GRAVITY AND SLICHTER MODES OF THE ROTATING EARTH

The exact two-potential description of the dynamics of the liquid oute r core (OC) is solved numerically, using a Galerkin method, for a rota ting spherical earth model (original and modified PREM). Coriolis effe cts are taken fully into account in the OC. Deformation of the inner c ore and mantle, incorporating Coriolis self-coupling, is included via internal load Love numbers. Special attention is given to conditions a t the geocentre in computing Love numbers at the inner core boundary ( ICB). Internal undertone oscillation eigenperiods are computed for PRE M modified to have a uniformly stable OC. For those modes involving no significant degree-1 spheroidal field, the assumption of rigid OC bou ndaries leads to smaller errors than adopting the subseismic approxima tion. Slichter mode eigenperiods are computed for PREM and for PREM mo dified to have a uniformly stable or unstable OC. The stability struct ure of the OC has little effect on Slichter eigenperiods, which are al most inversely proportional to the square root of the ICB density jump for earth models with the OC so modified. The effects of ellipticity and rotational potential on the Slichter eigenperiods are estimated us ing perturbation theory, and the effects of melting/freezing at the IC B during a Slichter oscillation are shown to be negligible.