均匀离散分布的平面应变过程和Fry法应变测量

本文运用 Apple Macitonsh 计算机对无应变的均匀离散点分布进行系列平面应变模拟,应变叠加模式分别采用具普遍意义的成岩压实+顺层缩短(LPS)+压溶作用和成岩压实+简单剪切+压溶作用。对各应变阶段的变形点分布进行相应的 Fry 法应变测量,并配合低变形砂岩样品的 Fry 法应变分析实例.证实 Fry 法应变测量方法为一非常有用的应变测量方法,其结果不仅能较好地揭示全岩总应变特征,而且能揭示出许多应变叠加的信息,Fry 法揭示的全岩有限应变椭球主面的方位也较为真实可靠。而 Fry 法运用于应变分布不均匀的劈理化岩石中时,能揭示不同变形域的应变特征,从而达到应变分解的目的。     

利用变形花岗岩体中的长石矿物进行有限应变测量初探

岩石有限应变测量的方法较多，相比之下，“长短轴法”最简单、快捷，野外易于操作，但是对所选的对象变形前要求近圆形，或者椭圆形，且随机分布。花岗岩区很难找到满足此条件的颗粒。在《1：25万玉门镇幅》调研的过程中，试以长石颗粒为研究对象，进行长短轴法变形测量，将其结果与相邻变形砾石、杏仁体和包体测量结果进行对比，发现它们具有相似的应变椭圆轴率，证实在变形花岗岩区可以用变形长石颗粒研究区域变形的特点。     

构造弱变形区自动有限应变测量-以石英砂岩为例

有限应变测量是研究岩石变形特征的重要研究内容。为了提高岩石有限应变测量的精度与速度,改变手工测量岩石有限应变耗时、枯燥的状况,应用多重图像限制的自动种子区域生长算法,以大青山地区为例,对如变形区内的石英砂岩有限应变进行了自动测量。该算法综合多个图像、利用色彩信息,不需要特殊设备即可对颗粒进行自动识别。算法还在叠加后的图像中,应用了修改的Canny边缘检测算法增强颗粒边界与内部的对比度。识别结果与手工测量的颗粒,在质心坐标、面积、长轴、短轴、有限应变测量方面具有很大的相似性。      

变形岩石有限应变的图解表示方法

自变形岩石的有限应变分析用于构造地质学研究以来,如何表示有限应变是构造地质工作者一直在讨论研究的问题之一。国外已经研究出了一整套表示方法。在国内这项研究工作还刚刚开始,部分构造地质工作者对于有限应变分析和图解的表示方法还不十分熟悉。为了使大家对有限应变图解表示法有一个较清楚的了解,本人谈一谈我们学习和研究过程中的点滴体会,以希起抛砖引玉之用。由于我们水平有限,文中难免有错误,乞望读者指正。归纳起来,有限应变的表示法有两类:一类是数字表示法,一类是图解表示法。如一个单位立方体受均匀有限变形后成为一个长柱体,其有限应变为: 三个主应变为ex,er和ez(ex≥er≥ez),用自然(或对数)应变表示则为:     

宣汉双石庙地区纵弯褶皱叠加特征及应力场、应变场分析

本文对川东北双石庙地区横跨褶皱特征作了详细论述,对其早晚两期褶皱形成时应变力场特征进行了较深入的讨论,并对岩石有限应变进行了Fry法研究、分析,指出了单个褶曲为平面应变,且核部应变程度大于翼部,复合地区应变程度大于非复合地区等特点。     

基于GIS的颗粒形状和应变分析

将GIS应用到岩石颗粒形状和有限应变分析, 使用了GIS地理数据库管理和空间对象叠置分析功能, 说明了在GIS环境中颗粒形状参数和属性参数的定义与获取方法; 对颗粒有限应变分析时, 使用了两种方法:最近邻弗莱法(TFry)和ASPAS法。以苏北盆地大丰—兴化勘探区块碎屑岩玻片为研究对象, 成功地分析了矢量化后的颗粒多边形形状及晶体塑性变形, 为构造地质分析和应用领域提供了一个方便快捷的工具。      

桂北元宝山花岗岩体中电英岩包体的应变测量和分析

在系统的野外地质调查基础上,通过对元宝山花岗岩体地质特征的分析,运用岩石有限应变测量、应变分析等方法,着重分析了元宝山花岗岩体中电英岩包体的应变特征,确定了电英岩包体的变形时代和原因.系统地开展了元宝山花岗岩体中电英岩包体的三维有限应变测量和应变分析.结果表明:电英岩包体的应变型式可分为3种:平面型应变(K=1)、压扁型应变(0＜K＜1)和收缩型应变(1＜K＜∞),且以平面型应变为主,有少量的压扁型应变和收缩型应变.     

辽南金州拆离带糜棱状花岗岩脉体变形特征及锆石SHRIMP U-Pb年龄——韧性拆离时限的新证据

辽南金州拆离断层带中发育糜棱状花岗岩脉。野外观察与显微构造分析显示该脉体为同构造变形脉体,与围岩太古宙片麻岩一起经历了伸展韧性剪切变形。长石Fry法的应变测量结果显示样品的付林参数K=0.83,罗德参数υ=0.09,应变强度Es=0.71,表明该岩石应变以平面应变为主,且有限应变较强;运动学涡度为Wk=0.89,表明剪切作用类型以简单剪切为主。对该花岗岩脉进行锆石SHRIMP U-Pb年代学测定,10颗岩浆锆石的206Pb/238U年龄加权平均值为129±2 Ma(MSWD=1.6),代表岩脉侵位年龄。结合该区研究的最新成果,表明金州拆离断层至少在129 Ma已经开始韧性变形,辽南地区构造体制在此时已经从缩短转折到伸展。     

米仓山构造带的应变与涡度分析

米仓山构造带东西向的断裂逆冲兼左旋走滑,西段的韧性变形较强,东段脆性为主。北东向三个主断裂带由北而南逆冲兼左行剪切,早期可能发生脆韧性变形,后期叠加了脆性变形。前震旦系基底岩系变形特征主要表现为透入性流变,碎斑结构和糜棱结构发育,镶嵌构造、S-C组构、带状构造、眼球构造为主,局部偶见"δ"和"σ"旋转碎斑以及矿物鱼。石英颗粒以亚颗粒旋转动态重结晶为主。显微特征反映岩石变形温度相当于绿片岩相。利用Fry法测定石英颗粒三维应变应变强度集中在1.35～1.60之间,显示出从北到南逐渐增强的趋势。Flinn指数K和Nadei-Hossack图解均表明应变类型为近似平面应变的拉长型。运动学涡度分析表明米仓山应变以简单剪切变形作用为主,具有由南向北递增趋势。     

胶东焦家金矿床有限应变分析及其意义

焦家金矿床构造岩中广泛发育变形石英颗粒，这些变形石英颗粒的三维有限应变分析表明，金矿定位于断裂带的扩容空间中，会林参数普遍表现为拉伸型，体积应变为增中型，金矿体就位于强应变与相对弱应变的转换部位，构造央垢有限应变椭球体拉伸轴主要中于ＮＥ－ＳＷ向，含矿热液运移方向与焦家断裂带平行，成矿过程中体系是开放的，有大量体系外物质迁入。     

A computer program for the determination of finite strain using fry method

Fry method enables rapid estimate of finite strain from deformed aggregates such as clastic grains, fossil colonies, oolitic or pisolitic aggregates, prophyroblastic minerals or phenocrysts. It has an advantage over the other methods of finite strain analysis in its very quality of enabling rapid estimation with a reasonable degree of accuracy. Details of the software to prepare a plot using Fry method are outlined. This program has an advantage over other computer based programs on the world wide web in its aesthetic getup, small size, user friendliness and a help file.     

Influence of object concentration on finite strain and effective viscosity contrast: insights from naturally deformed packstones

Deformed conglomerates and ooidal/oncoidal packstones are commonly used to evaluate finite strain in deformed sedimentary successions. In order to obtain a correct estimate of finite strain, it is necessary to consider not only the different behaviour of matrix and objects, but also object concentration. The analysis of two-component rocks characterised by high values of packing commonly results in a substantial underestimate of bulk strain and of viscosity contrast between objects and matrix. In this study, the effects of the volumetric fraction of competent inclusions on both object and bulk measured finite strain, as well as on apparent viscosity contrast, have been investigated in naturally deformed packstones characterised by variable object concentration on the scale of the hand specimen (and hence for homogenous viscosity contrast). Object finite strain has been obtained by Rf/ analysis, whereas the Fry method provides a measure of whole-rock strain that is also a function of inclusion concentration. Therefore, the finite strain measured by the Fry method is better termed effective bulk strain. In order to investigate the role of object concentration, this parameter has been plotted against object and effective bulk strain, and also against viscosity contrast. These diagrams show that: (i) for high values of packing, measured object and effective bulk strain show values that are significantly lower with respect to the calculated maximum value (that would result in the ideal case of no particle interaction and represents therefore the real bulk strain of the samples); (ii) the viscosity contrast shows lower values with respect to the calculated maximum one (that is equal for the three principal sections of the finite strain ellipsoid), and as packing reaches the maximum value, the viscosity contrast approaches a unit value. Empirical equations have also been found that link object concentration with both object and effective bulk finite strain.     

The Effect of finite strain and deformation history of HALABAN area,eastern Arabian shield,Saudi Arabia

The present study aims to evaluate a relationship between the mineralogy and structural analysis in the Halaban area and to document the tectonic evolution of Halaban and Al Amar faults. The collected samples were taken from deformed granitiods rocks (such as granite, gneisses and tonalite), metasedimentary, metavolcanic, metagabbro and carbonate rocks are trend to NE-SW with low dip angle in the Halaban area. These samples were 8 from granite, 14 metagabbro, 6 metavolcanics, 5 tonalite, 6 metasedimentary, 10 gneisses and 8 carbonate rocks. Our results are described for the different axial ratios of deformed rocks as the following: XZ sections range from 1.10 to 4.60 in the Fry method and range from 1.70 to 2.71 in the Rf/? method. YZ sections range from 1.10 to 3.34 in the Fry method and range from 1.62 to 2.63 in the Rf/Phi method. In addition, XY sections range from 1 to 3.51 in the Fry method and range from 1 to 1.27 in the Rf/? method for deformed granite rocks, metasedimentry rocks, and metagabbro. The stretch axes for measured samples in the X direction axes (S_X) variety from 1.06 to 2.53 in the Fry method and vary from 1.20 to 1.45 in the Rf/? method. The values of the Y direction axes (S_Y) vary from 0.72 to 1.43 in the Fry method, which indicates contraction and extension in this direction and vary from 1.13 to 1.37 in the Rf/? method which indicates extension in this direction. Furthermore, the Z direction axes (SZ) varies from 0.09 to 0.89 in the Fry method and from 0.52 to 0.71 in the Rf/? method. The stretches axes in the Z direction (SZ) show a vertical shortening about 11% to 91% in the Fry method and show vertical shortening about 29% to 48% in the Rf/? method. The studied rock units are generally affected by brittle-ductile shear zones, which are sub-parallel to parallel NW or NNW trend. It assumed that different rock types of have similar deformation behavior. Based on these results, it is concluded that the finite strain is accumulated during the metamorphism after that was started the deformation by thrusting activity. The contacts between the different rock types were deformed during thrusting under semi-brittle to ductile deformation conditions by simple shear. A component of vertical shortening is also involved causing subhorizontal foliation in the Halaban area.     

Strain analysis and microstructural evolution characteristic of neoproterozoic rocks associations of Wadi El Falek,centre Eastern Desert,Egypt

The estimation of finite strain in rocks is fundamental to a meaningful understanding of deformational processes and products on all scales from microscopic fabric development to regional structural analyses. The R_f/φ and Fry methods on feldspar porphyroclasts and mafic grains from 5 granite, 1 metavolcanic, 3 metasedimentary and 1 granodiorite samples were used in Wadi El Falek region. Finite-strain data shows that a high to moderate range of deformation of the granitic to metavolcano-sedimentary samples and axial ratios in the XZ section range from 1.60 to 4.10 for the R_f/φ method and from 2.80 to 4.90 for the Fry method. Furthermore, the short axes are subvertical associated with a subhorizontal foliation. We conclude that finite strain in the deformed granite rocks is of the same order of magnitude as that from metavolcano-sedimentary rocks. Furthermore, contacts formed during intrusion of plutons with some faults in the Wadi El Falek area under brittle to semi-ductile deformation conditions. In this case, finite strain accumulated during superimposed deformation on the already assembled nappe structure. It indicates that the nappe contacts formed during the accumulation of finite strain.     

Strain analysis from objects with a random distribution: A generalized center-to-center method

Existing methods of strain analysis such as the center-to-center method and the Fry method estimate strain from the spatial relationship between point objects in the deformed state. They assume a truncated Poisson distribution of point objects in the pre-deformed state. Significant deviations occur in nature and diffuse the central vacancy in a Fry plot, limiting the its effectiveness as a strain gauge. Therefore, a generalized center-to-center method is proposed to deal with point objects with the more general Poisson distribution, where the method outcomes do not depend on an analysis of a graphical central vacancy. This new method relies upon the probability mass function for the Poisson distribution, and adopts the maximum likelihood function method to solve for strain. The feasibility of the method is demonstrated by applying it to artificial data sets generated for known strains. Further analysis of these sets by use of the bootstrap method shows that the accuracy of the strain estimate has a strong tendency to increase either with point number or with the inclusion of more pre-deformation nearest neighbors. A poorly sorted, well packed, deformed conglomerate is analyzed, yielding strain estimate similar to the vector mean of the major axis directions of pebbles and the harmonic mean of their axial ratios from a shape-based strain determination method. These outcomes support the applicability of the new method to the analysis of deformed rocks with appropriate strain markers.     

Pure shear to simple shear-dominated transpression during the Eburnean major D2 deformation,Daléma sedimentary basin,eastern Senegal

Field studies in the Palaeoproterozoïc Daléma basin, Kédougou-Kéniéba Inlier, reveal that the main tectonic feature comprises alternating large shear zones relatively well-separated by weakly deformed surrounding rock domains. Analysis of the various structures in relation to this major D₂ phase of Eburnean deformation indicates partitioning of sinistral transpressive deformation between domains of dominant transcurrent and dominant compressive deformation. Foliation is mostly oblique to subvertical and trending 0–30° N, but locally is subhorizontal in some thrust-motion shear zones. Foliation planes of shear zones contain a superimposed subhorizontal stretching lineation which in places cross-cuts a steeply plunging stretching lineation which is clearly expressed in the metasedimentary rocks of weakly deformed surrounding domains. In the weakly deformed domains, the subhorizontal lineation is absent, whereas the oblique to subvertical lineation is more fully developed. Finite strain analyses of samples from surrounding both weakly deformed and shearing domains, using finite strain ratio and the Fry method, indicate flattened ellipsoid fabrics. However, the orientation of the long axis (X) of the finite strain ellipsoid is horizontal in the shear zones and oblique within the weakly deformed domains. Exceptionally, samples from some thrust zones indicate a finite strain ellipsoid in triaxial constriction fabrics with a subhorizontal long axis (X). In addition, the analysis of the strain orientation starting from semi-ductile and brittle structures indicates that a WNE–ESE (130° N to 110° N) orientation of strain shortening axis occurred during the Eburnean D₂ deformation.     

Least-squares center-to-center and mean object ellipse fabric analysis

The subjectivity of ellipse fitting in many strain techniques has hindered the determination of fabric anisotropy and tectonic strain. However, many sets of x, y co-ordinates can be approximated as an ellipse using a least-squares algorithm to calculate a best-fit ellipse and associated average radial error. For instance, the two dimensional shape of many objects can be approximated as an ellipse by entering digitized co-ordinates of the object margin into the ellipse algorithm.The rim of maximum point density in a normalized Fry diagram is defined by normalized center-to-center distances between touching or nearly touching objects. The enhanced normalized Fry (ENFry) method automates ellipse fitting by entering center-to-center distances between these “touching” objects into the least-squares ellipse algorithm. For homogeneously deformed populations of 200 objects, the ENFry method gives an accurate and precise measure of whole-rock fabric anisotropy, particularly for low ellipticities. When matrix strain exceeds clast strain, manual ellipse fitting of normalized Fry plots gives more accurate matrix anisotropies.The mean object ellipse (MOE) method calculates the best-fit ellipse from the geometry of the objects. Three points from the margin of each object ellipse, centered at the origin and expanded or reduced to unit volume, are used to calculate the best-fit fabric ellipse. The MOE method is very precise for small data sets, making it a good method for mapping heterogenous object strain. However, least-squares calculations maximize the influence of distal and spurious ellipticities, causing the MOE method to overestimate the fabric ellipticity of most aggregates.     

Density distribution techniques and strained length methods for determination of finite strains

For a homogeneously deformed rock composed initially of an isotropic distribution of object shapes, finite strain may be determined from the correlation between the orientations of either two-dimensional or one-dimensional sample cuts and the frequencies with which they intersect marker objects. Mimran previously published an incorrect method for planar samples under the heading ‘density distribution technique’. Methods are described by which the three-dimensional strain may be directly determined from six general samples, either linear or planar. Construction of two-dimensional ellipses as an intermediate step is unnecessary and enforces practical difficulties.These methods may be simplified by use of samples parallel to known principal axes or planes of the finite strain. In this case the same large errors may arise from slight misorientation of samples as with other methods of strain measurement. A new quick method is proposed, combining linear and planar measurements of frequencies of intersected objects, which is thought to be the first method to circumvent a large part of the error from this error source. For example, if true X:Z ratio is 9 : 1, and orientations in the XZ plane are misjudged by 8°, normal methods give 38% error where the new method gives, with care, an error of 1.9%. For methods of strain measurement such as are described here the concept of strain ellipsoid is unnecessarily limiting, and should be abandoned.     

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.     

Removal of finite deformation using strain trajectories

A technique is described for removing the effects of finite deformation, given the principal values and orientations of strain at a number of points throughout a deformed body.Using the principal orientations, strain trajectories are constructed for the deformed state. The body is divided into finite elements bounded by these trajectories. Each element is then unstrained without changing its orientation or position. This process creates artificial voids and overlaps, which are minimized by imparting rigid translations and rotations to the elements according to a least squares method.The result is the pattern of strain trajectories for the undeformed state. It is shown that the trajectories for the deformed and undeformed states may be used as reference coordinates in order to map the change in shape of any body as it passes from the deformed to the undeformed state or vice versa. The technique is tested using models of a folded layer and a shear zone. It is suggested that the technique is versatile enough to allow for errors in original strain data. Although the technique has so far been applied to two-dimensional deformations, a similar method should be usable in three dimensions.