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.     

衡山岩体西缘韧性剪切带磁性组构研究

本文对采自衡山花岗岩体西缘韧性剪切带的标本进行了岩石磁性组构研究,并将其与常规应变分析方法所得结果予以比较,表明了岩石磁化率各向异性椭球体与应变椭球体之间有一定的对应关系,岩石磁化率各向异性技术可望成为构造地质学的一种新手段。岩石磁性组构资料可应用于变形岩石的应变分析,特别是在没有宏观应变标志或者通常的岩石组构分析方法太费时间的情况下更显出其优越性。     

岩石的磁性组构及其在岩石变形分析中的应用

文本总结了对采自巴彦乌拉山韧性剪切带的部分标本进行岩石组构数据测定的分析结果,并将其与用常规应变分析方法所得结果予以比较,表明了岩石磁化率各向异性椭球体能够反映总的应变椭球体,证明岩石磁化率各向异性技术做为一种岩石组构因素的研究是有发展前景的。岩石磁性组构资料可应用于变形岩石的应变分析,特别是在通常的岩石组构分析技术太费时间和粗糙的情况下更显示了其优越性。     

The magnetic susceptibility anisotropy of deformed rocks from North Cornwall,England

The magnetic fabric of 306 samples from 51 sites was determined by means of a new, low-field anisotropy technique. The within-site consistency of the magnetic-fabric data was extremely high and was comparable with more tedious standard petrofabric analyses, where available, and with the structural properties of previously defined tectonic zones in North Cornwall. These data confirm the applicability of magnetic-fabric studies to structural problems, particularly in determining the orientation of the strain in the rocks. In areas of low strain, the technique appears applicable where standard petrofabric techniques are too coarse or time-consuming and indicates that direct estimates of both the magnitude and direction of the net strain ellipsoid should be possible in less deformed areas. Magnetic fabric studies therefore confirm the tectonic zonation in this region and provide a rapid method for similar structural evaluations.     

Strain determination using a density-distribution technique and its application to deformed Upper Cretaceous Dorset chalks

A simple and highly accurate finite-strain measurement technique is presented. The principle behind the technique is that the longer the dimension of a strain indicator in a certain orientation, the higher the probability of its being intersected by a plane perpendicular to this orientation. Strain indicators have to be counted in any three mutually perpendicular orientations and their populations are analytically transferred into the parameters describing the strain ellipses in the three orientations. Strain indicators might be of any shape, but they must have had predeformational random distribution and random orientation.The geological implications of the technique are discussed. The technique is applied to deformed Upper Cretaceous chalk from Dorset (southern England) using microfossils as strain indicators.     

湖北青峰韧性剪切带构造岩的磁性组构研究

通过对青峰韧性剪切带中糜棱岩的磁性组构研究,同时与常规主应变分析方法所测结果比较,表明岩石磁化率各向异性椭球体与应变椭球体之间有一定的对应关系。磁性组构的特征为构造岩变形机制,以及断裂带的运动学、动力学等的研究提供了一种比较可靠、准确、方便的方法。     

Graphic method for reconstruction of a strain ellipse from distorted regular polygons

A graphical method to determine the finite strain ellipse from deformed polygons of similar size is presented. This technique has been developed on sections normal to columnar joints of igneous rocks, but it can also be applied to any feature in which the corresponding unstrained polygons have their vertices located on a circumscribed circle.     

A comparison of intracrystalline deformation in naturally and experimentally deformed quartzites

A relatively undeformed quartzite sample from the Weverton formation was experimentally deformed in plane strain at a temperature of 700° C, a confining pressure of 15 kb and a constant strain rate of 10⁻⁶/sec, in a modified Griggs apparatus. A comparison of the known experimental strain for the sample with that measured from deformed rutile needles within the quartz grains shows fairly close agreement between the two values. This confirms the validity of using the needles as intracrystalline strain markers. A comparison has been made of the microstructures and preferred orientations in the experimentally deformed sample and a naturally deformed sample of the same quartzite which has undergone the same strain. The experimentally deformed sample exhibits more inhomogeneous intragranular deformation and a “double funnel” pattern of c axes, while the naturally deformed sample exhibits more homogeneous intragranular deformation and a broad great circle girdle of c axes normal to the foliation and lineation.     

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.     

Deformation path concepts in strain analysis: Applications for study of ductile shear zones

The internal fabric of a deformed rock represents the state of finite strain. In some special cases the fabrics also record the strain history of the deformed body. These special cases can profitably be utilized to compare the predictions of dynamic models and strain paths in natural deformations. In this contribution, the concept of deformation path in the study of ductile shear zones has been demonstrated.     

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。     

Factorization of finite strains in three dimensions—a computer method

Strain analysis using deformed objects is already well established. The more sophisticated techniques can resolve tectonic strains and indicate the nature of any pre-tectonic fabric. Methods that analyse in two dimensions can produce problems of incomparability when results from three faces of one sample are combined.A method for factorizing finite, non-coaxial strains is presented which overcomes these problems by analysing in three dimensions. Published data from deformed lapilli tuff from the English Lake District have been used to test the method.Results are as valid as those obtained originally from the data, and the technique enables strain analysis to be extended to areas which give imprecise results using existing methods.     

在变形岩石中确定应变椭球体方法的探讨

本文研究了四十年代以来确定变形岩石应变椭球体的方法,并结合实例给出一种简明、精度较高的从三个或更多任意截面上的二维应变测量数据,计算三维应变椭球体之主轴大小和方向的算法。     

在CorelDRAW平台上进行Fry法有限应变测量的新技术

有限应变测量是韧性变形定量估算的主要手段。Fry法有限应变测量以变形颗粒,如变形砾石、鲕粒、近等轴矿物等为应变标志体,地质实践中较容易获得,是岩石有限应变测量的最普遍手段。其传统测量过程极为繁琐,难以满足大范围应变测量的要求,数据精度也较低,限制了Fry法的应用。前人曾根据Fry法原理设计了计算机程序,但其程序相关编程语言如今已基本不能使用。本研究基于目前地质上较普遍使用的制图软件CorelDRAW平台的VBA编程,设计出一个基于CorelDRAW平台的Fry法应变测量宏程序FRY-1。在新图层上将所有变形颗粒的中心点标出后,运行FRY-1宏程序即可快速得到精确的Fry图解,并计算出相对精确的R值。通过实例与“最邻近心对心法”的测量结果进行的对比,证明该方法简便易操作,并可大幅提高有限应变测量的效率和有效减小误差。     

Tectonic deformation and recrystallisation of oligoclase

Naturally deformed and partially recrystallised oligoclase porphyroclasts were studied in a high voltage electron microscope. The oligoclases had a highly deformed outer mantle zone, which contained high densities of dislocations and albite and pericline deformation twins, and less deformed cores containing fewer dislocations and albite twins but no pericline deformation twins. There was little evidence for recovery; apparently the internal strain energy due to deformation was relieved by recrystallisation. Strain free nuclei developed in areas with the highest defect densities. The resultant new grains had a lower anorthite content than their parents. It is suggested that the recrystallisation processes were aided by strain enhanced diffusion.     

Analysis of the Variability of a Two-Dimensional Finite Strain Estimate

Finite strain estimation is a widely used technique for the study of rock deformation in structural geology. One particular algorithm proposed by Shimamoto and Ikeda uses the ‘average shape matrix’ of deformed markers. This paper provides a detailed error analysis for resulting strain estimates in two dimensions. When the number of markers exceeds 100, estimators of components of the strain tensor are shown to have an approximately Gaussian distribution with variances that increase with their mean. Equal variance estimators are obtained by applying a log transform for the elongation and an arcsin transformation for the orientation estimates. Confidence interval formulae for strain tensor components are proposed. Lithology specific constants arising in these formulae are estimated from undeformed samples. The results are validated by application to simulated data as well as observational data from thin sections of sandstone sampled from SE Ireland.     

利用惯量椭圆进行岩石有限应变分析

提出了利用惯量椭圆对任意形状矿物颗粒进行描述的方法,并利用惯量椭圆理论,计算了岩石薄片中任意形状矿物颗粒的惯量椭圆,通过颗粒面积对椭圆参数进行标准化,得到每一矿物颗粒的等效应变椭圆。等效应变椭圆能够有效地反映对应矿物颗粒的优选方位以及变形特征,进而利用椭圆的矩阵参数形式对等效应变椭圆进行统计分析,获得岩石的有限应变椭圆;同时给出了相应的数值计算方法,编制了软件Straindesk,并得到了成功的应用。该方法克服了先前应变测量中的局限性,方便实现计算机的自动分析,具有较强的有效性和广泛的适用性。     

Relationship of concretions and chlorite-muscovite porphyroblasts to the development of domainal cleavage in low-grade metamorphic deformed rocks from north-central Wales,Great Britain

Spaced or domainal cleavage is widespread in deformed rocks of low metamorphic grade. This study presents evidence on the origin of spaced cleavage in deformed pelites from Silurian turbidite sequences in north-central Wales. The variable development of cleavage folia is related to the presence of concretions, which served to concentrate strain effects of well-developed cleavage folia in the matrix in some zones and to produce ‘strain shadows’ (few or no cleavage folia) in others. Compositional differences between matrix, narrow transition zones, and concretions also influenced the development of cleavage folia. Chlorite-muscovite porphyroblast growth was initiated before cleavage formation, but its further growth and development took place during cleavage formation. The relationship of cleavage to the concretions and to the chlorite-muscovite porphyroblasts indicates that cleavage developed in a matrix that must have been in an advanced state of lithification (anchimetamorphic to lowermost greenschist facies of metamorphism) and not during soft-sediment deformation.     

The deformation matrix and the deformation ellipsoid

Homogeneous strain can be computed most easily by the methods of matrix algebra. Lines, planes and ellipsoids represented in matrix form can be homogeneously deformed by simple matrix multiplication by linear transformation matrices, the elements of which are the coefficients of the transformation equations. Deformation matrices or linear transformation matrices which cause geological-type homogeneous strain are divided into four classes based on the presence or absence of symmetry and/or orthogonality. The nature of the homogeneous strain caused by each class of deformation matrix is examined. Orthogonal-symmetrical and orthogonal matrices cause rotation. Symmetrical matrices cause irrotational strain with co-axial strain as a special case. Matrices which are neither orthogonal nor symmetrical cause many different types of rotational strain, some of which are examined.