Compositional Data Analysis of Geological Variability and Process: A Case Study

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.     

花岗岩型铀矿铀地球化学场分形奇异值分解研究

介绍了分形奇异值分解方法的原理和实现过程,在桃山花岗岩型铀矿矿集区开展了应用试验,利用该方法将桃山地区1/5万铀地球化学场分解为噪声场、区域地质背景场和局部异常场,在提取隐伏铀矿弱信息方面取得了较好的应用效果。     

Importance of Skewness and Kurtosis Statistical Tests for Outlier Detection and Elimination in Evaluation of Geochemical Reference Materials

A common characteristic of concentration data compilations for geochemical reference materials (GRM) is a skewed frequency distribution because of aberrant analytical data. Rejection of outlying results usually is required to obtain a better estimate of mean concentration values. The present work describes the application of an approach, based on skewness and kurtosis statistical tests, to establish reliable concentration values in study of rare-earth element compilations for GRM. Frequency histograms of initial concentrations for these elements differ significantly from a normal distribution, as deduced from their skewness and kurtosis coefficients. The statistical procedure shows that rejection of outliers yields normal distributions which can be used to provide mean concentrations with smaller standard deviations for a large number of cases, although for many elements our %RSD are similar (within 5%) to literature values. This procedure has been applied to derive new concentration data for rare-earth elements in 26 GRM, which are compared with earlier compilations to show that the statistical procedure proposed here provides mean values with greater quality value. Although most present mean concentrations are similar (within 5%) to those reported in previous literature, some of them are significantly different (with differences of up to 40%) in a few GRM.     

Relative Efficiency of Single-Outlier Discordancy Tests for Processing Geochemical Data on Reference Materials and Application to Instrumental Calibrations by a Weighted Least-Squares Linear Regression Model

Numerous studies report geochemical data on reference materials (RMs) processed by outlier-based methods that use univariate discordancy tests. However, the relative efficiency of the discordancy tests is not precisely known. We used an extensive geochemical database for thirty-five RMs from four countries (Canada, Japan, South Africa and USA) to empirically evaluate the performance of nine single-outlier tests with thirteen test variants. It appears that the kurtosis test (N15) is the most powerful test for detecting discordant outliers in such geochemical RM databases and is closely followed by the Grubbs type tests (N1 and N4) and the skewness test (N14). The Dixon-type tests (N7, N8, N9 and N10) as well as the Grubbs type test (N2) depicted smaller global relative efficiency criterion values for the detection of outlying observations in this extensive database. Upper discordant outliers were more common than the lower discordant outliers, implying that positively skewed inter-laboratory geochemical datasets are more frequent than negatively skewed ones and that the median, a robust central tendency indicator, is likely to be biased especially for small-sized samples. Our outlier-based procedure should be useful for objectively identifying discordant outliers in many fields of science and engineering and for interpreting them accordingly. After processing these databases by single-outlier discordancy tests and obtaining reliable estimates of central tendency and dispersion parameters of the geochemical data for the RMs in our database, we used these statistical data to apply a weighted least-squares linear regression (WLR) model for the major element determinations by X-ray fluorescence spectrometry and compared the WLR results with an ordinary least-squares linear regression model. An advantage in using our outlier procedure and the new concentration values and uncertainty estimates for these RMs was clearly established.     

应用奇异值分解与二维经验模型分解提取金矿化致矿重力异常

奇异值分解(singular value decomposition,SVD)和二维经验模型分解(bi-dimensional empirical mode decomposition,BEMD)2种方法用于鲁西铜石金矿田的金矿化致矿重力异常提取.通过对比研究得出如下结论:①基于重力数据,由BEMD和SVD 2种方法获...     

铀及伴生元素活动态分量探测在古宁浑迪砂岩型铀矿勘查中的应用

为了快速查明古宁浑迪地区砂岩型铀矿的有利成矿地段，并为钻探验证工程的部署提供依据，研究过程中采用了铀及伴生元素活动态分量探测地球化学勘查方法。通过系统采集样品和铀、钼、硒分量提取及测试，认为吸附态铀及伴生元素分量探测更适用于本地区砂岩型铀成矿有利地段的筛选。经钻探工程验证，绝大部分地表铀分量异常均与深部成矿目的层中的铀矿化或铀异常相对应，证实了铀及伴生元素活动态分量探测是适用于寻找隐伏砂岩型铀矿床的有效方法，尤其适用于古河道型砂岩铀矿的找矿勘查。