Scaling of viscous shear zones with depth-dependent viscosity and power-law stress–strain-rate dependence
Scaling of viscous shear zones with depth-dependent viscosity and power-law stress–strain-rate dependence
复制标题
具有与深度相关的粘度和幂律应力应变率依赖性的粘性剪切区缩放
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
B. Parsons
中科院分区：
文献类型：
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作者：
J. Moore;B. Parsons
关于断层变形的一个悬而未决的问题是断层下深部剪切的局部化程度和原因。对折返剪切带的地质观察表明，尽管运动不再是平面的，但仍可定位于断层下倾伸展附近，但定位程度尚不确定。我们使用简单的解析和数值模型来研究走滑断层下分布剪切的结构形式，以及有可能定位剪切带的物理机制的相对重要性。对于纯深度相关的粘度η=η0 EXP(−z/z 0)，我们fi发现，对于层底部的小z0，剪切带发展为半宽δw∼√z0，其中长度无量纲地由层厚度(D Km)确定。包括非线性应力-应变-速率关系(·(Cid：4)∝σn)，δw的比例为1/√n，与粘性薄板计算中的变形长度比例相当。我们fi发现，剪切带宽度的主要控制因素是粘度对深度的依赖关系，这种依赖关系源于粘度的温度依赖性和温度随深度的增加。由于这种关系是指数关系，标度关系给出了一个尺度近似为T12(K)为层中点温度，R(JmoL−1 K−1)为气体常数，Q(JmoL−1)为活化能，β(K Km−1)为地温梯度的维半宽度。这一关系预测了与大陆流变学一致的参数范围在2-5%以内，剪切带半宽度在2-6公里范围内的数值结果。剪切应力加热的加入仅使δw额外减少5-25%，这取决于剪切带的初始宽度。虽然剪切带的宽度可能不会明显减小，但由于剪应力加热的范围从50fiC到300◦C，局部温度的增加导致断层下的粘度减少了几个数量级，驱动运动所需的应力也随之减少。
SUMMARY 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 = η 0 exp ( − z / z 0 ), we find that a shear zone develops with a half-width δ w ∼ √ 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 (˙ (cid:4) ∝ σ n ) scales δ w by 1 / √ 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 where T 12 (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.