Paleosecular variation of field intensities and dipole moments

In order to use paleointensity data for paleosecular variation studies, we first obtain analytical for the intensity of the geomagnetic field and the corresponding dipole moment in terms of Gauss coefficients. Next, statistical parameters for these quantities are derived under the assumption that Gauss coefficients vary randomly with time and that the axial dipole component is much larger than all the other Gauss coefficients. Using these expressions, we construct a ‘homogeneous background model’ for paleosecular variation, in which Gauss coefficients other than the axial dipole term are zero mean random variables, with variances decaying exponentially with the degree of the harmonic. We compare this model with the present field and the data from the last 10 Ma collected in the paleointensity database. Although we have to make certain allowances, because some of the paleointensity data may not be characteristic of the time-averaged paleomagnetic field, we obtain a broad agreement between the observation and a slightly modified form of the homogeneous background model. From this match, we conclude that the amplitude of the non-dipole components may be about twice that predicted from the present field, and that the contribution from the equatorial dipole is very small. The present analysis suggests that a more rigorous selection criteria should be employed to secure the reliability of data and also that the data set should more adequately sample the time interval before we can obtain a more detailed knowledge of the structures of the ancient magnetic field.