Gravitational Constraints on the Earth's Inner Core Differential Rotation

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 alpha takes its degree 2, order 2 topography (peak-to-peak amplitude delta h) out of its gravitational alignment with the mantle. This creates a gravity variation of degree 2, order 2 proportional to delta h and to alpha. 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 delta h = 90 m, S2,2 provides upper bounds on alpha of 0.09 degrees, 0.3 degrees, and 0.4 degrees at periods of similar to 4, similar to 6, and similar to 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. The inner core (IC) is the solid part of the core at Earth's center. The IC rotates together with the rest of the Earth, albeit with small fluctuations with respect to the mantle. These small variations are suggested by observations of seismic waves traversing the IC. The angle of change (alpha) of the peak-to-peak topography at the surface of the IC (delta h) creates a change in the gravity field. By analyzing gravity variations recorded by satellites, we find upper limits on the possible values of alpha and delta h. These constraints suggest that the angle of IC reorientation is no more than 0.4 degrees at time periods between 4 and 12 years. Our results provide new constraints on the dynamics of the deepest part of our planet. Satellite gravity observations restrict the range of possible values of the inner core (IC) rotation angle alpha and peak-to-peak topography delta hThe limits on the IC differential rotation rates are 0.16 degrees yr-1, 0.31 degrees yr-1, and 0.21 degrees yr-1 at periods of similar to 4, similar to 6, and similar to 12 years, for delta h = 90 mTighter values for alpha and delta h can be obtained with a more accurate deconvolution of interannual hydrological effects from gravity data