We consider geomagnetic field reversal sequences from the last 160 Ma, and find the inter-reversal times to be well fit by a lognormal distribution. Such a distribution could arise from 'multiplicative noise' in the underlying geodynamo; and turbulent fluctuations within the core may be expected to provide such noise via the α-effect of dynamo theory. We investigate this mechanism by coupling a low order αω-type dynamo to a shell model of turbulence. This model reproduces field reversals varying in duration from subchrons to superchrons; these are reasonably fit by a lognormal distribution, consistent with the multiplicative noise mechanism proposed.