Alastair J. Sinclair

Selection of threshold values in geochemical data using probability graphs

Abstract A method of choosing threshold values between anomalous and background geochemical data, based on partitioning a cumulative probability plot of the data is described. The procedure is somewhat arbitrary but provides a fundamental grouping of data values. Several practical examples of real data sets that range in complexity from a single population to four populations are discussed in detail to illustrate the procedure. The method is not restricted to the choice of thresholds between anomalous and background populations but is much more general in nature. It can be applied to any polymodal distribution containing adequate values and populations with appropriate density distribution. As a rule such distributions for geochemical data closely approach a lognormal model. Two examples of the more general application of the method are described.

A fundamental approach to threshold estimation in exploration geochemistry: probability plots revisited

Several threshold estimation (and thus anomaly recognition) procedures are in use of exploration geochemistry. Experiential methods rely on absolute values in graphs or tables and are highly subjective in being dependent of the variable experience of explorationists. Model-based subjective techniques of threshold determination, including the mean plus two standard deviations, are arbitrary and inefficient: thus, they are not suitalbe despite the widespread use they have found in the past. Model-based objective methods include the gap statistic and the probability graph approaches, the latter finding much greater acceptance with the greatly increased ease of a recently available microcomputer software package that can treat many variables easily and rapidly. Many critical decisions in exploration geochemistry require a comprehensive interpretation of available data, including clear insight into the recognition of anomalous and background samples. Several decisions cannot be made in a vigorous and confident manner unless based on a fundamental approach to threshold selection. Examples include: (1) element zoning in geochemistry: (2) absolute estimation of geochemical contrast: (3) the recognition of the isotropic or anisotropic nature of anomalies: and (4) an estimation of areal extent of anomalies of various elements. Methods of threshold estimation which incorporate the philosophy that anomalous and background data are each characterized by their own probability density functions will be most successful in deriving a fundamental approach to threshold estimation. In the simplest general case, there are two overlapping populations, the overlapping character leading naturally to the extension of the single threshold concept to the definition of two thresholds that delimit the range of overlap. Such a concept, easily conceived and applied to individual variables, can be extended to the n-dimensional case. Univariate approaches will continue to dominate practical applications in the foreseeable future except in special circumstances.

Comparison of probability plots and the gap statistic in the selection of thresholds for exploration geochemistry data

Abstract Exploration geochemistry data commonly are treated statistically to select thresholds and identify anomalous samples. Previous research describing the various threshold selection techniques (e.g. Sinclair, 1976; Miesch, 1981) has relied on case histories to demonstrate the success of the technique in selecting geologically significant thresholds. Consequently, little effort has been made to contrast the relative merits and required assumptions of these techniques, or to evaluate their efficiencies and sensitivities under various data-distribution forms.

Anomaly recognition for multi-element geochemical data — A background characterization approach

Abstract Techniques for recognizing populations and defining anomalous samples in geochemical surveys are of two types: objective and subjective. Subjective techniques involve defining samples as anomalous if they have concentrations greater than a ‘certain percentile’ or greater than the mean plus ‘some multiple’ of the standard deviation. In both cases, the number of anomalous samples defined is dependent upon a subjective ‘rule’. Objective methods for defining geochemical populations include probability plots and the gap statistic. In both cases a model for the distribution of the data must first be assumed, and then the actual data distribution defines what samples may be anomalous. The Background Characterization Approach to anomaly recognition is an objective method designed for cases where significant overlap of multiple populations exists, or where no anomalous population can be recognized (unimodal distributions). It involves the determination of a background regression model for a pathfinder element using only background samples, and then applying this model to all possibly anomalous samples. Samples with element concentrations predicted successfully by the background model are classified as background, while those ‘reacting’ differently to the function are deemed to be from another population and therefore anomalous. A multi-element stream sediment exploration survey for stratabound Cu-Ag deposits in the Belt Basin of Montana is used to demonstrate the technique when the data are unimodally distributed.

Vein geochemistry, an exploration tool in Keno Hill camp, Yukon Territory, Canada

Abstract Seventy-two samples taken across the width of the Keno No. 18 vein at an average interval of 3 m and encompassing several Ag ore shoots and barren zones were analyzed for twenty-three elements. These samples were rearranged in order of decreasing silver values as a means of evaluating metal zonation patterns relative to an ideal ore shoot. This idealized zonation model is compared with four independent sets of data and found to apply throughout the deposit for ore shoots from 6 to 90 m in diameter. These results indicate that routine mine-sampling procedures, with samples analyzed for Pb, Zn, Ag, Ca, Hg and Co provide an adequate basis for use of the ideal ore shoot concept as an exploration tool. The approach appears useful in: (1) re-evaluating ends of existing underground workings and their possible proximity to undiscovered ore shoots; and (2) monitoring new workings. The methodology simply entails construction of profiles for Ag, Pb, Zn, Ca, Hg, Co, Zn/Ag and Co/Ag and comparison of these with patterns expected according to the ideal model. Most advantages of the procedure can be obtained in practice by supplementing normal assaying for Ag, Pb and Zn with Ca analyses.

Univariate Patterns in the Design of Multivariate Analysis Techniques for Geochemical Data Evaluation

The evaluation of regional geochemical data normally begins with a univariate analysis of each element. Patterns within the data are frequently recognized, but in cases where the patterns are obscure or not immediately understood, or where a large number of elements make interpretation difficult, a multivariate analysis is commonly undertaken. Unfortunately, this analysis is often made without consideration of the univariate results. Ignoring discernable univariate patterns in the design of subsequent multivariate analyses may lead to unneccessary ambiguities and/or complexities in the multivariate results and the subsequent interpretation. Geochemical concentration data from a soil survey in northern British Columbia are used to demonstrate this point. Univariate examination of the data reveals that most elements are bimodally distributed. However, the elements could be divided into two groups differing in the relative contribution of the two component populations (modes) making up their distributions. One group of elements has bimodal distributions with component populations of approximately equal size (55% and 45%); the other has bimodal distributions with component populations of vastly different size (90% and 10%).

Statistical Evaluation of the Significance of Categorical Field Parameters in the Interpretation of Regional Geochemical Sediment Data

ABSTRACT Matysek, P.F., Fletcher, W.K. and Sinclair, A.J., 1983. Statistical evaluation of the significance of categorical field parameters in the interpretation of regional geochemical sediment data. In: G.R. Parslow (Editor), Geochemical Exploration 1982. J. Geochem. Explor., 19: 383–401. In an attempt to study the value and utilization of categorical data collected during regional stream-sediment surveys, we have taken data from the Canadian Uranium Reconnaissance Program in S.E. British Columbia. After initial classification of the data into six subsets on the basis of catchment geology, probability plots were constructed for each of 11 elements (Zn, Cu, Pb, Ni, Co, Fe, Mn, Mo, W, Hg and U) and used to select thresholds to reject anomalous samples. The remaining background populations then were successively subdivided into groups according to their classification with respect to four sediment characteristics (abundance of fines, sand, organic matter and sediment colour) and six environmental parameters (physiography, water flow rate, stream class, drainage pattern, bank type and contamination). After calculation of log means for each group and a pooled common standard error, differences between group means were tested for significance using Duncans Multiple Range Test. The relative degree of confidence in the significance of difference between categorical means for any single field parameter were determined using a ratio method. Results of Duncans Multiple Range Test, show that, many field observations can be related systematically to metal content of drainage sediments. Some elements are more susceptible than others to environmental factors and some factors influence few or many elements. For example, in sediments derived from granites there are significant relationships between bank type and concentration of 8 elements (Zn, Cu, Ni, Pb, Co, Fe, Mn and Hg). In contrast, the texture of these sediments, using estimates of fines content as an index, did not significantly affect the concentration of any of the elements studied. In general, results indicate that groups of environmental factors acting collectively are more important than any single factor in determining background metal content of drainage sediments.