Benchmarking Horizontal and Vertical Deformation in Material Compressible Finite Element Models of Glacial Isostatic Adjustment of Iceland

Horizontal deformation data are not commonly used as constraints in Glacial Isostatic Adjustment
(GIA) studies. In GIA modelling, horizontal displacements are more sensitive to the elastic structure
of the Earth than vertical displacements. Reliable modeling of horizontal motion can therefore help
constrain further lithospheric elastic properties and allow for more realistic stress calculations, which
can be used in studies of e.g. fault stability and magma migration modulated by GIA induced stresses.
Previous GIA benchmarking studies have shown that, for incompressible models, vertical displace-
ments produced by flat-Earth Finite Element (FE) models compare well with solutions obtained using
the spherical harmonic method, whereas horizontal displacements may be significantly biased. The
more recent study by Reusen et al. (2023), focusing on compressible flat-Earth FE models, showed
good agreement in horizontal displacements between FE model with elastic foundations at each density
contrast and spherical harmonic solutions, with progressively improved agreement for decreasing load
radius. However, vertical displacements for the compressible case were not examined. In this specific
case, compressibility is implemented only partially through the so-called material compressibility, which
accounts for volume changes but neglects density variations.
Modelling present-day GIA in Iceland requires small load radii, low mantle viscosities, and thin
elastic lithospheres—parameter ranges that have not yet been fully benchmarked. Here, we extend the
study of Reusen et al. (2023) by considering glacier loads and Earth structures closer to those of Iceland
at the present day glacial retreat. In addition, we also benchmark the vertical displacement. We use a
flat-Earth, material compressible model with an elastic layer overlying a Maxwellian viscoelastic mantle,
applying spring foundations to every density contrast. Our goal is to identify strategies to obtain reliable
displacement and stress outputs from Icelandic GIA models, while quantifying uncertainties in mantle
viscosity and elastic thickness. Our study highlights the importance of benchmarking small icecaps and
thin lithospheres to be used in studies of small glaciated regions.

References
Reusen et al. (2023). “Simulating horizontal crustal motions of glacial isostatic adjustment using
compressible cartesian models”. In: Geophysical Journal International 235(1), pp. 542–553.