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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 (>∼300 km) 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.

Glacial Isostatic Adjustment (GIA) has a stabilizing effect on the evolution of the Antarctic Ice Sheet by reducing the grounding line migration that follows ice melt. The timescale and strength of this feedback depend on the spatially varying viscosity of the Earth’s mantle. Most studies assume a relatively high laterally homogenous response time of the bedrock. However, viscosity is spatially variable with a high viscosity beneath East Antarctica, and a low viscosity beneath West Antarctica. For this study, we have developed a new method to couple a 3D GIA model and an ice-sheet model to study the interaction between the Solid Earth and the Antarctic Ice Sheet during the last glacial cycle. The feedback effect into account on a high temporal resolution by using coupling time steps of 500 years. We applied the method using the ice-sheet model ANICE, a 3D GIA FE model, and results from a seismic model to determine the patterns in the viscosity. The results of simulations over the Last Glacial Cycle show that differences in viscosity of an order of magnitude can lead to differences in grounding line position up to 500 km, to differences in ice thickness in the order of 1.5 km. These results underline and quantify the importance of including local GIA feedback effects in ice-sheet models when simulating the Antarctic Ice Sheet evolution over the Last Glacial Cycle.

Changes in ice load over time deform the Earth’s crust and mantle. This effect, Glacial Isostatic Adjustment (GIA), induces vertical deformation of the bedrock of the Antarctic continent and impacts the grounding line position which is critical for the dynamical state of the Antarctic Ice Sheet (AIS). GIA introduces a negative feedback and stabilizes the ice sheet evolution, hence GIA modelling is important for transient studies. Most ice dynamic models use a two-layer flat Earth approach with a laterally homogenous relaxation time or a layered Earth approach with a laterally homogenous viscosity (1D) to compute the bedrock deformation. However, viscosity of the Earth’s interior varies laterally (3D) and radially with several orders of magnitude across the Antarctic continent. Here we present a new coupled 3D GIA – ice dynamic model which can run over hundred thousands of years with a resolution of 500 years. The method is applied using various 1D and 3D rheologies. Results show that the present-day ice volume is 3 % lower when using a 1D viscosity of 1021 Pa·s than using a 3D viscosity. However, local differences in grounding line position maybe up to a hundred kilometres around the Ronne and the Ross Ice Shelfs, and ice thickness differences are up to a kilometre for present day conditions when comparing 1D rheologies and 3D rheologies. The difference between the use of various 3D rheologies is significantly smaller. These results underline and quantify the importance of including local GIA feedback effects in ice dynamic models when simulating the Antarctic Ice Sheet evolution over the Last Glacial Cycle.

Accurate glacial isostatic adjustment (GIA) models are required for correcting measurements of mass change in Antarctica and for improving knowledge of the sub-surface, especially in areas of large current ice loss such as the Amundsen Sea Embayment (ASE). Regionally, seismic and gravity data suggests lateral differences in viscosity (3D). Furthermore, mantle flow laws allow for a stress-dependent effective viscosity which changes over time (3D-s). In this study we investigate whether models with 3D/3D-s have significant effects on the uplift in the region. We use a finite element model with composite rheology consisting of diffusion 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. Stress-dependent rheology 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 both increase or decrease the influence of stress-induced effective viscosity changes. For the ASE, fitting 1D models to 3D model uplift results in a best fitting model with viscosity that represents the average of a large area, while for 3D-s rheology, local viscosity is more influential. 1D models are statistically indistinguishable from 3D/3D-s viscosity with current GPS stations. However, 3D and 3D-s models should be taken into account when accurate uplift and gravity rate patterns are needed, as uplift can differ up to 45% compared to 1D models in between existing GPS stations.

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 t...

The Earth’s surface and interior deform due to a changing load of the Antarctic Ice Sheet (AIS) during the last glacial cycle, called Glacial Isostatic Adjustment (GIA). This deformation changes the surface height of the ice sheet and indirectly the groundling line position. These changes in surface height and grounding line position influence the evolution of the AIS and consequently, again the load on the Earth’s surface. As a result, GIA operates as a negative feedback loop and could stabilize the evolution of the AIS. This feedback maybe particularly relevant for relatively low viscosities of the mantle in West Antarctica which lead to a relatively fast response time of the bedrock due to changes in the West Antarctic Ice Sheet loading. Most studies capture this process by ignoring lateral variations in the viscosity of the mantle and the stabilizing GIA feedback loop. Here we present a new method to couple an ice sheet model to a GIA model at a variable timestep in the order of a thousand years. Several experiments have been done using different radial and lateral varying rheologies for simulations of the last glacial cycle. It is shown that the effect of including lateral variations and accounting for the stabilizing GIA feedback is up to 80 kilometers for the grounding line position and 400 meters for the ice thickness. The largest differences are observed close to the grounding line of the Ronne ice shelf and at several locations in East Antarctica. The total ice volume of the AIS increases by 0.5 percent over 5000 years when including the 3D GIA feedback loops in the coupled model. These results quantify the local importance of including GIA feedback effects in ice dynamic models when simulating the Antarctic Ice Sheet evolution over the full glacial cycle.

We present a finite-element model of postseismic solid Earth deformation built in the software package ABAQUS (version 2018). The model is global and spherical, and includes self-gravitation and is built for the purpose of calculating postseismic deformation in the far-field (> ~ 300 km) 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 postseismic model, 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.

Over glacial-interglacial cycles, the evolution of an ice sheet is influenced by Glacial isostatic adjustment (GIA) via two negative feedback loops. Firstly, vertical bedrock deformation due to a changing ice load alters ice-sheet surface elevation. For example, an increasing ice load leads to a lower bedrock elevation that lowers ice-sheet surface elevation. This will increase surface melting of the ice sheet, following an increase of atmospheric temperature at lower elevations. Secondly, bedrock deformation will change the height of the grounding line of the ice sheet. For example, a lowering bedrock height following ice-sheet advance increases the melt due to ocean water that in turn leads to a retreat of the grounding line and a slow-down of ice-sheet advance. GIA is mainly determined by the viscosity of the interior of the solid Earth which is radially and laterally varying. Underneath the Antarctic ice sheet, there are relatively low viscosities in West Antarctica and higher viscosities in East Antarctica, in turn affecting the response time of the above mentioned feedbacks. However, most ice-dynamical models do not consider the lateral variations of the viscosity in the GIA feedback loops when simulating the evolution of the Antarctic ice sheet. The method developed by Gomez et al. (2018) includes the feedback between GIA and ice-sheet evolution and alternates between simulations of the two models where each simulation covers the full time period. We presents a different method to couple ANICE, a 3-D ice-sheet model, to a 3-D GIA finite element model. In this method the model computations alternates between the ice-sheet and GIA model until convergence of the result occurs at each timestep. We simulate the evolution of the Antarctic ice sheet from 120 000 years ago to the present. The results of the coupled simulation will be discussed and compared to results of the uncoupled ice-sheet model (using an ELRA GIA model) and the method developed by Gomez et al. (2018).

The sea-level load in glacial isostatic adjustment (GIA) is described by the so called sea-level equation (SLE), which represents the mass redistribution between ice sheets and oceans on a deforming earth. Various levels of complexity of SLE have been proposed in the past, ranging from a simple mean global sea level (the so-called eu- static sea level) to the load with a deforming ocean bottom, migrating coastlines and a changing shape of the geoid. Several approaches to solve the SLE have been derived, from purely analytical formulations to fully numerical methods. Despite various teams independently investigating GIA, there has been no systematic intercomparison amongst the solvers through which the methods may be validated. The goal of this paper is to present a series of benchmark experiments designed for testing and comparing numerical implementations of the SLE. Our approach starts with simple load cases even though the benchmark will not result in GIA predictions for a realistic loading scenario. In the longer term we aim for a benchmark with a realistic loading scenario, and also for benchmark solutions with rotational feedback. The current benchmark uses an earth model for which Love numbers have been computed and benchmarked in Spada et al (2011). In spite of the significant differences in the numerical methods employed, the test computations performed so far show a satisfactory agreement between the results provided by the participants. The differences found can often be attributed to the different approximations inherent to the various algorithms.