Study of the impact of rheologies on GIA modeling

The Antarctic Ice Sheet (AIS) is the largest ice sheet on Earth that has known important mass changes during the last 26 kyrs. These changes deform the Earth and modify its gravity field, a process known as Glacial Isostatic Adjustment (GIA). GIA is directly influenced by the mechanical properties and internal structure of the Earth and is monitored using Global Navigation Satellite System positioning or gravity measurements. However, GIA in Antarctica remains poorly constrained due to the cumulative effect of past and present ice-mass changes, the unknown history of the past ice-mass change, and the uncertainties of the mechanical properties of the Earth. The viscous deformation due to GIA is usually modeled using a Maxwell rheology. However, other geophysical processes employ the Andrade rheology for tidal deformation or Burgers for post-seismic deformation which could result in a more rapid response of the Earth. We investigate the effect of using these different rheologies to model GIA-induced deformation in Antarctica.
We use the Love number and Green functions formalism to compute the radial surface displacements and the gravity changes induced by the past and present day ice-mass changes. We use the elastic properties and the radial structure of the Preliminary Reference Earth Model (PREM) and the viscosity profile VM5a given by Peltier et al., 2015 and a modified version of it to account for the recent results published regarding the present-day ice-mass changes. Deformations are computed for each rheological laws mentioned above using ICE6g deglaciation model and altimetry data from various satellite missions over the period 2002 to 2017 to represent the past and present changes of the AIS, respectively.
We find that the three rheological laws lead to significant discrepancies in the Earth response. The differences are the largest between Maxwell and Burgers rheologies during the 100 -1000 years following the beginning of the surface-mass change. First using a simple deglaciation model, we find that the deformations rates can be 3 times and 1.5 times greater using the Burgers and Andrade rheologies. However, the ratio between the gravity change rate and the displacement rate are similar for all rheologies (less than 5% difference). Results show that using the Andrade and Burgers rheologies can lead to a 5 and 10m difference in the radial displacement with regards to the Maxwell rheology, on a 200 year period after deglaciation using the ICE6g model. Regarding the response to present changes in Antarctica, the largest discrepancies are obtained in regions with the greatest current melting rates, namely Thwaites and Pine Island Glacier in West Antarctica. Using the Burgers and Andrade rheologies lead to deformations rates respectively 6 times and 2 times greater with respect to Maxwell rheology.