Anisotropic paleosecular variation models: implications for geomagnetic field observables

We present a family of statistical models for paleosecular variation (PSV) of the geomagnetic field that are compatible with paleodirectional and pale ointensity variations in lava flows sampling the last 5 Ma, and explore wha t paleomagnetic observables might be used to discriminate among the various family members. We distinguish statistical models with axial anisotropy, w hich provide a suitable description for an earth with homogeneous boundary conditions at the core-mantle interface from those with more general anisot ropy 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. Ge ophys, Res. 93, 11569-11581]. In CP88, secular variation is described by st atistical variability of each Gauss coefficient in a spherical harmonic des cription of the geomagnetic field, with each coefficient treated as a norma lly distributed random variable: the Gauss coefficients of the non-dipole p art of the field exhibit isotropic variability, and the variances are deriv ed from the present field spatial power spectrum. The dipole terms have a s pecial 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 te rms have zero mean except the axial-quadrupole. CP88 is untenable for two r easons: it fails to predict the observed geographic dependence of direction al variability in the magnetic field, and it grossly underpredicts the vari ance in paleointensity data. The new models incorporate large variance in t he 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 PS V, such as the flux lobes seen in the historical magnetic field, are simula ted using the non-zonal models. Both the zonal and non-zonal models fit sum mary statistics of the present dataset. We investigate the influence of per sistent non-zonal influences in PSV on various paleomagnetic observables. I t is shown that virtual geomagnetic pole (VGP) dispersion is rather insensi tive to longitudinal variations in structure of PSV, and that inclination d ispersion has the potential to be more informative given the right site dis tribution. There is also the possibility of using paleointensity and geogra phic variations in the frequency of occurrence of excursional directions to identify appropriate PSV models. (C) 1999 Elsevier Science B.V. All rights reserved.