T. Van Hoolst, V. Dehant, O. de Viron, S. Ponsar
Royal Observatory of Belgium, Brussels, Belgium
The Earth's core has an influence on the rotation of the planet. For example, an exchange of angular momentum between the core and the mantle is the likely cause of the decadal length-of-day variations. The observed correlation between the length-of-day variations and geomagnetic field variations is very suggestive of this core influence, and many studies have further developed and strengthened this model. The core also influences the nutations of the Earth (periodic motions of the rotation axis of the mantle in inertial space) through resonances with two rotational normal modes: the Free Core Nutation (FCN) and the Free Inner Core Nutation (FICN). These modes describe a relative rotation of the fluid outer core and the solid inner core, respectively, with respect to the mantle. Because their frequencies fall in the main nutation frequency band, the FCN and FICN resonantly enhance several nutations. Through this effect, the FCN and FICN frequencies and damping time scales can be determined. In this study, the paccuracy with which these can be determined from VLBI nutation observations is investigated. We use a resonance formula for the nutation amplitudes, in which the rotational normal mode complex frequencies appear, and deduce upper and lower bounds for these complex frequencies from the uncertainty on the nutation amplitudes. The frequencies and damping times of the FCN and FICN can be linked with several core properties, such as flattenings and electromagnetic coupling constants between inner core, outer core, and mantle, by using analytical theories for the relative rotations of these different regions of the Earth. From the accuracies on the rotational normal mode frequencies, bounds on core properties are then derived, such as the core flattening and the magnetic field at the inner core boundary and core-mantle boundary. For the magnetic field, different harmonic representations are considered.