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A new numerical method to calculate inhomogeneous and time dependent large deformations of two-dimensional geodynamic flows with application to diapirism
Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Mineralogy Petrology and Tectonics.ORCID iD: B-9710-2014
Goethe-University, Institute of Geoscience, Frankfurt am Main, Germany.
2013 (English)In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 194, no 2, 623-639 p.Article in journal (Refereed) Published
Abstract [en]

A key to understand many geodynamic processes is studying the associated large deformation fields. Finite deformation can be measured in the field by using geological strain markers giving the logarithmic strain f = log 10(R), where R is the ellipticity of the strain ellipse. It has been challenging to accurately quantify finite deformation of geodynamic models for inhomogeneous and time-dependent large deformation cases. We present a new formulation invoking a 2-D marker-in-cell approach. Mathematically, one can describe finite deformation by a coordinate transformation to a Lagrangian reference frame. For a known velocity field the deformation gradient tensor, F, can be calculated by integrating the differential equation DtFij = LikFkj, where L is the velocity gradient tensor and Dt the Lagrangian derivative. The tensor F contains all information about the minor and major semi-half axes and orientation of the strain ellipse and the rotation. To integrate the equation centrally in time and space along a particle's path, we use the numerical 2-D finite difference code FDCON in combination with a marker-in-cell approach. For a sufficiently high marker density we can accurately calculate F for any 2-D inhomogeneous and time-dependent creeping flow at any point for a deformation f up to 4. Comparison between the analytical and numerical solution for the finite deformation within a Poiseuille–Couette flow shows an error of less than 2 per cent for a deformation up to f = 1.7. Moreover, we determine the finite deformation and strain partitioning within Rayleigh–Taylor instabilities (RTIs) of different viscosity and layer thickness ratios. These models provide a finite strain complement to the RTI benchmark of van Keken et al. Large finite deformation of up to f = 4 accumulates in RTIs within the stem and near the compositional boundaries. Distinction between different stages of diapirism shows a strong correlation between a maximum occurring deformation of f = 1, 3 and 4, and the early, intermediate and late stages of diapirism, respectively. Furthermore, we find that the overall strain of a RTI is concentrated in the less viscous regions. Thus, spatial distributions and magnitudes of finite deformation may be used to identify stages and viscosity ratios of natural cases.

Place, publisher, year, edition, pages
2013. Vol. 194, no 2, 623-639 p.
Keyword [en]
Numerical modelling, Diapirism, Finite Deformation, Dynamics of lithosphere and mantle, Diapir and diapirism, convection currents, mantle plumes
National Category
Geosciences, Multidisciplinary
Research subject
Earth Science with specialization in Mineral Chemistry, Petrology and Tectonics
URN: urn:nbn:se:uu:diva-187593DOI: 10.1093/gji/ggt142ISI: 000321773500003OAI: oai:DiVA.org:uu-187593DiVA: diva2:575255
Available from: 2012-12-08 Created: 2012-12-08 Last updated: 2016-01-05Bibliographically approved

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Fuchs, Lukas
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