运动学涡度、极摩尔圆及其在一般剪切带定量分析中的应用

自然界中剪切带通常是由平行于剪切带方向的简单剪切和与之垂直的纯剪切共同作用的结果。利用运动学涡度(W_K)可以定量地分析两者间的比值大小。一般摩尔圆只能应用于共轴应变,而极摩尔圆可应用于共轴与非共轴变形,并为求取W_K提供了一种简便可行的方法。本文对一般剪切带的概念及其分类进行了描述,对运动学涡度和极摩尔国的原理及其应用进行了系统的论述,并在此基础上提出了几种新的实用的极摩尔国编制方法。      

运动学涡度在藏南冈底斯岩浆带中段谢通门-曲水韧性剪切带中的应用

一般剪切带主要由纯剪切和简单剪切共同作用,不同的剪切带及不同的构造位置两者所占有的比例不同。利用运动学涡度(Wk)可以定量地分析两者间的比值大小。本文通过极莫尔圆法和有限应变轴率Rs/石英c轴组构法对冈底斯岩浆带中段谢通门-曲水滑覆型韧性剪切带的运动学涡度进行了计算,两种方法获得了较为一致的结果。通过极莫尔圆法,对剪切带中的9组糜棱岩样品进行了运动学涡度计算,获得了Wk=0.73~0.96,平均值Wk=0.83。运用有限应变轴率Rs/石英c轴组构法对4个样品进行了分析,得到Wk=0.85~0.93,均值为0.88,两种方法获得了较为一致的应变结果。还根据极莫尔圆图解,计算了该韧性剪切带的减薄量S=0.09~0.35,平均减薄量为0.20。研究表明该韧性剪切带为典型的以简单剪切为主伴有部分纯剪切的一般剪切,该剪切带的形成可能与拉萨地体在中新世时从挤压到侧向伸展的转换有关。该剪切带变形特征和运动学涡度的确定深化了对藏南冈底斯地区的构造演化过程的理解,并对青藏高原中南部的地质研究具有推进作用。     

运动学涡度的理论与实践

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。     

运动学涡度和极摩尔圆的基本原理与应用

运动学涡度是岩石递进变形中非同性的一种量度，利用其对韧性剪切带进行应变分解，确定剪切作用类型是当今构造地质学研究的较新课题。极摩尔圆同时适用共轴和非共为形，是应变分析的一种有利工具，并特别适用于从应变测量数据求取运动学涡度；从力学理论角度对运动学涡度进行了系统而简明的论述，地极摩尔圆的原理进行了推导，提出了它们在韧性剪切带应变分析中的应用。     

运动学涡度及其在湘东雁林寺韧性剪切带中的应用

自然界中的剪切带通常是由简单剪切(simple shear)和纯剪切(pure shear)叠加的一般剪切带(general shear)。运动学涡度(kinematic vorticity)的引入提供了一个定量表示两种剪切成分的工具。通过测量剪切带的运动学涡度,可以清楚的了解一般剪切带中究竟是简单剪切还是纯剪切占优势。本文将运动学涡度的基本理论和极摩尔圆法对雁林寺金矿所在的湘东雁林寺韧性剪切带中所表现的运动学涡度进行测量,得出该韧性剪切带的Wk值为0.6,指示其变形以纯剪切为主,且简单剪切作用应变速率比纯剪切作用的应变速率慢。本文从微观运动学层面揭示了湘东雁林寺韧性剪切带对于雁林寺金矿的形成具有重要的意义。     

华北克拉通北缘医巫闾山韧性剪切拆离带的运动学涡度与韧性减薄量

医巫闾山韧性剪切拆离带位于华北克拉通北缘,为一走向NE、倾向WNW的低角度正断层系,由下盘的韧性剪切带(糜棱岩带)、未变形中生代的花岗岩体;脆性拆离断层面及上盘未变质的沉积岩系组成。以拆离断层带下盘韧性剪切带内糜棱岩长石碎斑为标志体的三维有限应变测量显示,应变主轴X轴伸长,Y轴不变,Z轴缩短。以极莫尔圆法估算拆离带内糜棱岩的运动学涡度值介于0.61到0.96,平均为0.80(涡度值是无量纲数),表明医巫闾山韧性剪切拆离带形成机制为以简单剪切为主的一般剪切作用。结合三维有限应变测量,医巫闾山韧性剪切拆离带为一加长减薄型剪切带。以有限应变测量与运动学涡度估算为基础,初步估算了该韧性剪切拆离带的韧性减薄量沿剪切拆离方向,减薄量从10%增加到40%,且减薄量与应变强度正相关、与运动学涡度负相关。     

鲁西青邑韧性剪切带运动学涡度及剪切作用类型

青邑韧性剪切带是晚太古代末期发育在鲁西前寒武纪基底花岗岩中一条规模较大的韧性剪切带。剪切带NW走向,面理直立,线理水平,剪切标志反映右行剪切。石英光轴法求得运动学涡度在0．96～0．99之间变化,极摩尔圆法求得糜棱岩化岩石运动学涡度为0．91,初糜棱岩运动学涡度为0．87,糜棱岩运动学涡度为0．81,超糜棱岩运动学涡度为0．60。运动学涡度表明,剪切带剪切作用类型为一般剪切,变形初期以单剪为主,随应变的增大,运动学涡度值逐渐减小,变形的纯剪分量不断增加,最后以纯剪为主。剪切作用类型及三维参照变形分析表明,青邑韧性剪切带属加长一变宽类型的一般剪切带并且在Y轴方向上有所增长。韧性剪切在太古代末期克拉通化过程中具有加厚陆壳的作用。     

韧性剪切带的剪切作用类型和韧性减薄量

韧性剪切带组构的演化和剪切作用类型受到许多研究者的关注。运用极莫尔圆法、有限应变法、刚性颗粒法、石英光轴组构结合有限应变测量法、拖尾形态法、剪切带内变形脉体(岩墙)法、碎斑法等方法可以估算剪切带变形过程中的运动学涡度,进而判别剪切带中单剪切组分与纯剪切组分的相对含量。自然界的剪切带一般介于单剪与纯剪之间,运动学涡度Wk介于0~1之间,表明韧性剪切带在变形过程中发生了垂直于剪切带边界(Z轴)方向的韧性减薄。剪切带变形过程中的韧性减薄量可依据有限应变测量与运动学涡度估算求得,也可依据剪切带内的石香肠(布丁)构造求解,还可依据构建极莫尔圆求解。以华北克拉通北缘的楼子店变质核杂岩及其韧性剪切带,以及希腊西奈山的Chelmos剪切带为例,介绍估算韧性剪切带韧性减薄的方法,这种韧性减薄是对大规模岩石圈减薄的有益补充和完善。研究结果表明,定量估算与变质核杂岩相关的韧性剪切带的剪切作用类型是分析变质核杂岩形成机制的有效途径和方法。     

结构面力学性质的定量鉴定

变形带力学性质的鉴定是地质力学研究中的先行基础步骤.近来出现一些新的概念和方法,可用以定量表征变形带的力学性质.天然变形带通常是一般剪切作用的产物,是纯剪切(共轴缩短或伸展)和简单剪切的组合.为了定量说明两者间的相对贡献,提出了运动学涡度(W_k)这一物理量,并简单地定义为cos υ.υ是主变形面内两特征方向间的夹角.纯剪切的υ=90°,W_k=0;简单剪切的υ=0°,W_k=1.一般剪切的υ介于0°和90°之间,W_k为0到1.运动学涡度符号的正负分别代表变形带的减薄和增厚.υ可通过极摩尔圆法求出.主压应力(σ₁)方向与W_k的关系为W_k=sin2ξ.ξ是σ₁与变形带法线间的夹角.因此,可用以确定变形带的W_k和力学性质.根据最大有效力矩准则,韧性变形带与主压应力(σ₁)方向间的夹角为55°,可用以确定古应力轴的方向,并可能确定变形时差应力的大小.      

亚干变质核杂岩的运动学涡度与剪切作用类型

运用极摩尔圆法、张量分析法和应力取向分析法对内蒙亚干变质核杂岩的剪切作用类型进行了定量分析。相关韧性剪切带的运动学涡度值为 0.53-0.87, 表明相关的剪切作用为减薄型一般剪切。其间的差异,表明主期以简单剪切为主,递进变形过程中, 纯剪切组分增加, 这很可能与因晚期脆性断层引起的位移分解作用有关。同向伸展褶劈理的取向与剪切带边界的夹角既不等于两流脊间的夹角,也不等于其值之半,但可据以确定主应力方向,从而确定两流脊间的夹角和对应的运动学涡度     

Kinematic,finite strain and vorticity analysis of the Sisters Shear Zone,Stewart Island,New Zealand

The Sisters Shear Zone (SSZ) on Stewart Island, New Zealand, is a greenschist-facies extensional shear zone active prior to and possibly during the development of the Pacific–Antarctica spreading ridge at ∼76 Ma. We report quantitative kinematic and rotation data as well as apatite fission-track (AFT) ages from the SSZ. Early kinematic indicators associated with the NNE-trending stretching lineation formed under upper greenschist-facies metamorphism and show alternating top-to-the-NNW and top-to-the-SSE senses of shear. During progressive exhumation lowermost greenschist-facies and brittle-ductile kinematic indicators depict a more uniform top-to-the-SSE sense of shear in the topmost SSZ just below the detachment plane. Deformed metagranites in the SSZ allow the reconstruction of deformation and flow parameters. The mean kinematic vorticity number (W_m) ranges from 0.10 to 0.89; smaller numbers prevail in the deeper parts of the shear zone with a higher degree of simple shear deformation in the upper parts of the shear zone (deeper and upper parts relate to present geometry). High finite strain intensity correlates with low W_m and high W_m numbers near the detachment correlate with relatively weak strain intensity. Finite strain shows oblate geometries. Overall, our data indicate vertical and possibly temporal variations in deformation of the SSZ. Most AFT ages cluster around 85–75 Ma. We interpret the AFT ages to reflect the final stages of continental break-up just before and possibly during the initiation of sea-floor spreading between New Zealand and Antarctica.     

Strain, Kinematic Vorticity and Ductile Thinning along the Detachment Zone of the Yunmeng Shan Metamorphic Core Complex, Beijing, China

The Yunmeng Shan metamorphic core complex (MCC) is composed of the lower plate, the upper plate and the detachment zone. The detachment zone consists of ductile shear zone (mylonite zone), chloritized microbreccias zone and the brittle fault plane. The ductile shear zone contains mylonitic rocks, protomylonites, and mylonites. Finite strain measurements of feldspar porphyroclasts from those rocks using the Rf/φ method show that the strain intensities increase from mylonitic rocks (Es=0.66–0.72) to protomylonites (Es=0.66–0.83), and to mylonites (Es=0.71–1.2). The strain type is close to flatten strain. Kinematic vorticity estimated by Polar Mohr diagrams suggest that foliations and lineation of mylonite (0.47相似文献   

The influence of matrix rheology and vorticity on fabric development of populations of rigid objects during plane strain deformation

The influence of vorticity and rheology of matrix material on the development of shape-preferred orientation (SPO) of populations of rigid objects was experimentally studied. Experiments in plane strain monoclinic flow were performed to model the fabric development of two populations of rectangular rigid objects with object aspect ratios (R_ob) 2 and 3. The density of the rigid object populations was 14% of the total area. Objects were dispersed in a Newtonian and a non-Newtonian, power law matrix material with a power law exponent n of 1.2. The kinematic vorticity number (W_n) of the plane strain monoclinic flow was 1, 0.8 and 0.6 with finite simple shear strain of 4.6, 3.0 and 0.9, respectively. In experiments with R_ob=3, the SPO is strongly influenced by W_n and the material properties of the matrix. Deformation of a power law matrix material and low W_n resulted in a stronger SPO than deformation of a linear viscous matrix and high W_n. Strain localization coupled with particle interaction plays a significant role in the development of a shape-preferred orientation. High strain simple shear zones separate trains of rigid objects that are surrounded by low strain zones with W_n lower than the bulk W_n. In fabrics involving populations of objects with R_ob=2, rheology of the matrix materials does not systematically influence the intensity of the SPO.     

南极普通球粒陨石风化等级的重新厘定

在南极格罗夫山普通球粒陨石的风化等级划分中出现了和Wlotzka(1993)标准矛盾的现象。部分普通球粒陨石的金属和陨硫铁氧化不足20%,然而硅酸盐却发生了蚀变。如果考虑金属的氧化量,这种风化程度应为W1,如果考虑硅酸盐的蚀变,这种风化程度应为W5。对于存在如此大的差异本文给出了折衷的解决办法——对金属和硅酸盐同时进行风化等级划分。金属的风化等级划分为W_m0-W_m4五个,硅酸盐风化等级划分为W_s0-W_s3四个。依据新方案,GRV 021588、021636、021772和021957等4块无法用Wlotzka(1993)标准来确定风化等级的陨石的风化等级均为W_m1-W_s1。而陨石GRV 023312的风化等级为W_m3-W_s0,其相当于Wlotzka(1993)标准中的W3。     

A general deformation matrix for three-dimensions

A deformation that is obtained by any simultaneous combination of two steady-state progressive deformations: simple shearing and a coaxial progressive deformation, involving or not a volume change, can be expressed by a single transformation, or deformation matrix. In the general situation of simple shearing in a direction non-orthogonal with the principal strains of the coaxial progressive deformation, this deformation matrix is a function of the strain components and the orientation of shearing. In this example, two coordinate systems are defined: one for the coaxial progressive deformation (x_i system), where the principal and intermediate strains are two horizontal coordinate axes, and another for the simple shear (x _i ^t’ system), with any orientation in space. For steady-state progressive deformations, from the direction cosines matrix that defines the orientation of shear strains in the x_i coordinate system, an asymmetric finite-deformation matrix is derived. From this deformation matrix, the orientation and ellipticity of the strain ellipse, or the strain ellipsoid for three-dimensional deformations, can be determined. This deformation matrix also can be described as a combination of a rigid-body rotation and a stretching represented by a general coaxial progressive deformation. The kinematic vorticity number (W _k is derived for the general deformation matrix to characterize the non-coaxiality of the three-dimensional deformation. An application of the deformation matrix concept is given as an example, analyzing the changes in orientation and stretching that variously-oriented passive linear markers undergo after a general two-dimensional deformation. The influence of the kinematic vorticity number, the simple and pure shear strains, and the obliquity between the two deformation components, on the linear marker distribution after deformation is discussed.     

Volume strain, strain type and flow path in a narrow shear zone

This study explores the state of finite strain and changes in the mean kinematic vorticity number, grain size, whole-rock chemistry and mineralogy across an upper amphibolite-facies shear zone in a metadiorite, northern Malawi, east-central Africa. P–T conditions during shear-zone formation and deformation were approximately 700–750^?°C and 5–7?kbar and are slightly less than P–T conditions for the regional peak of metamorphism. The major rock-forming minerals, plagioclase, hornblende, biotite, and quartz, were deformed by crystal-plastic processes accompanied by, except for hornblende, dynamic recrystallization. The modal abundance of all four major rock-forming minerals shows no systematic change from the country rock into and across the shear zone, indicating that shear-zone development was not associated with retrograde mineral reactions. The grain size of the major rock-forming minerals decreases within the shear zone. Plagioclase and hornblende, which occur as porphyroblasts outside the shear zone, exhibit a bimodal grain-size distribution within the shear zone. Quartz has a unimodal grain-size distribution in the shear zone. Major and trace element chemistry does not change systematically across the shear zone, implying no volume change in the mylonite. Matrix strain data for plagioclase and hornblende by the Fry method and fabric strain as deduced from R_f/φ analysis of plagioclase and quartz grains demonstrate a slightly constrictional strain type (K≈1.5) across the shear zone. The quantitative finite-strain data for the different residual minerals as obtained by unlike methods show no systematic variation, but recrystallized plagioclase grains record higher strain than the residual grains. The mean kinematic vorticity number changes from approximately 0.3 outside to approximately 0.8 within the shear zone, indicating that the bulk deformation path deviated from progressive simple shear. The estimates for finite strain and the degree of noncoaxiality account for approximately 50% of thinning normal to the shear zone.     

Soil CO2 efflux along an elevation gradient in Qinghai spruce forests in the upper reaches of the Heihe River,northwest China

This study was conducted in six plots along an elevation gradient in the Qinghai spruce (Picea crassifolia Kom.) forest ecosystem of the Qilian Mountains, northwest China. Soil CO₂ efflux over bare soil (R _s) and moss covered soil (R _s+m) were investigated from June to September in 2010 and 2011 by means of an automated soil CO₂ flux system (LI-8100). The results showed that R _s ranged from 1.51 to 3.96 (mean 2.64 ± 0.72) μmol m^?2 s^?1 for 2010, and from 1.41 to 4.09 (mean 2.55 ± 0.70) μmol m^?2 s^?1 for 2011. The daily change trend of R _s resembled that of air temperature (T _a), and there was a hysteresis between R _s and soil temperature (T _s). The seasonal variations of R _s at lowlands (i.e., Plot 1, Plot 2 and Plot 3) were driven by soil moisture and temperature (T _a and T _s), while that at highlands (i.e., Plot 4, Plot 5 and Plot 6) were obviously affected by temperature. There were higher values at Plot 2 and Plot 6, which were caused by the interaction between soil moisture and temperature. In addition, soil CO₂ efflux over moss covered soil (R _s+m) was 8.83 % less than that over bare soil (R _s), indicating that moss was another factor affecting R _s. It was concluded that R _s had temporal and spatial variations and was mainly controlled by temperature and soil moisture; the main determinants differed at different elevations; moss could reduce R _s.     

Usage of strain and vorticity analyses to interpret large‐scale fold mechanisms along the Sanandaj–Sirjan HP‐LT metamorphic belt,SW Iran

3D finite strain analyses and kinematic vorticity measurements were carried out on the Loghon Anticline within the HP‐LT Sanandaj–Sirjan metamorphic belt (Neyriz area, SW Iran). Rƒ/φ and Fry methods were used on the strain markers (e.g. deformed fossils) to interpret geometric relationships between the fold axis, strain ellipsoid axes and shear zone boundaries. The results indicate the predominance of prolate strain in the anticline. Quantitative kinematic analyses show that the W_k parameter is 0. 67 ± 0. 06 (i.e. pure‐shear dominated non‐coaxial flow). This study quantitatively supports the establishment of a dextral transpressive system, which is responsible for the development of the large‐scale right‐lateral shear zones that strike sub‐parallel to the major folds. Flexural shear combined with regional dextral‐shear is suggested to be the most common mechanism of folding in this area. Copyright © 2011 John Wiley & Sons, Ltd.     

Using the Maximum Effective Moment Criterion to Interpret Quartz <c>‐Fabric Patterns

The Maximum Effective Moment (MEM) criterion predicts that the initial orientation of ductile shear zones and shear bands is ~55° relative to the maximum principal stress axis (σ1) and that the kinematic vorticity number (Wk) is ~0.94. These preferred orientations should be reflected in the pattern of quartz -fabrics in shear zones and shear bands. Common quartz -fabrics in plane strain can be divided into low-temperature (L) and high-temperature (H) fabrics, with each group showing three patterns. A steady flow with a constant value of Wk≈0.94 gives rise to L-1 and H-1 patterns, which are commonly characterized by a single axis girdle normal to the shear zone and a single -point maximum parallel to the shear zone.Once the conjugate set develops, L-1 and H-1 have opening angles of ~70° and ~110°, respectively. L-2 and H-2 are asymmetric patterns associated with variable deformation partitioning and vorticity values of 0< Wk<0.94. In contrast, L-3 and H-3 are symmetric patterns associated with 100% deformation partitioning and Wk=0. The opening angle in quartz -fabrics is implicitly linked to the temperature during deformation. The opening angle is ~70° at low temperature and ~110° at high temperature. However, a linear correction between the opening angle and the temperature cannot be established. During deformation partitioning, synthetic shear bands form earlier than antithetic bands and are more easily developed. This may result in opening angles of <70° for low-temperature fabrics and of >110° for high-temperature fabrics. The following criteria can be used to recognize reworked shear zones that have experienced multiple orogenic phases and changes in the stress state: 1) the initial Wk is larger or smaller than ~0.94; 2) the change in Wk is abrupt, rather than progressive; 3) inconsistent shear senses are inferred for the different phases of deformation; and 4) a negative value of Wk is found in reworked shear zones.     

Structures,kinematic analysis,rheological parameters and temperature-pressure estimate of the Mesozoic Xingcheng-Taili ductile shear zone in the North China Craton

The NE to ENE trending Mesozoic Xingcheng-Taili ductile shear zone of the northeastern North China Craton was shaped by three phases of deformation. Deformation phase D₁ is characterized by a steep, generally E–W striking gneissosity. It was then overprinted by deformation phase D₂ with NE-sinistral shear with K-feldspar porphyroclasts forming a subhorizontal low-angle stretching lineation on a steep foliation. During deformation phase D₃, lateral motion accommodated by ENE sinistral strike-slip shear zones dominated. Associated fabrics developed at upper greenschist metamorphic facies conditions and show the deformation characteristics of middle- to shallow crustal levels. In some parts, the older structures have been in turn overprinted by late-stage sinistral D₃ shearing. Finite strain and kinematic vorticity in all deformed granitic rocks indicate a prolate ellipsoid (L-S tectonites) near plane strain. Simple shear-dominated general shear during D₃ deformation is probably of general significance. The quartz c-axis textures indicate prism-gliding with a dominant rhomb <a> slip and basal <a> slip system formed mainly at low-middle temperatures. Mineral deformation behavior, quartz c-axis textures, quartz grain size and the Kruhl thermometer demonstrate that the ductile shear zone developed under greenschist facies metamorphic conditions at deformation temperatures ranging from 400 to 500 °C. Dislocation creep is the main deformation mechanism at a shallow crustal level. Fractal analysis showed that the boundaries of recrystallized quartz grains had statistically self-similarities. Differential stresses deduced from dynamically recrystallized quartz grain size are at around 20–39 MPa, and strain rates in the order of 10⁻¹² to 10⁻¹⁴ s⁻¹. This indicates deformation of granitic rocks in the Xingcheng-Taili ductile shear zone at low strain rates, which is consistent with most other ductile shear zones. Hornblende-plagioclase thermometer and white mica barometer indicate metamorphic conditions of medium pressures at around ca. 3–5 kbar and temperatures of 400–500 °C within greenschist facies conditions. The main D₃ deformation of the ENE-trending sinistral strike-slip ductile shearing is related to the roll-back of the subducting Pacific plate beneath the North China Craton.