We present a family of statistical models for paleosecular variation (PSV) of the geomagnetic field that are compatible with paleodirectional and paleointensity variations in lava flows sampling the last 5 Ma, and explore what paleomagnetic observables might be used to discriminate among the various family members. We distinguish statistical models with axial anisotropy, which provide a suitable description for an earth with homogeneous boundary conditions at the core-mantle interface from those with more general anisotropy corresponding to geographically heterogeneous boundary conditions. The models revise and extend earlier ones, which are themselves descendants of CP88, devised by Constable and Parker [Constable, C.G., Parker, R.L., 1988. Statistics of the geomagnetic secular variation for the past 5 m.y. J. Geophys, Res. 93, 11569-11581]. In CP88, secular variation is described by statistical variability of each Gauss coefficient in a spherical harmonic description of the geomagnetic field, with each coefficient treated as a normally distributed random variable: the Gauss coefficients of the non-dipole part of the field exhibit isotropic variability, and the variances are derived from the present field spatial power spectrum. The dipole terms have a special status in CP88, with a non-zero mean for the axial-dipole, and lower variance than predicted from the spatial power spectrum. All non-dipole terms have zero mean except the axial-quadrupole. CP88 is untenable for two reasons: it fails to predict the observed geographic dependence of directional variability in the magnetic field, and it grossly underpredicts the variance in paleointensity data. The new models incorporate large variance in the axial-dipole, and in the non-axial-quadrupole Gauss coefficients, g1/2: and h1/2:. The resulting variance in paleomagnetic observables depends only on latitude (zonal models), unless the variance in h1/2: is different from that in g1/2 (non-zonal models). Non-zonal (longitudinal) variations in PSV, such as the flux lobes seen in the historical magnetic field, are simulated using the non-zonal models. Both the zonal and non-zonal models fit summary statistics of the present dataset. We investigate the influence of persistent non-zonal influences in PSV on various paleomagnetic observables. It is shown that virtual geomagnetic pole (VGP) dispersion is rather insensitive to longitudinal variations in structure of PSV, and that inclination dispersion has the potential to be more informative given the right site distribution. There is also the possibility of using paleointensity and geographic variations in the frequency of occurrence of excursional directions to identify appropriate PSV models. (C) 1999 Elsevier Science B.V. All rights reserved.

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