Shallow upper mantle rheology and secular ice sheets fluctuations

On time scales from decades to centuries, continental cryospheric forcing in response to climate change constitutes a major source of isostatic disequilibrium that may influence future regional sea level variations. Current vertical displacements and gravity field variations are often estimated neglecting rheological effects and thus assuming a fully elastic response of the Earth. In this study, we adopt a more general point of view, aiming at describing ongoing surface movements resulting from recent glacial instabilities, also taking into account the effects associated with shallow upper mantle and crustal rheologies. Our computations are based on the Post–Widder Laplace inversion formula, which permits the straightforward computation of load-deformation coefficients for steady state and transient rheologies up to very high harmonic degrees. Using a surface load with a simple geometry and time history, we compare the classical elastic solutions to those obtained considering the rheological response of the shallow upper mantle. While at the center of the ice sheet rheology only magnifies the elastic response, the pattern and time history of vertical displacement at the ice sheet margins show a greater complexity, mainly due to the development of lateral forebulges whose shape and amplitude are particularly sensitive to the rheology of the shallow upper mantle. In this region, assuming an elastic rheology is generally appropriate on a century time scale, but significant deviations from a purely elastic response (both sign and amplitude) are observed at longer time scales or when a low viscosity zone with Maxwell rheology is taken into account.