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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
2.
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. 相似文献
3.
Prakash P. Roday Manish K. Purohit K. K. Prajapati 《Journal of the Geological Society of India》2010,76(2):151-154
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. 相似文献
4.
《Journal of Structural Geology》1988,10(2):201-209
The resolution of conventional techniques of center-to-center strain analysis is limited by the degree of original anticlustering of centers on the analyzed plane. However, the three-dimensional anticlustering of packed objects does not result in equivalent anticlustering on two-dimensional planes through these aggregates. Size variations due to imperfect sorting further decrease the anticlustering of natural aggregates. For the Fry all-object-object separations method, these problems are manifested in vague point-density distributions and ambiguously defined strain ellipses.Normalization of center-to-center distances allows more precise determination of small initial and tectonic anisotropies in packed aggregates. On planes through packed aggregates, object spacing is a function of object size, shape and the distance between object margins. Dividing the center-to-center distance between two objects by the sum of their average radii eliminates variations due to object size and sorting. Analyses of synthetic aggregates of packed spheres and statically recrystallized iron show that normalized Fry diagrams form better-defined vacancy fields and sharper rims of maximum point density regardless of the original sorting and anticlustering in the aggregate. Normalized strain analyses of deformed aggregates also show greatly increased resolution, with variable initial and tectonic ellipticity resulting in a wider ring of high point-density. 相似文献
5.
K.C. Burmeister M.J. Harrison S. Marshak E.C. Ferr R.A. Bannister K.P. Kodama 《Journal of Structural Geology》2009,31(9):1028
In moderately to highly strained sandstones, both the long axis of the bedding-parallel finite-strain ellipse, as calculated by the normalized Fry method, and the projection of the long axis of the AMS ellipsoid on the plane of bedding, align well with local “structural grain” (trends of cleavage, folds, and faults). This relationship implies that results of both 2D Fry and AMS analyses represent the local layer-parallel tectonic strain component. Do both methods provide comparable results for very low-strain sandstone (e.g., <5%)? To address this question, Fry and AMS analyses were conducted in very low-strain sandstone from two localities in the Appalachian foreland fold–thrust belt: near Rosendale in New York and the Lackawanna synclinorium of Pennsylvania. We compared the map projections of both bedding-parallel Fry ellipses and AMS ellipsoids to the local structural grain. In both study areas, projections of the long axis of Fry strain ellipses do not cluster in a direction parallel to structural grain, whereas the projection of the long axes of AMS ellipsoids do cluster closely to structural grain. This observation implies that in very low-strain sandstone, AMS analysis provides a more sensitive “quick” indicator of tectonic fabric than does normalized Fry analysis. 相似文献
6.
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。 相似文献
7.
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
8.
How tightly should a sample be packed for strain estimation by the Fry method? We address this issue using synthetic simulations of 900 images such that each image contains 200 randomly distributed grains, but differs from other images with respect to the packing tightness and the degree of sorting. Each image is coaxially distorted by various known strain ratios and the strain estimates from distorted images are obtained by the Fry method. The statistical errors in the strain estimates are found to grow larger with the decrease in the packing tightness irrespective of the level of distortion. We demonstrate that a progressive decrease in the packing tightness results in an increasingly clustered nature of grain center distribution and hence the larger errors. These results, obtained from the synthetic images, are corroborated by two natural examples of sandstone, one loosely packed and the other tightly packed. Based on the results of tests on synthetic and natural examples, we recommend that the Fry method should be used only on those samples that have \({>}30\%\) packing density. 相似文献
9.
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
10.
An objective method is developed for identifying the shape of the void generated by analysis of the spatial arrangement of point distributions using the Fry method and in particular Delaunay triangulation nearest neighbour data. The method works by numerically minimising a weighted non-linear least-squares formulation which tends to selectively apply higher weights to points below the boundary and less weight to points above the boundary. Sampling errors are estimated using a bootstrap procedure. A simulation study indicates that the method works best for closely packed object arrangements and tends to underestimate the strain axial ratio at high imposed strains. Overall the method is found to be objective and consistent. 相似文献
11.
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。 相似文献
12.
Fractal modelling has been applied extensively as a means of characterizing the spatial distribution of geological phenomena
that display self-similarity at differing scales of measurement. A fractal distribution exists where the number of objects
exhibiting values larger than a specified magnitude displays a power-law dependence on that magnitude, and where this relationship
is scale-invariant. This paper shows that a number of distributions, including power-function, Pareto, log-normal and Zipf,
display fractal properties under certain conditions and that this may be used as the mathematical basis for developing fractal
models for data exhibiting such distributions. Population limits, derived from fractal modelling using a summation method,
are compared with those derived from more conventional probability plot modelling of stream sediment geochemical data from
north-eastern New South Wales. Despite some degree of subjectivity in determining the number of populations to use in the
models, both the fractal and probability plot modelling have assisted in isolating anomalous observations in the geochemical
data related to the occurrence of mineralisation or lithological differences between sub-catchments. Thresholds for the main
background populations determined by the fractal model are similar to those established using probability plot modelling,
however the summation method displays less capacity to separate out anomalous populations, especially where such populations
display extensive overlap. This suggests, in the geochemical data example provided, that subtle differences in the population
parameters may not significantly alter the fractal dimension. 相似文献
13.
In this paper, based on the concepts of uncertainty and reliability analyses, a method used for assessment of risk due to
debris flow events is proposed. First, procedures for obtaining the configuration of debris-flow fans are presented. Then,
the parameters affecting the configuration of debris-flow fans are identified and their corresponding means and standard deviations
are derived. Finally, the proposed method is applied to the Shih-Pa-Chung Creek in central Taiwan. The expected deposition
thickness at any point in the deposition area is computed and then the contours of risk for the 50-year and 100-year events
are constructed. Regarding the expected deposition thickness, it is found that the closer the distance from the canyon mouth,
the larger the debris-flow thickness becomes. The results also show that the contours of risk are of the shape of an ellipse
similar to the shape of deposition area, and the risk at a point decreases with increasing distance of that point from the
canyon mouth. In addition, when the return period of rainfall event is fixed, the variation in risk decreases as the distance
from the canyon mouth increases. For the assessment of risk due to debris flow events, the proposed method is recommended
as an alternative to the existing methods, because the influence of all the uncertainty of the parameters is considered. 相似文献
14.
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
15.
杨新岳 《大地构造与成矿学》1993,17(1):82-92
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。 相似文献
16.
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 (SX) 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 (SY) 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. 相似文献
17.
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 Rf/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 Rf/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. 相似文献
18.
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
19.
An eigenmethod for characterising the directional properties of convex polygons is described. Given a polygon, regular in the undeformed state, its image following a homogeneous strain transformation is an irregular polygon whose eigensolution (an ellipse) has the axis ratio and orientation of the strain ellipse. The eigenmethod can therefore be used for finite strain estimation using polygonal strain markers, and is compared with alternative methods recently proposed by Roder (1977) and Sanderson (1977). 相似文献
20.
Summary The theoretical model of the relationship between sub-surface and surface subsidence movements proposed earlier by the authors of this paper is briefly described and further tested against another case history example. Using this model, the magnitudes of the maximum subsidence, tilt and horizontal strain at sub-surface horizons between the ground surface and seam level are predicted in terms of the magnitudes of the corresponding components at the surface due to the extraction of subcritical panels with a wide range of width-depth ratios and the results presented in the form of nomographs and tables. These graphs and tables could be used to estimate the maximum subsidence, tilt and horizontal strain at any chosen sub-surface horizon associated with the extraction of a subcritical panel from the known corresponding maximum values at the surface.The proposed theoretical model can also be used to predict sub-surface subsidence components at any point within the zone influenced by the extraction of a panel from the corresponding surface subsidence components which may be obtained from field measurements or pre-calculated using any existing method of surface subsidence prediction. As an example, the profiles of surface and sub-surface subsidence at various horizons between the ground surface and the seam level resulting from the extraction of an assumed sub-critical longwall panel are predicted using the theoretical model together with the empirical method of surface subsidence prediction. The pattern of sub-surface subsidence movements in the strata overlying the panel is examined. 相似文献