Rheological implications for localization of strain in rock

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Rheological implications for localization of
strain in rock

• Ethan Coon
• (APAM)

Marc Spiegelman (LDEO/APAM)
Peter Kelemen (LDEO)
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Todays talk

• Big Picture viscoelasticity and complex
  rheologies in solid earth dynamics
• Small Picture shear zones in the upper
  mantle/lower crust
• Physics/Equations
• Numerical Results
• Where to next?

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Mid Ocean Ridge (the simple version)
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Shear Zones
(Regenauer-Lieb and Yuen, Earth Science Reviews
2003)
As a mechanism for deep earthquakes? (Whitehead
and Gans, Geophys. J. Roy. Astr. Soc 1974)
(Ogawa, JGR 1987) (Kameyama and Kaneda, Pure and
App. Geophysics 2002)
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(No Transcript)
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Shear Zones
U
U
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The Equations
( enthalpy balance )
( conservation of momentum )
( constitutive relation )
( grain size evolution )
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Creep Processes

• dislocation creep- movement of vacancies and
  defects through lattice

• diffusion creep- diffusion of atoms through
  lattice at areas of high stress

• grain boundary sliding- combination of diffusion
  and dislocation creep at grain boundaries

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Numerics

• Finite differences in space
• Irregularly spaced mesh (to resolve localization
  of strain
• Crank-Nicholson semi-implicit time stepping with
  adaptive time step
• Nonlinear solves go PETSc!

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Temperature feedback for localization
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Grain size feedback localization
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Grain size feedback localization
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Grain size feedback localization
grain boundary sliding
dislocation creep
diffusion creep
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Conclusions and Remarks on Future Work

• Nonlinear rheologies can cause localization of
  strain
• Given a localized region of small grain sizes,
  viscoelasticity can allow
• for quasi-periodic events which approach
  earthquake velocities deeper
• than brittle processes predict. These types
  of regions are observed in
• the upper crust, and may be present in the
  lower crust as well, causing
• deep earthquakes.
• Future models should allow evolution of grain
  size due to grinding and
• strain-equilibrium growth. Also, melting
  rock to form porosity occurs
• at high temperatures, which would feed back
  on viscosities.
• Dealing with complex rheologies may
  fundamentally change the
• dynamics of the system, and should be studied
  in depth for certain
• regions of the earth.

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Thanks to

• Marc Spiegelman, Peter Kelemen, and the
  Lamont/APAM Geodynamics Group
• PETSc people
• NSF IGERT and DOE/Krell CSGF for paying the
  present and future bills.