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1.
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
2.
Joaquín A. Cortés 《Mathematical Geosciences》2009,41(7):817-828
The current theoretical development of the analysis of compositional data in the article by Aitchison and Egozcue neglects
the use of Harker’s variation diagrams and other similar plots as “meaningless” or “useless” on compositional data. In this
work, it is shown that variation diagrams essentially are not a correlation tool but a graphical representation of the mass
actions and mass balances principles in the context of a given geological system, and, when they are used correctly, they
provide vital information for the igneous petrologist. The qualitative validity of the “spurious trends” in these diagrams
is also shown, when they are interpreted in their proper geological framework. The example previously used by Rollinson to
test the usefulness of the log-ratio transformation in the Aitchison and Egozcue article is revisited here in order to fully
illustrate the proper use of this tool. 相似文献
3.
J. A. Martín-Fernández V. Pawlowsky-Glahn J. J. Egozcue R. Tolosona-Delgado 《Mathematical Geosciences》2018,50(3):273-298
Compositional data analysis requires selecting an orthonormal basis with which to work on coordinates. In most cases this selection is based on a data driven criterion. Principal component analysis provides bases that are, in general, functions of all the original parts, each with a different weight hindering their interpretation. For interpretative purposes, it would be better to have each basis component as a ratio or balance of the geometric means of two groups of parts, leaving irrelevant parts with a zero weight. This is the role of principal balances, defined as a sequence of orthonormal balances which successively maximize the explained variance in a data set. The new algorithm to compute principal balances requires an exhaustive search along all the possible sets of orthonormal balances. To reduce computational time, the sets of possible partitions for up to 15 parts are stored. Two other suboptimal, but feasible, algorithms are also introduced: (i) a new search for balances following a constrained principal component approach and (ii) the hierarchical cluster analysis of variables. The latter is a new approach based on the relation between the variation matrix and the Aitchison distance. The properties and performance of these three algorithms are illustrated using a typical data set of geochemical compositions and a simulation exercise. 相似文献
4.
A class of multivariate nonparametric tests for spatial dependence, Multivariate Sequential Permutation Analyses (MSPA), is developed and applied to the analysis of spatial data. These tests allow the significance level (P value) of the spatial correlation to be computed for each lag class. MSPA is shown to be related to the variogram and other measures of spatial correlation. The interrelationships of these measures of spatial dependence are discussed and the measures are applied to synthetic and real data. The resulting plot of significance level vs. lag spacing, or P-gram, provides insight into the modeling of the semivariogram and the semimADogram. Although the test clearly rejects some models of correlation, the chief value of the test is to quantify the strength of spatial correlation, and to provide evidence that spatial correlation exists 相似文献
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6.
Tree-ring-based mass-balance estimates for the past 300 years at Peyto Glacier, Alberta, Canada 总被引：1，自引：0，他引：1
Tree rings were used to reconstruct mass balance for Peyto Glacier in the Canadian Rocky Mountains from A.D. 1673 to 1994. Summer balance was reconstructed from tree-ring estimates of summer temperature and precipitation in the Canadian Rockies. Winter balance was derived from tree-ring data from sites bordering the Gulf of Alaska and in western British Columbia. The models for winter and summer balance each explain over 40% of the variance in the appropriate mass-balance series. Over the period 1966-1994 the correlation between the reconstructed and measured net balances is 0.71. Strong positive mass balances are reconstructed for 1695-1720 and 1810-1825, when higher winter precipitation coincided with reduced ablation. Periods of reconstructed positive mass balance precede construction of terminal moraines throughout the Canadian Rockies ca. 1700-1725 and 1825-1850. Positive mass balances in the period 1845-1880 also correspond to intervals of glacier readvance. Mass balances were generally negative between 1760 and 1805. From 1673 to 1883 the mean annual net balance was +70 mm water equivalent per year (w.e./yr.), but it averaged −317 mm w.e./yr from 1884 to 1994. This reconstructed mass balance history provides a continuous record of glacier change that appears regionally representative and consistent with moraine and other proxy climate records. 相似文献
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8.
Amalgamation of parts of a composition has been extensively used as a technique of analysis to achieve reduced dimension,
as was discussed during the CoDaWork'03 meeting (Girona, Spain, 2003). It was shown to be a non-linear operation in the simplex that does not preserve distances
under perturbation. The discussion motivated the introduction in the present paper of concepts such as group of parts, balance
between groups, and sequential binary partition, which are intended to provide tools of compositional data analysis for dimension
reduction. Key concepts underlying this development are the established tools of subcomposition, coordinates in an orthogonal
basis of the simplex, balancing element and, in general, the Aitchison geometry in the simplex. Main new results are: a method
to analyze grouped parts of a compositional vector through the adequate coordinates in an ad hoc orthonormal basis; and the study of balances of groups of parts (inter-group analysis) as an orthogonal projection similar
to that used in standard subcompositional analysis (intra-group analysis). A simulated example compares results when testing
equal centers of two populations using amalgamated parts and balances; it shows that, in certain circumstances, results from
both analysis can disagree. 相似文献
9.
天山乌鲁木齐河源1号冰川物质平衡高度变化特征及其对径流的影响 总被引：1，自引：0，他引：1
利用天山乌鲁木齐河源1号冰川1980-2010年的物质平衡、水文气象实测资料, 分析了1号冰川1980-2010年的各高度带物质平衡特征, 进而分析了1984-2010年纯积累和纯消融的变化特点及其与气象要素、冰川融水径流变化的关系. 结果表明: 1号冰川物质平衡处于持续的负平衡, 纯积累量与年降水的相关系数为-0.16, 纯消融量与年均温的相关系数为0.61, 与夏季(6-8月)气温的相关系数为0.78. 2010年1号冰川为有观测记录以来的最强消融年(bn=-1 327 mm), 整个冰川处于消融区(平衡线高度大于海拔4 484 m, 积累区面积为0), 同时东、西支冰川各高度区间的物质平衡变化也与往年度显著不同, 说明2010年是1号冰川物质平衡变化的特殊年份, 也有可能1号冰川的物质平衡变化进入了一个新的亏损变化阶段. 对其径流数据的分析还表明, 温度对径流的影响大于降水对径流的影响. 相似文献
10.
Shuiwang Duan Rainer Amon Thomas S. Bianchi Peter H. Santschi 《Estuaries and Coasts》2011,34(1):78-89
Soluble reactive phosphorus (SRP) has recently been shown to be one of the limiting nutrients for the growth of phytoplankton
in the northern Gulf of Mexico. We show here that during the past decade, SRP concentrations in the lower reaches of North
America's largest river, the Mississippi River, were highest in summer and lowest in winter and positively correlated with
water temperature. Upstream data showed this coupling to increase in a downstream trend in the Mississippi main stem. Water
quality data analysis and phosphorus mass balances were conducted to examine the controls of this relationship. The results
showed that the positive SRP–temperature correlation in the Mississippi River system was largely a result of gradual dilution
of SRP-enriched upper Mississippi River waters, which contributed most to the Mississippi River during summer, by SRP-depleted
waters from the Ohio and other tributaries. Particle buffering and organic matter mineralization might play a role in the
observed SRP–temperature relationship, but their importance relative to tributary effects is not quantified. Future work on
the seasonal dynamics of SRP in large river systems needs to consider the effects of both tributary dilution and in situ processes. 相似文献
11.
Structural evaluation of the pegmatite-rich zones in a part of Lafiagi (Sheet 203), Central Nigeria, was carried out. It was aimed at identification of the structures responsible for the rich mineralization of the area. This work involved the qualitative and quantitative analysis of aeromagnetic data and pseudogravity transforms by using Oasis Montaj? software. The 3D Euler deconvolution results from acquired aeromagnetic data and pseudogravity transforms augmented with geological information obtained from reliable sources were employed in the structural interpretation work. The results have shown that the abundance of 2D and 3D structures that are commonly associated with gemstones and precious minerals explain why the study area is rich in mineral deposits. 相似文献
12.
地震资料处理中的并行计算机技术(综述) 总被引：1，自引：2，他引：1
作者在本文中从地震资料并行处理的工业需求，地震资料自身的特点和现代地震数据处理对高性能计算机的要求出发，简述了为什么要用并行机进行大规模并行处理的原因。通过分析目前国内外有代表性的两种并行机（IBM SP2和Intel Paragon)的体系结构，给出了并行机硬件的发展现状。作者在文中还着重对前苏联以及我国近几年引进的国外地震处理系统的并行功能和应用情况进行了阐述。并结合课题研究，提出了地震资料并行处理的一个发展方向-基于微机群的地震资料交互、并行处理系统。最后，作者对发展并行计算机提出了几点建议。 相似文献
13.
Gravity Recovery and Climate Experiment (GRACE) derived groundwater storage (GWS) data are compared with in-situ groundwater levels from five groundwater basins in Jordan, using newly gridded GRACE GRCTellus land data. It is shown that (1) the time series for GRACE-derived GWS data and in-situ groundwater-level measurements can be correlated, with R 2 from 0.55 to 0.74, (2) the correlation can be widely ascribed to the seasonal and trend component, since the detrended and deseasonalized time series show no significant correlation for most cases, implying that anomalous signals that deviate from the trend or seasonal behaviour are overlaid by noise, (3) estimates for water losses in Jordan based on the trend of GRACE data from 2003 to 2013 could be up to four times higher than previously assumed using estimated recharge and abstraction rates, and (4) a significant time-lagged cross correlation of the monthly changes in GRACE-derived groundwater storage and precipitation data was found, suggesting that the conventional method for deriving GWS from GRACE data probably does not account for the typical conditions in the study basins. Furthermore, a new method for deriving plausible specific yields from GRACE data and groundwater levels is demonstrated. 相似文献
14.
Chris Roth 《Mathematical Geology》1998,30(8):999-1009
Lognormal kriging was developed early in geostatistics to take account of the often seen skewed distribution of the experimental mining data. Intuitively, taking the distribution of the data into account should lead to a better local estimate than that which would have been obtained when it is ignored. In practice however, the results obtained are sometimes disappointing. This paper tries to explain why this is so from the behavior of the lognormal kriging estimator. The estimator is shown to respect certain unbiasedness properties when considering the whole working field using the regression curve and its confidence interval for both simple or ordinary kriging. When examined locally, however, the estimator presents a behavior that is neither expected nor intuitive. These results lead to the question: is the theoretically correct lognormal kriging estimator suited to the practical problem of local estimation? 相似文献
15.
Variogram Fitting by Generalized Least Squares Using an Explicit Formula for the Covariance Structure 总被引：4，自引：0，他引：4
Marc G. Genton 《Mathematical Geology》1998,30(4):323-345
In the context of spatial statistics, the classical variogram estimator proposed by Matheron can be written as a quadratic form of the observations. If data are Gaussian with constant mean, then the correlation between the classical variogram estimator at two different lags is a function of the spatial design matrix and the variance matrix. When data are independent with unidimensional and regular support, an explicit formula for this correlation is available. The same is true for a multidimensional and regular support as can be shown by using Kronecker products of matrices. As variogram fitting is a crucial stage for correct spatial prediction, it is proposed to use a generalized least squares method with an explicit formula for the covariance structure (GLSE). A good approximation of the covariance structure is achieved by taking account of the explicit formula for the correlation in the independent situation. Simulations are carried out with several types of underlying variograms, as well as with outliers in the data. Results show that this technique (GLSE), combined with a robust estimator of the variogram, improves the fit significantly. 相似文献
16.
Microdiamonds offer several advantages as a resource estimation tool, such as access to deeper parts of a deposit which may be beyond the reach of large diameter drilling (LDD) techniques, the recovery of the total diamond content in the kimberlite, and a cost benefit due to the cheaper treatment cost compared to large diameter samples. In this paper we take the first step towards local estimation by showing that micro-diamond samples can be treated as a regionalised variable suitable for use in geostatistical applications and we show examples of such output. Examples of microdiamond variograms are presented, the variance-support relationship for microdiamonds is demonstrated and consistency of the diamond size frequency distribution (SFD) is shown with the aid of real datasets. The focus therefore is on why local microdiamond estimation should be possible, not how to generate such estimates. Data from our case studies and examples demonstrate a positive correlation between micro- and macrodiamond sample grades as well as block estimates. This relationship can be demonstrated repeatedly across multiple mining operations. The smaller sample support size for microdiamond samples is a key difference between micro- and macrodiamond estimates and this aspect must be taken into account during the estimation process. We discuss three methods which can be used to validate or reconcile the estimates against macrodiamond data, either as estimates or in the form of production grades: (i) reconcilliation using production data, (ii) by comparing LDD-based grade estimates against microdiamond-based estimates and (iii) using simulation techniques.
相似文献17.
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
18.
The aim of this contribution is to explore the relationship among some concepts, often considered to be unrelated, such as weathering reactions, compositional data and fractals by means of distribution analysis.Weathering reactions represent the necessary transfer of heat and entropy to the environment in geochemical cycles. Compositional data express the relative abundance of chemical elements/species in a given total (i.e. volume or weight). Fractals are temporal or spatial objects with self-similarity and scale-invariance, so that internal structures repeat themselves over multiple levels of magnification or scales of measurement.Gibbs's free energy and the application of the Law Mass Action can be used to model weathering reactions, under the hypothesis of chemical equilibrium. Compositional data are obtained in the analytical phase after the determination of the concentrations of chemicals in sampled solid, liquid or gaseous materials. Fractals can be measured by using their fractal dimensions.In this paper, the presence of fractal structures is observed when the frequency distribution of isometric log-ratio coordinates is investigated, showing the logarithm of the cumulative number of samples exceeding a certain coordinate value plotted against the coordinate value itself. Isometric log-ratio coordinates (or balances) were constructed by using the sequential binary partition (SBP) method. The balances were identified to maintain, as far as possible, the similarity with a corresponding weathering reaction affecting the Arno river catchment (Tuscany, central Italy) as described by the Law of Mass Action. The emergence of fractal structures indicates the presence of dissipative systems, which require complexity, large numbers of inter-connected elements and stochasticity. 相似文献
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20.
近50年来北极斯瓦尔巴地区冰川物质平衡变化特征 总被引：3，自引：2，他引：1
利用长时间序列的冰川物质平衡资料,详细分析了北极斯瓦尔巴地区冰川的物质平衡变化特征以及气候因子对物质平衡的影响。结果表明：近50年来斯瓦尔巴地区冰川物质平衡变化主要呈负平衡、零平衡/略微增长两种状态。冰川净平衡一般为负值,年际变化波动幅度较大且呈负平衡趋势,累积物质平衡表现出长期稳定的负平衡增长态势。除Kongsvegen冰川外,其他冰川不存在短期内的平衡波动。季节变化表现为夏季消融、冬季积累,且夏季消融比冬季积累波动更大,冰川净平衡与夏季消融保持同步变化趋势。冰川净平衡与平衡线高度（ELA）呈负相关（平均相关系数为-0.89）,与积累区面积比率（AAR）呈正相关（平均相关系数为0.84）,该地区大多数冰川AAR减小,说明冰川物质补给处于劣势,冰川物质平衡向负平衡发展。夏季气温升高是斯瓦尔巴地区冰川表面物质加速亏损的直接原因。 相似文献