Frequency Dependent Mantle Viscoelasticity via the Complex Viscosity: cases from Antarctica and Western North America

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 lithosphere. However, different studies focused on similar locations have resulted in different estimates of these physical properties even when considering the same model of viscoelastic deformation. We argue that these different estimates infer apparent viscosities and apparent lithospheric 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 mantle viscosity and lithospheric thickness across a broad spectrum of geophysical timescales for three locations (Western North America, Amundsen Sea, and the Antarctic Peninsula). Our predictions require the self-consistent consideration of elastic, viscous, and transient deformation and also include non-linear steady state deformation, which have been determined by several laboratories. We demonstrate that these frequency dependent predictions of apparent lithospheric thickness and viscosity display a significant range and that they align to first order with estimates from GIA studies on different timescales. Looking forward, we suggest that observationally based studies could move towards a framework of determining the frequency trend in apparent quantities – rather than single, frequency independent values of viscosity – to gain deeper insight into the rheological behavior of Earth materials.