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。     

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     

Vorticity and non-coaxiality in progressive deformations

A measure of the non-coaxiality involved in progressive deformation histories is proposed in the form of the kinematical vorticity number, W_k. This number is a measure of the relative effects of rotation of material lines (relative to the instantaneous stretching axes) and of stretching of these material lines. As such, W_k, is a measure of the instantaneous degree of non-coaxiality. A detailed example is first presented in the form of a progressive simple shearing in which the shear plane rotates relative to an external coodinate system. This is followed by examples of more complicated deformation histories. Three specific types of progressive, isochoric (constant volume) deformation histories are recognized. Those for which 0 ≤ W_k < 1 correspond to deformation histories where no line that has been extended is shortened in future increments; W_k > 0 is a special case of these corresponding to a coaxial history. Histories with W_k > 0 are non-coaxial. Those histories with W_k = 1 correspond to progressive simple shearing. Those histories with 1 < W_k < ∞ are pulsating and lines that have been extended may be shortened in future increments.     

Investigations on the mechanical significance of crenulation cleavage

Measurements of total, incremental and progressive strains associated with the development of small scale crenulation cleavage in some low-grade metamorphic rocks from Australia and Switzerland are applied to a discussion of the mechanical significance of the cleavage.Limits are placed on the amount of incremental and total slip or simple shear possible along the cleavage by the observation that the XY principal plane trace of bulk total crenulation strain coincides within 4° of the crenulation cleavage trace in all cases where this strain has been measured or estimated. The measurements are made on eight specimens using deformed porphyroblasts, crystal fibres in pressure-shadows around pyrite and flattened folds and include deformations with coaxial and non-coaxial histories.Further measurements derived from pressure-shadow fibres (eight specimens) show that the style and orientation of incremental deformation are essentially independent of the crenulation cleavage, except for a limit (43°) to the obliquity of the principal incremental extension axis during a given cleavage episode. The only special deformation related to the cleavage is the coaxial one. An indication of passive cleavage behaviour at high strain is shown by the progressive strain history of one specimen. Evidence for passive rotation of a transected axial plane is shown by another. A model is proposed to account for these observations, especially the conditions necessary for initiation and continued development of a new cleavage fabric.Some further applications of existing strain measurement techniques are described: of the R_f/Ø_f method to heterogeneously superposed tectonic strains and of an improved procedure of t′_α/α flattening analysis.     

韧性剪切带的变形分域现象——以辽东的丹东韧性剪切带为例

丹东韧性剪切带的实例表明:韧性剪切带的持续变形包含了共轴与非共轴两种应变线路或状态,由于分布的不均匀性,导致变形分域现象,形成平面的变形岩石分区。持续变形过程中,又存在应变线路的转换和叠加。微构造是确定变形体制的主要依据。野外观测与应变分析证实,变形分域存在于不同尺度,在总体剪切(非共轴)变形条件下,初始糜棱岩往往表现以共轴变形占优势,而糜棱岩和超糜棱岩则以非共轴变形为主。持续变形导致从共轴向非共轴转变,最后形成后者的主体地位。     

被动椭圆形标志物应变分析的计算机模拟

本文采用计算机数学模拟的方法更深入地探讨了椭圆形标志物应变分析技术(R_f/Φ去应变法、Shimamoto等提出的代数法、调和平均值法和算术平均值法)的适用条件。一共形成了十一组有代表性的应变前数组,四种变形路径:纯剪、单剪、纯剪加单剪和体变。当应变前数组在(-90°,90°)内均匀分布或随机分布时,无论变形路径是哪一种(共轴的还是非共轴的),上述的所有方法都是适用有,且以代数法最佳。当应变前数组具有优选方位(单峰分布)且变形路径为共轴递进变形时,在一定条件下,R_f/Φ法能用来估计应变。经分析发现当应变足够大时,调和平均值法是一种简单快速的应变计算法。     

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   

Application of kinematic vorticity and gold mineralization for the wall rock alterations of shear zone at Dungash gold mining,Central Eastern Desert,Egypt

The use of porphyroclasts rotating in a flowing matrix to estimate mean kinematic vorticity number (Wm) is important for quantifying the relative contributions of pure and simple shear in wall rocks alterations of shear zone at Dungash gold mine. Furthermore, it shows the relationship between the gold mineralization and deformation and also detects the orientation of rigid objects during progressive deformation. The Dungash gold mine area is situated in an EW-trending quartz vein along a shear zone in metavolcanic and metasedimentary host rocks in the Eastern Desert of Egypt. These rocks are associated with the major geologic structures which are attributed to various deformational stages of the Neoproterozoic basement rocks. We conclude that finite strain in the deformed rocks is of the same order of magnitude for all units of metavolcano-sedimentary rocks. The kinematic vorticity number for the metavolcanic and metasedimentary samples in the Dungash area range from 0.80 to 0.92, and together with the strain data suggest deviations from simple shear. It is concluded that nappe stacking occurred early during the underthrusting event probably by brittle imbrication and that ductile strain was superimposed on the nappe structure during thrusting. Furthermore, we conclude that disseminated mineralization, chloritization, carbonatization and silicification of the wall rocks are associated with fluids migrating along shearing, fracturing and foliation of the metamorphosed wall rocks.     

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.     

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.     

三维参照变形及应变相研究评述

三维参照变形和应变相是最近构造地质学领域中取得的重要进展,三维参照变形是理想化的三维变形分类,每一参照变形是共轴级分（拉伸、压扁或纯剪）和与其垂直的简单切组分同时作用的产物,三种可能的面理取向和三种可能的线理取向的不同组合构成六咱应变相,三维参照变形和应变相研究证明糜陵面理未必平行剪切带,可与剪切带斜交,甚至垂直,线理未必与剪切方向一致,可与剪切方向斜交,甚至垂直,出现横向面理时,剪切指向标志位于该面理内,出现横向线理时,剪切指向出现在与线理垂直的ａｃ面理内,三维变形分析不公可解决三维分析难以解释的横向面理和线理,而且可确定共轴组分的类型及其与单剪组分的结合方式。     

The limitations of three-dimensional kinematic vorticity analysis

The kinematic vorticity number (W_k) can be calculated for three-dimensional as well as two-dimensional geologic deformations. For steady-state deformations, W_k can be correlated to and analyzed in terms of finite strains. The analysis shows that assumptions commonly made for two-dimensional deformations are not applicable to three-dimensional deformations. A single W_k describes an infinite number of three-dimensional deformations. Further, even knowledge of flow apophyses orientation, instantaneous stretching axes orientation, and/or W_k are not sufficient to describe deformation. Three-dimensional deformations also require knowledge of the deformation ‘type’ or boundary conditions of deformation (e.g. transpression). Hence, in addition to being difficult to estimate, the value of knowing W_k for three-dimensional deformations is greatly reduced compared with plane strain. The most useful methods of determining W_k from naturally deformed rocks are presented.     

总体非共轴持续变形产生的构造及其运动学意义——以金州韧性剪切带为例*

构造解析证实,金州韧性剪切带是以右行走滑为主的大型缓倾斜剪切带,带内发育的糜棱面理-小型褶皱-香肠构造及肿缩构造-S?C组构的系列,以及广泛分布的拉伸线理,是总体非共轴持续变形条件下,带内共轴与非共轴线路相结合的结果,并且后者占主要地位。糜棱面理是最早生成的透入性构造,对其他构造的形成有重要作用。剪应变量(γ)大小与糜棱岩化程度有直接关系。鞘褶皱多发育于γ≥10地段。微构造发育机制的变化是：γ 由低到高,石英变形从低温晶体-塑性转向塑性变形与重结晶作用; 而云母矿物从外形定向转向粘性颗粒-边界滑动。     

中蒙边界早白垩世不对称花岗岩穹隆的伸展时限、剪切作用类型和区域构造意义

东北亚大陆于晚中生代时期发生了大规模地壳伸展,发育变质核杂岩和不对称花岗岩穹隆,其伸展剪切机制一直是构造研究的重要内容之一。中蒙边界东南段沿北东向展布了罕乌拉、纳兰和宝德尔等3个不对称花岗岩伸展穹隆,主体均为晚中生代花岗岩侵入体,岩体西北缘发育韧性剪切(糜棱岩)带,并被后期高角度正断层所围限,整体为穹隆状。根据罕乌拉穹隆韧性剪切带内强变形中粗粒钾长花岗岩(133±1 Ma)和弱变形细粒花岗岩(128±2 Ma)的构造关系及其锆石U-Pb年龄,推测该穹隆内岩体可能为同伸展岩体,韧性伸展时间在133 Ma之后并持续至128 Ma或更晚,与同区其他穹隆发育时限相同。笔者用R_f/ф方法测量了3个穹隆剪切带内糜棱岩中长石的有限应变轴率,利用Hsu图解获得其应变类型为平面压扁应变(k=0.5)。用长石极莫尔圆法、刚性颗粒网法和C轴石英组构法估算了韧性剪切的长期变形过程,得到糜棱岩的平均运动学涡度值为0.68～0.74,表明这些穹隆的韧性剪切作用主要是纯剪切和简单剪切分量几乎相等的一般剪切作用。石英斜向条带法测得的韧性变形后期的运动学涡度值为0.87～0.99,平均值为0.93...     

Pulsating oblate and prolate three-dimensional strains

The progressive ductile deformation of competent spherical inclusions is modeled analytically. Results of this study may help to understand better the limitations connected to geological field methods using competent inclusions for strain analyses. Parameters studied and quantified here are the strain magnitude, the progressive change in inclusion shape, the orientation of the finite strain axes, the frequency of pulsation, and the coupling between the strain ellipticity and viscosity contrast. Competent inclusions develop pulsating apparent strains if the host material is subjected to a component of simple shear and provided time or strain rate is sufficient to complete the strain cycle. The disparity between the strain magnitude inferred from competent viscous inclusions and that undergone by the host rock, increases for larger viscosity between them. The pulsation of the inclusion may suggest zero strain after a strain cycle has been completed, even though strain in the host rock is extremely large. The inclusion will develop pulsating oblate strains if a shortening rate is superposed normal to the plane of pulsation. Conversely, pulsating prolate strains occur if an extension rate is superposed instead of shortening. Stretching lineations outlined by deformed competent inclusions within shear zones beneath collapsing nappe sheets may even point perpendicular to the direction of nappe transport. This finding offers an explanation for the occurrence of mutually perpendicular pebble elongations in nearby locations within the Bygdin conglomerate beneath the Jotun nappe, Norwegian Caledonides.     

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.     

Progressive deformation and the rotation of contemporary fold axes in the Ballybofey Nappe,north-west Ireland

Internal regions of orogenic belts may be characterized by an alignment of fold axes with mineral elongation lineations. This relationship is commonly interpreted as representing progressive tightening and rotation towards the shear direction of early buckle folds, the hinges of which were initiated orthogonal to this direction. Detailed structural analysis of lower amphibolite facies Dalradian metasediments of the Ballybofey (fold) Nappe, north-west Ireland, shows that an intense S₃ schistosity is developed axial planar to mesoscopic and minor F₃ folds. In areas of low D₃ strain, F₃ fold axes plunge gently towards the north-east, whereas in regions of greater strain plunges are towards the south-east subparallel to the constant mineral lineation. Minor folds which initiated at angles of 70–80° from the mineral lineation subsequently rotated towards the shear direction in a consistent clockwise sense. Progressive and variable non-coaxial deformation oblique to the original mean F₃ orientation has resulted in a unimodal distribution pattern of fold axes. Analysis of the angular rotation of fold axes enables estimates of the bulk shear strain to be evaluated and models of progressive deformation to be assessed.     

Rheological and kinematical responses to flow of two-phase rocks

Numerical simulations have been performed to investigate the strain-dependent behaviour of rheological and kinematical responses to flow of two-phase rocks using the commercial finite-difference program FLAC2D. It was assumed that the two phases have Maxwell rheology. Plane strain and velocity boundary condition, which produces a simple shear deformation, were also assumed. Two types of geometries were considered: strong phase supported (SPS) and weak phase supported (WPS). We calculated strain-dependent variations of effective viscosity and partitioning of strain rate, vorticity and kinematic vorticity number during deformation in both SPS and WPS structure models.The results show that the strain-dependent behaviour is largely influenced by the geometry of the composite. SPS models show both strain hardening and strain softening during the simulations, with strain hardening preceding strain softening. A critical shear strain is necessary to begin the strain softening behaviour. Strain hardening and strain softening are accompanied by a reduction and an increase of the partition of strain rate into the weak phase, respectively. On the other hand, WPS models show only weak strain hardening and strain softening, being the strain-dependent behaviour close to a steady state flow. In addition, the following results are obtained on vorticity and kinematic vorticity number; (1) in both SPS and WPS models the partition of vorticity into weak phase increases with progressive shear strain, i.e. the strong phase becomes less rotational, (2) in SPS models weak inclusions changes from sub-simple shear to super-simple shear with progressive strain, whereas the strong matrix changes from super-simple shear to sub-simple shear, (3) in WPS models the strong inclusions with high viscosity contrasts are less rotational but can be in super-simple shear condition to high strains.The observed strain-dependent behaviours have been compared with previous proposed analytical models. The degree of agreement is variable. Balshin and Ryshkewitch–Duckworth models are only applicable to SPS models. Ji-generalized mixture rule model is applicable to both models.The results suggest that polyphase rocks with SPS structure during ductile shear deformation respond as strain softening materials, after an initial strain hardening stage that may drive to the strain localization into the material.     

The simulation of fabric development during plastic deformation and its application to quartzite: the influence of deformation history

The effect of deformation history on the development of crystallographic preferred orientation in quartzities has been simulated using a computer program based on the Taylor-Bishop-Hill analysis. Model quartzities with different combinations of glide systems have been subjected to various coaxial and non-coaxial deformation histories. It is possible to obtain information from the fabrics that develop during simple histories; for example, the location of the axis of extension is generally associated with a pole free area on a c-axis plot, and progressive axial shortening, plane strain and axial shortening produce characteristic fabrics. In progressive simple shear the fabric skeleton becomes asymmetric relative to the sense of shear and a-axes preferentially align in the flow plane parallel to the flow direction. However, this example illustrates that the fabric orientation and characteristics are controlled by the kinematic framework and bear only an indirect relationship to the finite strain accumulated to that point in the history.The imprint of the closing stages of deformation limits to some degree the use of crystallographic fabrics as a tool for structural geologists, but in favourable circumstances data can be obtained concerning characteristics of the deformation history, on the scale of the hand-specimen, for the last part of this history.     

Three‐dimensional vorticity and time‐constrained evolution of the Main Central Thrust zone,Garhwal Himalaya (NW India)

Vorticity estimates based on porphyroclasts analysis are limited by the extrapolation to three dimensions of two‐dimensional data. We describe a 3D approach based on the use of X‐ray micro‐computed tomography that better reflects the real 3D geometry of the porphyroclasts population. This new approach for kinematic vorticity analysis in the Munsiari Thrust mylonites, the lower boundary of the Main Central Thrust zone (MCTz) in Indian Himalaya, indicates a large pure shear component during non‐coaxial shearing. ⁴⁰Ar/³⁹Ar ages of micas along the mylonitic foliation of the Munsiari and Vaikrita thrusts (the upper boundary of the MCTz) constrain thrust activity to 5–4 and 8–9 Ma, respectively. Available kinematic vorticity analyses of the Vaikrita mylonites suggest the dominance of a simple shear component. Combining these data, we suggest that the southward and structurally downward shift of deformation along the MCTz was accompanied by a progressive increase in the pure shear component in a general shear flow.