Strain analysis of passive elliptical markers: success of de-straining methods

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.     

Error estimation in stratigraphic correlation

Correlation in coalfields depends on the recognition of suitable reference points in the succession. In the East Midlands coal seams and marker horizons provide the most dependable reference points recognizable in borehole records. Distinctive marker horizons provide especially useful reference points as they may be considered to mark points of absolute time equivalence, but their use is limited owing to their irregular distribution. A graphic technique is used to formulate ‘confidence limits of correlation’ between marker horizons where correlation is uncertain. Functions are derived which describe the confidence limits. Coal-seam correlation data from a set of boreholes are used to derive confidence curves in a number of cases. It is concluded that one set of curves may be used for all the Middle Coal Measures of the East Midlands Coalfield. Use of these curves as general tools in correlation is demonstrated.     

A mathematical model for orientation data from macroscopic elliptical conical folds

An iterative least-squares technique to fit circular and elliptical conical surfaces to orientation data from folds is presented. A statistical model is used which assumes that each data point is an observation from a Fisher distribution. The mean of this distribution is assumed to lie on the curve to be fitted. Estimates of variances and covariances for the fitting parameters are calculated, and confidence intervals for the cone axis and half apical angle are estimated from variances and covariances. A normal test with null hypothesis that the cone angle is 90° determines if a conical model fits the data better than a cylindrical model. AnF test is used to determine whether an elliptical cone is a better model than a circular cone. In this fashion, macroscopic folds are classified into cylindrical, circular conical, or elliptical conical folds. Examples of these three types of fold are given. The Wynd Syncline near Jasper, Alberta is the first natural elliptical conical fold described as such.     

用OpenGL绘制物化探数据等值线

在Visual C 6．0环境下调用OpenGL库用网格法绘制标准物化探数据等值线，以图示形式给出数据集的二维和三维方式的等值线图，并给出相应的数字高程模型图，方便用户分析和理解数值分布情况。用线性内差法计算所有网格边上的等值点，横边上的等值点到前一个最近网格点的距离存放在二维数组X中，纵边上的等值点到下一个最近网格点的距离存放在二维数组Y中。调用自编的搜索函数在网格边上搜索等值线的线头，用追踪函数对这个线头所在线上的点进行追踪，并把追踪到的等值点的坐标按顺序存放在二维数组DW中，用OpenGL中绘制Bezier曲线的方法分段连接DW数组中的等值点，并按颜色从红到蓝递变的顺序在屏幕上绘制等值线。     

Tests of computerised strain analysis methods by the analysis of simulated deformation of natural unstrained sedimentary fabrics

Axial ratio—fluctuation measurements made on markers (oncolites, oolites, quartz grains, and accretionary lapilli) on bedding-perpendicular sections of unstrained sedimentary rocks have been homogeneously strained mathematically by set amounts, using published transformation equations, to provide a simulation of natural tectonic deformation. The resultant data have been used as test input to the strain analysis computer programs of Dunnet and Siddans (1971) and Matthews et al. (1974), which were devised to assess tectonic strain in assemblages of strained elliptical markers, with the use of limited specific assumptions concerning the nature of the pre-tectonic fabrics of the markers. The tests have shown that even slight deviations in the initial fabrics from the assumptions involved in the use of the strain analysis methods may lead to significant errors in the strain determinations. Errors are particularly large when fabrics which were imbricate in the unstrained state are used with the mistaken assumption that they were bedding-symmetric.     

A volume-conserving representation of cell faces in corner point grids

Corner point grids is currently the standard grid representation for use in reservoir simulation. The cell faces in corner point grids are traditionally represented as bilinear surfaces where the edges between the corner points all are straight lines. This representation has the disadvantage that along faults with varying dip the cell faces on either side will not precisely match, giving overlapping cells or gaps between cells. We propose an alternative representation for the cell faces. The four vertical cell faces are still represented as bilinear surfaces, but instead of having linear edges between the cell corners along the top and bottom faces, we propose a representation of the vertical cell faces where any horizontal intersection will give a straight line, giving column faces whose shape is independent of the corner point locations of the individual grid cells. This ensures that the grid columns match up and that there are no gaps or overlapping volumes between grid cells. This representation gives a local parameterization for the whole grid column, and the top and bottom grid cell surfaces are modeled as bilinear using this parameterization. A set of local coordinates for the grid cell permits all the common grid operations like volume calculation, area calculation for cell faces, and blocking of well traces.     

Adaption of polygonal strain markers

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.     

Interpolation by regularized spline with tension: II. Application to terrain modeling and surface geometry analysis

A general approach to the computation of basic topographic parameters independent of the spatial distribution of given elevation data is developed. The approach is based on an interpolation function with regular first and second order derivatives and on application of basic principles of differential geometry. General equations for computation of profile, plan, and tangential curvatures are derived. A new algorithm for construction of slope curves is developed using a combined grid and vector approach. Resulting slope curves better fulfill the condition of orthogonality to contours than standard grid algorithms. Presented methods are applied to topographic analysis of a watershed in central Illinois.     

基于Gauss-Chebyshev积分的道路平曲线计算

道路平曲线坐标计算中可能会采用线元法,其中线元类型有直线、圆曲线和缓和曲线。本文采用改进的线元表对平曲线数据进行预处理,讨论了Gauss-Chebyshev积分公式的应用并通过数值计算实验研究了高斯点数量对待定点计算的影响,在此基础上使用Gauss-Chebyshev积分方法和5点改进型GaussChebyshev积分方法解决平曲线计算中的定积分计算问题。为验证Gauss-Chebyshev积分的计算效果,选取某铁路一段平曲线作为计算数据,指定16个临近点作为数值实验对象,实验结果显示反算所得各点里程和偏距与起始给定的数值一致。     

Log-normal interpolation in grain size analysis

A computer program is described for the display of grain size distributions by log-probability plots. These plots are useful to recognize and interpret log-normal subpopulations. Because log-probability plots of the cumulative curves often show two or more straight line segments we suggest a method of ‘log-normal’interpolation for use in computing statistical parameters. The method combines advantages of graphical methods with those of mathematical moments. Finally, the frequency curve is derived by approximating the log-probability plot of the cumulative curve with spline functions.     

Inversely-Mapped Analytical Solutions for Flow Patterns around and within Inclined Elliptic Inclusions in Fluid-Saturated Rocks

In this paper, an inverse mapping is used to transform the previously-derived analytical solutions from a local elliptical coordinate system into a conventional Cartesian coordinate system. This enables a complete set of exact analytical solutions to be derived rigorously for the pore-fluid velocity, stream function, and excess pore-fluid pressure around and within buried inclined elliptic inclusions in pore-fluid-saturated porous rocks. To maximize the application range of the derived analytical solutions, the focal distance of an ellipse is used to represent the size of the ellipse, while the length ratio of the long axis to the short one is used to represent the geometrical shape of the ellipse. Since the present analytical solutions are expressed in a conventional Cartesian coordinate system, it is convenient to investigate, both qualitatively and quantitatively, the distribution patterns of the pore-fluid flow and excess pressure around and within many different families of buried inclined elliptic inclusions. The major advantage in using the present analytical solution is that they can be conveniently computed in a global Cartesian coordinate system, which is widely used in many scientific and engineering computations. As an application example, the present analytical solutions have been used to investigate how the dip angle of an inclined elliptic inclusion affects the distribution patterns of the pore-fluid flow and excess pore-fluid pressure when the permeability ratio of the elliptic inclusion is of finite but nonzero values.     

Some applications of the Mohr diagram for three-dimensional strain

The Mohr diagram for strain is rarely used in its full form, as a representation of three-dimensional strain. Recent attention has focused on various uses of the Mohr circle to express two-dimensional strain tensors. This contribution redescribes the Mohr diagram for three-dimensional strain and illustrates some new applications. The Mohr diagram for any strain ellipsoid provides an immediate method for ellipsoid shape classification. However, its greatest new potential is considered to be in the representation of strain ellipses as sections of ellipsoids.Any plane section of a strain ellipsoid can be plotted on the ellipsoid's Mohr diagram: it is here called a ‘Mohr locus’ because it is constructed as a locus of points representing the sheaf of lines which can be considered to define the plane. Mohr loci for sectional ellipses have a variety of forms, according to their orientation in the strain ellipsoid. Generally oblique sections are represented by loops bounded by the three principal circles. Their most leftward and rightward points are the plane's principal axes. Any Mohr locus can be transformed into a Mohr circle for the sectional ellipse.Mohr diagrams with Mohr loci have considerable potential as a graphical method of deriving best-fit strain ellipsoids from natural strain data. This is illustrated in three examples.     

基于多因素椭圆堆叠的岩土细观建模方法

天然岩土体具有复杂的细观结构和组成特征,现有细观建模方法难以解决任意粒径、长短轴比、倾角以及平面分布特征的多因素岩土体细观建模问题。为此基于椭圆的4段圆弧等效,结合改进的分组波前堆叠法,实现了任意粒径、长短轴比、倾角以及平面分布的快速高体积率椭圆堆叠,并以此建立了与堆叠椭圆粒径、长短轴比、倾角以及平面分布一致的凸多边形结构。与现有的椭圆堆叠ALA法和圆盘堆叠ODR方法相比,提出的方法具有更高的椭圆堆叠体积率和堆叠效率,MATLAB环境下椭圆堆叠效率为500～600个/s。与现有仅能考虑颗粒粒径分布的岩土细观建模GBM法相比,提出的方法可以同时考虑颗粒的粒径、长轴、倾角,以及平面分布4个因素,快速生成任意粒径、长短轴比、倾角以及平面分布的颗粒堆积,并建立与椭圆分布一致的岩石细观结构。通过两个岩土体细观建模案例分析表明,所提方法可以提高岩土体模型的细观建模精度与生成效率。     

The dynamics of conservative mixing in estuaries

Mixing plots, in which a dissolved constituent is plotted against salinity or chlorinity, are commonly used to interpret conservative and non-conservative processes in estuarine systems. A bend in the resulting curve is generally interpreted as indicative of the reactive or non-conservative nature of the constituent or the presence of multiple sources or sinks within the estuary. This paper demonstrates analytically that bends in mixing curves may also result from temporal variations in end-member (river or ocean) constituent concentrations even for conservative constituents. A one-dimensional dispersion equation is used to calculate the distribution of salinity and a conservative constituent in a model estuary. Both straight and bent mixing curves are shown resulting simply from changing the variability of the river constituent concentration. For no variability the curve is straight. For variability with a period much less than the flushing time, the average curve for a general data set straight, whereas the curve for a synoptic data set is bent. For variability with a period greater than the flushing time a bent curve results. Since bent mixing curves can occur for conservative properties, the use of these curves for interpretation of estuarine processes must be undertaken with an understanding of the temporal variability of the river and ocean constituents and their relationship to the estuary mixing properties and flushing time.     

A new early Holocene cryptotephra from northwest Scotland

Clarification of the temporal relationships amongst records of environmental change is dependent on accurate timescales. Event markers such as tephra layers are extremely important for constraining chronologies and providing tie points. In this report we present evidence of a previously unknown early Holocene Icelandic cryptotephra from a lake in northern Scotland—the ‘An Druim Tephra’. The calibrated radiocarbon age of 9560 cal. yr BP for this new cryptotephra makes it an important addition to the suite of cryptotephras now recorded from the last glacial termination and early Holocene in northwest Europe. In addition we report evidence in support of a ‘Younger Borrobol Tephra’ from Lateglacial sediments of Allerød age. Copyright © 2005 John Wiley & Sons, Ltd.     

First attempt to combine terrestrial cosmogenic nuclide (10Be) and Schmidt hammer relative-age dating: Strauchon Glacier, Southern Alps, New Zealand

This study provides the first attempt to combine terrestrial (in situ) cosmogenic nuclide (¹⁰Be) surface exposure dating with Schmidt hammer relative-age dating for the age estimation of Holocene moraines at Strauchon Glacier, Southern Alps, New Zealand. Numerous Schmidt hammer tests enable a multi-ridged lateral moraine system to be related to three late-Holocene ‘Little Ice Age’-type events. On the basis of cosmogenic ¹⁰Be ages, those events are dated to c. 2400, 1700, and 1100 years ago. Linear age-calibration curves are constructed in order to relate Schmidt hammer R-values to cosmogenic ¹⁰Be ages. The high explanation yielded reveals the causal link between both data sets. The potential of combining both methods in a ‘’multiproxy approach’ is discussed alongside possible future improvements. Terrestrial cosmogenic nuclide dating delivers absolute ages needed as fixed points for Schmidt hammer age-calibration curves. The Schmidt hammer technique can be used to crosscheck the boulder surfaces chosen for surface exposure dating by terrestrial cosmogenic nuclides. It should, therefore, reduce the number of samples necessary and costs.     

用双椭圆方法确定反射点位置

在反射波地震勘探中使用动校正确定反射点位置用到很多假设,如勘探深度要远远大于炮检距;假定倾斜反射界面的反射点与水平反射界面反射点都位于炮检距的中点;近似认为倾斜反射界面的动校正量等于水平反射界面的动校正量;假定反射面倾角固定且较小等,上述假设一定会造成勘探误差。由于反射点位置和反射面倾角未知,所以理论上无法唯一地确定反射点位置。如果反射波传播的介质的波速一定,从炮点发出的地震波,经反射点后,在接收点被接收,其可能的反射点是椭圆的一部分,但还不能唯一确定反射点;再取炮点和另外一个接收点,其可能的反射点是另外一个椭圆的一部分。如果假定反射面是平面,可以是水平面,也可以是有固定倾角的倾斜平面,该平面在地震波射线平面内是一条直线,该直线一定是两椭圆的公切线。把两椭圆方程和切线方程联立,就可以求解出公切点位置,公切点位置就是反射点位置,这就是用双椭圆确定反射点位置的方法。通过建立模型对勘探方法进行了检验,证实了用双椭圆方法确定反射点位置的有效性。双椭圆方法有一个重要的副产品,就是在确定反射面位置的同时计算出反射面的视倾角。     

用双椭圆方法确定反射点位置

在反射波地震勘探中使用动校正确定反射点位置用到很多假设,如勘探深度要远远大于炮检距;假定倾斜反射界面的反射点与水平反射界面反射点都位于炮检距的中点;近似认为倾斜反射界面的动校正量等于水平反射界面的动校正量;假定反射面倾角固定且较小等,上述假设一定会造成勘探误差。由于反射点位置和反射面倾角未知,所以理论上无法唯一地确定反射点位置。如果反射波传播的介质的波速一定,从炮点发出的地震波,经反射点后,在接收点被接收,其可能的反射点是椭圆的一部分,但还不能唯一确定反射点;再取炮点和另外一个接收点,其可能的反射点是另外一个椭圆的一部分。如果假定反射面是平面,可以是水平面,也可以是有固定倾角的倾斜平面,该平面在地震波射线平面内是一条直线,该直线一定是两椭圆的公切线。把两椭圆方程和切线方程联立,就可以求解出公切点位置,公切点位置就是反射点位置,这就是用双椭圆确定反射点位置的方法。通过建立模型对勘探方法进行了检验,证实了用双椭圆方法确定反射点位置的有效性。双椭圆方法有一个重要的副产品,就是在确定反射面位置的同时计算出反射面的视倾角。