Theory of slickenline patterns based on the velocity gradient tensor and microrotation
Theory of slickenline patterns based on the velocity gradient tensor and microrotation
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基于速度梯度张量和微旋转的光滑线图案理论
DOI：
10.1016/0040-1951(91)90360-5
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发表时间：
1991
期刊：
影响因子：
2.9
通讯作者：
S. Hurst
中科院分区：
文献类型：
--
作者：
R. Twiss;G. M. Protzman;S. Hurst
脆性断裂带的特征通常是多个线理剪切面，且方向分布广泛。在我们的模型中，我们假设断层岩石包括一个刚性块体的集合体，其表面是剪切面。我们定义了两个独立的运动尺度，以区分块与其剪切平面的局部刚性旋转（“微动”）与宏观尺度上的材料的平均变形（“宏动”）。宏观运动由宏观速度梯度张量、形变率和宏观自旋张量定义，宏观速度梯度张量分为对称和反对称两部分;微运动由微自旋张量定义。在任何剪切平面上，光滑线形成平行于最大剪切速率的方向，我们假设它是由切向于剪切平面的宏观速度梯度张量的最大分量的方向和剪切中的微自旋分量决定的。飞机对于一个受约束的运动学模型，滑移线取向的模式由D和W的值定义在剪切面取向的均匀分布上，D是变形速率张量的主值之差的比值，W是净自旋与宏观剪切的最大速率的比值。我们区分瞬时光滑线模式和有限变形模式。如果剪切面相对于主变形速率轴旋转，则这两者是不同的，在这种情况下，有限变形滑移线形成弯曲的或交叉的线理。当W = 0时，瞬时滑线花样具有正交对称性（0 <D< 1），或更高对称性（D= 1或0）。当W ≥ 0时，瞬时滑移线花样具有单斜对称性，当剪切为纯剪切时，瞬时滑移线花样具有正交对称性（W= 0，D= 0.5），而对于平面各向异性上的剪切调节的纯剪切，（W =-1，D= 0.5）时，图案为单斜。对于简单剪切，由剪切诱导自旋定义的局部剪切面刚性旋转，（W= 0，D= 0.5），瞬时滑线花样为斜方晶系，而有限变形花样为单斜晶系。对于没有剪切面旋转的简单剪切（W=-1，D= 0.5），瞬时图形是单斜的。我们假设的特殊情况等价于滑移线平行于最大分解剪应力方向的假设（例如Angelier，1979，1984）。在这种情况下预测的滑线图案总是正交或更高的对称性，并相当于我们的瞬时图案，其中W = 0和我们的有限变形图案，其中，此外，没有微自旋。
Brittle fault zones commonly are characterized by a multitude of lineated shear planes having a wide distribution of orientations. In our model, we assume the faulted rock comprises an aggregate of rigid blocks whose surfaces are the shear planes. We define two independent scales of motion to distinguish the local rigid rotation of the blocks with their shear planes (the “micromotion”) from the average deformation of the material on a macroscopic scale (the “macromotion”). The macromotion is defined by the macrovelocity gradient tensor, which is separated into symmetric and antisymmetric parts, the deformation rate and the macrospin tensors respectively; the micromotion is defined by a microspin tensor.On any shear plane, slickenlines form parallel to the direction of the maximum rate of shear, which we assume is determined by the direction of the maximum component of the macrovelocity gradient tensor tangent to the shear plane and by a component of the microspin in the shear plane. For a restricted kinematic model, patterns of slickenline orientations are defined on a uniform distribution of shear plane orientations by the values ofDandW.Dis a ratio of differences in the principal values of the deformation rate tensor, andWis a ratio of the net spin to the maximum rate of macroshear. We distinguish between instantaneous slickenline patterns and finite-deformation patterns. The two are different if the shear planes rotate relative to the principal deformation rate axes, in which case finite-deformation slickenlines form curved or crossing lineations. IfW= 0, the instantaneous slickenline patterns have orthorhombic symmetry (0 <D< 1), or higher symmetry (D= 1or0). IfW≠ 0, the instantaneous slickenline patterns have monoclinic symmetry.For pure shear in an isotropic body, instantaneous slickenline patterns have orthorhombic symmetry (W= 0,D= 0.5) whereas for pure shear accommodated by shear on a planar anisotropy (W = −1,D= 0.5), the pattern is monoclinic.For simple shear with the rigid rotation of local shear planes defined by the shear-induced spin (W= 0,D= 0.5), the instantaneous slickenline pattern is orthorhombic but the finite-deformation pattern is monoclinic. For simple shear with no shear plane rotation (W= −1,D= 0.5), the instantaneous pattern is monoclinic.Special cases of our hypothesis are equivalent to the hypothesis that slickenlines are parallel to the direction of maximum resolved shear stress (e.g. Angelier, 1979, 1984). The slickenline patterns predicted for this case are always of orthorhombic or higher symmetry, and are equivalent to our instantaneous patterns for whichW= 0 and to our finite-deformation patterns for which, in addition, there is no microspin.