Accurate GIA models are required for correcting measurements of mass change in Antarctica and for improving our knowledge of the sub-surface, especially in areas of large current ice loss such as the Amundsen Sea Embayment. There, seismic and gravity data suggests lateral differences in viscosity. Furthermore, mantle flow laws allow for time-varying viscosity. In this study we investigate whether spatial and temporal variations in viscosity (4D viscosity) have significant effects on the measured uplift in the region. We use a finite element model with composite rheology consisting of diffusion on and dislocation creep, forced by an ice deglaciation model starting in 1900. We use its uplift predictions as synthetic observations to test the performance of 1D model inversion in the presence of viscosity variations. Introducing time-varying viscosity results in lower viscosity beneath the load and a more localized uplift pattern. We demonstrate that the background stress from earlier ice load changes, can increase and decrease the influence of stress-induced viscosity changes. For the ASE, fitting 1D models to 3D model uplift results in a best fitting model with viscosity that is equal to the average of a large contributing area, while for 4D the local viscosity is more crucial. 1D models are statistically indistinguishable from 3D/4D models with current GPS stations. However, 3D and 4D models should be taken into account when accurate uplift and gravity rate patterns are needed for correcting satellite measurements or predicting relaxation times, as uplift can differ up to 45\% compared to 1D models.

In Southeast Alaska, extreme uplift rates are primarily caused by glacial isostatic adjustment (GIA), as a result of ice thickness changes from the Little Ice Age to the present combined with a low-viscosity asthenosphere. Previous GIA models adopted a 1-D Earth structure. However, the actual Earth structure is likely more complex due to the long history of subduction and tectonism and the transition from a continental to an oceanic plate. Seismic evidence shows a laterally heterogenous Earth structure. In this study a numeral model is constructed for Southeast Alaska, which allows for the inclusion of lateral viscosity variations. The viscosity follows from scaling relationships between seismic velocity anomalies and viscosity variations. We use this scaling relationship to constrain the thermal effect on seismic variations and investigate the importance of lateral viscosity variations. We find that a thermal contribution to seismic anomalies of 10% is required to explain the GIA observations. This implies that non-thermal effects control seismic anomaly variations in the shallow upper mantle. Due to the regional geologic history, it is likely that hydration of the mantle impact both viscosity and seismic velocity. The best-fit model has a background viscosity of 5.0×10^19 Pa-s, and viscosities at ~80 km depth range from 1.8×10^19 to 4.5×10^19 Pa-s. A 1-D averaged version of the 3-D model performed slightly better, however, the two models were statistically equivalent within a 2σ measurement uncertainty. Thus, lateral viscosity variations do not contribute significantly to the uplift rates measured with the current accuracy and distribution of sites.

The long-wavelength negative gravity anomaly over Hudson Bay coincides with the area depressed by the Laurentide ice sheet during the Last Glacial Maximum, suggesting that it is, at least partly, caused by Glacial Isostatic Adjustment (GIA). Additional contributions to the static gravity field stem from dynamic topography and density anomalies in the subsurface. Previous estimates of the contribution of GIA to the gravity anomaly range from 25 percent to more than 80 percent. However, these estimates did not include uncertainties in all components that contribute to the gravity field. In this study, we develop a forward model for the gravity anomaly. We combine density anomalies, isostatic balance, and non-isostatic contributions from GIA and dynamic topography. The largest uncertainty in the predicted gravity anomaly is due to the lower mantle viscosity; uncertainties in the ice history, the crustal model, the lithosphere-asthenosphere boundary and the conversion from seismic velocities to density are found to have a smaller effect. A preference for lower mantle viscosities >10^22 Pa s is found, in which case at least 60 percent of the observed long-wavelength gravity anomaly can be attributed to GIA. This lower bound on the lower mantle viscosity has implications for models employing a viscosity profile in the mantle, such as models for mantle convection and GIA, and inferences based on these models.