1. Rheological implications for localization of strain in rock Ethan Coon (APAM) Marc Spiegelman (LDEO/APAM) Peter Kelemen (LDEO)

2. Today’s 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?

3. Mid Ocean Ridge (the simple version) ? visco-elastic rheology (temperature, grain size, and stress- dependent viscosity) brittle/microcracks/damage fluid flow/porosity

4. (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) Shear Zones

6. U U

7. The Equations: ( enthalpy balance ) ( conservation of momentum ) ( constitutive relation ) ( grain size evolution )

8. 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

9. 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!

10. Temperature feedback for “localization”

11. Grain size feedback localization

13. grain boundary sliding dislocation creep diffusion creep

14. 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. Conclusions and Remarks on Future Work

15. 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.