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1.
J. Aitchison 《Mathematical Geology》1984,16(6):617-635
The high-dimensionality of many compositional data sets has caused geologists to look for insights into the observed patterns of variability through two dimension-reducing procedures: (i)the selection of a few subcompositions for particular study, and (ii)principal component analysis. After a brief critical review of the unsatisfactory state of current statistical methodology for these two procedures, this paper takes as a starting point for the resolution of persisting difficulties a recent approach to principal component analysis through a new definition of the covariance structure of a composition. This approach is first applied for expository purposes to a small illustrative compositional data set and then to a number of larger published geochemical data sets. The new approach then leads naturally to a method of measuring the extent to which a subcomposition retains the pattern of variability of the whole composition and so provides a criterion for the selection of suitable subcompositions. Such a selection process is illustrated by application to geochemical data sets. 相似文献
2.
B. Chattopadhyay 《Mathematical Geology》1990,22(5):589-598
The Main Hill Arkasani Granophyre Pluton (MAG), a product of Proterozoic intraplate acid magmatic activity, represents an anatectic melt of the enveloping rocks of dominantly pelitic composition with subordinate trondhjemitic gneiss and basic rocks. Petrography, chemistry, correlation between compositional attributes, areal variation of volume percent granophyric intergrowth, and varimax rotated factor analysis of compositional attributes of these rocks suggest that in the MAG pluton, plagioclase phenocrysts and biotite crystallized first, followed by change of level of emplacement of the magma when the groundmass started crystallizing at a rapid rate. The rapid growth of quartz and alkali feldspar crystallizing from the residual melt gave rise to the ubiquitous granophyric intergrowth in the late stage of crystallization. The alkali-rich residual liquid tended to concentrate toward the margin of the pluton where there is a profusion of granophyric intergrowths. 相似文献
3.
Developments in the statistical analysis of compositional data over the last two decades have made possible a much deeper
exploration of the nature of variability and the possible processes associated with compositional data sets from many disciplines.
In this paper, we concentrate on geochemical data. First, we explain how hypotheses of compositional variability may be formulated
within the natural sample space, the unit simplex, including useful hypotheses of sub-compositional discrimination and specific
perturbational change. Then we develop through standard methodology, such as generalised likelihood ratio tests, statistical
tools to allow the systematic investigation of a lattice of such hypotheses. Some of these tests are simple adaptations of
existing multivariate tests but others require special construction. We comment on the use of graphical methods in compositional
data analysis and on the ordination of specimens. The recent development of the concept of compositional processes is then
explained, together with the necessary tools for a staying-in-the-simplex approach, such as the singular value decomposition
of a compositional data set. All these statistical techniques are illustrated for a substantial compositional data set, consisting
of 209 major oxide and trace element compositions of metamorphosed limestones from the Grampian Highlands of Scotland. Finally,
we discuss some unresolved problems in the statistical analysis of compositional processes. 相似文献
4.
Compositional Data Analysis of Some Alkaline Glasses 总被引：1，自引：0，他引：1
The approach to the analysis of compositional data involving log-ratio transformation of the data has not been generally adopted by researchers wishing to analyse such data. In the context of exploratory methods of multivariate analysis, such as principal components analysis, where the hope is to identify (cluster) structure in the data, this may be because traditional methods can produce more interpretable results than the log-ratio approach. After illustrating this with an example, circumstances under which the log-ratio approach performs poorly when traditional approaches work well are identified. Log-ratio analysis can be dominated by variables having low absolute presence and high relative variation that do not contribute to, and can obscure, structure in the data. Traditional methods can detect certain kinds of structure in the data that correspond to structure on a ratio scale, after a suitable redefinition of the composition. Since traditional methods often detect such structure more directly than log-ratio analysis it can be concluded that claims that the traditional analysis is inappropriate or meaningless are exaggerated. This conclusion is based on empirical experience rather than theoretical concerns. The arguments are illustrated using compositional data for alkaline glasses, but have more general application. 相似文献
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7.
稀土元素在韧性剪切带体积亏损研究中的应用：以胶南造山带构造岩为例 总被引：10，自引：1，他引：9
稀土元素在韧性剪切带中发生有规律的成分变异,随着变形程度的增强,单个稀土元素,轻稀土,重稀土,稀土元素的总量均明显增加,而稀土配分模式不变。通过花岗质构造岩变形前后的等比分析,稀土元素的成分变异主要是由于较大的体积亏损而引起,并根据成分变异与体积亏损之间的函数关系,进一步确定了构造岩变形前后的体积亏损率。 相似文献
8.
利用稳定同位素大气水平衡模式（iAWBM）的模拟数据,分析了在不同的下垫面蒸发和不同的凝结分馏条件下降水中δ18O的时间变化、降水量效应、负温度效应和大气水线。并通过与长沙站5年实测数据的比较以及模拟试验结果之间的相互比较,揭示下垫面蒸发水汽中稳定同位素的季节性变化和云中稳定同位素分馏对降水中稳定同位素变化的可能影响,增进对季风区水稳定同位素效应的理解和认识。iAWBM给出的4个模拟试验均很好地再现了监测站降水中δ18O的时间变化,模拟出季风区降水中稳定同位素在暖半年被贫化、在冷半年被富集的基本特点。与平衡分馏相比,动力分馏下降水中稳定同位素被贫化的程度加强、季节差和离散程度减小;由下垫面蒸发水汽中稳定同位素δe季节性变化所引起的降水中稳定同位素的变化在不同季节完全相反：在长沙,暖半年降水中δ18O更低,冷半年降水中δ18O更高,使得降水中稳定同位素季节差和离散程度增大。4个模拟试验均很好地再现了季风区的降水量效应和负温度效应。与平衡分馏相比,动力分馏下模拟的降水量效应和负温度效应的斜率相对较小;δe季节性变化导致模拟的降水量效应和负温度效应的斜率增大。利用iAWBM,模拟出季风区湿热气候条件下的MWL。动力分馏以及δe季节变化均使模拟得到的MWL的斜率和截距减小。 相似文献
9.
The simplex with the Aitchison geometry is a natural sample space for compositional data, that is, observations carrying only
relative information (especially proportions, percentages, etc., often occurring in the geosciences). For this reason, standard
statistical methods that rely on Euclidean structure of the real space cannot be used directly for statistical analysis. At
first, compositional data need to be expressed in coordinates of an orthonormal basis on the simplex (with respect to the
Aitchison geometry). The mathematical interpretation of the orthonormal coordinates is derived from the procedure by which
they are constructed (called sequential binary partition), and they act as balances between groups of compositional parts.
The goal of this paper is to describe the covariance structure of coordinates and, consequently, to provide a complementary
interpretation based on log-ratios of parts of the original composition. It must be noted that, in a composition, the ratios
themselves contain all the relevant information. The possibilities as well as the limitations of this approach are demonstrated
through illustrative examples. 相似文献
10.
Application of Compositional Techniques in the Field of Crystal Chemistry: A Case Study of Luzonite, a Sn-Bearing Mineral 总被引：1，自引：1，他引：0
Miria Borgheresi Antonella Buccianti Francesco Di Benedetto David John Vaughan 《Mathematical Geosciences》2013,45(2):183-206
Out-of-equilibrium crystallization often produces complex compositional variability in minerals, generating zoning and other mixing phenomena. The appropriate microchemical characterization of the resulting out-of-equilibrium patterns is of critical importance in understanding the overall physical and chemical properties of the host crystalline phases. In this framework, the modeling of compositional changes assumes a fundamental role. However, when compositional data are used, their management with standard exploratory, statistical, graphical, and numerical tools may give misleading results attributable to the phenomenon of induced correlations. To avoid these problems, methods able to extract compositional data from their constrained space (the simplex) in order to apply standard statistics, have to be adopted. As an alternative, the use of tools having properties able to work in the simplex geometry has to be considered. A luzonite single crystal (ideal composition, Cu3AsS4) exhibiting concentric and sector zoning was studied using electron probe microanalysis in order to understand the mechanisms which give rise to chemical variability and conditions in the developing environment. Compositional variations were determined by collecting data along three different transects. The major and minor elements (Cu, As, S, Fe, Sb, Sn) were analyzed with the aim of characterizing their patterns of association in the crystal and, hence, crystal evolution. The whole covariance structure as well as the chemical relationships between the successive zones was investigated by means of compositional methods, considering both data transformation and the stay in the simplex approach. Results indicate that the crystal grew under quiescent conditions, where chemical control was primarily exercised by the mineral’s surface and only minor effects were due to changes in the composition of the surrounding fluid. Consequently, an oscillatory uptake of chemical components occurred in which a competition between famatinite-like (Cu3SbS4) and kuramite-like (Cu3SnS4) domains characterized the As-poor zones. 相似文献
11.
Rajib Kar 《Journal of the Geological Society of India》2012,80(5):653-666
Stock-like granite plutons in the Eastern Ghats belt and their host granulites exhibit similar solid state fabric. Both mineralogically and chemically these plutons are peraluminous and granitic in composition with S-type granite affinities. The granite plutons are product of a variety of mica dehydration melting reactions, as evident from their (1) compositional plots in the (FeO + MgO) ?? Na2O.Al2O3 ?? K2O.Al2O3 (MNK) pseudoternary diagram and (2) trace element contents. Muscovite and/or biotite breakdown reaction with or without plagioclase are the characteristic melting reactions. Restitic signature is evident in the host metapelitic granulites, locally known as khondalites (Qtz-Kfs-Grt-Sil-Fe-Ti oxides-bearing gneisses). The compositional variability of the associated khondalites can be a result of (1) original compositional variation and (2) they represent different stages of restites. Trace element monitoring following restite separation model suggests that these granite plutons are largely saturated equilibrium melts. The granites are chemically discriminated as syn-collisional. The plutons could also be the product of segregation during the regional exhumation of the Eastern Ghats terrain. 相似文献
12.
John Maclennan 《Geochimica et cosmochimica acta》2008,72(16):4159-4176
The lead isotope and trace element compositions of a suite of olivine-hosted melt inclusions in primitive lava flows from the Reykjanes Peninsula in Iceland show extreme variability. Much of this variability is present in the composition of inclusions from one hand specimen of Háleyjabunga, a depleted picrite lava shield that erupted 13 ka. 208Pb/206Pb compositions in this sample span 50-90% of the total range found in Atlantic MORB, indicating that high-amplitude compositional heterogeneity is present in the mantle source of melts that aggregated to form a single eruption. The trace element and isotopic trends in the melt inclusions are coincident with those in whole rock samples from young lava flows of the Reykjanes Peninsula, and extend the total range of variation towards more depleted compositions. The incompatible trace element and lead isotope compositions of the inclusions are strongly coupled and lie close to binary mixing trends between the extreme melt inclusion compositions. These relationships indicate that the trace element variation in the melt inclusions reflects heterogeneity in the composition of the mantle source entering the melting region under the Reykjanes Peninsula. Large positive Sr concentration anomalies are present in three of the inclusions, but do not correlate with indicators of mantle melting or source variations and are likely to arise by reaction with plagioclase during crustal storage. Fractional melting of heterogeneous mantle is predicted to generate melts with a wide range of compositions, filling a large volume in trace element-isotope space. However, the compositional variations observed in the melt inclusions lie close to binary mixing curves. These observations may be accounted for by a two-stage model of melt mixing. The first stage occurs in porous channels that transport melt in the mantle and takes place before inclusion entrapment. This mixing stage generates a bimodal distribution of melt compositions that is supplied from the channels to sub-Moho and lower crustal magma lenses. The second stage of mixing occurs in these chambers, producing the binary mixing trends recorded in the inclusion compositions. The distribution of isotopic compositions observed in the melt inclusions and whole rock samples from the Reykjanes Peninsula is therefore controlled by melt mixing. These results have important implications for the interpretation of basalt composition in terms of distinct compositional entities within the upwelling solid mantle under mid-ocean ridges and ocean islands. 相似文献
13.
Correlation coefficients are most popular in statistical practice for measuring pairwise variable associations. Compositional data, carrying only relative information, require a different treatment in correlation analysis. For identifying the association between two compositional parts in terms of their dominance with respect to the other parts in the composition, symmetric balances are constructed, which capture all relative information in the form of aggregated logratios of both compositional parts of interest. The resulting coordinates have the form of logratios of individual parts to a (weighted) “average representative” of the other parts, and thus, they clearly indicate how the respective parts dominate in the composition on average. The balances form orthonormal coordinates, and thus, the standard correlation measures relying on the Euclidean geometry can be used to measure the association. Simulation studies provide deeper insight into the proposed approach, and allow for comparisons with alternative measures. An application from geochemistry (Kola moss) indicates that correlations based on symmetric balances serve as a sensitive tool to reveal underlying geochemical processes. 相似文献
14.
Gas associated with Carboniferous coal seams and younger Miocene sediments in the SW Upper Silesian Basin in Czech Republic shows wide compositional variation. Coal-related gas extracted from cross-measure degassing boreholes, as well as gas released during canister desorption of coal samples from three different mines was analyzed to evaluate the genetic origin and the influence of sorption/desorption processes on the gas composition. Analyses comprised the compositional and stable carbon and isotope composition of coal-related gases. The isotopic composition of gas from cross-measure boreholes indicates thermogenic origin in the southern part of the basin and microbial CO2 reduction and mixed type origin in the northern part. Gas from canister desorption shows similar origins, but larger compositional and isotopic variation. No consistent isotopic fractionation due to desorption could be observed. Differences in geochemical composition of thermogenic gases could indicate a contribution of gas migrated from deeper formations below the Carpathian overthrust. 相似文献
15.
A crystal fractionation model for the basaltic rocks of the New Georgia Group,British Solomon Islands 总被引：1，自引：0，他引：1
Study of the data provided by Stanton and Bell (1969) for certain basaltic rocks from the New Georgia Group reveals an apparent discrepancy between compositional variation and the sequence of phenocryst phases available for fractionation. The discrepancy none-the-less appears explicable in terms of two low-pressure crystal fractionation mechanisms. The first of these we term compensated crystal settling, a process which, it is postulated, allows a substantial amount of magma undergoing crystal settling to maintain its overall composition since crystals settling from it are continually replaced by compositionally similar crystals which settle into it from higher levels. The second process involves selective fractionation of phases sinking at different rates. Slow sinking of plagioclase relative to ferromagnesian minerals is believed to produce cumulus enrichment in plagioclase in the upper part of the chamber, the resultant magmas being erupted as highly porphyritic, high-alumina, basaltic andesites. 相似文献
16.
Two picrite flows from the SW rift zone of Mauna Loa containxenoliths of dunite, harzburgite, lherzolite, plagioclase-bearinglherzolite and harzburgite, troctolite, gabbro, olivine gabbro,and gabbronorite. Textures and olivine compositions precludea mantle source for the xenoliths, and rare earth element concentrationsof xenoliths and clinopyroxene indicate that the xenolith sourceis not old oceanic crust, but rather a Hawaiian, tholeiitic-stagemagma. Pyroxene compositions, phase assemblages and texturalrelationships in xenoliths indicate at least two different crystallizationsequences. Calculations using the pMELTS algorithm show thatthe two sequences result from crystallization of primitive MaunaLoa magmas at 6 kbar and 2 kbar. Independent calculations ofolivine Ni–Fo compositional variability in the plagioclase-bearingxenoliths over these crystallization sequences are consistentwith observed olivine compositional variability. Two parentsof similar bulk composition, but which vary in Ni content, arenecessary to explain the olivine compositional variability inthe dunite and plagioclase-free peridotitic xenoliths. Xenolithsprobably crystallized in a small magma storage area beneaththe rift zone, rather than the large sub-caldera magma reservoir.Primitive, picritic magmas are introduced to isolated rift zonestorage areas during periods of high magma flux. Subsequenteruptions reoccupy these areas, and entrain and transport xenolithsto the surface. KEY WORDS: xenolith; Hawaii; volcano plumbing; mineral composition; picrite 相似文献
17.
The recent development of activity–composition relations for mineral and melt phases in high‐grade metamafic rocks allows mineral equilibria tools to be used to further aid our understanding of partial melting and the mineralogical consequences of melt segregation in these rocks. We show that bulk compositional data from natural amphibolites cover a wide compositional range, with particular variability in the content and ratios of Ca, Na and K indicating that low‐grade metasomatic alteration can substantially alter the igneous protolith chemistry and potentially affect the volume and composition of melt generated. Mineral equilibria calculations for five samples that span the compositional variability in our data set indicate that melting occurs primarily via the fluid‐absent breakdown of amphibole+quartz to produce a pressure‐sensitive peritectic assemblage of augite, orthopyroxene and/or garnet. The introduction of orthopyroxene at the onset of the amphibolite‐to‐granulite‐facies transition at lower pressure results in an increased rate of melt production until quartz is typically exhausted, and this is similarly seen for the introduction of garnet at higher pressure. Calculated melt compositions are dependent on the protolith composition, but initial solidus melting and biotite breakdown produce 1–3 mol.% of K‐rich granitic melts. As hornblende melting proceeds, 15–20 vol.% of either more granodioritic‐to‐tonalitic or granodioritic‐to‐trondhjemitic melt is produced. Once quartz is exhausted, intermediate to mafic melt compositions are produced at ultrahigh‐temperature conditions. Quartz‐rich lithologies with high Ca coupled to low Na and K are the most fertile under orogenic conditions, yielding up to 25 mol.% of sub‐alkalic granitic melt by 850°C. Such rocks did not experience significant subsolidus alteration. Altered compositions with low Ca and elevated Na and K are not as fertile, yielding less than 15 mol.% of alkalic granitic melt by 850°C. These melt volumes are enough to be segregated, and can make a contribution to granite magmatism and intracrustal differentiation that should not be overlooked. 相似文献
18.
Garnet porphyroblasts in sillimanite‐bearing pelitic schists contain complex textural and compositional zoning, with considerable variation both within and between adjacent samples. The sillimanite‐bearing schists locally occur in regional Barrovian garnet zone assemblages and are indicative of a persistent lack of equilibrium during prograde metamorphism. Garnet in these Dalradian rocks from the Scottish Highlands preserves evidence of a range of metamorphic responses including initial growth and patchy coupled dissolution–reprecipitation followed by partial dissolution. Individual porphyroblasts each have a unique and variable response to prograde metamorphism and garnet with mainly flat compositional profiles co‐exists with those containing largely unmodified characteristic bell‐shaped Mn profiles. This highlights the need for caution in applying traditional interpretations of effective volume diffusion eliminating compositional variation. Cloudy garnet with abundant fluid inclusions is produced during incomplete modification of the initial porphyroblasts and these porous garnet are then particularly prone to partial replacement in sillimanite‐producing reactions. The modification of garnet via a dissolution–reprecipitation process releases Ca into the effective whole‐rock composition, displacing the pressure–temperature positions of subsequent isograd reactions. This represents the first report of internal metasomatism controlling reaction pathways. The behaviour of garnet highlights the importance of kinetic factors, especially deformation and fluids, in controlling reaction progress and how the resulting variability influences subsequent prograde history. The lack of a consistent metamorphic response, within and between adjacent schists, suggests that on both local and regional scales these rocks have largely not equilibrated at peak metamorphic conditions. 相似文献
19.
中国沙漠物源研究:回顾与展望 总被引：1，自引：0，他引：1
沙漠物源研究不仅在风沙地貌学上有重大的理论和实践意义,而且对联结大气粉尘排放、黄土堆积、气候系统和海洋生物地球化学循环也有重要价值。在简要回顾中国沙漠研究的基础上,梳理了中国沙漠物源研究的理论、方法和主要成果,结合国际上沉积物物源分析的趋向,指出目前世界沙漠物源的研究都是基于沉积物组份属性统计的反演模型,这种研究范式在数据获取、处理与解释方面存在缺陷,如沉积物的取样设计与测试分析、未消除"粒级依赖"对沉积物组份影响、数据未进行对数变换、忽视Dickinson图解应用的前提条件等。提出今后中国沙漠物源研究的方向:①采用正确统一的取样设计和分析方法对各沙漠的沉积物组份属性进行系统研究,建立中国沙漠沉积物组份的属性数据库;②选择若干典型沙漠,利用其周边山地详尽的地质构造、母岩和气候数据,定量构建沉积物生成的正演模型,模拟源区生成沉积物的数量、成分和结构,并用建成的沉积物组份属性数据验证和校正;③定量评估河流冲积物、冲积-湖积物、洪积-冲积物和基岩风化的残积、坡积物对中国各沙漠物源的贡献率与迁移路径,研究中国各沙漠中细颗粒物质的形成机制,对比中国沙漠与低纬度沙漠物源的形成机制;④定量研究历史和地质时间尺度沙漠-黄土-深海沉积物物源的内在联系及其驱动因素,建立陆地-大气-海洋物质循环的机理模型。 相似文献
20.
《International Geology Review》2012,54(8):703-714
A worldwide data set of major element and sulfur analyses of undegassed lavas, pumices, and melt inclusions from 14 volcanic locations was selected to investigate the compositional effects on sulfur solubility in magmas. We utilized analyses on calc-alkaline, alkaline, and tholeiitic rocks, with a range of 3400 ppm S variation. There is a strong correlation between chemical composition and the sulfur concentration: the less silicic and the more alkaline the rocks are, the more dissolved sulfur they can carry. Also, sulfur concentration is higher in rocks that represent less polymerized melts. Elemental correlations between FeO and S, well-defined for tholeiites, do not hold for alkaline melts. The compositional effects are at least as important as the better-known pressure, temperature, and f(O2) dependencies. 相似文献