运动学涡度的理论与实践

Theory and practice of kinematic vorticity (W_k).

一般剪切作用下，碎斑或顺剪切作用方向向前或逆向旋转向两特征方向或流脊（非旋转方向）靠拢。高应变条件下，二长比大于一特定值的碎斑，当其顺向或逆向旋转至以特征方向为渐近线的双曲线的稳定翼上时，便稳定下来不再旋转。二长比小于该值的碎斑将不断向前旋转。这一特定值位于该双曲线的顶点，相应的临界形态因子（B＊）或／和两特征方向间夹角的余弦定义为运动学涡度（Wk）。Wk是确定一相关韧性变形带纯剪切和简单剪切组分相对大小的重要度量，是根据内旋转（涡度）与线应变速率之间的比值而定的数值度量。就变形带而言，一般剪切带的运动学涡度变化为0～1，纯剪切为零，简单剪切为1。这是一非线性尺度，纯剪切和简单剪切各占50％的运动学涡度为0．71，而不是0．5。运动学涡度可通过计算、图解（双曲线网（PHD）、刚性颗粒网（RGN）法、Passchier图解、wallis图解）、极摩尔圆法和应力或瞬时增量应变方向获得。运动学涡度与有限应变测量相结合很可能是估算一地地壳减薄/伸展量或增厚/缩短量的最佳途径。变形过程中运动学涡度很可能变化，应根据不同时期形成的构造获得相应时期的运动学涡度。

In the case of a general shearing, the porphyroclasts can either rotate backwards or forwards towards the two eigenvectors or the flow apophyses （non-rotated orientations）. The porphyroclasts with their aspect ratios above a specific value may become stationary at high strain as they rotate forward or backward into the sta- ble limb of the hyperbola that takes one of the two eigenvectors as its asymptotic line. The porphyroclasts whose aspect ratios are less than the specific value are expected to totate forwards indefinitely. The specific value is located at the hinge of the hyperbola, and the related shape factor called the critical shape factor （B＊） or/ and the cosine of the angle between the two eigenvectors is defined as the kinematic vorticity （Wk）, which is important for quantifying the relative contributions of the pure shear and the simple shear in a ductile deformation zone. It is a dimensionless numerical measure, based on the ratio of the internal rotation （vorticity） to the rate of stretching strain. For general shear zones, Wk is measured on a scale between 0 and 1, with 0 being pure shear and 1 being simple shear. The Wk scale is not linear and at the midway between simple and pure shear Wk is 0. 71. The kinematic vorticity （Wk） can be estimated by means of any of the following methods： calculating, plotting （such as the Passchier plot, Wallis plot, the Porphyroclast Hyperbolic Distribution （PHD） method and the rigid grain net （RGN））, polar Mohr constructions and ISA or al-orientation method. The combination of Wk analysis and finite strain measurements probably is the best way to estimate the contraction/thickening or extension/thinning of the crust in the study area. Since Wk is most likely changeable during a tectonic event, the features formed at different stages of a progressive deformation should be separately treated.