The effect of the differential rotation of the earth inner core on the free core nutation

Seismic observations shows that the inner core rotates faster than the mantle and the rotation axis of the inner core may not align with the rotation axis of the mantle. Free core nutation reflects core's information. We discuss the effect of the inner core's differential rotation on free core nutation from two aspects: rotation speed and deflection angle. Our result shows it is in accordance with the observations when the inner core's rotation speed doesn't exceed 10∘faster than mantle's per year, and the deflection angle is less than 1∘, if the rotation speed and the deflection angle are respectively considered separately.