The Earth's Normal Modes: Wobble/Nutation revisited

A Galerkin method is used to solve the equations describing the dynamics of the Earth's interiors. We solve the momentum and Poisson equations in the solid inner core and the mantle. In the fluid core, however, we solve the 3PD (the Three Potential Description) which describes, without approximation, the linearized dynamics of the rotating, self gravitating, compressible and inviscid fluid bodies via three scalar potentials: the dilatation and the perturbations in pressure and gravitational potential. In the Earth models available the derivatives of the profiles describing the Earth's material properties such as density and Lamé parameters are not well defined. In order to minimize the effects of these derivatives a (non-orthogonal) Clairaut coordinate system is used. We will show that in this coordinate system the boundary conditions are implemented consistent with the approach in solving the equations throughout the Earth model. We will also show that, using a Galerkin method, it is straightforward to test the possibility that the second order terms in the ellipticity may have significant effects on the predicted periods of some of the Earth's wobble and nutation modes.