1. Rheology of the Earth

2. Schedule Rheology Viscous, elastic & plastic Viscous, elastic & plastic Deformation maps and “Christmas tree’s” for mantle & lithosphere Constrains of rheology of the Earth from geology & geophysics

3. Rheology: what is it? The study of how material flows Examples

4. Viscous creep law Experimental data: Viscosity is strongly dependent on pressure temperature, stress (strain-rate), grain size, water, melt, & mineralogy … Viscosity is strongly dependent on pressure temperature, stress (strain-rate), grain size, water, melt, & mineralogy …

5. Empirical fit to Mohr Coulomb Byerlees law

6. Strength of the Lithosphere and Mantle (Kohlstedt et al., 1995) Strength curves for different materials: lithosphere

7. Difference 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’)

8. Constraints on rheology from geophysics

9. Post-Glacial Rebound (PGR)

10. Rate of rebound: sensitive to absolute viscosity. sensitive to absolute viscosity. Depends on: ice-load size/shape, sea-level measurements & unloading history. ice-load size/shape, sea-level measurements & unloading history. lateral variations in elastic plate properties. lateral variations in elastic plate properties. From: http://www.pgc.nrcan.gc.ca/geodyn/ docs/rebound/glacial.html

11. PGR Haskell (1935): 10 21 Pas Kaufman & Lambeck, PEPI (2000)

12. Geoid From M. Billen

13. Geoid Range +/- 120 meters

14. Geoid Observations from seismic studies Long wave length geoid LOWS correlate with seismically FAST regions, ie cold dense regions Long wave length geoid LOWS correlate with seismically FAST regions, ie cold dense regions Long wave length geoid HIGHS correlate with seismically SLOW regions, ie.hot buoyant regions. Long wave length geoid HIGHS correlate with seismically SLOW regions, ie.hot buoyant regions. This is initially counter intuitive

16. Geoid Layer 1 Layer 2 Sensitive to radial and lateral viscosity structure. From: M. Billen (MYRES)

17. “Robust” Constraints on Viscosity Structure Geoid: Very long wavelength structure explained by lower mantle structure. Very long wavelength structure explained by lower mantle structure. Jump or increase in viscosity from upper to lower mantle (+/- factor 30). Jump or increase in viscosity from upper to lower mantle (+/- factor 30). From: Hager & Richards, phil trans 1989, (fig 1, 5a) Observed Predicted

18. Plate motions Purely radial viscosity structure poloidal motion (divergence/ convergence). poloidal motion (divergence/ convergence). 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

19. Plate motions & mantle viscosity structure Becker (2006) Invert for radial viscosity structure Invert for rheolgy Assume free slip boundary at CMB and surface Choose flow laws

20. Plate motions & mantle viscosity structure

21. Observables: summary Geoid Plate motion Postglacial rebound Lab experiments, but large extrapolation involved.

22. Rheology: Viscous, 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 experiments Difficulties of extrapolating Difficulties of extrapolating YSE & consequences of rheology for deformation of the lithosphere Geophysical constraints Geoid, plate motion, PGR Geoid, plate motion, PGR