  Field reversals are the most spectacular changes in the geomagnetic field but
remain little understood. Paleomagnetic data primarily constrain the reversal
rate and provide few additional clues. Reversals and excursions are
characterized by a low in dipole moment that can last for some 10kyr. Some
paleomagnetic records also suggest that the field decreases much slower before
an reversals than it recovers afterwards and that the recovery phase may show
an overshoot in field intensity. Here we study the dipole moment variations in
several extremely long dynamo simulation to statistically explored the reversal
and excursion properties. The numerical reversals are characterized by a switch
from a high axial dipole moment state to a low axial dipole moment state. When
analysing the respective transitions we find that decay and growth have very
similar time scales and that there is no overshoot. Other properties are
generally similar to paleomagnetic findings. The dipole moment has to decrease
to about 30% of its mean to allow for reversals. Grand excursions during which
the field intensity drops by a comparable margin are very similar to reversals
and likely have the same internal origin. The simulations suggest that both are
simply triggered by particularly large axial dipole fluctuations while other
field components remain largely unaffected. A model at a particularly large
Ekman number shows a second but little Earth-like type of reversals where the
total field decays and recovers after some time.
