Robert G. Garrett

Factor analysis applied to regional geochemical data: problems and possibilities

Abstract Cluster analysis can be used to group samples and to develop ideas about the multivariate geochemistry of the data set at hand. Due to the complex nature of regional geochemical data (neither normal nor log-normal, strongly skewed, often multi-modal data distributions, data closure), cluster analysis results often strongly depend on the preparation of the data (e.g. choice of the transformation) and on the clustering algorithm selected. Different variants of cluster analysis can lead to surprisingly different cluster centroids, cluster sizes and classifications even when using exactly the same input data. Cluster analysis should not be misused as a statistical “proof” of certain relationships in the data. The use of cluster analysis as an exploratory data analysis tool requires a powerful program system to test different data preparation, processing and clustering methods, including the ability to present the results in a number of easy to grasp graphics. Such a tool has been developed as a package for the R statistical software. Two example data sets from geochemistry are used to demonstrate how the results change with different data preparation and clustering methods. A data set from S-Norway with a known number of clusters and cluster membership is used to test the performance of different clustering and data preparation techniques. For a complex data set from the Kola Peninsula, cluster analysis is applied to explore regional data structures.

Multivariate outlier detection in exploration geochemistry

A new method for multivariate outlier detection able to distinguish between extreme values of a normal distribution and values originating from a different distribution (outliers) is presented. To facilitate visualising multivariate outliers spatially on a map, the multivariate outlier plot, is introduced. In this plot different symbols refer to a distance measure from the centre of the distribution, taking into account the shape of the distribution, and different colours are used to signify the magnitude of the values for each variable. The method is illustrated using a real geochemical data set from far-northern Europe. It is demonstrated that important processes such as the input of metals from contamination sources and the contribution of sea-salts via marine aerosols to the soil can be identified and separated.

Natural Sources of Metals to the Environment

Almost all metals present in the environment have been biogeochemically cycled since the formation of the Earth. Human activity has introduced additional processes that have increased the rate of redistribution of metals between environmental compartments, particularly since the industrial revolution. However, over most of the Earths land surface the primary control on the distribution of metals is the geochemistry of the underlying and local rocks except in all but the worst cases of industrial contamination and some particular geological situations. Fundamental links between chemistry and mineralogy lead to characteristic geochemical signatures for different rock types. As rocks erode and weather to form soils and sediments, chemistry and mineralogy again influence how much metal remains close to the source, how much is translocated greater distances, and how much is transported in solutions that replenish ground and surface water supplies. In addition, direct processes such as the escape of gases and fluids along major fractures in the Earths crust, and volcanic related activity, locally can provide significant sources of metals to surface environments, including the atmosphere and sea floor. As a result of these processes the Earths surface is geochemically inhomogeneous. Regional scale processes lead to large areas with enhanced or depressed metal levels that can cause biological effects due to either toxicity or deficiency if the metals are, or are not, transformed to bioavailable chemical species.

The chi-square plot: a tool for multivariate outlier recognition

Abstract In large multi-element regional surveys statistically derived threshold levels of the form that define, for example, the top 2% of the data for each element as worthy of further investigation have led to the generation of inordinately large lists of geochemical samples for detailed study. This problem is compounded when a number of geological and secondary environments exists of sufficiently different character that separate thresholds should be estimated for each. Additionally, single-element thresholds for multi-element surveys can, in certain circumstances, lead to obviously out-of-character individuals not being recognized. Numerical approaches to the problem of anomaly recognition have commonly used a principal-component or regression analysis procedure as their basis. These, as indeed do all such approaches, have a common drawback in that the outliers being sought can distort the analysis being used to detect them. In addition, regression models have the further problem that there may be outliers in both the response and explanatory variables. A relatively simple approach would be to prepare a multivariate cumulative probability plot where each multi-element geochemical sample is represented as a single value. The resulting diagram would be interpreted much as a univariate probability plot where the presence of more than one straight-line segment is taken as evidence of multiple populations, and outliers as individuals or small groups are separated from the remaining data by gaps on the plot. Such a diagram may be prepared by plotting the rank-ordered values of the generalized or Mahalanobis distance, a multivariate distance measure, versus values of the chi-square statistic. This procedure is based on the covariance matrix of the data, a measure that underlies both principal-component and regression model approaches. In order to work effectively a statistically robust starting covariance matrix is essential. The procedure is described in detail with two examples, one a synthetic bivariate data set containing known outliers, and the other a small, well studied stream sediment data set from Norway extensively used in methodological comparison studies. The result of the procedure is to identify statistical outliers, which are candidates for interpretation as true geochemical anomalies, and to isolate a multi-element subset that is representative of the geochemical background.

Robust factor analysis for compositional data

Factor analysis as a dimension reduction technique is widely used with compositional data. Using the method for raw data or for improperly transformed data will, however, lead to biased results and consequently to misleading interpretations. Although some procedures, suitable for factor analysis with compositional data, were already developed, they require pre-knowledge of variable groups, or are complicated to handle. We present an approach based on the centred logratio (clr) transformation that does not build on this pre-knowledge, but still recognizes the specific character of compositional data. In addition, by using the isometric logratio transformation it is possible to robustify factor analysis using a robust estimation of the covariance matrix. A back-transformation of the results to the clr space allows an interpretation of the results with compositional biplots. The method is demonstrated with data from the Kola project, a large ecogeochemical mapping project in northern Europe.

From geochemical prospecting to international geochemical mapping: a historical overview

This paper provides a history of the development of regional geochemical mapping. Modern geochemistry was born in the Soviet Union in the 1930s, and the basic methodologies for regional mapping had been developed by the late 1960s, with important extensions being made in the 1980s. The paper records the development of regional geochemical surveys, or mapping, in the context of spatial scale and transition from a mineral exploration and resource assessment tool to an environmental mapping exercise supporting multi-disciplinary research. Attention is drawn to the role of the International Geological Correlation Programs Projects 259 and 360, and the continuing role of the International Union of Geological Sciences, in providing an international focus and dimension to global geochemical mapping. The paper closes with a section on some of the current research issues, opportunities and challenges for regional geochemical mapping.

A prediction model for estimating the cadmium content of durum wheat from soil chemistry

A non-linear prediction model for the Cd content of durum wheat grain has been developed based on the 0.1 M Na4P2O7-extractable Cd and organic carbon in the <2 mm fraction of the soil ploughed horizon. The extraction is selective for metals held as metal–organic complexes in the soil, and will also extract more loosely held metal. The prediction model explains 74% of the variability of the durum grain data (N=34), and confirms the importance of the metal-organically held Cd, organic carbon and pH in influencing the uptake of Cd by durum wheat in Canadian Prairie soils.

Assessment of the 1 M NH4NO3 extraction protocol to identify mobile forms of Cd in soils

Extraction of soils by leaching 20 g in 50 ml of unbuffered 1 M NH4NO3 for 2 h has become the standard German protocol (DIN 19730) to estimate mobile and potentially hazardous forms of trace elements. This protocol was examined using soil controls of chernozem and podzol character collected in the Canadian Prairies and Ontario. It was found that this procedure was not robust with respect to change in sample weight per unit volume of reagent or to contact time. A 3- to 15-fold increase in Cd extracted was produced by decreasing sample weight from 10 g to 1 g in 50 ml of reagent. This change in extractable-Cd was more pronounced with increasing pH of the soil, ranging from 5.2 to 8.1 amongst the control samples. Leach period was less significant in determining results but longer time (1–3 h) generally produced lower extractable-Cd, suggesting readsorption. Lack of stability of Cd in this reagent was further demonstrated by spiking experiments where Cd was added at the beginning of the leach. Recoveries of Cd at 50 and 200 ppb were below 20% for soils of pH 6.1 and 6.9. Such severe adsorption of Cd was not encountered with another unbuffered reagent, 1 M NH4Cl, operating at a similar initial pH of 5. Cadmium levels extracted from soils by NH4Cl and 0.1 M Na4P2O7 were comparable and could be used to predict uptake in durum wheat on the Canadian Prairies, whereas data by the 1 M NH4NO3 leach were generally near the detection limit of 0.1 ppb (ng g−1) Cd. Readsorption of Cd and lack of equilibrium in the 1 M NH4NO3 extraction could lead to underestimation of plant-available Cd in neutral and alkaline soils.

The management and analysis of regional geochemical data

Abstract Experiences in the U.S. National Uranium Resource Evaluation Program and Canadian Uranium Reconnaissance Program related to the use of geochemical exploration methods are drawn upon to review concepts and standards for data management and analysis. The topics discussed include: (a) field data acquisition; (b) quality control; (c) data management; (d) univariate statistical analysis; (e) initial data presentation; (f) multivariate statistical analysis; and (g) derivative maps. It is concluded that computer usage is essential if the data are to be compiled to desired levels of quality assurance in a timely and efficient fashion for interpretation and distribution. In general the costs for data management and analysis are some 10% of total costs; of this 10% some three-quarters is expended on compilation, quality control, editing and archiving. The use of the mathematical and statistical methods, with appropriate presentation techniques, can greatly assist the geochemist in interpretation. The objective of geochemical data analysis in the context of this paper is to identify that small proportion of the samples which relate to mineralization. A variety of tools, both simple and complex, are illustrated and discussed from this viewpoint. However, it is stressed that data analysis is only a tool and the results must be critically reviewed in terms of their geochemical implications before acceptance and incorporation into an interpretation.

The relationship between zinc and organic content in centre-lake bottom sediments

Abstract The relationship between Zn and organic content, the latter measured by percentage weight loss on ignition (LOI) is investigated in a suite of 3844 centre-lake bottom sediments from east-central Saskatchewan. The data indicate that Zn values have a strong sympathetic increase with LOI below 12% LOI. Zn values tend to stabilize above 12% LOI, in actuality they decrease slowly from 12 to 50% LOI before decreasing at an accelerated rate over 50% LOI. It is proposed that the change from a sympathetic Zn vs. LOI relationship to an antipathetic relationship occurs because there is insufficient Zn available, from weathering, etc., in the lake water of sampled lakes to maintain the sympathetic relationship. Therefore, the lack of Zn, together with the increasing availability of organic material, creates an excess adsorption capacity of the lake sediments. Below 12% LOI, in lake sediments that do not have an excess adsorption capacity, Zn distribution patterns will be partly controlled by the amount of organic material present. Thus, Zn in these lake sediments may not truly reflect the chemistry of a drainage basin. Whereas, above 12% LOI, where there is an excess adsorption capacity in the sediments, the Zn distribution patterns will more closely reflect the chemistry of a drainage basin. The observed decrease in Zn values obvious over 50% LOI may be reflecting a dilution factor introduced by the ever increasing load of organic material to a system which is not receiving more Zn. It is concluded that centre-lake bottom sediments whose organic content is dominantly in the range of 12–50% LOI form the most effective sample media for regional lake sediment surveys.