Dealing with outliers and censored values in multi-element geochemical data – a visualization approach using XmdvTool

Dealing with geochemical data also means coping with their underlying limitations that are related to sampling, analytical techniques, and other characteristics of the data. This paper discusses the issue of data cleaning, using a regional geochemical dataset of 6 heavy metals in glacial till. Interactive data manipulation techniques provided in the freeware visualization system XmdvTool were used for exploring both metal concentrations reported as under the detection limit, and high or extreme values (outliers) in the dataset. The proposed integrated visual evaluation (IVE) approach for selective removal of outliers outperformed simple removal of the highest concentrations of metals, showing that existing spatial multi-element fingerprints in data could be recognized and preserved by IVE. The uniqueness of visualization is in simultaneous display of both multivariate and spatial information. Being simple and interactive, integrated visual evaluation can be recommended as a valuable complementary tool in cleaning and analysing multi-element geochemical data.     

Geochemical background in soils: a linear process domain? An example from Istria (Croatia)

Definition of geochemical background in exploration and environmental geochemistry has always been regarded as contingent upon scale and investigated locality but mostly under assumption that hosts of processes that produce the data more or less conform individually to Gaussian law of “central tendencies”. Recently, understanding of pedogenesis as synergetic process being characterized by non-linear dynamics renders thermodynamic approach directly applicable in assessment of geochemical thresholds, with concepts of linearity and normality set alongside in solving the problems of soil geochemistry. Seen from this perspective the work is an attempt to relate conceptual fundamentals of non-linear dynamical theory to basic statistical methods in order to elucidate the nature and origins of element subpopulations hidden in the original geochemical data from the soils of Istrian Peninsula (western Croatia). To this purpose the two major groups of soils were selected for analysis depending on the type of bedrock as one of the main soil-forming factors. Geochemical data were subjected to the trimming procedure by which the outliers were removed from the total data collective and attributed to non-linear causes precluding simple cause-and-effect relationships as the sine qua non of Gaussian distribution. Geochemical background is then defined as the normal range of data of the remaining (trimmed) dataset indicating the “thermodynamic branch” of the specific soil processes as opposed to outliers being described as dissipative structures.     

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.     

Selection of threshold values in geochemical data using probability graphs

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.     

The detection and correction of outlying determinations that may occur during geochemical analysis

‘Wild’, ‘rogue’ or outlying determinations occur periodically during geochemical analysis. Existing tests in the literature for the detection of such determinations within a set of replicate measurements are often misleading. This account describes the chances of detecting outliers and the extent to which correction may be made for their presence in sample sizes of three to seven replicate measurements. A systematic procedure for monitoring data for outliers is outlined. The problem of outliers becomes more important as instrumental methods of analysis become faster and more highly automated; a state in which it becomes increasingly difficult for the analyst to examine every determination. The recommended procedure is easily adapted to such analytical systems.     

Models of Spatial Structures of Regional Multi-element Geochemical Anomalies over Copper-Polymetallic Orefields

Regional stream sediment surveys at a 1:200,000 scale reveal positive and negative regional multi-element geochemical anomalies over medium to large copper-polymetallic orefields of different genetic types in China. Regional geochemical anomalies of orefield refer to those geochemical anomalies that are related to metallogenesis of an orefield in a certain area. The anomaly area is typically 10 to 100 km2. The regional multi-element anomalies related to mineralization can be divided into three groups, that is, the ore-element anomaly association, indicator element anomaly association, and metallogenic environmental element anomaly association. Their common spatial distributions over ore deposits or orefields possess unique structures.The model of spatial structure of regional multi-element geochemical anomalies (RAGSS) of an orefield delineates structural feature possessed by orderly spatial distributions of different groups of multi-element anomaly associations related to orefield metallogenesis. It is     

Adjustment of geochemical background by robust multivariate statistics

Conventional analyses of exploration geochemical data assume that the background is a constant or slowly changing value, equivalent to a plane or a smoothly curved surface. However, it is better to regard the geochemical background as a rugged surface, varying with changes in geology and environment. This rugged surface can be estimated from observed geological, geochemical and environmental properties by using multivariate statistics.A method of background adjustment was developed and applied to groundwater and stream sediment reconnaissance data collected from the Hot Springs Quadrangle, South Dakota, as part of the National Uranium Resource Evaluation (NURE) program. Source-rock lithology appears to be a dominant factor controlling the chemical composition of groundwater or stream sediments. The most efficacious adjustment procedure is to regress uranium concentration on selected geochemical and environmental variables for each lithologic unit, and then to delineate anomalies by a common threshold set as a multiple of the standard deviation of the combined residuals. Robust versions of regression and RQ-mode principal components analysis techniques were used rather than ordinary techniques to guard against distortion caused by outliers Anomalies delineated by this background adjustment procedure correspond with uranium prospects much better than do anomalies delineated by conventional procedures. The procedure should be applicable to geochemical exploration at different scales for other metals.     

A machine learning approach for regional geochemical data:Platinum-group element geochemistry vs geodynamic settings of the North Atlantic Igneous Province

Whilst traditional approaches to geochemistry provide valuable insights into magmatic processes such as melting and element fractionation, by considering entire regional data sets on an objective basis using machine learning algorithms(MLAs), we can highlight new facets within the broader data structure and significantly enhance previous geochemical interpretations.The platinum-group element(PGE) budget of lavas in the North Atlantic Igneous Province(NAIP) has been shown to vary systematically according to age, geographic location and geodynamic environment.Given the large multi-element geochemical data set available for the region, MLAs were employed to explore the magmatic controls on these shifting concentrations.The key advantage of using machine learning in analysis is its ability to cluster samples across multi-dimensional(i.e., multi-element)space.The NAIP data set is manipulated using Principal Component Analysis(PCA) and t-Distributed Stochastic Neighbour Embedding(t-SNE) techniques to increase separability in the data alongside clustering using the k-means MLA.The new multi-element classification is compared to the original geographic classification to assess the performance of both approaches.The workflow provides a means for creating an objective high-dimensional investigation on a geochemical data set and particularly enhances the identification of metallogenic anomalies across the region.The techniques used highlight three distinct multi-element end-members which successfully capture the variability of the majority of elements included as input variables.These end-members are seen to fluctuate in prominence throughout the NAIP, which we propose reflects the changing geodynamic environment and melting source.Crucially, the variability of Pt and Pd are not reflected in MLA-based clustering trends, suggesting that they vary independently through controls not readily demonstrated by the NAIP major or trace element data structure(i.e., other proxies for magmatic differentiation).This data science approach thus highlights that PGE(here signalled by Pt/Pd ratio) may be used to identify otherwise localised or cryptic geochemical inputs from the subcontinental lithospheric mantle(SCLM) during the ascent of plume-derived magma, and thereby impact upon the resulting metallogenic basket.     

Evaluation of Interlaboratory Geochemical Data: Some Considerations on the Abbey-Rousseau Debate, the Meaningfulness of the Median and Other Topics

This paper discusses the methods most commonly used to evaluate interlaboratory geochemical data for a search of "best" values. It suggests that the Select-Laboratories, Dybczyński, median and mode methods integrated by the visual inspection of the plot of the ordered data can be regarded as general, complementary approaches to data handling. Because of the elusive nature of the problem, a multiple method approach to be accepted and standardized by the geoscientist community is suggested. The importance of ascribing realistic confidence intervals to any derived value is also pointed out.     

Robust statistics and geochemical data analysis

Advantages of robust procedures over ordinary least-squares procedures in geochemical data analysis is demonstrated using NURE data from the Hot Springs Quadrangle, South Dakota, U.S.A. Robust principal components analysis with 5% multivariate trimming successfully guarded the analysis against perturbations by outliers and increased the number of interpretable factors. Regression with SINE estimates significantly increased the goodness-of-fit of the regression and improved the correspondence of delineated anomalies with known uranium prospects. Because of the ubiquitous existence of outliers in geochemical data, robust statistical procedures are suggested as routine procedures to replace ordinary least-squares procedures.     

Geochemical mapping in China

China's National Geochemical Mapping Project (Regional Geochemistry-National Reconnaissance, RGNR project) was initiated in 1979. From 1978 to 1982, cooperative research projects were carried out for the preparation and distribution of standard reference samples and for the development of field sampling techniques, multi-element analytical methodology and a unified data quality monitoring procedure. Large pilot surveys were also commenced in several provinces. After five years of technical preparation, the project came into its full implementation. More than 5 million km² of Chinese land surface has been covered by this project. During 1993–1995, another national geochemical project, under the name of ‘Environmental geochemical monitoring network and dynamic geochemical maps in China’ as a pilot survey to choose the suitable sampling medium for the global geochemical mapping application, was carried out in China. The remarkable achievements of China's geochemical mapping projects are widely recognized. Nearly 66% of new discoveries of economic mineralization by MGMR were attributed to the RGNR project. New concepts and new methodologies have emerged through these projects. They also made a great contribution to the international activity toward standardization of geochemical mapping methodology and the possible realization of wide-spaced global geochemical mapping.     

分形求和法及其在地球化学数据分组中的应用

分形建模广泛地应用于具有自相似性不同尺度测量的地质现象空间分布特征。分形分布的特点要求大于等于某一尺度的数目,与物体大小之间存在幂函数关系,这种关系具有尺度不变性。这里提出的分形求和法可以确定地球化学数据分组界限。应用澳大利亚新南威尔士东北地区汇水沉积物地球化学数据,采用分形求和法确定其分组界限,并与传统的概率图模型结果进行比较。铜(Cu)元素数据划分二个部分,一部分是元素含量少于20 ppm的正态分布数据,另一部分是元素含量大于20 ppm的多个对数正态分布数据,能识别第三纪玄武岩区域和铜的主要矿化区。这一结论与使用传统的概率图模型方法得到的结论一致。该方法不仅适用于地球化学铜元素数据,而且还适用于其它元素和地质数据,具有普遍的意义。     

Recent advances in geochemical exploration in China

This paper outlines the recent advances in geochemical exploration in China.The Regional Geochemistry—National Reconnaissance (RGNR) Project first proposed in 1978, continues to be the focus of geochemical exploration activities in China. Several rapid quantitative multi-element analysis systems using conventional equipment available in most Chinese geological laboratories, have been developed. Eight Geochemical Standard Reference Samples of Drainage Sediments were prepared. Large-scale orientation or pilot surveys are being carried out by nearly 2/3 of the provincial geological bureaus in China. Methods of regional and follow up surveys for high and cold mountainous terrain have been worked out.Special attention has been given to the improvement and application of mercury vapour detection techniques. A new sampler was used to enhance anomalous values. A new Zeeman effect mercury detector was constructed and tested in routine analysis of mercury. Experiments of the application of soil gas mercury survey in petroleum and uranium prospecting are briefly described.Some examples of recent geochemical success in China are given.     

分区背景校正法及其对化探异常圈定的意义

化探中目前常用的用平面或曲线来拟合地球化学背景的作法从理论上是有严重缺陷的。地球化学背景应是一个随地质和景观变化而因点各异、崎岖不平的面。借助于稳健多元统计方法可以由观察到的地质、地化及环境变量来估计出这个背景面,即进行背景校正。本文介绍了对美国南达科达州黑山地区铀矿地球化学普查数据进行背景校正试验的结果。地层—岩性看来是控制地下水及系沉积物的地球化学特征的主要因素。从提高异常与矿化的吻合程度的角度来说,分区背景校正法的效果最好。这种方法对各个地层一岩性分区分别用可溶铀含量对选择出的地化—环境变量进行回归,然后将全区的剩余值合起来统一圈定异常。文中对这种方法成功的原因作了解释。用稳健统计学方法来代替经典统计学方法对于提高背景校正的效果也是很有帮助的。分区背景校正法是一种理论上有依据、实践上简便易行的异常圈定方法,值得进一步在不同地区对不同的目标矿种、不同的采样对象和比例尺进行试验。     

珠江水系沉积物重金属元素背景值估算及污染特征分析

估算水系沉积物的地球化学背景值和识别其异常对人为污染判别与环境风险评估非常重要。采集并分析了珠江58件水系沉积物样品,经分析检验,Al、Fe和Sc被选作参考元素,并对比了确定地球化学背景及识别异常值的方法。其中,基于最小截断二乘法的回归分析是定义地球化学背景的有效方法,它是一种对异常值不敏感的稳健统计方法,而基于局部富集因子的箱线图和回归诊断图更适用于识别异常值。珠江不同河段重金属污染存在差异,北江和河网区主要受As、Cd、Cu、Pb和Zn污染,东江主要受Cu、Cr和Ni污染,而西江几乎不存在重金属污染。水系沉积物的主要污染类型是点源污染,主要污染来源是采矿和电镀等相关的工业活动。     

勘查地球化学数据挖掘与弱异常识别

我国积累的大量高质量、多元素、多尺度的地球化学数据,为矿产勘查与环境评价提供了有效的数据支撑。如何对这些数据进行二次开发和再利用,提取有价值的地球化学异常信息并带动找矿突破,是缓解当前矿产资源短缺的重要途径之一。在覆盖区和深部的找矿实践中,由于矿体埋深和覆盖层的影响,往往在表生介质中形成弱小的地球化学异常,识别和评价弱小地球化学异常是当前勘查地球化学数据处理的重要方向之一。本文围绕地球化学异常信息的提取和评价,主要从以下几个方面讨论了相关的国内外研究进展和发展趋势:勘查地球化学数据处理与异常识别方法和模型,勘查地球化学数据闭合效应的影响及其解决方案,基于大数据和机器学习的勘查地球化学数据处理以及弱小地球化学异常的识别和评价。研究发现,在地质环境的约束下,基于大数据思维和机器学习相结合的方法,注重地球化学空间分布模式与已发现矿床的相关关系,同时使用所有地球化学变量能有效刻画具有非线性特征的地球化学空间分布模式,可识别出传统方法无法识别的异常,为开展地球化学空间模式识别与异常提取提供了新的途径。     

Geochemical prospecting in complex sample media-multivariate data analysis of indirect observations (PLS-regression between modal mineralogy and geochemistry)

Geochemical exploration in secondary environments can be viewed as a particular manifestation of indirect geological observation. Geochemical anomalies in complex sample media reflect dispersion signatures, generally much disguised by secondary or higher-order mechanical and physico-chemical processes such as mixing, comminution, dilution, (re)transportation, weathering etc. Such complexities often make a thorough understanding of the origin of any particular sample type difficult ot obtain. The objective of data analysis in this context is to convert the geochemical data into a meaningful “signal”, particularly useful for prospecting, and other, in this case irrelevant, variability or “noise”. The experience of the last decades of practical exploration has clearly shown that statistical as well as geographical geochemical anomaly patterns are multi-element signatures. Using suitable multivariate statistical procedures (in the present case principal components modelling), it is possible to simultaneously define both a background data model and to quantify multivariate geochemical anomalies. This type of data analysis is guided very strongly by geological interaction, in which the emphasis is on modelling the background population(s), coupled with geographic plotting facilities. This outlier-screening facility is critical for many types of geochemical data evaluation. An example of this approach is described below. Another application of indirect multivariate data analysis is represented by PLS (Partial Least Squares) regression, which is a supervised pattern recognition and regression technique. We use it here to predict modal scheelite occurrences from regional stream-sediment data.     

Multivariate statistical techniques applied to pisolitic laterite geochemistry at Golden Grove, Western Australia

Multivariate statistical procedures are applied to pisolitic laterite geochemistry in a study of the Golden Grove massive sulphide district. The objective is to optimize identification of geochemical anomalies caused by base metal mineral deposits.The statistical approach used in this paper depends upon geochemical data for appropriate reference groups (or training sets) being available. The target group consists of orientation data from pisolitic laterite about the Gossan Hill Cu-Zn massive sulphide deposit. A group representing background sequence was selected by combining three subareas in a geochemically quiet part of the prospective acid volcano-sedimentary sequence.A multi-element allocation procedure was set up using data from the reference groups. The exploration samples are then allocated, one sample at a time, to either one of the reference group categories, using the probability of group membership. A map showing the relative probability values for each sample site is the final product for interpretation, aided by ancillary use of an index of typicality.The allocation procedures were carried out using different element combinations, these being based on a procedure for subset selection to give maximum separation of reference groups, and on geochemical insight. Whilst many versions of the allocation procedure gave positive identification of the anomaly related to the blind Scuddles Cu-Zn deposit, allocation using only Cu, Pb, Zn and Ag did not. The results emphasize the importance of pathfinder elements in geochemical studies in weathered terrain.The allocation procedure using the most appropriate element combinations provided more positive identification of the main areas of known mineralization than had the previously used empirically derived methods of Smith and Perdrix (1983). The formal allocation procedure has the following additional advantages: results are not markedly affected by a very high value for any single element since robust procedures are incorporated into the analysis; better discrimination appears to be possible for weaker anomalies; separation of target from background can be optimized by formal calculations instead of by trial and error; and better suppression of background variation results.     

Analysis and mapping of geochemical anomalies using logratio-transformed stream sediment data with censored values

There is lack of research and documentation of actual (as opposed to theoretical) benefits (e.g., mineral deposit discovery) of developments in compositional data analysis and imputation of censored values to mineral exploration geochemistry. In the present study, analyses of logratio- and ln-transformed stream sediment geochemical data containing ca. 30% of samples with censored values of a pathfinder element for the mineral deposit-type of interest yielded the following findings. Exclusion of those samples supports interpretation of multi-element anomalies reflecting the presence of mineralization. However, the multi-element anomaly maps obtained by exclusion of those samples are barely better than the multi-element anomaly maps derived by inclusion of those samples after replacing the censored values with 1/2 of detection limit or with imputed values. Logratio (i.e., alr, clr, or ilr) transformation, compared to ln-transformation, of stream sediment geochemical data does not improve mapping of pathfinder element anomalies reflecting the presence of mineralization. However, stream sediment geochemical data, excluding or including censored values (replaced with 1/2 of detection limit or with imputed values), should be clr- or ilr-transformed to enhance recognition of anomalous multi-element associations reflecting the presence of mineralization. The anomaly maps of multi-element associations derived from ilr-transformed data are better, albeit slightly, than the anomaly maps of multi-element associations derived from clr-transformed data. In the present study, the main benefit of either clr- or ilr-transformation, compared to either ln- or alr-transformation, of stream sediment geochemical data is the enhancement of anomalous multi-element associations reflecting the presence of mineralization. This is an important benefit because variations in trace element concentrations in regional-scale stream sediment geochemical data are mostly due to lithology and other factors (or processes) unrelated to mineralization. Further investigations of various exploration geochemical data are needed to demonstrate and document the actual (as opposed to theoretical) benefits of developments in compositional data analysis and imputation of censored values to mineral exploration.