Since the work of William Gilbert in 1600 (ref. 1), it has been widely beli
eved that the Earth's magnetic field, when suitably time-averaged, is that
of a magnetic dipole positioned at the Earth's centre and aligned with the
rotational axis. This 'geocentric axial dipole' (GAD) hypothesis has been t
he central model for the study of the Earth's magnetic field-it underpins a
lmost all interpretations of palaeomagnetic data, whether for studies of pa
laeomagnetic secular variation, for plate tectonic reconstructions, or for
studies of palaeoclimate(2). Although the GAD hypothesis appears to provide
a good description of the Earth's magnetic field over at least the past 10
0 Myr (ref. 2), it is difficult to test the hypothesis for earlier periods,
and there is some evidence that a more complicated model is required for t
he period before 250 Myr ago(3). Kent and Smethurst(3) suggested that this
additional complexity might be because the inner core would have been small
er at that time. Here I use a numerical geodynamo model and find that reduc
ing the size of the inner core does not significantly change the character
of the magnetic field. I also consider an alternative process that could le
ad to the breakdown of the GAD hypothesis on this timescale, the evolution
of heat-flux variations at the core-mantle boundary, induced by mantle conv
ection. I find that a simple pattern of heat-flux variations at the core-ma
ntle boundary, which is plausible for times before the Mesozoic era, result
s in a strong octupolar contribution to the field, consistent with previous
findings(3).