The asthenosphere delayed response to the periodic oscillations of global surface loads

Until recently the constraints from geodesy on the mantle viscosity come mostly from analyses of postglacial rebound and postseismic relaxation. The viscoelastic relaxation that follows large earthquakes allows us to probe the properties of the Earth's interior only at spotty locations and mostly at depths shallower than 100km. The rebound over Fennoscandia and the Great Lakes offers only a single event to study the phenomenon. Here, we show that modern geodesy can provide a continuous and repeatable measurement of the effect of the asthenosphere and upper mantle to the continental deformation. The time series of GPS data can record a displacement that results from large-scale plate motion combined to co- and postseismic deformation episodes. But additionally, an analysis of GPS time series in California reveals an oscillatory signal at annual and semi-annual frequencies with a spatially coherent direction pointing towards the Pacific Ocean. The amplitude of horizontal displacement is compatible with the elastic response to a distributed load on the nearby ocean floor but time series of GPS and water level exhibit a phase lag of several months. Owing to the large wavelength of the forcing, the continental deformation may be sensitive to the inelastic properties of the Earth's deep interior. The phase delay may be explained by the viscoelastic, delayed, response of the mantle to superficial oscillatory loading. To investigate the effect of a viscoelastic mantle to the response of oscillatory surface loading, I develop a numerical tool to solve the viscoelastic equations under gravity in spherical coordinates. Resolving simultaneously the large-wavelength of the loading and the small distance between the GPS stations requires extensive computations. I implement a fully parallelized multi-grid method that can reconcile these constraints while providing an efficient and accurate numerical solution. I use the Ocean Bottom Pressure, as estimated by the ECCO project, to identify the annual variations of loading at the solid Earth's surface. I compare the solutions of an elastic Earth and a viscoelastic one and show that the viscous properties of mantle rocks give rise to a significant phase delay of the continental deformation. A thorough modeling of the viscoelastic coupling between ocean loading and continental surface displacement may provide strong constraints on the viscoelastic properties of the lower crust and upper mantle and expand our current means to image the Earth's interior.