Frequency Dependent Mantle Viscoelasticity via the Complex Viscosity: Cases From Antarctica

Studies of glacial isostatic adjustment (GIA) often use paleoshorelines and present‐day deformation to constrain the viscosity of the mantle and the thickness of the elastic lithosphere. However, several studies focused on similar locations have resulted in different estimates of these physical properties. We argue that these different estimates infer apparent viscosities and apparent lithospheric elastic thicknesses, dependent on the timescale of deformation. We use recently derived relationships between these frequency dependent apparent quantities and the underlying thermodynamic conditions to produce predictions of viscoelastic properties and lithospheric thickness across a broad spectrum of geophysical timescales for two Antarctic locations (Amundsen Sea Embayment and the Antarctic Peninsula). Our predictions are constrained by input from seismic tomography, require the self‐consistent consideration of elastic, viscous, and transient rheological behavior and also include non‐linear steady state viscosity, which have been determined by several laboratories. We demonstrate that when the full spectrum of viscoelasticity is considered, lithospheric thickness displays a significant range across frequency and that transient creep may play an important role across the timescales relevant for the GIA studies we explore. We suggest that observational studies could move toward a framework of determining the frequency dependence of viscoelastic quantities—rather than single, frequency independent values of viscosity. There remains much work to accomplish this both theoretically and observationally, but the eventual result would provide deeper insight into the rheological behavior of Earth. Plain Language Summary The viscoelastic structure of the solid Earth has important consequences for ice‐melting events, and other processes that involve shifting mass on Earth's surface. As mass moves on Earth's surface, the Earth subsides or rebounds, where the degree and time‐scale of these responses depend on Earth's viscosity. Inferences of Earth's viscosity often consider a single viscosity that does not take into account the time‐scale effects of how slowly or quickly mass is exchanged on Earth's surface (e.g., ice sheet collapse compared with slow melt spanning thousands of years). Using a new theoretical framework and applying it to cases in Antarctica (in particular, the Antarctic Peninsula and Amundsen Sea Embayment), we demonstrate that such time‐scale factors shoul