Scaling of viscous shear zones with depth-dependent viscosity and power-law stress–strain-rate dependence

• Published in: Geophysical journal international 2015-07, Vol.202 (1), p.242-260
• Main Authors: Moore, James D.P., Parsons, Barry
• Format: Article
• Language: English
• ISSN: 0956-540X; 1365-246X
• DOI: 10.1093/gji/ggv143

One of the unresolved questions concerning fault deformation is the degree and cause of localization of shear at depth beneath a fault. Geologic observations of exhumed shear zones indicate that while the motion is no longer planar, it can still be localized near the down-dip extension of the fault; however, the degree of localization is uncertain. We employ simple analytic and numerical models to investigate the structural form of distributed shear beneath a strike-slip fault, and the relative importance of the physical mechanisms that have the potential to localize a shear zone. For a purely depth dependent viscosity, η = η0 exp (−z/z 0), we find that a shear zone develops with a half-width $\delta _w\sim \sqrt{z_0}$ for small z 0 at the base of the layer, where lengths are non-dimensionalized by the layer thickness (d km). Including a non-linear stress–strain-rate relation ( $\dot{\epsilon }\propto \sigma ^n$ ) scales δ w by $1/\sqrt{n}$ , comparable to deformation length scales in thin viscous sheet calculations. We find that the primary control on the shear-zone width is the depth dependence of viscosity that arises from the temperature dependence of viscosity and the increase in temperature with depth. As this relationship is exponential, scaling relations give a dimensional half-width that scales approximately as \begin{equation*} \tilde{\delta }_w\approx T_{\frac{1}{2}}\sqrt{\frac{Rd}{nQ\beta }}\text{ km}, \end{equation*} where $T_{\frac{1}{2}}$ (K) is the temperature at the midpoint of the layer, R (J mol−1 K−1) the gas constant, Q (J mol−1) the activation energy and β (K km−1) the geothermal gradient. This relation predicts the numerical results for the parameter range consistent with continental rheologies to within 2–5 per cent and shear-zone half-widths from 2 to 6 km. The inclusion of shear-stress heating reduces δ w by only an additional 5–25 per cent, depending on the initial width of the shear zone. While the width of the shear zone may not decrease significantly, local temperature increases from shear-stress heating range from 50 to 300 °C resulting in a reduction in viscosities beneath the fault of several orders of magnitude and a concomitant reduction in the stresses needed to drive the motion.