The figure of the Earth : Gravimetry, stress regime and free oscillations.

The link between the shape of the Earth and stress is studied without any a priori rheological hypothesis. The external gravity potentiel is written harmonic by harmonic at second order as a function of lateral variations of density on the equipotentials and of altitude of interfaces. These lateral variations are linked with stress tensor components thanks to the equilibrium equation. The general expression of the potential as a function of stress is inferred. The importance of second order of this potential is emphasised.

The inversion of geopotential and topography data is carried out up to degree 360 minimising the deviatoric stress, or, more exactly, the difference between nearly-vertical and nearly-horizontal stress. In general, the crustal thickness ---best determined quantity--- is more important bellow reliefs, where the tectonic state is vertical compression. Compilations of `moho' seismic depths confirm our results. This methodology is applied to the Moon up to degree 70. Positive mass anomalies under major bassins are clearly visible down to great depth.

Free oscillations frequencies calculus for a laterally heterogeneous Earth is extended in order to take deviatoric stress into account. Under transverse isotropy assumption the observables are written has functions of lateral variations of elastic coefficients on the equipotentials, of deviatoric stress and altitude of stress surfaces. The corresponding data inversion allows to infer the first even degrees of Earth mechanical parameters lateral variations.

Key-words : Perturbations, spherical harmonics, gravity potential, density, stress, topography, altitude, lateral variations , free oscillations.