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Implementation of the glacial rebound pre-stress advection correction in general-purpose finite element analysis software: Springs versus foundations
Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics. (Seismology)
Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
2012 (English)In: Computers & Geosciences, ISSN 0098-3004, E-ISSN 1873-7803, Vol. 40, 97-106 p.Article in journal (Refereed) Published
Abstract [en]

When general-purpose finite element analysis software is used to model glacial isostatic adjustment (GIA), the first-order effect of prestress advection has to be accounted for by the user. We show here that the common use of elastic foundations at boundaries between materials of different densities will produce incorrect displacements, unless the boundary is perpendicular to the direction of gravity. This is due to the foundations always acting perpendicular to the surface to which they are attached, while the body force they represent always acts in the direction of gravity. If prestress advection is instead accounted for by the use of elastic spring elements in the direction of gravity, the representation will be correct. The use of springs adds a computation of the spring constants to the analysis. The spring constant for a particular node is defined by the product of the density contrast at the boundary, the gravitational acceleration, and the area supported by the node. To be consistent with the finite element formulation, the area is evaluated by integration of the nodal shape functions. We outline an algorithm for the calculation and include a Python script that integrates the shape functions over a bilinear quadrilateral element. For linear rectangular and triangular elements, the area supported by each node is equal to the element area divided the number of defining nodes, thereby simplifying the computation. This is, however, not true in the general nonrectangular case, and we demonstrate this with a simple 1-element model. The spring constant calculation is simple and performed in the preprocessing stage of the analysis. The time spent on the calculation is more than compensated for by a shorter analysis time, compared to that for a model with foundations. We illustrate the effects of using springs versus foundations with a simple two-dimensional GIA model of glacial loading, where the Earth model has an inclined boundary between the overlying elastic layer and the lower viscoelastic layer. Our example shows that the error introduced by the use of foundations is large enough to affect an analysis based on high-accuracy geodetic data.

Place, publisher, year, edition, pages
2012. Vol. 40, 97-106 p.
National Category
Geophysics
Research subject
Geophysics with specialization in Solid Earth Physics
Identifiers
URN: urn:nbn:se:uu:diva-159553DOI: 10.1016/j.cageo.2011.07.017ISI: 000301624600009OAI: oai:DiVA.org:uu-159553DiVA: diva2:445553
Available from: 2011-10-04 Created: 2011-10-04 Last updated: 2017-12-08Bibliographically approved
In thesis
1. Glacial Isostatic Adjustment: Inferences on properties and processes in the upper mantle from 3D dynamical modeling
Open this publication in new window or tab >>Glacial Isostatic Adjustment: Inferences on properties and processes in the upper mantle from 3D dynamical modeling
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Observations of glacial isostatic adjustment (GIA) offers a powerful window into the properties of the Earth's interior. Combined with dynamical modeling of the GIA process we can use the observations to infer properties such as the elastic structure of the lithosphere, the rheology of the mantle and changes in the stress conditions in the Earth. This information aids our understanding of the long term evolution of the Earth, e.g. mantle convection, but also illuminates short term processes such as magma generation, earthquakes and shoreline migration. As present day warming trends causes glacier retreat world wide, GIA offers the opportunity to gain local insight into the Earth.

In this thesis I develop an implementation of the pre-stress advection term in finite element modeling. I apply this to current GIA in Iceland, and conclude that local variations in the elastic thickness of the lithosphere can potentially be detected close to the largest ice cap. I study the magnitude of dehydration stiffening in the uppermost Icelandic mantle. The results indicate that the increase in viscosity over the dry solidus is of small magnitude, implying a non-linear rheology in the uppermost mantle beneath Iceland. The present deglaciation in Iceland causes additional melting of the mantle. I find an increased melt production rate of 100-140% at present, although the melt supply rate at the base of the lithosphere is found to be delayed, with estimated present day perturbations ranging from neglible up to 120%.

In the last section of the thesis I focus on the role of ice sheet reconstructions in GIA modeling. I compare three reconstruction of the Weichselian ice sheet and discuss similarities and difference as well as the fit to present day uplift rates in Fennoscandia. The results provide input to improvements in the ice sheet models.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2012. 83 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 906
National Category
Geophysics
Identifiers
urn:nbn:se:uu:diva-169790 (URN)978-91-554-8294-7 (ISBN)
Public defence
2012-04-20, Hamberg, Geocentrum, Villavägen 16, Uppsala, 10:00 (English)
Opponent
Supervisors
Available from: 2012-03-29 Created: 2012-03-06 Last updated: 2012-04-19Bibliographically approved

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Schmidt, PeterLund, BjörnHieronymus, Christoph

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