Environmental Monitoring and Peat Assessment Using Multivariate Analysis of Regional-Scale Geochemical Data

A compositional multivariate approach was used to analyse regional-scale soil geochemical data obtained as part of the Tellus Project generated by the Geological Survey of Northern Ireland. The multi-element total concentration data presented comprise X-ray fluorescence (XRF) analyses of 6862 rural soil samples collected at 20-cm depth on a non-aligned grid at one site per \(2\,\hbox {km}^{2}\). Censored data were imputed using published detection limits. Each soil sample site was assigned to the regional geology map, resulting in spatial data for one categorical variable and 35 continuous variables comprised of individual and amalgamated elements. This paper examines the extent to which soil geochemistry reflects the underlying geology or superficial deposits. Since the soil geochemistry is compositional, log-ratios were computed to adequately evaluate the data using multivariate statistical methods. Principal component analysis (PCA) and minimum/maximum autocorrelation factors (MAF) were used to carry out linear discriminant analysis (LDA) as a means to discover and validate processes related to the geologic assemblages coded as age bracket. Peat cover was introduced as an additional category to measure the ability to predict and monitor fragile ecosystems. Overall prediction accuracies for the age bracket categories were 68.4 % using PCA and 74.7 % using MAF. With inclusion of peat, the accuracy for LDA classification decreased to 65.0 and 69.9 %, respectively. The increase in misclassification due to the presence of peat may reflect degradation of peat-covered areas since the creation of superficial deposit classification.     

Surficial and Deep Earth Material Prediction from Geochemical Compositions

Prediction of true classes of surficial and deep earth materials using multivariate spatial data is a common challenge for geoscience modelers. Most geological processes leave a footprint that can be explored by geochemical data analysis. These footprints are normally complex statistical and spatial patterns buried deep in the high-dimensional compositional space. This paper proposes a spatial predictive model for classification of surficial and deep earth materials derived from the geochemical composition of surface regolith. The model is based on a combination of geostatistical simulation and machine learning approaches. A random forest predictive model is trained, and features are ranked based on their contribution to the predictive model. To generate potential and uncertainty maps, compositional data are simulated at unsampled locations via a chain of transformations (isometric log-ratio transformation followed by the flow anamorphosis) and geostatistical simulation. The simulated results are subsequently back-transformed to the original compositional space. The trained predictive model is used to estimate the probability of classes for simulated compositions. The proposed approach is illustrated through two case studies. In the first case study, the major crustal blocks of the Australian continent are predicted from the surface regolith geochemistry of the National Geochemical Survey of Australia project. The aim of the second case study is to discover the superficial deposits (peat) from the regional-scale soil geochemical data of the Tellus Project. The accuracy of the results in these two case studies confirms the usefulness of the proposed method for geological class prediction and geological process discovery.

     

Spatial and multivariate analysis of geochemical data from metavolcanic rocks in the Ben Nevis area, Ontario

A study of the lithogeochemistry of metavolcanics in the Ben Nevis area of Ontario, Canada has shown that factor analysis methods can distinguish lithogeochemical trends related to different geological processes, most notably, the principal compositional variation related to the volcanic stratigraphy and zones of carbonate alteration associated with the presence of sulphides and gold. Auto- and cross-correlation functions have been estimated for the two-dimensional distribution of various elements in the area. These functions allow computation of spatial factors in which patterns of multivariate relationships are dependent upon the spatial auto- and cross-correlation of the components. Because of the anisotropy of primary compositions of the volcanics, some spatial factor patterns are difficult to interpret. Isotropically distributed variables such as CO ₂ are delineated clearly in spatial factor maps. For anisotropically distributed variables (SiO ₂ ), as the neighborhood becomes smaller, the spacial factor maps becomes better. Interpretation of spatial factors requires computation of the corresponding amplitude vectors from the eigenvalue solution. This vector reflects relative amplitudes by which the variables follow the spatial factors. Instability of some eigenvalue solutions requires that caution be used in interpreting the resulting factor patterns. A measure of the predictive power of the spatial factors can be determined from autocorrelation coefficients and squared multiple correlation coefficients that indicate which variables are significant in any given factor. The spatial factor approach utilizes spatial relationships of variables in conjunction with systematic variation of variables representing geological processes. This approach can yield potential exploration targets based on the spatial continuity of alteration haloes that reflect mineralization.List of symbols c _i Scalar factor that minimizes the discrepancy between andU _i - D Radius of circular neighborhood used for estimating auto- and cross-correlation coefficients - d Distance for which transition matrixU is estimated - d _ij Distance between observed valuesi andj - E Expected value - E _i Row vector of residuals in the standardized model - F(d _ij) Quadratic function of distanced _ij F(d _ij)=a+bd _ij+cd _ij ² - L Diagonal matrix of the eigenvalues ofU - _i Eigenvalue of the matrixU;ith diagonal element ofL - N Number of observations - p Number of variables - Q Total predictive power ofU - R Correlation matrix of the variables - R _0j Variance-covariance signal matrix of the standardized variables at origin;j is the index related tod andD (e.g.,j=1 ford=500 m,D=1000 m) - R _1j Matrix of auto- and cross-correlation coefficients evaluated at a given distance within the neighborhood - R _m ² Multiple correlation coefficient squared for themth variable - S _i Column vectori of the signal values - s _k ² Residual variance for variablek - T _i Amplitude vector corresponding toV _i;ith row ofT=V ^–1 - T Total variation in the system - U Nonsymmetric transition matrix formed by post-multiplyingR ₀₁ ^–1 byR _ij - U _i Componenti of the matrixU, corresponding to theith eigenvectorV _i;U _i= _iV_iT_i - U* _i ComponentU _i multiplied byc _i - U _ij Sum of componentsU _i+U _j - V _i Eigenvector of the matrixU;ith column ofV withUV=VL - w Weighting factor; equal to the ratio of two eigenvalues - X _i Random variable at pointi - x _i Value of random variable at pointi - y _i Residual ofx _i - Z _i Row vectori for the standardized variables - z _i Standardized value of variable     

Recognition of geochemical footprints of mineral systems in the regolith at regional to continental scales

Understanding the character of Australia's extensive regolith cover is crucial to the continuing success of mineral exploration. We hypothesise that the regolith contains geochemical fingerprints of processes related to the development and preservation of mineral systems at a range of scales. We test this hypothesis by analysing the composition of surface sediments within greenfield regional-scale (southern Thomson Orogen) and continental-scale (Australia) study areas. In the southern Thomson Orogen area, the first principal component (PC1) derived in our study [Ca, Sr, Cu, Mg, Au and Mo at one end; rare earth elements (REEs) and Th at the other] is very similar to the empirical vector used by a local company (enrichment in Sr, Ca and Au concomitant with depletion in REEs) to successfully site exploration drill holes for Cu–Au mineralisation. Mapping of the spatial distribution of PC1 in the region reveals several areas of elevated values and possible mineralisation potential. One of the strongest targets in the PC1 map is located between Brewarrina and Bourke in northern New South Wales. Here, exploration drilling has intersected porphyry Cu–Au mineralisation with up to 1 wt% Cu, 0.1 g/t Au, and 717 ppm Zn. The analysis of a comparable geochemical dataset at the continental scale yields a compositionally similar PC1 (Ca, Sr, Mg, Cu, Au and Mo at one end; REEs and Th at the other) to that of the regional study. Mapping PC1 at the continental scale shows patterns that (1) are spatially compatible with the regional study and (2) reveal several geological regions of elevated values, possibly suggesting an enhanced potential for porphyry Cu–Au mineralisation. These include well-endowed mineral provinces such as the Curnamona and Capricorn regions, but also some greenfield regions such as the Albany-Fraser/western Eucla, western Murray and Eromanga geological regions. We conclude that the geochemical composition of Australia's regolith may hold critical information pertaining to mineralisation within/beneath it.     

Classification problems of samples of finite mixtures of compositions

A discriminant technique based on mixture models is presented to be applied when observations are a sample of a mixture of compositions with each component following an additive logistic normal distribution on the d-dimensional simplex. The efficiency of this discriminant technique is compared empirically with the efficiency of the standard discriminant technique based on logcontrast. Simulated compositional data and a real dataset are used to carry out these comparisons.     

Integrated Spatial and Spectrum Method for Geochemical Anomaly Separation

A new approach for separating geochemical anomalies from background has been developedon the basis of integration of spatial and spectrum analysis. A map generated from geochemicaldata can be transformed into a frequency domain in which a spatial concentration-area fractalmethod can be applied to distinguish the patterns on the basis of the power-spectrum distribution.Distinct classes can be generated, such as lower, intermediate, and high power-spectrum valuesapproximately corresponding to background, anomalies, and noises of geochemical values ina spatial domain. An irregular filter then can be constructed on these distinct patterns withthe background and noises related to low- and high-power-spectrum values being removed.The image converted back to a spatial domain with the filter applied can show patterns which,after the removal of background and noise, mainly reflect a residual area that representsanomalous or atypical geochemical patterns. This method is demonstrated using a case studyof soil geochemical data from the Mudik area, on the island of Sumatra, Indonesia. The resultsobtained from this method in comparison with those obtained from other methods have shownthat the newly developed method can separate overlapping populations without using a singlecutoff value.     

Classification of distinct eruptive phases of the diamondiferous Star kimberlite, Saskatchewan, Canada based on statistical treatment of whole rock geochemical analyses

Discrete eruptive events of the Star kimberlite, Saskatchewan, Canada have been classified into five distinctive clusters using statistical methods applied to whole rock geochemical data. The data set consists of 270 kimberlite samples from 38 drill holes that were analysed for whole rock major- and trace-element geochemistry. The data set was analysed by multivariate statistical techniques after a log-ratio transformation, including principal component analysis and linear discriminant analysis. Data analysis using principal component analysis recognized five distinct classes, confirmed by petrographic study, which correspond to unique mineralogical compositions. Based on relationships from detailed drill core logging results, these five geochemical classes are the Cantuar, Pense, early Joli Fou (eJF), mid Joli Fou (mJF) and late Joli Fou (lJF) equivalent age eruptive phases of the Star kimberlite. Subsequent statistical analysis utilizing linear discriminant analysis supports the distinctions between the classes. For the four kimberlite eruptive phases (Pense, early Joli Fou, mid Joli Fou and late Joli Fou) for which there is macrodiamond data from bulk sampling, there is an excellent correlation between the amount of lithospheric mantle contamination (as defined by the geochemistry) and the diamond grade.     

Some aspects of transformations of compositional data and the identification of outliers

The statistical analysis of compositional data is based on determining an appropriate transformation from the simplex to real space. Possible transfonnations and outliers strongly interact: parameters of transformations may be influenced particularly by outliers, and the result of goodness-of-fit tests will reflect their presence. Thus, the identification of outliers in compositional datasets and the selection of an appropriate transformation of the same data, are problems that cannot be separated. A robust method for outlier detection together with the likelihood of transformed data is presented as a first approach to solve those problems when the additive-logratio and multivariate Box-Cox transformations are used. Three examples illustrate the proposed methodology.