Rheology of the EarthRheology of the Earth

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

Rheology: what is it?Rheology: what is it?

The study of how material flowsThe study of how material flows

ExamplesExamples

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 ……

Empirical fit to Mohr Coulomb Empirical fit to Mohr Coulomb Byerlees lawByerlees law

Strength of the Lithosphere and Mantle

(Kohlstedt et al., 1995) Strength curves for different materials: lithosphere

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’)

Constraints on rheology from Constraints on rheology from geophysicsgeophysics

Post-Glacial Rebound (PGR)Post-Glacial Rebound (PGR)

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

PGRPGRHaskell (1935): 10Haskell (1935): 102121 Pas Pas

Kaufman & Lambeck, PEPI (2000)

GeoidGeoid

From M. Billen

GeoidGeoid

Range+/- 120 meters

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

GeoidGeoid

Layer 1

Layer 2

Sensitive to radial and lateral viscosity structure.

From: M. Billen (MYRES)

““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

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

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

Plate motions & mantle viscosity Plate motions & mantle viscosity structurestructure

Observables: summaryObservables: summaryGeoidGeoid

Plate motionPlate motion

Postglacial reboundPostglacial rebound

Lab experiments, but large extrapolation Lab experiments, but large extrapolation involved.involved.

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