Impact of the Earth's mantle transient rheology on surface deformation induced by decades of hydrological mass redistribution

Over the past decades, modern geodetic observations have provided crucial constraints on the Earth's rheological properties over a wide range of time scales. Whole mantle steady-state viscosity has been inferred from geodetic observations related to glacial isostatic adjustment. More recently, geodesy has helped probing Earth’s upper mantle transient response to stresses induced by rapid regional changes in hydrology, including recent ice melting, during which viscosity rapidly increases from an elastic to a viscous regime. Here we investigate the potential of using decades of global hydrological mass redistributions, mainly driven by recent ice melting, to constrain the Earth's mantle transient rheology. We quantify the sensitivity of the Earth surface deformation and gravity field to mass redistribution at very large spatial scales to variations in the Earth’s mantle rheology using a spherically layered model and considering Maxwell and Burgers behaviors. Mass redistribution is estimated using low-degree spherical harmonics of the Earth’s gravity field inferred from over 30 years of Satellite Laser Ranging (SLR) observations. We discuss the importance of accounting for the Earth's lower mantle transient rheology at timescales of a few decades and evaluate to what extent it can be constrained by combining long geodetic time series of the Earth’s gravity field and surface deformation.