Limits on differential rotation of the inner core from an analysis of the Earth's free oscillations

Differential rotation of the Earth's inner core has been inferred by severa l seismic 'body-wave' studies(1-6) which indicate that the inner core is ro tating at a rate between 0.2 degrees and 3 degrees per year faster than the Earth's crust and mantle. The wide range in inferred rotation rate is thou ght to be caused by the sensitivity of body-wave studies to local complexit ies in inner-core structure(3,7). Free-oscillation 'splitting functions: on the other hand, are insensitive to local structure and therefore have the potential to estimate differential rotation more accurately. A previous fre e-oscillation study(3), however, was equivocal in its conclusions because o f the relatively poor quality and coverage of the long-period digital data available 20 years ago. Here we use a method for analysing free oscillation s' which is insensitive to earthquake source, location and mechanism to con strain this differential rotation. We find that inner-core differential rot ation is essentially zero over the past 20 years (to within +/-0.2 degrees per year), implying that the inner core is probably gravitationally locked to the Earth's mantle(10).