Analytical approach to the computation of the Earth, the outer core and the inner core rotational motions

Abstract

We have investigated the rotational motions of a simple Earth model composed of three homogeneous layers: an elastic inner core, a liquid outer core and an elastic mantle. Taking into account the various pressure and gravitational torques appearing between the different parts of the model as well as the elasto-gravitational deformations with the help of a Love number approach, we propose a fully developed set of equations for the conservation of angular momentum. The homogeneous system relative to the free case yields four normal modes: besides the classical Chandler Wobble and Free Core Nutation, two new eigenmodes appear: the Inner Core Wobble and the Free Inner Core Nutation. The simplicity of our model allows us to find analytical expressions for these rotational modes and to show the relative importance of the various coupling mechanisms which are involved. We also compare our values to numerical values proposed by two recent studies. The rotational response is then computed as a function of two different forcing mechanisms: one derived from an external potential like the tidal gravitational potential of nearly diurnal frequency, and another associated with a surface pressure like the pressure induced by atmospheric or oceanic loading.