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Many geological phenomena are regularly measured over time to follow developments and changes. For many of these phenomena, the absolute values are not of interest, but rather the relative information, which means that the data are compositional time series. Thus, the serial nature and the compositional geometry should be considered when analyzing the data. Multivariate time series are already challenging, especially if they are higher dimensional, and latent variable models are a popular way to deal with this kind of data. Blind source separation techniques are well-established latent factor models for time series, with many variants covering quite different time series models. Here, several such methods and their assumptions are reviewed, and it is shown how they can be applied to high-dimensional compositional time series. Also, a novel blind source separation method is suggested which is quite flexible regarding the assumptions of the latent time series. The methodology is illustrated using simulations and in an application to light absorbance data from water samples taken from a small stream in Lower Austria.
相似文献2.
Detecting subcropping mineralizations but also deeply buried mineralizations is one important goal in geochemical exploration. The identification of useful indicators for mineralization is a difficult task, as mineralization might be influenced by many factors, including location, investigated media and depth. Here, a statistical method is proposed which indicates chemical elements related to mineralization along a transect. Moreover, the method determines the potential area of the deposit along a transect. The identification is based on general additive models (GAMs) for the element concentrations across the spatial coordinate(s). The log-ratios of the GAM fits are taken to compute the curvature, where high and narrow curvature is supposed to indicate the mineralization area. By defining a measure for the quantification of high curvature, the log-ratios can be ranked, and elements can be identified that are indicative of the anomaly patterns.
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Julie Sucharovà Ivan Suchara Marie Hola Sarka Marikova Clemens Reimann Rognvald Boyd Peter Filzmoser Peter Englmaier 《Applied Geochemistry》2012
High top-/bottom-soil ratios, or high values of “enrichment factors” (EFs), are used as a proof for major anthropogenic impact on the geochemistry of the Earth surface. The idea behind calculating such ratios is that soils taken at depth or “average crust” can provide the geochemical background for the soils collected at the Earth surface. However, a soil profile is not a closed system, element exchange between the different layers, depending on and varying with the chemical properties of the different elements, and their turnover in the biosphere is the essence of soil formation. High top-/bottom-soil ratios, or EFs, may thus highlight the geochemical de-coupling of the lithosphere from the biosphere rather than contamination. This is demonstrated by using regional data from 258 soil O- and B-horizon samples collected from the Czech Republic (76,800 km2). Results show no relationship between the ratios and the magnitude of anthropogenic emissions. The visible relationship between element concentrations and sources in a map of the spatial distribution of the elements is lost when maps for the top-/bottom-soil ratio or EFs are constructed. The value of the data lies in the spatial elemental distribution, and not in ratios calculated based on misconceptions. 相似文献
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Normal and lognormal data distribution in geochemistry: death of a myth. Consequences for the statistical treatment of geochemical and environmental data 总被引：13，自引：0，他引：13
All variables of several large data sets from regional geochemical and environmental surveys were tested for a normal or
lognormal data distribution. As a general rule, almost all variables (up to more than 50 analysed chemical elements per data
set) show neither a normal or a lognormal data distribution. Even when different transformation methods are used more than
70 % of all variables in every single data set do not approach a normal distribution. Distributions are usually skewed, have
outliers and originate from more than one process. When dealing with regional geochemical or environmental data normal and/or
lognormal distributions are an exception and not the rule. This observation has serious consequences for the further statistical
treatment of geochemical and environmental data. The most widely used statistical methods are all based on the assumption
that the studied data show a normal or lognormal distribution. Neglecting that geochemcial and environmental data show neither
a normal or lognormal distribution will lead to biased or faulty results when such techniques are used.
Received: 21 June 1999 · Accepted: 14 August 1999 相似文献
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Julie SucharováIvan Suchara Clemens Reimann Rognvald BoydPeter Filzmoser Peter Englmaier 《Applied Geochemistry》2011,26(7):1205-1214
Lead concentrations were determined in samples of soil B-horizon (N = 258), forest-floor humus (O-horizon, N = 259), grass (Avenella flexuosa, N = 251) and spruce (Picea abies, N = 253) needles (2nd year) collected at the same locations evenly spread over the territory of the Czech Republic at an average density of 1 site/300 km2. Median Pb concentrations differ widely in the four materials: soil B-horizon: 27 mg/kg (3.3-220 mg/kg), humus: 78 mg/kg (19-1863 mg/kg), grass: 0.37 mg/kg (0.08-8 mg/kg) and spruce needles: 0.23 mg/kg (0.07-3 mg/kg). In the Pb distribution maps for humus, grass and spruce a number of well-known Pb-contamination sources are indicated by unusually high concentrations (e.g., the Pb smelter at Pribram, the metallurgical industry in the NE of the Czech Republic and along the Polish border, as well as the metallurgical industry in Upper Silesia and Europe’s largest coal-fired power plant at Bogatynia, Poland). The ratio 206Pb/207Pb was determined in all four materials. The median value of the 206Pb/207Pb isotope ratio in the soil B-horizon is 1.184 (variation: 1.145-1.337). In both humus and grass the median value for the 206Pb/207Pb isotope ratio is 1.162 (variation: 1.130-1.182), in spruce needles the median ratio is 1.159 (variation: 1.116-1.186). In humus, grass and spruce needles the known contamination sources are all marked by higher 206Pb/207Pb isotope ratios in the maps. Furthermore, the soil B-horizon, humus, grass and spruce needles show distinctly different spatial distribution patterns of the 206Pb/207Pb isotope ratios. The B-horizon does not provide a viable background value for metal concentrations in the O-horizon or plant materials. None of the maps provides evidence for the importance of traffic-related emissions for the observed isotope ratios at the scale of the Czech Republic. 相似文献
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Correlation Analysis for Compositional Data 总被引：1，自引：0，他引：1
Compositional data need a special treatment prior to correlation analysis. In this paper we argue why standard transformations
for compositional data are not suitable for computing correlations, and why the use of raw or log-transformed data is neither
meaningful. As a solution, a procedure based on balances is outlined, leading to sensible correlation measures. The construction
of the balances is demonstrated using a real data example from geochemistry. It is shown that the considered correlation measures
are invariant with respect to the choice of the binary partitions forming the balances. Robust counterparts to the classical,
non-robust correlation measures are introduced and applied. By using appropriate graphical representations, it is shown how
the resulting correlation coefficients can be interpreted. 相似文献
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A test comparing concentrations of 57 chemical elements (Ag, Al, As, B, Ba, Be, Bi, Ca, Cd, Ce, Co, Cr, Cs, Cu, Dy, Er, Eu, Fe, Ga, Gd, Ge, Hf, Ho, I, K, La, Li, Lu, Mg, Mn, Mo, Na, Nb, Nd, Ni, Pb, Pr, Rb, Sb, Se, Sm, Sn, Sr, Ta, Tb, Te, Th, Ti, Tl, Tm, U, V, W, Y, Yb, Zn and Zr) determined by inductively coupled plasma quadrupole mass spectrometry (ICP-QMS) in 294 samples of the same bottled water (predominantly mineral water) sold in the European Union in glass and PET bottles demonstrates significant (Wilcoxon rank sum test, α = 0.05) differences in median concentrations for Sb, Ce, Pb, Al, Zr, Ti, Th, La, Pr, Fe, Zn, Nd, Sn, Cr, Tb, Er, Gd, Bi, Sm, Y, Lu, Dy, Yb, Tm, Nb and Cu. Antimony has a 21× higher median value in bottled water when sold in PET bottles (0.33 vs. 0.016 μg/L). Glass contaminates the water with Ce (19× higher than in PET bottles), Pb (14×), Al (7×), Zr (7×), Ti, Th (5×), La (5×), Pr, Fe, Zn, Nd, Sn, Cr, Tb (2×), Er, Gd, Bi, Sm, Y, Lu, Yb, Tm, Nb and Cu (1.4×). Testing an additional 136 bottles of the same water sold in green and clear glass bottles demonstrates an important influence of colour, the water sold in green glass shows significantly higher concentrations in Cr (7.3×, 1.0 vs. 0.14 μg/L), Th (1.9×), La, Zr, Nd, Ce (1.6×), Pr, Nb, Ti, Fe (1.3×), Co (1.3×) and Er (1.1×). 相似文献
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Pieter-Jan van Helvoort Peter Filzmoser Pauline F.M. van Gaans 《Applied Geochemistry》2005,20(12):2233-2251
Sequential Factor Analysis (seqFA) is presented here as an enhanced alternative to multivariate factorial techniques including robust and classical Factor Analysis (FA) or Principal Component Analysis (PCA). A geochemical data set of 145 sediment samples from very heterogeneous, mainly riverine, deposits of the Rhine-Meuse delta (The Netherlands) analyzed for 27 bulk parameters was used as a test case. The innovative approach explicitly addresses the priority issues when performing PCA or FA: heterogeneity and overall integrity of the data, the number of factors to be extracted, and which optimum minimal set of key variables to be included in the model. The stepwise decision process is based on quantitative and objectively derived statistical criteria, yet also permitting arguments based on geochemical expertize. The results show that seqFA, preferably in combination with robust methods, yields a highly consistent factor model, and is favorable over classical methods when dealing with heterogeneous data sets. It optimizes rotation of the factors, and allows the extraction of less distinct factors supported by only a few variables, thus uncovering additional geochemical processes and properties that would easily be missed with other approaches. The identification of key variables simplifies the geochemical interpretation of the factors, and greatly facilitates the construction of a geochemical conceptual model. For the case of the fluvial deposits, the conceptual model effectively describes their bulk chemical variation in terms of a limited number of governing processes. 相似文献