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.

We present a finite-element model of post-seismic solid Earth deformation built in the software package Abaqus (version 2018). The model is global and spherical, includes self-gravitation and is built for the purpose of calculating post-seismic deformation in the far field (1/4300gkm) of major earthquakes. An earthquake is simulated by prescribing slip on a fault plane in the mesh and the model relaxes under the resulting change in stress. Both linear Maxwell and biviscous (Burgers) rheological models have been implemented and the model can be easily adapted to include different rheological models and lateral variations in Earth structure, a particular advantage over existing models. We benchmark the model against an analytical coseismic solution and an existing open-source post-seismic model code, demonstrating good agreement for all fault geometries tested. Due to the inclusion of self-gravity, the model has the potential for predicting deformation in response to multiple sources of stress change, for example, changing ice thickness in tectonically active regions.

In Antarctica, Global Positioning System (GPS) vertical time series exhibit non-linear signals over a wide range of temporal scales. To explain these non-linearities, a number of hypotheses have been proposed, among them the short-term rapid solid Earth response to contemporaneous ice mass change. Here we use GPS vertical time series to reveal the solid Earth response to variations in surface mass balance (SMB) in the Southern Antarctic Peninsula (SAP). At four locations in the SAP we show that interannual variations of SMB anomalies cause measurable elastic deformation. We use regional climate model SMB products to calculate the induced displacement assuming a perfectly elastic Earth. Our results show a reduction of the misfit when fitting a linear trend to GPS time series corrected for the elastic response to SMB variations. Our results imply that, for a better understanding of the glacial isostatic adjustment signal in Antarctica, SMB variability must be considered.

The Antarctic Ice Sheet is an important indicator of climate change and driver of sea-level rise. Here we combine satellite observations of its changing volume, flow and gravitational attraction with modelling of its surface mass balance to show that it lost 2,720 ± 1,390 billion tonnes of ice between 1992 and 2017, which corresponds to an increase in mean sea level of 7.6 ± 3.9 millimetres (errors are one standard deviation). Over this period, ocean-driven melting has caused rates of ice loss from West Antarctica to increase from 53 ± 29 billion to 159 ± 26 billion tonnes per year; ice-shelf collapse has increased the rate of ice loss from the Antarctic Peninsula from 7 ± 13 billion to 33 ± 16 billion tonnes per year. We find large variations in and among model estimates of surface mass balance and glacial isostatic adjustment for East Antarctica, with its average rate of mass gain over the period 1992-2017 (5 ± 46 billion tonnes per year) being the least certain.

Differences in predictions of Glacial Isostatic Adjustment (GIA) for Antarctica persist due to uncertainties in deglacial history and Earth rheology. The Earth models adopted in many GIA studies are defined by parameters that vary in the radial direction only and represent a global average Earth structure (referred to as 1-D Earth models). Oversimplifying the actual Earth structure leads to bias in model predictions in regions where Earth parameters differ significantly from the global average, such as West Antarctica. We investigate the impact of lateral variations in lithospheric thickness on GIA in Antarctica by carrying out two experiments that use different rheological approaches to define 3-D Earth models that include spatial variations in lithospheric thickness. The first experiment defines an elastic lithosphere with spatial variations in thickness inferred from seismic studies.We compare the results from this 3-D model with results derived from a 1-D Earth model that has a uniform lithospheric thickness defined as the average of the 3-D lithospheric thickness. Irrespective of the deglacial history and sublithospheric mantle viscosity, we find higher gradients of present-day uplift rates (i.e. higher amplitude and shorter wavelength) in West Antarctica when using the 3-D models, due to the thinner-than-1-D-average lithosphere prevalent in this region. The second experiment uses seismically inferred temperature as an input to a power-law rheology, thereby allowing the lithosphere to have a viscosity structure. Modelling the lithosphere with a powerlaw rheology results in a behaviour that is equivalent to a thinner lithospheremodel, and it leads to higher amplitude and shorter wavelength deformation compared with the first experiment. We conclude that neglecting spatial variations in lithospheric thickness in GIA models will result in predictions of peak uplift and subsidence that are biased low in West Antarctica. This has important implications for ice-sheet modelling studies as the steeper gradients of uplift predicted from the more realistic 3-D model may promote stability in marine-grounded regions of West Antarctica. Including lateral variations in lithospheric thickness, at least to the level of considering West and East Antarctica separately, is important for capturing shortwavelength deformation and it has the potential to provide a better fit to Global Positioning System observations as well as an improved GIA correction for the Gravity Recovery and Climate Experiment data.