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1.
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. 相似文献
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The Fry method, based on the relative movement of different material points, typically grain centers, with reference to each other graphically yields a point distribution that displays the finite strain ellipse as a central vacancy. The diffused nature of the central vacancy induces subjectivity in strain estimation, particularly, if the point population when undeformed lacked an isotropic anticlustered distribution. Most existing methods use analytical and/or iterative approaches for improving the sharpness of the central vacancy and positioning the best-fit strain ellipse in a Fry plot. We provide an image-analysis method that is independent of any iteration or analytical solution. It is also an efficient technique for extraction of the central vacancy without any subjectivity. The method is more direct, simple and easy-to-use than most existing techniques.The image-analysis method uses Gaussian blur filter for distinction between the areas of largest and smallest pixel intensities in a Fry plot image. It then applies the optimal threshold value and an inversion filter for extraction of the sharp central vacancy. The method also searches for the best-fit strain ellipse through the extracted central vacancy and displays axial ratio and orientation of the ellipse in a separate window. The validity of the method is tested using several computer-simulated and natural examples. 相似文献
4.
Mostafa E. Mostafa 《Tectonophysics》1984,110(3-4):317-331
A method is presented for the determination of the shape and orientation of the ellipse on a central plane section across a triaxial ellipsoid (such as a strain ellipsoid) of known orientation and magnitude. Conditional extremal values of longitudinal strain (λ) are obtained in the plane section and these are the principal axes of the strain ellipse. In solving this variational problem, the arbitrary cosntants (two undetermined Lagrange multipliers) are found to have physical meaning in themselves as proved in a complementary geometric solution. The two roots of the first constant directly determine the magnitude of the principal axes of the strain ellipse in terms of the normal to the cross section. The two arbitrary constants together define shear strains and orientation of these axes.
Strain computation uses simple, single-line equations in either frames of strained or unstrained states. 相似文献
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For some strain in the strike slip zone is difficult to be determined accurately in the classification scheme of the 7 elements of the ellipse of the strike slip strain ellipse (PDZ, R, R', P, T, Y and local contraction), the properties of the strain elements in all directions in the strained ellipse were reunderstood by analyzing the causal relationship between the mechanical state and the strain properties in a certain direction. A new model of the Riedel shear system was proposed, which contained 4 pure strain zones (pure right walk slip, pure left walking slip, pure extrusion, pure Stretch Strain Zone) and 4 complex strain zones (both stretching and right walking, both stretching and left walking, both extrusion and left walking, both extrusion and right walking slip strain zone). The closer the crack was to the direction of a single strain band, the stronger the corresponding property. The model included all the elements of the traditional model and made up for its vacancy. It proved the rationality of the left (right) row left (right) order and the double tectonic belt rule. At the same time, three research examples of Bohai Sea were cited to illustrate the application of the model: (1) The synchronous and perpendicular spatial-temporal relationship between compressive and extensional stress fields in strike-slip zones, as well as the unified but not contradictory dialectical relationship between them, were illustrated through the example of the co-controlled cycle formation of northeastern depression in Laizhou Bay Depression; (2) The Bohai Sea walk was enumerated. The research results of the slip transition zone illustrated the strain trend law of the extensional or compressive transition zone in the strike-slip zone; (3) The relationship between the strike of the effective fracture and the extensional strain zone in the present strike-slip stress field was illustrated by giving an example of the effective fracture research results of a buried hill structure in the Bohai Sea. 相似文献
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Gregory H. Roder 《Tectonophysics》1977,43(3-4)
Two methods are presented whereby finite-strain data may be determined from naturally occurring irregular strain markers (polygons) which are of unknown pre-deformation shape and distribution, without assumptions as to the orientation of the finite-strain ellipse. The first method describes “construction” of ellipses within the polygons, these ellipses providing the basis for analysis by already developed techniques. The second method is a simple extension of Wellman's method, which graphically establishes a strain ellipse from angle and line data. 相似文献
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考虑到颗粒形状对粗粒料的力学特性有重大影响,提出了一种新的表征颗粒形状的方法,即在椭圆上随机选取一系列点连接成多边形颗粒,表征狭长扁平的颗粒。新方法较圆上取点的方法能代表更多类型的颗粒形状,适用范围更广。提出了一种新的粗粒料投放算法,即先缩小颗粒,然采用随机算法将缩小的颗粒投放至给定区域,对颗粒划分好网格后,将颗粒放大到原来的大小,然后采用有限元-离散元(FEM/DEM)方法计算稳定后即生成了相应的试样。通过将上述颗粒生成及投放算法与FEM/DEM结合,应用于粗粒料的数值模拟。分析表明,FEM/DEM是研究粗粒料力学性质的较好方法,对复杂的颗粒形状也可简单建模,且因在颗粒内部划分了有限元网格,复杂的接触判断及接触力计算转化为标准统一的三角形和三角形之间的接触判断及接触力计算,所有的计算均可标准化、统一化。同时因为颗粒是可以变形的,依然保留了连续介质力学中应力和应变的概念,无须像PFC那样需通过测量圆来间接表示某点的应力、应变。最后,通过粗粒料的侧限压缩试验的数值模拟,展现了文中提出的一整套解决方案在模拟粗粒料方面的巨大潜力。 相似文献
9.
岩石有限应变测量反向轮法的计算机CSD软件设计 总被引：4，自引：0，他引：4
用计算机实现反向轮法测岩石有限应变的过程, 可提高有限应变测量的准确性和效率.开发出了用Visual Basic 5.0编写的CSD软件, 利用岩石薄片图像或者矿物颗粒轮廓图测出岩石有限应变的大小及应变椭圆长轴方向, 同时测出矿物颗粒分布的优选方位.其操作相当简便, 首先统计出图像中0°~180°各方向上矿物颗粒的边界数目; 然后在方位-边界坐标系中投点, 并利用最小二乘法进行数据点的多项式曲线拟合; 最后求出曲线的极值点坐标, 并根据坐标绘制相应的应变椭圆.软件运行中, 统计出的边界数据和拟合曲线以及应变椭圆图形都是可视的, 并能进行相应的保存. 相似文献
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Nicholas J. Milton 《Tectonophysics》1980,64(1-2)
An ellipsoid is defined by, and may be re-constructed from, any three sections through it. In the field, calculation of the strain ellipsoid from general sections (two-dimensional strain ellipses determined from measured strain markers) is complicated by the fact that, due to experimental error and/or strain inhomogeneity, the three ellipses may not come from the same ellipsoid. The ellipses must first be adjusted to make them compatible. A method is suggested by which an adjustment ellipse is determined analytically for each of the three sections. Application of these adjustment ellipses makes the three sections compatible, and the strain ellipsoid may be determined. The principal axes of the ellipsoid are derived from the ellipsoid matrix by eigenvector analysis. Examples are given of practical applications of this method. 相似文献
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A unified development of the subject of the algebraic strain analysis methods using Rf/ɸ data is outlined, embodying the main features the theories of Shimamoto and Ikeda, Mulchrone et al. and Yamaji. It is shown that the theories yields an identical strain ellipse from the same data set. However, error estimation in that of Shimamoto and Ikeda is difficult owing to the distortion of its parameter space: Resolution of their method depends on the choice of a reference orientation in the plane where strain markers are observed. In this respect, the remaining two theories have advantages. The hyperbolic vector mean method was developed in the Minkowski 3-space, thereby linked seamlessly with the visualizing methods of Rf/ɸ data, optimal strain and its confidence region. In addition, the residuals of the optimal strain ellipse determined by this method have clear physical meanings concerning logarithmic strains needed to transform a unit circle to given ellipses. 相似文献
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Graham John Borradaile 《Journal of Structural Geology》1984,6(4):433-437
Where passive elliptical markers are homogeneously and coaxially strained the strain ellipse ratio may be estimated to within 10%. This takes account of inaccuracies in measurement and does not assume knowledge of the strain ellipse's orientation. Between 50 and 75 markers are needed to achieve this accuracy and larger sample sizes do not significantly improve on this. The de-straining methods use two different tests for randomness of the de-strained fabric. One of these, the runs test, is particularly sensitive to clustering in the angular distribution and may be of particular value in de-straining sedimentary fabrics. De-straining methods are warranted where the strain ellipse ratio is ?3.0 in natural data. 相似文献
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If the particle paths are known for deforming continuous media such as rocks, the strain is determined at all stages of the deformation. The particle paths are studied for various types of simultaneous combinations of pure shear and simple shear. Any kind of progressive plane homogeneous strain can be expressed as a simultaneous superposition of pure shear and simple shear by selecting the proper ratio between the two strain rates and the proper angle between the slide direction of the simple-shear part and the principal axes of the pure-shear part. In the cases studied — except one — the angle between the slide direction of the simple-shear part and the principal strain rate
of the pure-shear part is 45°. Several combinations of the simple-shear rate, γ, and the pure-shear rate,
, are tested. These combinations give particle paths varying from sets of straight parallel lines to orthogonal hyperbolas. Distorted hyperbolas, ellipses and circles constitute the particle paths at intermediate
ratios. From the particle-path equations — which are found by integration of the rate-of-deformation equations — the strain ellipse is readily determined at any stage of the deformation. One particularly intriguing result is the rotating and pulsating strain ellipse found in the cases when the particle paths are closed curves (ellipses). Application of the results to various fold-, thrust- and inclusion structures is suggested. In an appendix the treatment of rotational deformation as a superposition of irrttational strain and rigid rotation is considered for comparison. 相似文献
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J. Wheeler 《Journal of Structural Geology》1984,6(4):417-423
A modification of the Elliott grid for plotting ellipse shape data are described. The effects of strain on elliptical markers are easy to visualize when the data are plotted on the new grid, and this allows clear interpretation of displayed data. New graphical methods for manipulating distributions of elliptical markers are directly related to an existing numerical method. When a distribution on the grid is strained, all the points move along straight, parallel lines. An initial distribution in which all the points lie on a straight line is strained into a distribution with the points lying on a hyperbola. Such curves include the analogues of ‘theta curves’. If the points lie on a circle centred at the grid origin, they are strained so as to lie on an ellipse. These are the analogues of ‘onion curves’. 相似文献
16.
Fissure veins are very important source of mineral deposits particularly that of hydrothermal deposits. The average depth vs. average strike-length of fissure vein, which is an interesting topic, was discussed in Bateman (1962). Some say that depth is equal to length while others opined that depth may be equal to half the length. Here the question arises whether the ratio depth/ length which is loosely used refers to depth to length at any given point of time or average depth vs. average length on a statistical basis. Infact these are empirical rules. The empirical rules hold good for an average basis only. Such problems are dealt under geometric probability. The ore body is more like a lens. Infact none of these hold good. The authors developed a method statistically for ore bodies of two geometries namely a circle and an ellipse. In the case of ellipse, three cases are considered namely, (i) the major axis of ellipse is horizontal to X–axis (ii) the major axis of ellipse is parallel to Y axis and (iii) the ellipse is inclined and whose major axis makes an angle q with the X–axis. In any case, only circular ore body is considered in Bateman (1962). In the case of circular body it is shown that the ratio is neither equal to one or ½ as pointed in Bateman (1962). 相似文献
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本文讨论了一种新的数学工具,即惯量投影椭球（和椭圆）,在具有任意形状构造变形体的变形描述与应变分析中的意义。论证了在均匀的递进变形过程中,构造标志体惯量投影椭球的变形与其自身的变形保持一致,两者遵循同样的均匀变形方程。在进行构造变形描述和分析时,构造标志体形状与其惯量投影椭球是等效的。惯量投影椭球具有有限应变椭球相同的性质,可以用来描述任意形状构造标志体的变形,并可以替代具有任意形状构造标志体进行变形分析。先前适用于椭圆形标志体变形分析的方法均可应用于具有任意形状的构造标志体。这将为我们对具有任意形状的构造标志体变形的描述和分析提供方便和有用的数学工具。 相似文献
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Foliation and total strain patterns of diapiric structures are very sensitive to pre- or post-diapiric deformation. This is illustrated quantitatively by superimposing homogeneous pure and simple shear on Mareschal and West's (1977) finite-element model of an antiformal diapiric ridge.
In models with post-diapiric homogeneous deformation (type 1) the foliation patterns typical for diapirism are obliterated. In models with pre-diapiric homogeneous deformation (type 2) diapiric deformation was too weak to overprint pre-diapiric foliation patterns. However, total strain patterns can be used successfully for identifying a diapiric component in the deformation history of both type 1 and type 2 models provided post- or pre-diapiric deformation is not too high. 相似文献
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This paper considers the basic principles of the strain analysis method based on the analysis of antitaxial regeneration fibrous fringes around linear rigid inclusions in a low-viscosity rock matrix. This method has been developed for pressure shadows composed of fibrous minerals, whose orientation is controlled by the major elongation direction rather than the orientation of rigid inclusions. This approach is applicable only for rocks exposed to uniform coaxial straining. The strain ellipse is calculated in two ways: for three variably oriented strain markers, it is calculated using Mohr’s circles, and for numerous strain markers by average body ellipse. The strain ellipsoid is calculated using the parameters of a few strain ellipses calculated with three and more non-parallel planes. This paper provides the data on the method testing in reference sites of Dora–Pil’ ore field in the Upper Indigirka district and Vangash area in the Yenisei Range. Regeneration fibrous fringes around fragments of fern fossils and linear rutile metacrystals were used as markers. The results of strain analysis obtained for the reference sites in the Upper Indigirka district made it possible to describe the signs of variable strain stages of developing strike-slip zones making up the Adycha–Taryn Fault Zone. Sublatitudinal ore-bearing strike-slip zones are characterized by a subvertical orientation of the elongation axes X of elongated strain ellipsoids, which are subperpendicular to quartz–carbonate veins and slope kink zones. NW-trending strike-slip zones are characterized by subhorizontal orientation of the Z shortening axes of flattened strain ellipsoids, which are subparallel to the normals of quartz–carbonate veins and veinlets. The results of strain analysis obtained for reference sites in the Vangash area made it possible to describe the thrust strain environment following the metamorphism stage and to reveal specific features in the formation of the strain textures of ore-bearing rocks based on their rheological properties. 相似文献
