Normal modes of realistic Earth models: an advanced treatment of elasticity, rotation and fluid core compressibility

Abstract

We apply the Galerkin method to solve the linear momentum description (LMD) of the dynamics of the Earth's layers and expand the Galerkin formulation of the LMD to include the first order ellipticity using the Clairaut coordinate system in order to study the Earth's normal modes. We show that the computed frequencies of the inertial modes may be significantly affected by the elasticity of the mantle and inner core. Traditionally, a liquid core with rigid boundaries is considered to study these modes. Our computed periods of the Chandler wobble (CW) and the free core nutation (FCN) are not affected by the density stratification of the fluid core. The computed period of the FCN, 432.28 sd, is almost identical to the observed value. This indicates that the Earth is indeed in hydrostatic equilibrium which is in contrast to previous work suggested that the Earth deviated from hydrostatic equilibrium. The great advantage of our method is that we can ensure the frequencies are converged.