An application of R-mode factor analysis to the study of metamorphic petrogenesis

R-mode factor analysis of modal and chemical data clarifies the trends of mineralogical evolution and associated chemical variations in amphibolites from the Northwest Adirondack Mountains, New York and the Willyama Complex, Broken Hill District. In both areas the principal mineralogical reaction attending metamorphism, as described by the first factor, appears to have been Hornblende + Quartz → Calcic pyroxene + Orthopyroxene + Plagioclase. For the Adirondack amphibolites, the derived reaction coefficients viewed against the modal contents of the pyroxenes suggest another hornblende breakdown reaction producing calcic pyroxene, which is corroborated by the first appearance of the phase a little NE of Emeryville. The other factors extracted reveal the underlying parameters responsible for the development of biotite, sphene, opaques and quartz in the Adirondack metabasites and albite, anorthite, ilmenite and quartz in the Willyama Complex amphibolites.The analysis also demonstrates that the principal mineralogical reactions in both the areas have been combinations of thermal and ionic types and further that to decipher the net mineralogical changes in high grade metamorphic basic and pelitic rocks it is necessary to extend the integration of the ‘part reactions’ occurring in different domains to the level of a hand specimen.     

R-mode factor analysis applied to uranium exploration in the Montrose quadrangle, Colorado

R-mode factor analysis is used to describe the relationships among 18 remotely sensed and geochemical data sets (variables) for the Montrose 1° × 2° quadrangle, Colorado, a region that covers 19 000 km². The data sets contain reconnaissance-scale information and include Landsat imagery, airborne geophysical information (eU, eTh, K40, aeromagnetics), elevation, and hydrogeochemical and stream sediment analyses. The elements U, K, Dy, Hf, V, Th, Ca and Ba in sediments and U in waters were selected.The results of the factor analysis for the entire quadrangle are compared to the results for a 50 km × 50 km test area containing several known uranium occurrences. Four factors account for 70.0% of the total variance in the data. These are interpreted as a felsic factor, Landsat factor, economic or mineralization factor (in terms of uranium mineralization and potential mineralized areas), and a volcanic factor.Graphical representations (maps) of the raw data, factor approximations, residuals for each data set, and the four-factor model greatly aid interpretation of the analytic results. We find that data integration techniques and R-mode factor analysis can be used with some success in uranium resource appraisal.     

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.     

An effect of closure on the structure of principal components

The principal components transformation generates, from any data array, a new set of variables—the scores of the components—characterized by a total variance exactly equal to that of the initial set. It is in this sense that the transformed variables are said to contain, preserve, or account for, the variance of the original set. The scores, however, are uncorrelated. In the course of the transformation, what becomes of the strong interdependence of variance and covariance so characteristic of closed arrays? The question seems to have attracted little attention; we are aware of no study of it in the earth sciences. Experimental work reported here shows quite clearly that the overall equivalence of variance and covariance imposed by closure, though absent from the component scores,may emerge in relations between the coefficientsof each of the lower-order components; if the raw data are complete rock analyses, the sum of all the covariances of the coefficients of such a component is negative, and is very nearly equal to the sum of all the variances in absolute value. (In all cases so far examined, the absolute value of the first sum is a little less than that of the second.) The principal components transformation provides an elegant escape from closure correlation if a petrographic problem can be restated entirely in terms of component scores, but not if a physical interpretation of the component vectors is required.     

降雨对路堤斜坡稳定性影响的时间效应

以某高速公路填筑试验路堤为例,基于非饱和土渗透及强度理论,采用渗流场与应力场、稳定性计算耦合的方法,对两种不同透水特性的路堤在降雨过程中孔隙水压力和稳定性系数随时间变化的特点及规律进行较为深入的探讨。结果表明,（1）透水性能较好的路堤斜坡下部降雨入渗要强于斜坡上部,透水性能较差的路堤斜坡,雨水往往以近似于均匀的形式入渗;（2）透水能力强的路堤斜坡在短暂的超强降雨或者强度较低但持续时间超长的降雨过程中,其最小稳定性系数易于出现滞后现象,一般滞后0.5～3 d,透水能力差的路堤斜坡最小稳定性系数有显著滞后特点,一般滞后7～15 d;（3）总降雨量一定、雨强大于等于50 mm/d条件下透水能力强斜坡能达到的最小稳定性系数随降雨时间增长而降低,而透水能力差的斜坡最小稳定性系数受雨强和降雨时间共同影响。     

Viscosity effect on consolidation of poroelastic soil due to groundwater table depression

In this study, the viscosity effect on consolidation of poroelastic soil due to groundwater table depression is examined. A viscoelastic consolidation numerical model is developed to conduct this examination. By nondimensionalizing the governing equations the viscosity number that depends on hydraulic conductivity, viscous moduli, and thickness of soil is obtained to represent the viscosity effect on consolidation of poroelastic soil. The case of clay stratum sandwiched between sandy strata subjected to sudden and gradual groundwater table depressions is used to investigate the importance of viscosity effect to poroelastic consolidation. The results show that the displacement and pore water pressure of clay stratum are strongly related to the viscosity effect. The overestimation of soil displacement will occur if the viscosity effect is neglected. Hence, the viscosity effect needs to be considered in modeling consolidation of poroelastic soil under groundwater table depression.     

Land subsidence due to groundwater pumping and recharge: considering the particle-deposition effect in ground-source heat-pump engineering

With the rapid development and use of ground-source heat-pump (GSHP) systems in China, it has become imperative to research the effects of associated long-term pumping and recharge processes on ground deformation. During groundwater GSHP operation, small particles can be transported and deposited, or they can become detached in the grain skeleton and undergo recombination, possibly causing a change in the ground structure and characteristics. This paper presents a mathematical ground-deformation model that considers particle transportation and deposition in porous media based on the geological characteristics of a dual-structure stratum in Wuhan, eastern China. Thermal effects were taken into consideration because the GSHP technology used involves a device that uses heat from a shallow layer of the ground. The results reveal that particle deposition during the long-term pumping and recharge process has had an impact on ground deformation that has significantly increased over time. In addition, there is a strong correlation between the deformation change (%) and the amount of particle deposition. The position of the maximum deformation change is also the location where most of the particles are deposited, with the deformation change being as high as 43.3%. The analyses also show that flow of groundwater can have an effect on the ground deformation process, but the effect is very weak.     

Using robust staged R-mode factor analysis and logistic function to identify probable Cu-mineralization zones in Khusf 1:100,000 sheets,east of Iran

Factor analysis method is a multivariate analysis technique that is widely used for the interpretation of stream sediment geochemical data. The purpose of factor analysis is describing the changes in a set of multi-element geochemical data by reducing the dimension of the data and variables to a number of factors that can present the hidden association between elements. Differences in mobility, physical, and chemical properties of the elements and the nature of the factor analysis method in which the matrix of all data is used cause paragenes elements not to be found on the output of factor analysis. In this research, to improve the output of factor analysis for deriving the best reagent multi-element mineralization, robust staged factor analysis method was used according to the close nature of geochemical data in order to identify the Cu-mineralization potential in Khusf 1:100,000 sheets located at the east of Iran. The robust staged factor analysis enhances the recognition of anomalous geochemical signatures and increases geochemical anomaly intensity and the percentage of the total explained variability of data. As indicated by the results of the study, few anomalous zones have been found in the study area. The observation of chalcopyrite and malachite mineralization in andesite and dacite–andesite rocks in a region during the field study confirms the effectiveness of the robust SFA technique. Such studies can be used by mine engineers and geologists for designing an optimum grid exploration on the next exploration steps.     

隧道盾构施工引起土体力学效应的计算分析

随着市政建设的快速发展,地铁盾构越来越多的穿越密集的建（筑）物和地下管线,隧道施工对周围环境的影响已经引起人们足够的重视。视隧道开挖引起的土体移动为一随机过程,应用随机介质理论,根据土体损失的空间分布规律,得到土体损失引起的位移计算公式;在此基础上,结合弹性理论基本方程推导了隧道开挖引起周围土体应力变化的计算公式。最后,结合算例,对盾构推进过程中引起的土体位移和附加应力分别进行计算,旨在了解盾构施工引起的环境力学效应,为采取措施减小这种影响提供依据。     

基坑开挖对邻近地下管线影响的变形控制标准

基坑开挖会引起邻近区域地埋管线的附加受力和变形,甚至会引起管线的开裂破坏。基于位移控制理论,对板式支护体系由于基坑开挖而引起的周边自由土体位移场的分布规律进行了探讨,通过位移控制两阶段简化分析方法与位移控制有限元方法的对比,验证了简化方法的合理性。其次对最近修订的《上海市基坑工程技术规范》的基坑环境保护标准进行了探讨,利用简化方法通过算例计算以分析其仍需改进的方面,在此基础上,基于地下管线的自身承受能力,提出了基坑开挖对管线保护的变形控制标准,给出了为保证管线正常使用,基坑开挖深度与基坑允许侧向变形的关系,从而可以为基坑开挖环境影响评价标准的建设提供相应的理论依据。     

表面约束下的沉桩挤土效应数值模拟研究

采用数值方法对表面约束下的沉桩挤土效应进行了研究。以道路约束为例，讨论了不同宽度道路以及道路与浅基础共同约束时，对沉桩挤土引起的地表隆起及水平位移的影响，得出若干有参考价值的结论。     

岩石裂纹闭合效应及其定量模型研究

岩石的裂纹闭合效应对于岩石的变形以及强度性质具有重要影响。主要研究了岩石内部微裂纹的闭合压密效应及其定量评价方法。首先,基于有效介质理论将岩石的轴向应变分为基质轴向应变和裂纹轴向应变两部分;然后通过3组岩石压缩试验资料,建立裂纹轴向应变随轴向应力变化的负指数模型。分析发现,负指数模型可以较好地描述岩石裂纹闭合压密阶段的非线性。裂纹闭合应变可以在一定程度上反映岩石内部的微裂纹数量(密度),能够描述微裂纹密度在单轴、三轴压缩条件下的变化规律。     

R-mode factor analysis of lithologic variables from cyclically deposited Late Paleozoic Barakar sediments in Singrauli Gondwana sub-basin,Peninsular India

The quantitative relationships between lithological variables from the Late Paleozoic coal bearing cycles have been investigated using factor analysis in an attempt to analyze net subsidence during the deposition of these cycles. The results suggest that there are only two non-zero eigenvalues in varimax matrix which indicate that the hyper ellipsoid enclosing the data points have seven axes of zero length and exists an ordinary two dimensional ellipsoid. The data points can be located with reference to two mutually perpendicular axes. Loading on thickness of sandstones, thickness of shale, number of sandstone beds and number of shale beds are extremely high on RF-I and low on the other factor. This would lead to the interpretation that a balance was maintained throughout the Barakar sedimentation between the rate of deposition and the rate of subsidence. On the other hand, loading on number of coal beds is high on ‘ suggesting that the development of peat swamps (coal beds) is not a normal feature during the Late Paleozoic Barakar sedimentation in this Gondwana sub-basin.     

基于加载动力效应对孔压滞后现象的一个解释

在底部可测孔压的固结仪内进行单面排水固结试验时,观测到试样底部的孔压可出现滞后现象。为分析其原因,考虑加载引起的动力效应,建立以竖向应变为求解对象的一维动力固结方程,并用有限差分法进行求解。引入新指标CD来综合考虑试样压缩模量、渗透系数、密度以及土样厚度等4个参数对动力效应的影响,探讨了该指标对固结过程中孔隙水压力的影响。计算结果表明,瞬时加载引起的动力效应是引起试样内孔压滞后的一个原因,并且对于压缩模量或渗透系数较大的试样,更易出现孔压滞后现象,同时动力效应对固结度的影响则主要体现在固结的前期。最后讨论了固结分析时可以忽略动力效应的范围。     

Subsidence due to crack closure and depressurization of hydrothermal systems: a case study from Mt Epomeo (Ischia Island,Italy)

Levelling surveys carried out between 1990 and 2003 on the Mt Epomeo resurgent block (Ischia Island) record negative dislocations on its northern and southern flanks with a maximum subsidence rate of 1.27 cm yr⁻¹. This deformation is not associated with the cooling, crystallization or lateral drainage of magma and cannot be explained by a pressure point or prolate ellipsoid source. Results from dislocation models and the available structural and geochemical information indicate that the subsidence is due to crack closure processes along two main ENE–WSW and E–W preexisting faults, which represent the preferred pathway of CO₂ degassing from the hydrothermal system located beneath Mt Epomeo. The monitoring of the dislocations and CO₂ flux along these faults could give useful information on the dynamics of the hydrothermal system.     

Publication bias in the neighbourhood effects literature

There is a strong belief amongst policy makers regarding the existence of neighbourhood effects, i.e., that above and beyond other influence, the neighbourhood in which they live influences individuals’ life chances. The evidence from scientific reviews leans towards the idea that it is likely that neighbourhoods indeed affect life chances of their residents. Yet, amongst scientists there is no consensus about the neighbourhood effects hypothesis because of differences in methodological and theoretical approaches. I ask why, when there is no consensus, the evidence leans towards supporting the neighbourhood effects hypothesis within policy circles. To test whether the scientific evidence for the neighbourhood effects hypothesis is driven by publication bias, I employ a meta-analysis over all studies that test for a relation between neighbourhood characteristics and educational outcomes. The results show that around the arbitrary boundary for statistical significance (p-value is less than 0.05), there is an unlikely large share of studies that are significant compared to the share of studies that are insignificant. This finding strongly suggests that there is publication bias in the neighbourhood effects literature.     

雅砻江垮山堵江及溃泄洪水

１９６７年６月８日在四川西部的雅砻江发生了垮山堵江,堆积体达６８００万ｍ＾３,形成了３００多ｍ的高坝,蓄水量６．８亿ｍ＾３,溃坝最大流量５７００ｍ＾３／ｓ,溃泄洪水演进至下游１７００多ｋｍ的长江重庆后始消除其影响,这是一次罕见的特大型垮山堵江事件。由于初夏少雨,下游来水量不大,预报、抢救及时,使灾害减轻到最低限度。分析了垮山的原因,论述了垮山江的蓄水历史经验,对于类似地区尤其是对下游正在兴建中的二     

Improvement in the radial accuracy of altimeter-satellite orbits due to the geopotential

The application of satellite altimetry in geosciences needs a precise computation of the orbit positions of the satellites with altimeters. In particular the knowledge of the radial orbit error is of high interest in this context. Rosborough's theory [Rosborough, G.W., 1986 Satellite Orbit Perturbations due to the Geopotential, CSR-86-1 rep., Center for Space Research, Univ. of Texas, Austin.], ammended by our newer works, describes Earth static gravity induced radial orbit error as a function of latitude, longitude and pass direction. Using this theory applied to precise long-term measurements of crossover altimetry we demonstrate the improvement in the accuracy of the orbit radius due to Earth gravity models, from the early 1980s (order of tens of meters), to the present (order of centimeters and less). The early models, with higher correlations between potential coefficients, show strong variations of the error in longitude as well as latitude, compared to the more recent fields. Currently the static gravity errors in the best of the Earth models are believed to be below the systematic environmental errors in the long-term altimetry.     

Subsidence hazards due to evaporite dissolution in the United States

Evaporites, including gypsum (or anhydrite) and salt, are the most soluble of common rocks; they are dissolved readily to form the same type of karst features that typically are found in limestones and dolomites, and their dissolution can locally result in major subsidence structures. The four basic requirements for evaporite dissolution to occur are: (1) a deposit of gypsum or salt; (2) water, unsaturated with CaSO₄ or NaCl; (3) an outlet for escape of dissolving water; and (4) energy to cause water to flow through the system. Evaporites are present in 32 of the 48 contiguous states of the United States, and they underlie about 35–40% of the land area. Karst is known at least locally (and sometimes quite extensively) in almost all areas underlain by evaporites, and some of these karst features involve significant subsidence. The most widespread and pronounced examples of both gypsum and salt karst and subsidence are in the Permian basin of the southwestern United States, but many other areas also are significant. Human activities have caused some evaporite–subsidence development, primarily in salt deposits. Boreholes may enable (either intentionally or inadvertently) unsaturated water to flow through or against salt deposits, thus allowing development of small to large dissolution cavities. If the dissolution cavity is large enough and shallow enough, successive roof failures above the cavity can cause land subsidence or catastrophic collapse.