The attraction of the Moon and the Sun on the Earth induces deformations of the Earth body. At the surface of the Earth, these effects are described using tital parameters which are observed by tidal instruments and estimated using a Earth model. These tidal parameters are indeed computed from a linear combination of the displacement field, the stress field, and the potential due to the mass readjustment associated with the tides. The theoretical tidal parameter values depend crucially on the model used for the interior of the Earth. The system of equations used in the computation contains a stress-strain relationship. This equation is the only one which changes when considering mantle inelasticity instead of elasticity. For an inelastic mantle, the stress-strain relationship is a Hooke law with complex and frequency dependent rheological parameters. The numerical values of these rheological parameters depend on the hypotheses formulated on the Earth body. Even after the introduction of mantle inelasticity in the equations, there are still some differences between the theory and the observations.

By increasing the complexity of the model, scientists want to decrease the difference between the theory and the observations. This comparison brings answers to very important points in geophysics. In particular, the resonances at the free core nutation frequency and at the free inner core nutation frequency in tidal response give the values of these Earth normal mode periods and the comparison between the observed and the computed period constrains the core flattening and the jump in the density at the inner core-outer core boundary, respectively. ¿American Geophysical Union 1991