About gravity rates to vertical velocities ratio induced by ice-sheet changes in Antarctica

The Glacial Isostatic Adjustment (GIA) is the deformation of the Earth in response to changes in the cryosphere. It can produce significant uplift rates up to 1.5 cm/yr in North America. Therefore, it is crucial to remove these signals from space-based gravimetry and altimetry missions to improve our understanding of sea-level changes or to better assess other geophysical processes like ice-mass loss in Antarctica. Specifically, GIA in Antarctica remains poorly constrained due to the lack of in situ observations and the absence of paleo-shorelines dating. To compensate this observational gap, combinations of geodetic and gravimetry observations have been proposed. Wahr et al. (1995, doi:10.1029/94GL02840) introduced the ratio between rates of surface gravity changes and vertical displacements with a value of –0.15 microGal/mm and Sato et al. (2012, doi:10.1029/2011JB008485) theoretically showed that this ratio varies spatially and temporally. In this study, we investigate this ratio more thoroughly. We use the Love number formalism to compute gravity rates and vertical velocities induced by several ice-loading histories for a radially layered spherical Earth using the ALMA and TABOO software packages. We specifically assess the effect of different viscosity profiles and rheological laws such as Maxwell, Andrade, and Burger as a function of spatial wavelength and timing of the glacial history.