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Rheology of the EarthRheology of the Earth
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ScheduleScheduleRheologyRheology Viscous, elastic & plasticViscous, elastic & plastic
Deformation maps and “Christmas tree’s” for Deformation maps and “Christmas tree’s” for mantle & lithospheremantle & lithosphere
Constrains of rheology of the Earth from Constrains of rheology of the Earth from geology & geophysics geology & geophysics
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Rheology: what is it?Rheology: what is it?
The study of how material flowsThe study of how material flows
ExamplesExamples
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Viscous creep lawViscous creep law
Experimental data:Experimental data:Viscosity is strongly dependent on Viscosity is strongly dependent on pressurepressure temperaturetemperature, , stress (strain-rate),stress (strain-rate), grain size, grain size, waterwater, , melt, melt, && mineralogymineralogy ……
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Empirical fit to Mohr Coulomb Empirical fit to Mohr Coulomb Byerlees lawByerlees law
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Strength of the Lithosphere and Mantle
(Kohlstedt et al., 1995) Strength curves for different materials: lithosphere
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Difference between compression/extensionDifference between compression/extension
Burov Treatise on Geophysics V. 6 (2007)
-> Difference in come from the dependence of Byerlee’s law on normal stress. Compression results in larger normal stress (‘tectonic loading’)
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Constraints on rheology from Constraints on rheology from geophysicsgeophysics
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Post-Glacial Rebound (PGR)Post-Glacial Rebound (PGR)
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Post-Glacial Rebound (PGR)Post-Glacial Rebound (PGR)Rate of rebound:Rate of rebound: sensitive to sensitive to absolute absolute
viscosityviscosity..
Depends on:Depends on: ice-load size/shape, ice-load size/shape,
sea-level sea-level measurements & measurements & unloading history. unloading history.
lateral variations in lateral variations in elastic plate elastic plate properties.properties.
From:http://www.pgc.nrcan.gc.ca/geodyn/docs/rebound/glacial.html
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PGRPGRHaskell (1935): 10Haskell (1935): 102121 Pas Pas
Kaufman & Lambeck, PEPI (2000)
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GeoidGeoid
From M. Billen
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GeoidGeoid
Range+/- 120 meters
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GeoidGeoidObservations from seismic studiesObservations from seismic studies Long wave length geoid Long wave length geoid LOWSLOWS correlate correlate
with seismically with seismically FAST FAST regions, ie cold regions, ie cold dense regionsdense regions
Long wave length geoid Long wave length geoid HIGHS HIGHS correlate with seismically correlate with seismically SLOW SLOW regions, ie.hot buoyant regions.regions, ie.hot buoyant regions.
This is initially counter intuitiveThis is initially counter intuitive
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GeoidGeoid
Layer 1
Layer 2
Sensitive to radial and lateral viscosity structure.
From: M. Billen (MYRES)
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““Robust” Constraints on Robust” Constraints on Viscosity Structure Viscosity Structure
Geoid:Geoid: Very long Very long
wavelengthwavelength structure structure explained by lower explained by lower mantle structure.mantle structure.
Jump or increaseJump or increase in in viscosity from upper to viscosity from upper to lower mantle (+/- lower mantle (+/- factor 30).factor 30).
From:Hager & Richards, phil trans 1989, (fig 1, 5a)
Observed
Predicted
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Plate motionsPlate motionsPurely radial viscosity structure Purely radial viscosity structure poloidal motion poloidal motion (divergence/ (divergence/
convergence) .convergence) .
How to use in modelling?How to use in modelling? Impose as boundary conditions.Impose as boundary conditions. Predict from model (defined plate regions).Predict from model (defined plate regions).
Predicted
From: Conrad &Lithgow-Bertelloni, Science 2003
Observed
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Plate motions & mantle viscosity Plate motions & mantle viscosity structurestructure
Becker (2006)
Invert for radial viscosity structureInvert for rheolgy
Assume free slip boundary at CMB and surfaceChoose flow laws
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Plate motions & mantle viscosity Plate motions & mantle viscosity structurestructure
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Observables: summaryObservables: summaryGeoidGeoid
Plate motionPlate motion
Postglacial reboundPostglacial rebound
Lab experiments, but large extrapolation Lab experiments, but large extrapolation involved.involved.
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Rheology:Rheology:Viscous, elastic, plastic & combinationsViscous, elastic, plastic & combinations Viscous: diffusion creep & powerlaw creep.Viscous: diffusion creep & powerlaw creep. Plastic: stress-limiting mechanism.Plastic: stress-limiting mechanism. Elastic: recoverable.Elastic: recoverable.
Mostly based on lab experimentsMostly based on lab experiments Difficulties of extrapolatingDifficulties of extrapolating
YSE & consequences of rheology for YSE & consequences of rheology for deformation of the lithospheredeformation of the lithosphere
Geophysical constraintsGeophysical constraints Geoid, plate motion, PGRGeoid, plate motion, PGR