Length of day variations due to zonal tides for an inelastic earth in non-hydrostatic equilibrium

We present a refined theoretical model for length-of-day (lod) variations induced by the zonal part of the tide-generating potential. The model is computed from a numerical integration, from the Earth's centre up to the surface, of the equation of motion, the rheological equation of state and Poisson’s equation. The Earth is modelled as a three-layered body, with an inelastic inner core, an inviscid fluid core and an inelastic mantle sustaining convection, which induces deviations from hydrostatic equilibrium. The model also incorporates ocean corrections deduced from dynamic ocean models. It is shown that the non-hydrostatic structure inside the Earth has an effect of less than 0.1 per cent on the transfer functions, while the different modellings of mantle inelasticity (different combinations of possible values for the inelastic parameters) can lead to a wide range of results. Finally, we show that the precision of the geodetic observations of UT1 and the precision of the oceanic and atmospheric corrections are not yet sufficient to obtain information about mantle inelasticity from the comparison between theoretical models and geodetic observations.