Degree-one deformations of the Earth

Abstract

The degree one deformations of the Earth, in a reference frame related to the center of mass of the planet, are computed using a theoretical approach (Love numbers formalism) at short time-scale (from the month up to the century), where the Earth has an elastic behavior. The translations at each interface of the layers of the Earth's model (especially at the surface, at the Core-Mantle boundary (CMB) and at the Inner Core boundary (ICB)) are computed when the excitation source is the atmospheric pressure or a magnetic pressure acting at the CMB and at the ICE. The effects of external and internal tangential tractions are also investigated. The total force, resulting from the excitation sources, in a geographic frame (centered at the center of mass) has to be equal to zero, in order to conserve the center of mass of the Earth. This involves a relation between the different forcing mechanisms; we obtain a Consistency Relation, i.e., a special condition that the degree-one valid solutions have to obey (Farrell, 1972). As geophysical application, we have computed the degree-one static deformations induced by atmospheric loading. To end, at secular and geological timescales, where the Earth has a viscoelastic behaviour, we have computed the secular and geological variations of the geocenter induced by postglacial rebound and by mantle density heterogeneities.