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Lectures on Rheology of Earth Materials Fundamentals and frontiers in the study of deformation of minerals and rocks (at Tohoku University) Shun-ichiro Karato Yale University Department of Geology & Geophysics New Haven, CT, U.S.A. June 25-27, 2003. Lecture Outline. 1. Why rheology?

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Lectures onRheology of Earth MaterialsFundamentals and frontiers in the study of deformation of minerals and rocks(at Tohoku University)Shun-ichiro KaratoYale UniversityDepartment of Geology & GeophysicsNew Haven, CT, U.S.A.June 25-27, 2003

lecture outline
Lecture Outline

1. Why rheology?

2. General background

defects and plastic deformation


3. Some fundamentals of creep

3-1. Diffusion and diffusion creep

3-2. Dislocations, slip systems, and dislocation


3-3. Deformation mechanism maps

3-4. Effects of phase transformations

3-5. Effects of pressure, water


4. Physical processes controlling the grain size

4-1. Grain-growth

4-2. Dynamic recrystallization

4-3. Nucleation-growth

5. Some applications

5-1. Lithosphere-asthenosphere

5-2. Rheology subducting slabs

5-3. Some unresolved problems

要点 1。スケーリング則







要点 2。
  • レオロジー的性質は温度、水、相転移、結晶粒径などをとおして地球の進化、ダイナミクスと密接に関係している。(密度や弾性的性質などと違う。)
why rheology
Why rheology?
  • Rheology controls mantle convection.
    • Mixing of geochemical reservoirs
  • Rheology has strong influence on the way in which seismic wave propagation is affected by mantle convection.
    • anelasticity, anisotropy

What causes velocity heterogeneity: thermal or chemical origin (or both) ?

Much of the velocity heterogeneity in the upper mantle has chemical origin (ocean vs. continent).

To what extent is the deep mantle chemically heterogeneous?

In regions where there is chemical heterogeneity, what is the cause of heterogeneity (which elements or which minerals)?

Ritsema et al. (1999)


Upper mantle

Transition zone

Trampert and van Heijst (2002)

Pattern of anisotropy is very different between

the upper mantle and the transition zone.

What does it tell us?

what do we want to know
What do we want to know?
  • How does rheology control convection pattern?
    • What is the rheological stratification in Earth?
    • How can we infer flow pattern from seismological observations?
  • How does rheology affect mixing?
    • Where are geochemical reservoirs and how have they survived (or not survived)?
  • Why plate tectonics on Earth and not on Venus?
    • What are the mechanisms of localization of deformation?
  • How have continents survived for billions of years?
    • Is continental lithosphere ”dry” or “wet”?
frontiers in the study of deformation of minerals and rocks
Frontiers in the study of deformationof minerals and rocks
  • Extreme conditions
    • High-pressure (whole Earth dynamics)
    • Large strain (anisotropy, grain-size evolution, strain partitioning)
    • Small strain (seismic tomography-anelasticity

post-glacial rebound)

  • Complexities
    • deformation  chemical reaction(s) [metamorphism, phase transformations, partial melting, hydrogen redistribution---]
    • deformation microstructural evolution

[instability, localization: “plate” formation, deep earthquakes]

some fundamentals of mineral and rock rheology
Some fundamentals of mineral and rock rheology
  • T-P dependence of plastic deformation
  • Stress, grain-size dependence
  • Dependence on chemical environment
  • Effects of phase transformations

Elastic deformation

Plastic deformation: involves atomic jumps

thermally activated processes


T-dependence  time-dependence


Temperature dependence of elastic constant

and viscosity: ductile strength (viscosity) is highly

sensitive to T


Pressure dependence of elastic constant

and viscosity: ductile strength (viscosity) is highly

sensitive to P

basic physics of plastic deformation
Basic physics of plastic deformation
  • Defects and plastic deformation
    • thermo-chemical equilibria
    • law of mass action
    • fugacity
  • Thermally activated processes
    • origin of t-T dependence
    • Boltzmann statistics

Diffusion creep

m=2 for diffusion inside of grains, m=3 for diffusion along the grain-boundary