On low-degree spherical harmonic models of paleosecular variation

Abstract Geomagnetic field directions over the past few millions of years have recently been compiled and these data bases can be used to build low-degree spherical harmonic models of the time-averaged field (TAF) and its paleosecular variation (PSV) variance structure. Such models can be constrained by a number of statistical distributions derived from the data, such as latitude variations of the angular standard deviation (ASD) of virtual geomagnetic poles (VGP), which is widely used in paleomagnetism. Our approach has been to test predictions of the giant Gaussian field model of Constable and Parker ( J. Geophys. Res. , 93: 11569–11581, 1988) with respect to six such distributions: ASD of VGPs, VGP distribution with latitude and longitude and in so-called ‘common-site’ longitude, and standard deviations of declination and inclination. Model predictions have been calculated at the actual sites and for the actual number of lava flows recorded in the database. We have next explored modifications of the TAF model when a single persistent term is added (up to degree and order four), or a combination of a few such terms. No model with persistent terms and the Constable and Parker (1988) PSV structure can fit the data satisfactorily, and a change in that variance structure is required. We explore several hypotheses, and find that assuming isotropic PSV in the non-dipole field components improves the situation significantly. This could be related to systematic underestimation of paleomagnetic uncertainties. However, the best fit is obtained if one assumes that the PSV structure of spherical harmonic terms is non-uniform. An excellent fit is obtained if the standard deviation of the (2, 1) quadrupole is assumed to be significantly larger than that of the (2, 0) and (2, 2) terms. This is in good agreement with recent theoretical findings. The significance of persistent harmonics of degree equal to or higher than three in the TAF is doubtful. There are also indications that the lack of symmetry between the normal and reverse states of the paleofield may have been overestimated. It remains to be seen how much of the TAF and PSV structure that is found is still biased by the poor geographical distribution of the sites, as is clearly the case for the so-called ‘right-handed effect’ in VGP distribution.