Detailed knowledge of the long-term spatial configuration and temporal variability of the geomagnetic field is lacking because of insufficient data for times prior to 10 ka. We use realisations from suitable numerical simulations to investigate three important questions about stability of the geodynamo process: is the present field representative of the past field; does a time-averaged field actually exist; and, supposing it exists, how long is needed to define such a field. Numerical geodynamo simulations are initially selected to meet existing criteria for morphological similarity to the observed magnetic field. A further criterion is introduced to evaluate similarity of long-term temporal variations. Allowing for reasonable uncertainties in the observations, observed and synthetic axial dipole moment frequency spectra for time series of order a million years in length should be fit by the same power law model. This leads us to identify diffusion time as the appropriate time scaling for such comparisons. In almost all simulations, intervals considered to have good morphological agreement between synthetic and observed field are shorter than those of poor agreement. The time needed to obtain a converged estimate of the time-averaged field was found to be comparable to the length of the simulation, even in non-reversing models, suggesting that periods of stable polarity spanning many magnetic diffusion times are needed to obtain robust estimates of the mean dipole field. Long term field variations are almost entirely attributable to the axial dipole; nonzonal components converge to long-term average values on relatively short timescales (15-20 kyr). In all simulations, the time-averaged spatial power spectrum is characterised by a zigzag pattern as a function of spherical harmonic degree, with relatively higher power in odd degrees than in even degrees. We suggest that long-term spatial characteristics of the observed field may emerge on averaging times that are within reach for the next generation of global time-varying paleomagnetic field models. (C) 2014 Elsevier B.V. All rights reserved.

}, keywords = {boundary heat-flow, convection, core evolution, dipole-moment, dynamos, Earth{\textquoteright}s core, earths magnetic-field, geodynamo models, geomagnetic frequency spectrum, mantle, models, numerical, reversals, secular variation}, isbn = {0012-821X}, doi = {10.1016/j.epsl.2014.07.042}, url = {