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) (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 E a = activation energy P = pressure V a = activation volume d = grain diameter D 0 = 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 E a = activation energy b = dislocation density V a = activation volume n ~ 3 D 0 = 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 f H2O 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.
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. Brittle-field (Amonton’s or Byerlee’s law) assumes elastic-plastic constitutive law Ductile assumes Newtonian or non-Newtonian viscous flow
Buehler & Shearer, JGR 2010Schutt et al., Geology in prep P n velocity variation Moho temperature from P n & mineral physics Moho temperature T Moho from P n phase:
Schutt et al., Geology in prep Moho temperature from P n & mineral physics Wait… What? Temp under ND > NV-UT? (Partly, but not entirely, because the Moho is deeper in the stable part of the continent…)
Pyroxene DryWet Feldspar Quartz 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!