Viscosity of the Earth's inner core: Constraints from nutation observations

The gravitational torque applied on the Earth by the other celestial bodies generates periodic variations in the orientation of the Earth's rotation axis in space which are called nutations. Observations of Earth's nutations allow for insights into the physical properties of the inner core because of the presence of a normal mode, the Free Inner Core Nutation (FICN), which is characterized by a tilt of the inner core figure and rotation axes with respect to the mantle and outer core. The frequency of the FICN is controlled by the strength of the mechanical coupling acting at the inner core boundary (ICB) and by the ability of the inner core to deform under the action of centrifugal and gravitational forces. Attenuation of the FICN reflects energy dissipated by electromagnetic (EM) and viscous friction at the ICB and through viscous relaxation of the inner core. Here, we show that it is possible to explain the observed frequency and damping of the FICN by a combination of EM coupling at the ICB and viscoelastic deformation of the inner core. This imposes a strong constraint on the viscosity of the inner core which has to be in the range ~ 2-7 × 10 ¹⁴ Pa s. We also obtain an estimate of the RMS strength of the radial magnetic field at the ICB, which has to be between 4.5 and 6.7 mT. Interestingly, if a viscoelastic Maxwell rheology is assumed for the inner core, our estimated inner core viscosity is in very good agreement with the shear quality factor inferred from seismic normal modes observations. This suggests that the viscous deformation of the inner core at the nutation (diurnal) time scale and at the seismic normal modes time scale may be due to the same physical mechanisms.