Dynamic mantle density heterogeneities and global geodetic observables

We investigate the influence of mantle dynamics on low degree deformations of the Earth at geological timescale. We first compute surface deformations, and discuss the analytical form of the tangential surface displacement induced by internal loads, in a reference frame related to the centre of mass of the planet. We use the theoretical Love numbers formalism since the Earth has a viscoelastic behaviour at geological timescale. Then we quantify degree-one and degree-two deformations induced by upwelling domes and subducted plates sinking into the mantle. We use a simple model in which the slabs are modelled as blobs diving vertically through the mantle, and in which the domes are assumed to be stable over the last 120 Ma. Their location is modelled from seismic tomography within the lower mantle. The temporal evolutions of the J(2) gravitational potential coefficient and of the geocentre motion are plotted since 120 Ma. We find that: (1) The mantle density heterogeneities within the mantle can explain the present-day non-hydrostatic flattening of the Earth. However they vary at a too slow timescale to significantly perturb the. J(2) coefficient. (2) Although there is a significant discrepancy of about a few hundred metres between the centre of figure and the centre of mass of the Earth, the secular variation of the geocentre motion is one order of magnitude smaller than the one induced by surface loads.