Significance tests for multivariate normality of clusters from branching patterns in dendrograms

A significance test is presented for whether, based on levels of branches in a dendrogram, a cluster is from a multivariate normal distribution. The method compares the observed cumulative graph of number of branches with a graph derived from a simple logistic function. Provided the number of objects or variables is not small, the difference between graphs can be tested by the Kolmogorov-Smirnov, Cramér-von Mises, and Lilliefors statistics.Logistic functions were obtained by simulation and are available for three similarity measures: (1) Euclidean distances, (2) squared Euclidean distances, and (3) simple matching coefficients, and for five cluster methods: (1) WPGMA, (2) UPGMA, (3) single linkage (or minimum spanning trees), (4) complete linkage, and (5) Ward's increase in sums of squares. For simple matching coefficient, the mean intracluster similarity also is required.The method allows a test of whether the dendrogram could be from a cluster of smaller dimensionality due to character correlations. Good fit of the data to abnormally large or small dimensionality provides an important warning to interpretation of the dendrogram. Quantiles of test statistics were found by simulation to be well-approximated by logistic functions. The Lilliefors test is recommended for general use; if a conservative test is required, the two-tailed Kolmogorov-Smirnov test is most suitable. The method is suitable for use with a hand calculator, and a computer program for it is available from the author.     

Conodont distributions,and ages of Silurian and Devonian limestones in the Palmers Oakey district,N.S.W.

Limestones in the Palmers Oakey District, N.S.W., range in age from Middle Silurian to Early Devonian. They occur as sheet‐like, bioclastic beds and/or isolated clasts in three facies: a volcaniclastic facies, a mudstone‐limestone facies, and a limestone‐mudstone breccia facies. Multielement conodont taxa, not previously reported from Australia, include Kockelella absidata, Kockelella stauros, Ozarkodina asymmetrica, Ozarkodina stygia, Ozarkodina transitans, Pseudooneotodus bicornis, and Pseudooneotodus tricornis.     

A method for testing the distinctness of clusters: A test of the disjunction of two clusters in Euclidean space as measured by their overlap

A method is described for testing the distinctness of two clusters in Euclidean space. One first calculates the projections, q,of the N₁ and N₂ members of the clusters onto the line joining the cluster centroids. From the distributions of qan index of disjunction, W,is calculated, which corresponds to an index of overlap, V_G.The quantity W√(N₁+N₂)is distributed as noncentral tsubject to assumptions on the multivariate normal distribution of the clusters. This allows a test of whether the observed disjunction is significantly greater than a chosen figure, which is equivalent to testing whether the overlap of the clusters is significantly less than a corresponding value of V_G.Two clusters that appear distinct may be produced simply by the partitioning of a homogeneous swarm into two contiguous regions. Provided that the clusters form a dichotomy in a dendrogram, and that the clustering method yields geometrically convex clusters, a conservative test of this situation can be derived by determining the excess of Wover the value expected for a rectangular distribution.     

西秦岭铀成矿带中志留系硅岩灰岩的成因研究

通过大量的剖面测制和室内分析,从岩石的地质产状、岩石学及地球化学特别是稀土元素地球化学方面研究了西秦岭铀成矿带中硅、灰岩的成因。原始沉积的泥晶灰岩和球粒泥晶灰岩沉积于水下高地较低能环境,球粒主要为粪球粒及少量硅质生物体。硅岩具生物化学沉积（Ｉ类）和由灰岩硅化（交代）成因（Ｉ类）两种成因类型,它们在地质产状、结构构造、常量元素及稀土元素地球化学等方面都存在显著差异。在综合分析的基础上建立了西秦岭铀成矿带早志留世沉积环境模式     

基于最小熵理论和未确知测度理论的泥石流敏感性分析

为了合理确定各影响因子权重,客观分析泥石流敏感性,基于最小熵分析原理和未确知测度理论建立泥石流敏感性分析模型。选取金沙江流域26条典型泥石流沟,确定9个主要影响因子,利用最小熵分析原理分析各因子对泥石流系统贡献率及权重,然后基于未确知测度理论计算各泥石流沟的多指标综合评价尺度向量,最后根据置信度识别准则确定各泥石流沟敏感度水平。将分析结果与已有成果进行对比可知,仅有7条泥石流沟敏感性结果有所差异。将评价结果与现场实际调查情况对比分析可知,22条泥石流沟的敏感度水平与泥石流实际发育情况相符,仅有4条沟评价结果偏于“保守”,因此,利用所提出的模型进行泥石流敏感度分析是十分有效的,并可对泥石流的防治提供合理的建议,可以在实际工程中推广应用。     

结构面粗糙度统计测量最小样本数确定方法

由于结构面粗糙度具有各质异性、各向异性、非均一性和尺寸效应等特征,结构面粗糙度系数(JRC)取值具有不确定性,工程中广泛采用统计方法来分析结构面粗糙度性质,然而以往研究往往忽略样本数不足对统计结果的影响。针对结构面粗糙度统计测量时无法确定合理样本数的问题,分别提出基于变异系数级比分析及简单随机抽样原理的最小样本数确定方法。以实际工程岩体结构面表面数据为研究对象,对比分析两种方法在系列尺寸下确定的统计测量最小样本数。实例分析表明:小尺寸样本的变异系数(CV)值明显大于大尺寸样本,且CV值随取样尺寸的增大而减小,取样尺寸为10～50cm的CV值基本稳定在0.31～0.47之间,取样尺寸为60～100cm的CV值基本稳定在0.21～0.31之间;最小样本数与取样尺寸基本满足幂函数关系,且最小样本数随取样尺寸的增大而减少;系列尺寸下级比分析方法在允许误差为±2%时确定的最小样本数与简单随机抽样原理在最大允许误差为10%、置信度为95%时计算的最小样本数是一致的,相似度大于0.997。该研究方法可为工程岩体中定量获取结构面粗糙度统计测量最小样本数提供依据,保证了JRC(结构面粗糙度系数)统计测量...     

郯庐断裂带对华北板内变形及煤田构造的影响

郯庐断裂是华北板内重要变形，也是华北煤田重要控煤构造，它将华北晚古生代聚煤盆地东段切割推移，使之成为相对独立的构造单元；控制了华北板内变形：断裂旁侧派生的旋卷构造，构成新颖的煤田构造样式。从华北晚古生代聚煤盆地沉积和变形的视角看，郯庐断裂中生代走滑平移，估算最大水平位移量达５００ｋｍ，东盘辽吉块体岩壳消减量２５０ｋｍ，走滑运动时限，从印支期始，燕山晚期走滑速度增快达到高潮，并向伸展运动转化。     

Analysis of multivariate point distributions and chemical grouping of rocks

Large sets of rock compositions can be grouped by the analysis of corresponding point distributions in multidimensional space, where the separate dimensions represent the chemical variables. The point density around each composition is estimated in a small, multivariate, rectangular interval. Establishment of the identity of specimens contained in the interval, and systematic comparison of the point densities surrounding each of them, leads to the recognition of density maxima, which represent the statistical modes of the rock types present in the set. The remaining specimens by the same operations can be assigned to the groups formed. Experimental results are given for two sets, one comprising a wide variety of metasedimentary and metavolcanic rocks from the ore-bearing Skellefte district and adjacent parts of V?sterbotten, Sweden, and the other representing a less variable population of basic rocks from Norrbotten, Sweden. Linear discriminant analysis and existing geological information indicate that the groups obtained are statistically and geologically valid.     

基桩低应变法三维干扰最小点位置的影响因素及确定方法

通过工程实测信号和数值模拟分析,证明了瞬态集中荷载敲击下,桩顶三维干扰速度信号的强度沿径向先递减后递增,存在干扰最小点,并对比了不同学者提出的干扰最小点位置处的信号。参数分析表明,三维干扰最小点的位置与桩径、桩长、荷载脉宽、桩身混凝土弹性模量、土层剪切波速及土层泊松比等桩、土参数几乎无关,但与桩身混凝土泊松比密切相关,且泊松比越大,干扰最小点的位置越靠近桩中心。给出了干扰最小点位置与桩身混凝土泊松比之间的函数表达式,可方便应用于实际工程。     

适用倾斜滑面的刚性抗滑桩最小嵌固深度计算方法

为计算确定桩前滑面倾斜情况下加固边坡的抗滑桩最小嵌固深度,基于倾斜地面条件的抗滑桩计算地基系数法,确定嵌固段桩侧土层压力,同时采用塑性极限分析方法,推导与滑面倾角密切相关的嵌固段土层极限抗力,并根据桩侧地层最大压力不超过其极限抗力的条件,建立了抗滑桩最小嵌固深度计算方法,并确定了其与滑面倾角的关系。实例分析表明,抗滑桩最小嵌固深度随滑面倾角呈非线性增大,在倾角为10°～30°范围内变化显著;嵌固段地层黏聚力、内摩擦角和重度对抗滑桩最小嵌固深度均有明显影响,且呈负相关关系;本文方法所得桩体最小嵌固深度比传统考虑桩前滑面倾斜影响的方法约小18%。     

鄂尔多斯盆地西南缘早志留世酸性凝灰岩的确定及其构造意义

在鄂尔多斯盆地西南缘六盘山断裂带内的两处灰绿色“岩脉”实际上是流纹质岩屑晶屑凝灰岩,对其进行的LA-ICP-MS锆石U-Pb测年给出了最年轻的主峰年龄443 Ma和加权平均年龄441 Ma,说明这套地层形成于早志留世,这是在鄂尔多斯盆地西南缘地区初次识别出的下志留统地层。流纹质岩屑晶屑凝灰岩具有弧后盆地岩浆岩的地球化学特征,应该形成于北祁连洋盆东段向北俯冲诱发的弧后环境,推断火山碎屑应该来自陇山构造带内同时代的酸性火山作用。综合区域地质资料分析认为,流纹质岩屑晶屑凝灰岩在当时沉积于近南北向延伸的深海槽之中,该深海槽东西两侧在晚奥陶世—早志留世呈现出来完全不同的构造活动性。海槽西侧陇山地区强烈伸展并发育大规模岩浆活动;东侧鄂尔多斯地块抬升剥蚀,基本缺失上奥陶统—志留系。西部陇山地区强烈的构造活动几乎没有影响到东部的鄂尔多斯地块,海槽两侧呈现出来几乎完全不同的沉积—构造格局。中—新生代六盘山断裂带的斜向走滑活动使该流纹质岩屑晶屑凝灰岩抬升并以脉状形态出露地表。

     

施工爆破对确定海底隧道最小岩石覆盖厚度的影响研究

确定海底隧道的最小岩石覆盖厚度是在确保海底隧道安全的基础上减少工程造价的关键。施工爆破对上覆岩石的振动影响着海底隧道最小岩石覆盖厚度的确定。采用FLAC3D模拟了宁波海底隧道钻爆法施工对上覆岩层的动力学影响,分析了海底隧道的底板标高和装药量对上覆岩层交界面的稳定性影响,得到了振动速度、应力波动历时曲线和塑性区大小。通过与萨道夫斯基公式计算结果的对比,综合经济、安全方面的考虑,建议降低装药量,底板线下降2 m。     

东南极中山站-昆仑站断面最高和最低气温变化特征

利用中山站-昆仑站断面自动气象站2 m气温和同期再分析资料分析了南极沿海到内陆高原的最高和最低气温的变化特征, 并通过个例讨论了气温出现极端过程的天气背景. 结果表明: 南极中山站-昆仑站断面最高和最低气温季节变化趋势基本相似, 年际变化不明显. 最高气温标准偏差大于最低气温, 冬季气温标准偏差明显大于夏季, 且夏季气温变化幅度远小于冬季. 随海拔的增加, 最高气温年较差逐渐增大, 最低气温年变化的无芯率(气温没有明显的最小值程度)呈增大趋势, 夏季气温变化幅度逐渐增大, 冬季气温变化幅度的区域性差异不明显; 2005年7月25-31日的极端降温过程主要受到极涡、地面冷高压及下降风的共同影响.     

安徽宿松志留系—泥盆系碎屑锆石物源分析及其大地构造意义*

安徽宿松志留系—泥盆系分布于下扬子地层区西部,大别造山带东南缘,郯庐断裂带南端东侧。为了获得宿松地区志留系—泥盆系的物源信息,对出露于宿松地区的坟头组、茅山组及五通组细砂岩及粉砂岩进行了碎屑锆石LA-ICP-MS U-Pb定年。结果显示,3个样品均获得了约970 Ma、820 Ma的主要峰值年龄和约450 Ma的次要峰值年龄。碎屑锆石主要来源于花岗质岩石。根据花岗岩中锆石的判别图,研究层段碎屑锆石大多属于I型和S型花岗岩锆石,而江南造山带内新元古代及华南地区加里东期的花岗质岩石大多为I型和S型。通过与华南碎屑锆石年龄谱的对比,认为研究地层物源主要来自华南板块内部。根据锆石结晶年龄与沉积年龄差异模式图,判别出安徽宿松志留系—泥盆系形成于碰撞背景。     

Data manipulation in cluster analysis and the concept of zero presence

A zero presence results from mathematical manipulation of a zero datum due to centering and normalizing the data for each site. Ecologically it can be interpreted as having the same importance as any other presence, where any presence results from the interaction of environmental factors.     

川东南地区志留系小河坝组砂岩特征及物源分析

通过对川东南地区小河坝组砂岩的碎屑组分、岩屑类型、重矿物组合、地球化学（稀土元素、微量元素）及古流向的研究,分析了小河坝组砂岩的物源方向、母岩类型及源区的构造背景。结果显示：源区为盆地东边江南－雪峰山隆起西侧上元古界板板溪群及其侵入板溪群中的基性岩体、中基性喷出岩体。具有活动大陆边缘、大陆岛弧及被动大陆边缘的构造背景。地球化学研究进一步证明,母岩主要为更老的沉积岩再旋回沉积物及少量岩浆岩。在早志留世小河坝期以华南板块缓慢向扬子板块蠕动方式相拼接,致使扬子板块整体缓慢抬升,同时沉积中心不断向西北方向迁移,造成研究区具有明显沉积旋回性的物源供给特征。     

模糊聚类分析法与舒卡列夫法在小范围内岩溶水化学分类中的比较分析

以西龙河峄山断层带水源地岩溶水系统为例,着重利用模糊聚类分析法进行了岩溶水化学分类,并且与舒卡列夫分类法得到的结果作了比较分析,最后得出结论:模糊聚类分析法分类更合理,更能系统地、全面地反映地下水各种属性、含水层间的水力联系以及地下水的补排关系.