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\begin{document}

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



\author[1]{Harriet C.P. Lau}%
\author[2]{Jacqueline Austermann}%
\author[3]{Benjamin Kamine Holtzman}%
\author[4]{Cameron Book}%
\author[5]{Christopher Havlin}%
\author[6]{Emily Hopper}%
\author[3]{Andrew J Lloyd}%
\affil[1]{University of California, Berkeley}%
\affil[2]{Columbia University}%
\affil[3]{Lamont-Doherty Earth Observatory, Columbia Univ.}%
\affil[4]{University of California Berkeley}%
\affil[5]{University of Illinois}%
\affil[6]{Lamont-Doherty Earth Observatory of Columbia University}%


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  \date{May 25, 2024}


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\begin{abstract}
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 laboraties. 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.%
\end{abstract}%



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