Geodynamical models and seismic observations suggest that the Earth's solid inner core rotates at a different rate than the mantle. However, discrepancies exist in rotation rate estimates based on seismic waves produced by earthquakes. Here we investigate the inherent assumption of a constant rotation rate using earthquake doublets - repeating earthquakes that produce similar waveforms. We detect that the rotation rate of the Earth's inner core with respect to the mantle varies with time. We perform an inverse analysis of 7 doublets observed at the College station, Alaska, as well as 17 previously reported doublets, and reconstruct a history of differential inner-core rotation between 1961 and 2007. We find that the observed doublets are consistent with a model of an inner core with an average differential rotation rate of 0.25-0.48° yr~(-1) and decadal fluctuations of the order of 1° yr~(-1) around the mean. The decadal fluctuations explain discrepancies between previous core rotation models and are in concordance with recent geodynamical simulations.
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