Geomagnetic field model for the last 5 My: time-averaged field and secular variation

Structure of the geomagnetic field has bee studied by using the paleomagetic direction data of the last 5 million years obtained from lava flows. The method we used is the nonlinear version, similar to the works of Gubbins and Kelly [Nature 365 (1993) 829], Johnson and Constable [Geophys. J. Int. 122 (1995) 488; Geophys. J. Int. 131 (1997) 643], and Kelly and Gubbins [Geophys. J. Int. 128 (1997) 315], but we determined the time-averaged field (TAF) and the paleosecular variation (PSV) simultaneously. As pointed out in our previous work [Earth Planet. Space 53 (2001) 31], the observed mean field directions are affected by the fluctuation of the field, as described by the PSV model. This effect is not excessively large, but cannot be neglected while considering the mean field. pose that the new TAF+PSV model is a better representation of the ancient magnetic field, since both the average and fluctuation of the field are consistently explained. In the inversion procedure, we used direction cosines instead of inclinations and declinations, as the latter quantities show singularity or unstable behavior at the high latitudes. The obtained model gives reasonably good fit to the observed means and variances of direction cosines. In the TAF model, the geocentric axial dipole term (g10) is the dominant component; it is much more pronounced than that in the present magnetic field. The equatorial dipole component is quite small, after averaging over time. The model shows a very smooth spatial variation; the nondipole components also seem to be averaged out quite effectively over time. Among the other coefficients, the geocentric axial quadrupole term (g20) is significantly larger than the other components. On the other hand, the axial octupole term (g30) is much smaller than that in a TAF model excluding the PSV effect. It is likely that the effect of PSV is most clearly seen in this term, which is consistent with the conclusion reached in our previous work. V model shows large variance of the (2,1) component, which is in good agreement with the previous PSV models obtained by forward approaches. It is also indicated that the variance of the axial dipole term is very small. This is in conflict with the studies based on paleointensity data, but we show that this conclusion is not inconsistent with the paleointensity data because a substantial part of the apparent scatter in paleointensities may be attributable to effects other than the fluctuations in g10 itself.