Influence of the inner core viscosity on the rotational eigenmodes of the Earth

Abstract

The equations governing the rotation of the Earth, of the fluid outer core and of the inner core are generalized to include electromagnetic torques at the core-mantle and inner core boundary and to take into account the viscous relaxation of the inner core. The four rotational eigenmodes (especially the eigenperiods and their quality factor) are investigated. The free core nutation (FCN) and the Chandler mode are not significantly perturbed by these effects. The torques due to the magnetic field at the core-mantle (CMB) and inner core (ICB) boundaries are frictional torques and depend on the radial component of the magnetic field, respectively, at the CMB and ICB. An increase in the amplitude of the radial magnetic field at the ICB involves an increase of the period of the free inner core nutation (FICN). Using a simple Maxwell model of rheology for the inner core with an effective viscosity ranging from 10 12 up to 10 17 Pa s, we have found that, in the absence of electromagnetic torque, the period of the FICN varies from 75 days (quasi-fluid inner core) up to 485 days (quasi-elastic inner core), and that the inner core wobble disappears for a quasi-fluid rheological behavior of the inner core. The simultaneous influence of both the electromagnetic torques and the inner core viscosity on the FICN is investigated and discussed.