Integration of the Gravitational Motion Equations for An Elliptic Uniformly Rotating Earth With An Inelastic Mantle

We present numerical integration solutions of the deformation equations for an elliptical uniformly rotating Earth with an inelastic Mantle. Inelasticity is introduced in Wahr's model by using complex rheological parameters in the frequency domain. Many choices for their profile inside the Earth are analysed. We conclude that the cut gaussian form of the stress relaxation time distribution of Zschau for the mantle shear modulus profile, combined with any realistic value for the bulk modulus profile and the elastic profile inside the outer core and inner core are the best choice. The corresponding increase of the tidal gravimetric factor is of the order of one or two tenth of a percent. Mantle inelasticity can thus explain a part of the discrepancy between observations and computations.