共查询到20条相似文献，搜索用时 28 毫秒
1.
John C. Butler 《Lithos》1979,12(1):33-39
Chemical analyses of igneous rocks have been expressed in a variety of units and many previous workers have expressed a preference for one transformation form or another (oxide weight percentages, molecular amounts, grams per 100 cc, etc.). Transformations which operate on the columns of a data matrix (containing the measured chemical constituents) can be described as simple linear transformations which change the means and variances of the columns but not the coefficients of variation of the columns or the correlation coefficients between columns. Such transformations include changing from oxide weight percentage to molecular amounts or normalizing to some constant value. If the investigator applies a numerical or graphical method of analysis to the original and column transformed forms of the same data set any differences must be attributed to the transformation itself. If the column transformed data are converted to percentage form (such as forming molecular percentages from molecular amounts) all of the summary statistics are likely to change.Transformations which operate on a row of the data matrix (such as multiplication by sample density to convert oxide weight percentages to grams/100 cc) result in changes in the summary statistics of each column and the correlations between all pairs of columns. Equations can be written which express the properties of the columns of the row transformed data matrix in terms of the properties of the non-transformed (parent) data matrix.An investigator may have a preference as to the units in which to express chemical variations(s) of igneous rocks but such preference must be based on petrogenetic criteria and not on a comparison of the statistics of the transformed and non-transformed forms of the same data set. 相似文献
2.
瀑布沟大坝心墙拱效应分析 总被引：2，自引：0，他引：2
在总结前人提出的拱效应系数基础上,对拱效应系数的公式进行了改进,认为拱效应系数应该是实测土压力与上覆土压力和孔隙水压力之和的比值。结合瀑布沟大坝监测资料,用改进的拱效应系数计算公式对大坝心墙拱效应进行计算,并对心墙内拱效应进行动态分析。在施工期,施工工艺是影响大坝心墙拱效应系数的主要因素,填土在仪器埋设以上0～20 m时,拱效应系数较大,随着填土的增加拱效应系数减小,施工期坝体内应力分布在蓄水初期起决定性作用。在蓄水期,心墙上游侧拱效应系数与水位变化呈反相关联,拱效应系数比下游同高程和0+001 m处大;0+001 m处拱效应系数与水位变化呈正相关联,且此处拱效应系数最小;心墙下游处拱效应系数与水位变化呈正关联的关系,在心墙与基岩接触处拱效应系数大于100%。产生这种规律的原因主要有湿化、渗流、水力劈裂作用,三者共同影响,从而导致心墙内应力发生变化。 相似文献
3.
Donald H. Eckhardt 《Mathematical Geology》1984,16(2):155-171
Studies of correlation coefficients between different sets of global geophysical data may lead to useful inferences concerning their relationship or independence. If one data set is allowed to rotate with respect to another, the statistical theory is complicated and extra care is required before one can conclude that there is any statistical significance to a maximized correlation coefficient. If, for some relative rotation, two spherical harmonic fields are significantly correlated, then their individual degree component harmonics of dominant power must also be significantly correlated. Rotations can be found that result in high correlations between the dominant low-degree spherical harmonics of the geomagnetic and tertestrial gravity field potentials, but rotations can also be found that result in equally high, yet meaningless, correlations if the lunar gravity field is substituted for the geomagnetic field. To explain such high correlations, the theoretical correlation distribution function between normally distributed component harmonics is derived and then verified for lowdegree harmonics by using a Monte Carlo technique which takes into account the three-dimensional rotation group. Some curious properties surface: (1)the correlation distribution function for all possible relative orientations is almost the same between identical and uncorrelated fields; and (2)a system for determining the correlation distribution function from randomly selected fields or from randomly rotated fields is almost ergodic. 相似文献
4.
Rosenbleuth's point‐estimate method has become widely used in geotechnical practice for reliability calculations. Although the point‐estimate method is a powerful and simple method for evaluating the moments of functions of random variables, it is limited by the need to make 2n evaluations when there are n random variables. Modifications of the method reduce this to 2n evaluations by using points on the diameters of a hypersphere instead of at the corners of the inscribed hypercube. However, these techniques force the co‐ordinates of the evaluation points farther from the means of the variables; for a bounded variable, the points may easily fall outside the domain of definition of the variable. The problem can be avoided by using other techniques for some special cases or by reducing the number of random variables that must be considered. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
5.
A method for determining the reversibility of a Markov sequence 总被引：1，自引：0，他引：1
This paper describes, given a tally matrix with strictly positive entries, a method to determine whether the associated Markov process is reversible, and (for reversible Markov processes) methods to compute the reversibility matrix from the tally matrix. If the tally matrixN is symmetric, then it is shown that the Markov process must be reversible and the reversibility matrixC equalss (R
–1NR–1), whereR is the diagonal matrix whosei
th diagonal entry is the sum of the entries of thei
th row ofN (for everyi) ands denotes the sum of all the entries ofN. Because a symmetric tally matrix is of special importance in applications, a 2 test is proposed for determining, in the presence of experimental errors, whether such a matrix is symmetric. 相似文献
6.
研究多变量干旱特性联合分布的推求方法。选择干旱历时、干旱烈度和烈度峰值为水文干旱特性变量。单变量的边际分布参数分别采用矩法、概率权重法、极大似然法和遗传算法进行计算和优化。应用检验、Kolmogorov-Smirnov等6种检验法进行单变量分布的拟合度检验。采用Pearson’s古典相关系数,Spearman秩相关系数,Kendall’s,Chi-Plots和K-Plots进行变量间的相依性度量。选择4种常用的3维Archimedean Copula函数进行干旱特性变量联合分布拟合。根据RMSE、AIC和BIC准则选择最优copula。在此基础上,采用基于Rosenblatt变换的Bootstrap法进行3维copula的拟合度检验。模型应用于渭河流域北洛河状头站径流序列,结果表明:Gumbel-Hougaard copula拟合效果最好,可以描述洛河状头站3维干旱变量的联合分布。 相似文献
7.
Scaling variables and interpretation of eigenvalues in principal component analysis of geologic data
A. T. Miesch 《Mathematical Geology》1980,12(6):523-538
The dominant feature distinguishing one method of principal components analysis from another is the manner in which the original data are transformed prior to the other computations. The only other distinguishing feature of any importance is whether the eigenvectors of the inner product-moment of the transformed data matrix are taken directly as the Q-mode scores or scaled by the square roots of their associated eigenvalues and called the R-mode loadings. If the eigenvectors are extracted from the product-moment correlation matrix, the variables, in effect, were transformed by column standardization (zero means and unit variances), and the sum of the p-largest eigenvalues divided by the sum of all the eigenvalues indicates the degree to which a model containing pcomponents will account for the total variance in the original data. However, if the data were transformed in any manner other than column standardization, the eigenvalues cannot be used in this manner, but can only be used to determine the degree to which the model will account for the transformed data. Regardless of the type of principal components analysis that is performed—even whether it is Ror Q-mode—the goodness-of-fit of the model to the original data is given better by the eigenvalues of the correlation matrix than by those of the matrix that was actually factored. 相似文献
8.
A regionalized composition is a random vector function whose components are positive and sum to a constant at every point of the sampling region. Consequently, the components of a regionalized composition are necessarily spatially correlated. This spatial dependence—induced by the constant sum constraint—is a spurious spatial correlation and may lead to misinterpretations of statistical analyses. Furthermore, the cross-covariance matrices of the regionalized composition are singular, as is the coefficient matrix of the cokriging system of equations. Three methods of performing estimation or prediction of a regionalized composition at unsampled points are discussed: (1) the direct approach of estimating each variable separately; (2) the basis method, which is applicable only when a random function is available that can he regarded as the size of the regionalized composition under study; (3) the logratio approach, using the additive-log-ratio transformation proposed by J. Aitchison, which allows statistical analysis of compositional data. We present a brief theoretical review of these three methods and compare them using compositional data from the Lyons West Oil Field in Kansas (USA). It is shown that, although there are no important numerical differences, the direct approach leads to invalid results, whereas the basis method and the additive-log-ratio approach are comparable. 相似文献
9.
John C. Butler 《Mathematical Geology》1976,8(1):25-36
The application of R-mode principal components analysis to a set of closed chemical data is described using previously published chemical analyses of rocks from Gough Island. Different measures of similarity have been used and the results compared by calculating the correlation coefficients between each of the elements of the extracted eigenvectors and each of the original variables. These correlations provide a convenient measure of the contribution of each variable to each of the principal components. The choice of similarity measure (variance-covariance or correlation coefficient)should reflect the nature of the data and the view of the investigator as to which is the proper weighting of the variables—according to their sample variance or equally. If the data are appropriate for principal components analysis, then the Chayes and Kruskal concept of the hypothetical open and closed arrays and the expected closure correlations would seem to be useful in defining the structure to be expected in the absence of significant departures from randomness. If the data are not multivariate normally distributed, then it is possible that the principal components will not be independent. This may result in significant nonzero covariances between various pairs of principal components. 相似文献
10.
基于地统计学烟区土壤养分及pH值空间异质性分析——以重庆市酉阳县岩溶区为例 总被引：2，自引：2，他引：0
调查了解土壤养分及pH值空间异质性特征是制定烟区土壤养分管理与施肥决策的前提。本研究基于经典统计学和地统计学方法,分析了酉阳烟区土壤表层pH值及土壤养分要素的空间异质性特征。结果表明:酉阳烟区土壤有机质含量丰富,有效磷较缺乏;土壤养分指标的变异系数在13.11%～71.46%之间,有效磷的变异系数最大,而有机质、全氮、碱解氮在土壤中比较稳定;土壤有机质和全氮、全磷、碱解氮和有效磷呈极显著的正相关,pH值和有效磷和速效钾呈极显著的负相关;有机质、全氮、全磷及速效钾的变异函数曲线理论模型符合指数模型,而pH值和碱解氮则与球状模型拟合较好;全氮、碱解氮、全磷及有效磷表现出中等空间相关性,而有机质、全钾及速效钾的空间相关性表现较弱;分维数大小表现为:全钾的分维数最大,pH值、速效钾、有机质其次,全氮、碱解氮最少;土壤养分及pH值空间分布在东西和南北方向具有显著性差异,且在东西方向上的变异要高于南北方向。酉阳烟区土壤养分空间相关性不强,说明地形、施肥及耕作等随机性因素能够显著影响烟区土壤养分空间异质性。 相似文献
11.
In the present paper, the analysis of a strip footing resting on a layered soil system has been carried out considering the elastic moduli of soil layers as random variables. Three layers of soil have been considered and the analysis employs Monte Carlo simulation. The modulus of elasticity has been considered as random variable having lognormal distribution. Factors of safety with respect to settlement of footing and the interfacial stresses have been determined and have been related to the associated risk factor and coefficient of variation of the random variable. A detailed parametric study revealed that for a given risk level, the factors of safety is strongly dependent on the coefficient of variation of elastic modulus and only mildly upon other parameters of the soil?Cfoundation system. This facilitated the development of closed form equations for the upper bounds on factors of safety only in terms of allowable risk of failure and the coefficient of variation of elastic modulus. 相似文献
12.
DIRK GOOSSENS 《Sedimentology》1987,34(1):155-167
In this paper interference phenomena between particle flattening and particle rounding during the free vertical sedimentation of natural particles are investigated. Particle flattening is measured by the Corey Shape Factor (CSF), particle rounding by the Powers Index (P). Using Dietrich's equation, the effect of the flattening and the effect of the rounding on the terminal fall velocity of the particle can be studied separately. This is done by examining the influence of particle flattening and particle rounding on the Particle Sedimentation Coefficient (PSC), which is the ratio of the nominal diameter Dn of the particle to the equivalent sedimentation diameter Db. It appears that particle flattening and particle rounding are interdependent so that interference phenomena occur. In the case of positive interference, the combined effect of flattening and rounding on the PSC is larger than the sum of the effects of both parameters separately. If, on the other hand, the combined effect is smaller than the sum of the single effects, negative interference occurs. For fine-grained particles, the more the shape of a particle differs from a sphere in one variable (flattening or rounding), the higher will be the influence of the other variable on the free vertical fall. For coarse-grained particles, the inverse occurs. For very fine-grained particles (Dn < 200 μm (air) or < 370 μm (water)) the influence of particle rounding on free vertical settling is negligibly small. For coarser grained particles, flattening is the most important parameter if the grains are strongly flattened. If not, rounding will be the governing parameter. 相似文献
13.
边坡稳定性分析的条块稳定系数法 总被引：4，自引：2，他引：2
鉴于传统条分法对边坡安全系数定义和使用的局限性,引入了条块稳定系数的概念。分析了条间力推力线高度的影响因素,假定条间力传递时都具有相同的条间力稳定系数 ,并考虑了条块重力偏心矩的影响。根据条块的力和力矩平衡关系以及条间力假定,建立了求解条块稳定系数的四元方程组。在此基础上,求得条块稳定系数随滑动面的分布状况。根据条块稳定系数随滑动面的分布规律划分了滑体的主滑段、抗滑段和牵引段,大致判断滑坡的滑动模式。根据滑面上抗滑力和下滑力之比的定义,求解边坡整体稳定系数。采用传统条分法和所建立的条块分析法分别以圆弧滑动和折线形滑动的两个实例进行了验算,说明了条块分析法的优越性和可靠性。 相似文献
14.
Joint Consistent Mapping of High-Dimensional Geochemical Surveys 总被引：1，自引：0，他引：1
Geochemical surveys often contain several tens of components, obtained from different horizons and with different analytical techniques. These are used either to obtain elemental concentration maps or to explore links between the variables. The first task involves interpolation, the second task principal component analysis (PCA) or a related technique. Interpolation of all geochemical variables (in wt% or ppm) should guarantee consistent results: At any location, all variables must be positive and sum up to 100 %. This is not ensured by any conventional geostatistical technique. Moreover, the maps should ideally preserve any link present in the data. PCA also presents some problems, derived from the spatial dependence between the observations, and the compositional nature of the data. Log-ratio geostatistical techniques offer a consistent solution to all these problems. Variation-variograms are introduced to capture the spatial dependence structure: These are direct variograms of all possible log ratios of two components. They can be modeled with a function analogous to the linear model of coregionalization (LMC), where for each spatial structure there is an associated variation matrix describing the links between the components. Eigenvalue decompositions of these matrices provide a PCA of that particular spatial scale. The whole data set can then be interpolated by cokriging. Factorial cokriging can also be used to map a certain spatial structure, eventually projected onto those principal components (PCs) of that structure with relevant contribution to the spatial variability. If only one PC is used for a certain structure, the maps obtained represent the spatial variability of a geochemical link between the variables. These procedures and their advantages are illustrated with the horizon C Kola data set, with 25 components and 605 samples covering most of the Kola peninsula (Finland, Norway, Russia). 相似文献
15.
岩土力学数值模拟结果的概率评估方法研究 总被引：1，自引：1，他引：0
提出了一种用于评估多参数随机变异情况下岩土力学非线性数值模拟结果可靠性的多维高效直接积分型随机分析方法.它首先根据多维积分理论和可靠性分析的直接积分法确定多维随机输入参数的计值点;然后利用非线性数值模拟方法,比如有限元法或有限差分法等,完成所有计值点上的计算任务,据此就可以利用多维高效积分程序计算待评估响应量的前几阶矩(一般包括1～6阶矩);最后利用多种方法,包括曲线拟合法、加权余量法及最大熵法计算响应量的概率分布,并据此算出响应量的概率置信区间,用于定量评估响应量的可靠性.数值算例表明,此法具有精度和计算效率较高的优点. 相似文献
16.
Guocheng Pan 《Mathematical Geology》1995,27(5):609-632
A basic task in earth-science data integration is to quantify variable associations. Although manv measures have been used to determine the associations between quantitative variables, the ability to quantify qualitative attributes (e.g., categorical) is limited. Moreover, most traditional association measures are restricted to linear correlations or similarities, for example, correlation coefficient. The measures proposed in this report are designed on the basis of Shannon's entropy concepts, including directional related information, ordinary related information, and partial related information. The directional related information quantifies the association of one variable in terms of another. The ordinary related information determines the mutual association of two variables. The partial related information characterizes the association of an individual stale of one variable in terms of another variable. The properties of these measures are discussed and their sample estimates are derived from both maximum likelihood and Bayesian methods. The relations between these measures are illustrated by using synthetic examples. Two applications of these measures also are developed, including the selection of variables and evaluation of mineral resources. Finally, a case study is given to demonstrate the use of the measures in mineral resources evaluation. 相似文献
17.
利用便携式土壤盐分计测量膜下滴灌棉田不同位置和不同深度的土壤电导率,来研究膜下滴灌条件下表层土壤电导率的日内变化特征.结果显示:干旱区一膜两管膜下滴灌条件下,窄行处土壤电导率值最低,膜间最大,宽行居中,表层土壤电导率值存在显著的日内变化特征,早晚土壤电导率值低,中午电导率值高,上午的上升速率大于下午的下降速率;窄行处相对变化幅度大,膜间绝对变化幅度大,土壤电导率值日内变化幅度随深度呈减小趋势;膜下滴灌情况下,表层土壤电导率值的变化受土壤温度和气温的影响显著,但二者相关性复杂,不同深度、不同时间段的相关性不同,膜间大多呈显著正相关,窄行大多呈非显著正相关,宽行处上午呈非显著正相关,但下午呈显著负相关. 相似文献
18.
Correlation coefficients of modal variables from several suites of granitic rocks have been calculated and tested for significance using the Chayes-Kruskal and Chayes methods. The results show that although Chayes' remaining-space transformation does, in general, weaken the original proportion correlations, the positive and low-negative original proportion correlations tend to increase in absolute value because of a tendency of positive increment of the covariance by such transformation. However, no satisfactory procedure for choosing the variable to be transformed (V2)could be determined, and testing of the significance of remaining-space correlations is found to be highly problematic. It is shown also that the Vistelius-Sarmanov procedure of calculation of correlation coefficients from closed-table data does not effectively eliminate the closure effect. It is concluded that assigning statistical significance to the correlation coefficients between modal variables is, in general, unsatisfactory, except where the number of variables 8,the sample size is large (say, 30),and there is no negative element in the variance vector of the corresponding open variables. 相似文献
19.
Eighteen samples of the McMurdo volcanics on Ross Island, Antarctica consisting of basanitoid, trachybasalt and phonolite have been analyzed for rare earth elements (REE) in order to determine the details of differentiation using quantitative trace element modeling. The basanitoids have REE patterns similar to those for alkali basalts or nephelinites from ocean islands. Since there is no correlation between REE and silica contents among five basanitoids, some of the variability in the REE contents must be related to the extent of partial melting, variation in the residual mineralogies of the mantle during melting, or to inhomogeneities in the REE composition of the mantle.In order to explain the data, more than one differentiation sequence is necessary. In each case a basanitoid melt is the parent which differentiates to trachybasalt upon separation of olivine, clinopyroxene, spinel, ±kaersutite±plagioclase±apatite. If clinopyroxene, kaersutite, anorthoclase, plagioclase and apatite separate from a trachybasalt melt, a mafic phonolite results.If, however, no kaersutite is involved, an anorthoclase phonolite results. A distinct type of mafic phonolite results if kaersutite is one of the minerals that separates from the anorthoclase phonolite. If the anorthoclase phonolite precipitates plagioclase and anorthoclase and if the melt reacts with plagioclase-rich continental rocks, a trachyte results.Formerly spelled: Shine Soon Sun 相似文献
20.
为研究导热系数与影响因素之间的相关关系,建立导热系数的推算公式,以长春地区粉质黏土为研究对象,对原状土样的导热系数与其物理参数之间的相关性进行回归分析。制作9个重塑土样,测其相关的参数值,以验证回归方程的适用性。结果表明,回归分析建立导热系数与2个物理参数之间的关系式不成立;考虑天然密度、含水率和孔隙度为自变量,其分别对应的相关性系数T检验显著值(Sig)都0. 05,复决定系数为0. 886,建立的回归方程成立,自变量能准确解释因变量的变化,且含水率与导热系数呈负相关,天然密度和孔隙度呈正相关。重塑土样相关参数代入回归方程得到的导热系数值与实验实测值之间相对误差低于4%,验证了该回归方程的普遍性和适用性。 相似文献