How complex is the time-averaged geomagnetic field over the past 5 Myr?

A basic tenet of palaeomagnetism is that the Earth's magnetic field behaves on average like that of a central axial dipole (g(1)(0)). Nevertheless, the question of possible persistent second-order features is still open. Recently Johnson & Constable (1995, 1996) performed a regularized non-linear inversion and found evidence for persistent non-zonal features. Formal uncertainties would indicate that there are significant (non-zero) terms at least up to degree and order 4. Using a recent compilation of two different data sets from lavas (0 to 5 Ma) and the Johnson & Constable codes, we test the robustness of this result. The data set has been divided into three subsets: the Brunhes polarity data (B), all normal polarity data (N) and all reverse data (R). In each subset of data, a prominent g(2)(0), of the order of 5 per cent of g(1)(0), is clearly present, as previously established by several authors. In some subsets, smaller terms appear: g(2)(2) and g(1)(1) in the Brunhes data, h(3)(1) and h(2)(1) in N, and h(2)(1), g(3)(0) and g(3)(3) in R. A threshold under which terms resulting from the inversion cannot yet be considered as robust appears to be of the order of 300 nT. Indeed, tests show that many terms, which are different for each epoch (B, N or R), may be artefacts due to aliasing because of poor site distribution, or due to the underestimation of a priori errors in the data; these could result from undetected tectonic rotations, non-horizontal palaeoslopes, or viscous overprints. Because of these limitations in resolution, it may not yet be possible to identify robustly terms other than the axial dipole and quadrupole. The persistence of high-latitude flux concentrations, hemispheric asymmetry or normal versus reversed field asymmetry cannot yet be considered as demonstrated.