| The tensor strain rate edot in a ductile shear zone is directly related to its width w and the
displacement rate V by edot = V /2w. If the strain-rate is related to stress via a constitutive
relationship, or flow law, then we should be able to predict w as a function of temperature and
depth by w = V /2f(sigma), where sigma is the second invariant of the deviatoric stress
tensor, and f is the rheology. The rheology has the general form f(sigma) = A
exp(-Q/RT) sigmand−m, where Q is the activation energy, Ris the gas constant, T is
temperature, and d is grain-size. The prefactor A is a function of the properties of the
mineral and its grain-boundaries, and may incorporate some dependency on water
content.
If we have constraints on the variation of temperature and stress with depth, in a shear
zone for which the slip rate is likely to have been constant with depth and time, we should be
able to calculate edot, and hence w, as a function of depth. The Whipple Mountains
metamorphic core complex provides an example of this, as the temperature and stress as a
function of depth in the exhumed shear zone are known (Behr & Platt, EPSL, 2011), and the
slip rate is well constrained over a 9 m.y. period. To calculate edot, I used a range of possible
rheologies, including various published flow laws for quartz, and composite flow laws for
granite or granitic gneiss based on several published approaches to the rheology of
quartz-feldspar mixtures spanning the full range of physically viable solutions.
These different rheologies give values for edot spanning many orders of magnitude,
but more importantly, they all predict increasing strain-rate (and hence decreasing
w) with depth and temperature. It is widely accepted that shear zones increase in
width with temperature and depth, so this appears to be an example of a failed
model. Some possible reasons for this, and approaches for the future, are discussed. |