  The geomagnetic field's dipole undergoes polarity reversals in irregular time
intervals. Particularly long periods (of the order of $10^7$yrs) without
reversals, named superchrons, have occurred at least three times in history. We
provide observational evidence for high non-Gaussianity in the vicinity of a
transition to and from a geomagnetic superchron, consisting of a sharp increase
in high-order moments (skewness and kurtosis) of the dipole's distribution.
Such increase in the moments is a universal feature of crisis-induced
intermittency in low-dimensional dynamical systems undergoing global
bifurcations. This suggests temporal variation of the underlying parameters of
the physical system. Through a low dimensional system that models the
geomagnetic reversals we show that the increase in the high-order moments
during transitions to geomagnetic superchrons is caused by the progressive
destruction of global periodic orbits exhibiting both polarities as the system
approaches a merging bifurcation. We argue that the non-gaussianity in this
system is caused by the redistribution of the attractor around local cycles as
global ones are destroyed.
