GEO 5/6690 Geodynamics 10 Oct 2014 Last Time: RHEOLOGY Laboratory studies & mineral physics suggest two main types of thermally-activated, stress-driven creep (flow) in “solid” rock: • Diffusion creep can occur as diffusion of exotic atoms or vacancies through a grain or movement of atoms along grain boundaries (“Coble creep”). The relationship of stress to strain rate is linear, viscoelastic, and sensitive to grain size: • Dislocation creep describes movement of dislocations through a lattice, is nonlinear, & dominates unless grain size << 1 mm: Read for Wed 15 Oct: T&S 339-355 © A.R. Lowry 2014

Next Journal Article Reading: For Monday Oct 13: Watts & Burov (2003) Lithospheric strength and its relationship to the elastic and seismogenic layer thicknesses. Earth Planet. Sci. Lett. 213(1-2) 113-131. (Xiaofei will prep discussion materials)

Laboratory studies & mineral physics suggest two dominant “flavors” of non-recoverable strain: (1) Linear viscoelastic creep: “Diffusion” where viscosity Here: R = gas constant T = temperature Ea = activation energy P = pressure Va = activation volume d = grain diameter D0 = frequency factor m = 2 in crystal interiors (rock mat’l prop’s) 3 on crystal boundaries

Laboratory studies & mineral physics suggest two dominant “flavors” of non-recoverable strain: (2) Nonlinear Viscoelastic: “Dislocation creep” where effective viscosity Here: R = gas constant T = temperature P = pressure Ea = activation energy b = dislocation density Va = activation volume n ~ 3 D0 = frequency factor  = shear modulus (rock mat’l prop’s) Edge dislocation Screw dislocation

Laboratory studies of rock strain use roughly the same equations as those derived from first principles in mineral physics, but collapse them to observable constant params depends on: • Lithology (pyroxene > olivine > feldspar > quartz) • Water fugacity fH2O • Temperature T (and to a lesser extent) • Strain rate  • Grain size d • Pressure P . Ideally, we would like to use geophysics to determine each in situ! But it’s not so simple.

Brittle-field (Amonton’s or Byerlee’s law) assumes elastic-plastic constitutive law In Yield Strength Envelopes, we essentially assume a steady-state (i.e., constant strain rate) That assumption is valid for problems in which time- scales are long and stress is ~ constant. Ductile assumes Newtonian or non-Newtonian viscous flow

Moho temperature TMoho from Pn phase: Pn velocity variation Moho temperature from Pn & mineral physics Buehler & Shearer, JGR 2010 Schutt et al., Geology in prep

Wait… What? Temp under ND > NV-UT? Moho temperature from Pn & mineral physics (Partly, but not entirely, because the Moho is deeper in the stable part of the continent…) Schutt et al., Geology in prep

Dry Wet These temperatures are sufficiently high to ensure lower crustal flow for all likely crustal lithologies, wet or dry… Viscosity is very sensitive also to lithology & water! Pyroxene Feldspar Quartz 1019 1022