Gravitational Constraints on the Earth's Inner Core Differential Rotation

Abstract

The differential axial rotation of the solid inner core (IC) is suggested by seismic observations and expected from core dynamics models. A rotation of the IC by an angle α takes its degree 2, order 2 topography (peak-to-peak amplitude δh) out of its gravitational alignment with the mantle. This creates a gravity variation of degree 2, order 2 proportional to δh and to α. Here, we use gravity observations from Satellite Laser Ranging, the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On to reconstruct the time-variable S2,2 Stokes coefficient. We show that for δh = 90 m, S2,2 provides upper bounds on α of 0.09°, 0.3°, and 0.4° at periods of ∼4, ∼6, and ∼12 years, respectively. These are overestimates, as our reconstructed S2,2 signal likely remains polluted by hydrology, although viscous relaxation of the IC can permit larger amplitudes.