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1.
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
2.
A.W.B. Siddans 《Tectonophysics》1980,64(1-2)
It has been suggested (Oertel, 1971, 1972;Owens, 1974; Shimamoto and Ikeda, 1976) that some methods for analysis of finite homogeneous strain from deformed ellipsoidal objects (Ramsay, 1967; Dunnet, 1969a; Elliott, 1970; Dunnet and Siddans, 1971; Matthews et al., 1974) require sections to be cut in principal planes of the finite strain ellipsoid. A mathematical model is presented which enables the homogeneous deformation of a randomly oriented ellipsoid to be investigated. In particular the elliptical shapes that result on any three mutually perpendicular sections through the ellipsoid, in the deformed state, can be computed, together with the corresponding strain ellipses. The resulting ellipses can be unstrained in the section planes by applying the corresponding reciprocal strain ellipses. It is shown that these restored ellipses are identical with the elliptical shapes that result on planes through the original ellipsoid when the planes are parallel to the unstrained orientation of the section planes.The model is extended to investigate the finite homogeneous deformation of a suite of 100 randomly oriented ellipsoids of constant initial axial ratio. The pattern of elliptical shapes that result on any three mutually perpendicular section planes, in the deformed state, is computed. From this data the two-dimensional strain states in the section planes are estimated by a variety of methods. These are combined to recalculate the three-dimensional finite strain that was imposed on the system. It is thus possible to compare the results of the two- and three-dimensional analyses obtained by the various methods. It is found that providing all six independent combinations of the two-dimensional strain data are used to compute a best finite strain ellipsoid, the methods of Dunnet (1969a), Matthews et al. (1974) and Shimamoto and Ikeda (1976) provide accurate estimates of the three-dimensional finite strain state.It is concluded that measurement of the two-dimensional data on section planes parallel to the principal planes of the finite strain ellipsoid is not necessary and that all six independent combinations of the two-dimensional strain data should always be made and used to compute a best finite strain ellipsoid. 相似文献
3.
Kingshuk Roy Choudhury 《Mathematical Geosciences》2009,41(5):535-553
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. 相似文献
4.
The available methods for measuring strains in two and three dimensions from passive ellipsoidal objects are compared in an attempt to determine the most useful and precise procedure for the structural geologist. A comparison of data collection techniques showed that the use of thin orthogonally cut slabs or mylar overlays used with a monocomparater provides the most reproducible data. Lisle's theta-curve and Shimamoto and Ikeda's algebraic methods provided the most precise, and probably most accurate, two-dimensional data while Miller and Oertel's procedure and possibly Dunnet's PHASE 5 program gave the best three-dimensional results.An examination of errors encountered in strain analyses suggests that all of the available methods give accurate orientations of the finite strain ellipsoid. However, the magnitudes of strain ratios show large variations that are dependent on the sample size and procedure used. Shimamoto and Ikeda's method again proved to be the most precise, giving reproducible results with as few as ten elliptical objects.The samples used in the above comparison are part of a larger analysis of strains occurring in southeastern Maine. Structural elements observed in four selected areas of Avalonian belt rocks and the strain data collected suggest that the region has undergone at least three non-coaxial deformations with D1 >D2 >D3. 相似文献
5.
被动椭圆形标志物应变分析的计算机模拟 总被引：1，自引：0，他引：1
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。 相似文献
6.
A major problem in strain analysis of ellipsoidal fabrics is how to separate the effects of initial preferred orientation of objects from the effects of strain. New algebraic methods are presented here which apply to many of the situations previously analysed by graphical and iterative techniques. The algebraic solutions are simple and highlight some assumptions implicit in previous methods, and the relations between those methods. It is shown that many final ellipsoidal fabrics cannot be produced from initial fabrics which were symmetric with respect to bedding, and that a three-dimensional analysis is preferable to analysis on two-dimensional section planes. 相似文献
7.
Norman Fry 《Journal of Structural Geology》1979,1(3):221-229
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. 相似文献
8.
J. Wheeler 《Tectonophysics》1986,126(2-4)
Many rocks contain ellipsoidal objects (such as pebbles or reduction zones) which display a variety of shapes and orientations. In deformed rocks such objects may be used for strain analysis by using the concept of an average ellipsoid (here called the “fabric ellipsoid”). Two fabric ellipsoids are defined which are the results of two different algebraic averaging processes. During deformation of ellipsoidal distributions, the fabric ellipsoids change as if they were themselves material ellipsoids and are therefore of fundamental importance in strain analysis.In most studies to date, such 3-D fabric ellipsoids have been obtained from 2-D average ellipses determined on section planes cut through the rock sample. Previous work has assumed that the average ellipses will approximate to section through a single fabric ellipsoid. I show here that this is not the case as sectioning introduces a systematic bias into the section ellipse data. This bias is distinct from the statistical errors (due to finite sample size and measurement errors) discussed in other work and must be considered in any method of strain analysis using section planes. 相似文献
9.
10.
为提高传统频率域激电信号接收机的通用性,设计了一种可采集和处理变频信号、双频信号和伪随机多频信号等多种频率域激电信号的采集平台。该平台以STM32微控制器为核心设计硬件电路,实现低通滤波、程控放大、模数转换以及数据通信等功能;在LabVIEW中设计上位机,进行参数设置、数字滤波、频谱分析、幅值测量、求值计算等处理,得到幅频率等目标参数,并具有波形显示与回放、数据存储与查看等功能;设计了阻容网络模拟实验,3种激电法幅频率实测值与理论值绝对误差均小于0.5%。实验表明,平台能够灵活选取不同方法进行采集和处理,测量精度较高,在资源勘查以及煤矿水害探测等方面具有良好的应用前景。 相似文献
11.
In this paper we first estimate the strain rate field with 1202 GPS vectors from 1999 to 2005 in the Chinese continent. Then we propose a method to make error analysis of the strain rates computed from GPS vectors based on the Monte Carlo technique. In general, the orientations of compressive principal strain rates are in agreement with those of present tectonic stresses. The strain rates in the paper confirm the tectonic features of Tibetan Plateau such as NE–W compression and shortening, E–W extension, and normal faulting along near N–S faults. At the same time, the eastward extrusion in the east part of Tibet can also be seen from the strain rate field. In the error analysis, independent computation of strain rates is repeated for a large number of times, both the absolute and relative errors as well as the mean value of strain rates are obtained through statistical theory. The error result shows that the errors of strain rates may be associated with the uncertainties of GPS measurement and the distribution of GPS stations in space. The magnitude of the strain rate error is in the range of 3–8 × 10?9/yr across China in general. However, we found that the relative errors are much larger in East China than those in the west of China. In addition, the relative errors of maximum shear strain rates are smaller than those of surface dilation rates. Also, we found that there may be some correlations between maximum shear strain rates and seismic activities. Where the maximum shear strain rates are higher, there the earthquakes occur more frequently. The computed GPS strain rates reveal the distributed nature of deformation across the whole Chinese continent, and can represent the main present-day tectonic features. The strain rate and its error in the paper may provide important constraints to geodynamical modeling. 相似文献
12.
B. Paláncz A. Somogyi N. Rehány T. Lovas B. Molnár 《Australian Journal of Earth Sciences》2016,63(5):665-673
Environmental, engineering and industrial modelling of natural features (e.g. trees) and man-made features (e.g. pipelines) requires some form of fitting of geometrical objects such as cylinders, which is commonly undertaken using a least-squares method that—in order to get optimal estimation—assumes normal Gaussian distribution. In the presence of outliers, however, this assumption is violated leading to a Gaussian mixture distribution. This study proposes a robust parameter estimation method, which is an improved and extended form of vector algebraic modelling. The proposed method employs expectation maximisation and maximum likelihood estimation (MLE) to find cylindrical parameters in case of Gaussian mixture distribution. MLE computes the model parameters assuming that the distribution of model errors is a Gaussian mixture corresponding to inlier and outlier points. The parameters of the Gaussian mixture distribution and the membership functions of the inliers and outliers are computed using an expectation maximisation algorithm from the histogram of the model error distribution, and the initial guess values for the model parameters are obtained using total least squares. The method, illustrated by a practical example from a terrestrial laser scanning point cloud, is novel in that it is algebraic (i.e. provides a non-iterative solution to the global maximisation problem of the likelihood function), is practically useful for any type of error distribution model and is capable of separating points of interest and outliers. 相似文献
13.
Sammen Saad Sh. Mohamed T. A. Ghazali A. H. Sidek L. M. El-Shafie A. 《Natural Hazards》2017,87(1):545-566
The study of dam-break analysis is considered important to predict the peak discharge during dam failure. This is essential to assess economic, social and environmental impacts downstream and to prepare the emergency response plan. Dam breach parameters such as breach width, breach height and breach formation time are the key variables to estimate the peak discharge during dam break. This study presents the evaluation of existing methods for estimation of dam breach parameters. Since all of these methods adopt regression analysis, uncertainty analysis of these methods becomes necessary to assess their performance. Uncertainty was performed using the data of more than 140 case studies of past recorded failures of dams, collected from different sources in the literature. The accuracy of the existing methods was tested, and the values of mean absolute relative error were found to be ranging from 0.39 to 1.05 for dam breach width estimation and from 0.6 to 0.8 for dam failure time estimation. In this study, artificial neural network (ANN) was recommended as an alternate method for estimation of dam breach parameters. The ANN method is proposed due to its accurate prediction when it was applied to similar other cases in water resources.
相似文献14.
Shahab Shahbeik Peyman Afzal Parviz Moarefvand Mania Qumarsy 《Arabian Journal of Geosciences》2014,7(9):3693-3704
Estimation of mineral resources and reserves with low values of error is essential in mineral exploration. The aim of this study is to compare inverse distance weighted (IDW) and ordinary kriging (OK) methods based on error estimation in the Dardevey iron ore deposit, NE Iran. Anisotropic ellipsoid and variograms were calculated and generated for estimation of Fe distribution by both methods. Density, continuity of ore and waste, the number of points involved, and the discretization factor in the estimation of ore and waste boundaries were determined and the resource estimated by IDW and OK methods. Estimation errors were classified based on JORC standard, and both methods were compared due to distribution of error estimation. Results obtained by the study indicate that error estimation of OK method is less than IDW method and that the results of OK method are reliable. 相似文献
15.
Denis Marcotte 《Mathematical Geology》1995,27(6):749-762
Conditional simulation with data subject to measurement error has received little attention in the geostatistical literature. The treatment of measurement error in simulation must be different from its treatment in estimation. Two approaches are examined: pre- and post-simulation filtering of data measurement error. The pre-simulation filtering is shown to be inefficient. The post-simulation filtering performs best. It is done by factorial kriging and a modified version of factorial kriging which ensures predetermined theoretical variance for the filtered data. It also is shown that the theoretical variogram of the filtered data reproduces the underlying variogram (i.e., without noise) almost perfectly. A simulation with a high level of correlated noise is used for validation and comparison. The post-simulation filtered values show an experimental variogram in agreement with the previously identified underlying variogram. Moreover, the filtered image compares well with the true image. The theoretical variogram corresponding to the post-simulation filter can be computed beforehand. Thus, the size of the simulation grid and of the filter neighborhood can be adjusted to ensure good reproduction of the underlying variogram. 相似文献
16.
扩散是低渗透系数情况下溶质迁移的主要方式,目前尚没有测定高塌落度防渗墙填料扩散系数的试验方法。根据沥出试验原理,将处于流动状态的填料用半透膜包裹进行透析试验,通过有限圆柱中溶质迁移解析解对溶质迁移过程进行拟合求其扩散系数,探讨了试验和数据处理的相关问题,研究了膨润土含量和盐浴浓度对扩散系数的影响规律。结果表明,随拟合天数增加,填料中NaCl有效扩散系数减小,而误差增大;高塌落度填料中溶质迁移明显比压实土样中快,按拟合误差小于0.5%作为试验数据取舍依据,这一误差要求实际上是对溶质迁移以扩散为主导这一条件的量化,保证了采用纯扩散解析解进行数据拟合的合理性;扩散系数随填料中膨润土含量增加而减小,随盐浴浓度增加而减小,但在试验范围内数值变化不大,透析试验是快速测定防渗墙填料中溶质有效扩散系数的可行方法。 相似文献
17.
18.
David J. Sanderson 《Mathematical Geology》1977,9(5):483-496
Arrays or rosettes of lines along which the extension or relative extension can be determined constitute finite strain gauge rosettes. Expressions for the principal strains and their orientation in terms of three nonparallel gauge extensions can be established in a suitable form for algebraic evaluation, thus replacing graphical methods based on Mohr construction. Three types of strain rosette problems, including one which utilizes angles, are particularly relevant to the study of deformed rocks. These, together with their relation to grid methods, are discussed and simple examples of their use given. Finally, an approach to the problem of finding best-fitting solutions to overdetermined regular strain rosettes is discussed. 相似文献
19.
The differential code bias (DCB) is the differential hardware (e.g., the satellite or receiver) delay that occurs between two different observations obtained at the same or two different frequencies. There are two approaches used to estimate DCBs for receivers and satellites: the relative and absolute methods. The relative method utilizes a GPS network, while the absolute method determines DCBs from a single station (zero difference). Three receiver types based on the pseudo-range observables were used here to collect the GPS data: Codeless Tracking, Cross Correlation, and Non-Cross Correlation styles. According to its types, GPS receivers have responded to restrictions on the GPS signal structure in different ways. The main goal of the current research is providing a method to determine the DCBs of GPS satellites and dual frequency receivers. The developed mathematical model was based on spherical harmonic function and geometry-free combination of pseudo-range observables (C/A or/and P-code) according to receiver type. A new elevation-dependent weighting function with respect to GPS satellites in our algorithm was applied. The applied weighting function was used to consider the quality variation of satellite DCBs, which is caused by pseudo-range measurement errors. The code of the proposed mathematical model was written using MATLAB and is called “zero difference differential code bias estimation (ZDDCBE)”. This code was tested and evaluated using data from IGS GNSS stations and different types of GPS stations out of IGS network installed in Egypt and Saudi Arabia. The estimated values from the ZDDCBE code show a good agreement with the IGS analysis centers with a mean error of estimation for the receiver DCB equal 5.94%. Therefore, the ZDDCBE code can be used to estimate the DCB for any type of receiver regardless if the receiver is from IGS network or not. 相似文献
20.
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