Elongation in distributions of paleomagnetic field directions and corresponding poles

Properties of paleosecular variation (PSV), mainly derived from lava flow data for the last few million years, were often discussed in terms of the latitudinal dependence of angular standard deviation (ASD) of virtual geomagnetic poles (VGPs) distributions after Cox (1970). Generally the ASD of VGP has a feature that it is smallest in the equatorial region and becomes higher in the higher latitude (e.g. McFadden et al., 1988). However mapping of each directional datum into the corresponding VGP is nonlinear and distorted on the unit sphere. Therefore it is not feasible that both distributions become synchronously circular except for sites around the geomagnetic poles. Recent accumulation of reliable paleomagnetic directional data has enabled us to discuss the more details of the nature of PSV, not only the ASD but also the shape of the distributions (Kono, 1997; Tanaka, 1999; Khokhlov et al., 2001). In this study, by using Bingham statistics (Bingham, 1973; Onstott, 1980) we made a comparison in the shape of distributions between actual paleomagentic data obtained from several sites on the Earth, where data from enough flows are available, and our recent PSV model (Hatakeyama and Kono, 2002) which was derived by nonlinear inverse procedures. Some important characteristics of the PSV appearing in the data and relation to the remarkable components in the Gauss coefficients were indicated as following, (1) the shape of the VGP distribution shows much circular than that of the field directions especially in the low latitude region, (2) the distribution of paleodirections is elongated to the direction of the meridian, while that of VGPs is distorted toward the perpendicular direction, and (3) the circular nature of the pole distributions depends on the ``isotropic'' PSV (Constable and Parker, 1988) but the elongation perpendicular to the meridian is likely to be caused by large variances of a special component (l=2, m=1) of spherical harmonics. This component is also regarded as important for the latitudinal dependence of the ASD of VGP (Kono and Tanaka, 1995; Hulot and Gallet, 1996).