This chapter reviews glacial isostatic adjustment (GIA) and post-seismic deformation in Antarctica. It discusses numerical models and their inputs, and observations and inferences that have been made from them. Both processes are controlled by mantle viscosity but their forcings are different. Ongoing GIA induced by the loss of ice since the last glacial maximum (LGM) could have amounted to 5–15 m of global sea-level rise. However, mantle viscosity is so low in parts of West Antarctica (c. 10¹⁸ Pa s) that changes in ice thickness over the last centuries and decades have controlled the current uplift rates there. The uplift due to GIA has promoted ice-sheet stability since the LGM, and in West Antarctica GIA is a significant negative feedback on the current decline of the ice sheet. Post-seismic deformation following the 1998 earthquake near the Balleny Islands south of New Zealand has been detected in global navigation satellite system (GNSS) data and compared to model outputs. The best-fitting viscosity for this area is c. 10¹⁹ Pa s, similar to GIA-based estimates for the Antarctic Peninsula. Future work should focus on unifying descriptions of viscosity across geodynamic models, and integrating information from seismic, gravity, experimental and geological data.

The Barents Sea is situated on a continental margin and was home to a large ice sheet at the Last Glacial Maximum. Studying the solid Earth response to the removal of this ice sheet (glacial isostatic adjustment; GIA) can give insight into the subsurface rheology of this region. However, because the region is currently covered by ocean, uplift measurements from the center of the former ice sheet are not available. The Gravity Recovery and Climate Experiment (GRACE) gravity data have been shown to be able to constrain GIA. Here we analyze GRACE data for the period 2003-2015 in the Barents Sea and use the data to constrain GIA models for the region. We study the effect of uncertainty in non-tidal ocean mass models that are used to correct GRACE data and find that it should be taken into account when studying solid Earth signals in oceanic areas from GRACE. We compare GRACE-derived gravity disturbance rates with GIA model predictions for different ice deglaciation chronologies of the last glacial cycle and find that best-fitting models have an upper mantle viscosity equal or higher than <span classCombining double low line"inline-formula">3×1020</span>&thinsp;<span classCombining double low line"inline-formula">Pa s</span>. Following a similar procedure for Fennoscandia we find that the preferred upper mantle viscosity there is a factor 2 larger than in the Barents Sea for a range of lithospheric thickness values. This factor is shown to be consistent with the ratio of viscosities derived for both regions from global seismic models. The viscosity difference can serve as constraint for geodynamic models of the area.