and of a variance and cross-correlation contribution, which cannot be distinguished from one another unless additional information is being used. In the case of the VGP scatter of the last 5 Myr, available mean field models show that the mean field contribution is very weak. But assuming an isotropic-with-no-correlations statistical model of the field cannot account for the corresponding VGP scatter curve, whatever the spectrum of the non-dipole field. Anisotropy and/or cross-correlations are thus required. We show examples of statistical models incorporating such ingredients. It appears that the separation into dipole and quadrupole (antisymmetric and symmetric) families along the line suggested by McFadden et al. (1988) is not the most appropriate. Rather, it is likely that the pre-eminence of the order 1 terms suggested by the observation of the historical field is responsible for the VGP scatter curve of the past 5 Myr. This study somewhat follows and completes the very recent work of Kono and Tanaka (1995).