Abstract
Analogue and numerical models show that strong or weak domains in a deforming ductile material cause stress concentrations that may promote strain localization. Such domains commonly occur in the lithosphere through variations in composition or mineral fabric. Here we use a 2D plane-stress, non-Newtonian, viscous model to explore how strain localization develops from an initial isolated weak inclusion. We use a temperature-dependent rheological law for which the material weakens as a result of work done by shear converted to heat. The progress of strain localization follows a power-law growth that is strongly non-linear and may be regarded as an instability. Although this localization mechanism is ultimately limited by thermal diffusion, this parametrization permits a robust criterion for the conditions in which localized shear zones can form within the lithosphere. Shear zones in the lower crust are typically depicted as the downward continuation of faults. We argue that the depth-extent of narrow shear zones within the lithosphere is limited by the stability criteria that we infer from 2D numerical experiments. When applied to the rheological laws for common lithospheric minerals, the combination of temperature and stress-dependence provides a direct means of predicting the depth below which the localization instability does not occur. For an olivine based rheology, the maximum depth at which rapid localization is expected is in the range of ~20 to 60 km, depending on heat flow, strain-rate and water fugacity. We apply our calculations to two major continental strike-slip zones, the San Andreas Fault and North Anatolian Fault, and compare our predicted maximum localization depths with published seismological images. Strain localization in the lower crust requires a dry rheology comparable to plagioclase. Observations that imply localized strain in the uppermost mantle beneath these fault zones are consistent with the localization criteria and the rheological properties of dry olivine.
Highlights
Large scale deformation of the continents is reasonably well explained by simplified models in which the lithosphere behaves as a thin viscous sheet that responds to plate boundary stresses and internal variation of gravitational forces (e.g. England et al, 2016; England and Molnar, 2005)
In considering deformation of the continental lithosphere we have shown that a region with a weak inclusion subjected to simple-shear can develop localized zones of high strain-rate near parallel to the direction of shear
The strain rate in the shear zone follows a power-law growth curve, whose exponent p is dependent on the inclusion strength (Λ), strain exponent (n), initial strain-weakening parameter (Γ0′) and the rate at which it changes (Tref) with temperature, and the distance from the inclusion
Summary
Large scale deformation of the continents is reasonably well explained by simplified models in which the lithosphere behaves as a thin viscous sheet that responds to plate boundary stresses and internal variation of gravitational forces (e.g. England et al, 2016; England and Molnar, 2005). Strain typically localizes near domain boundaries between regions of different effective viscosity (Vauchez et al, 1998; Vauchez et al, 2012) Sustained deformation in this situation can create lithospheric-scale shear zones, such as the Altyn Tagh fault of Central Asia (Dayem et al, 2009) or the Borborema shear zone in Brazil (Tommasi and Vauchez, 1997; Tommasi et al, 1995). We quantify the rate of shear localization by focusing on the strain rate within a sheared region and show that it increases at a rate that is primarily determined by a dimensionless variable dependent on rheological parameters and environmental variables like temperature, pressure and background strain-rate These experiments may be compared with similar experiments reported by Kaus and Podladchikov (2006) who obtained scaling laws for the rate of temperature increase and showed that the weakening mechanism may be suppressed by the effect of diffusive cooling. We compare maximum depths of shear localization inferred from seismic observations with the predictions of this simplified theory, for two major continental strikeslip systems
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