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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
##### Identifiers
ISI: 000321773500003OAI: oai:DiVA.org:uu-187593DiVA: diva2:575255
Available from: 2012-12-08 Created: 2012-12-08 Last updated: 2017-12-07Bibliographically approved

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Fuchs, Lukas

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Mineralogy Petrology and Tectonics
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Geophysical Journal International
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