Appendix 07 Principal components analysis

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1 Appendix 07 Principal components analysis Data Analysis by Eric Grunsky The chemical analyses data were imported into the R ( statistical processing environment for an evaluation of possible multi-element relationships and spatial patterns that might be extracted from the data. The data were screened for values that were less than detection limit. Where such analyses were found, one half of the detection limit was chosen as a replacement value. Sanford et al. (1993) and Lee and Helsel (2005) have developed a method that allows for the calculation of a suitable replacement value based on a maximum likelihood approach. Replacement values using these methods become important if the number of samples that are less than the detection limit becomes significant (i.e. >5%). In addition, elements that were expressed as weight per cent were transformed to parts per million by using a multiplication factor of 10,000. The weight per cent major element oxides were not converted to major element cation values, although this should be done for a more complete evaluation of the data. As the data are compositional (weight% and parts per million), the data was transformed using a logcentered transformation. Aitchison (1986, 1997, 1999) and others have clearly demonstrated that any statistical inference of petrological processes based on compositions reported as weight percent oxide or ppm are subject to spurious correlations. This can lead to false interpretations from the apparent relationships of the data. Thus any analysis of data that is compositional in nature should be transformed using logarithms. The utility of taking this approach (Aitchison, 1986, 1997, 1999) has been confirmed by many other studies (Barcelo-Vidal, 1996; Aitchison et al., 2000, 2003; von Eynatten et al., 2002, 2003; Egozcue et al., 2003; Pawlowsky and Olea, 2004; Pawlowsky-Glahn, 2005; Tolosana-Delgado et al., 2005; Martin-Fernandez et al., 2005; Buccianti and Pawlowsky-Glahn, 2005; Aitchison and Egozcue, 2005). In this study, the log-centered transformation was used. Given 53 elements and 366 observations, it is helpful to describe the variability and patterns observed in these data in a way that defines the processes that produced these compositions. One way of summarizing these processes/patterns is by the application of multivariate methods such as principal components analysis. As well, the data were analyzed using partial extraction and a more complete three-acid digestion methods. Evaluating the differences of these two digestion methods can provide additional insight into the data, by inferring the presence/absence of resistant silicates and clay minerals. The objective of principal components analysis is to reduce the number of variables necessary to describe the observed variation within a set of data. This is done by forming linear combinations of the variables (components) that describe the distribution of the data based on the covariance structure of the data. Ideally, each component might be interpreted as describing a geological process such as differentiation (partial melting, crystal fractionation, mineral sorting/winnowing), contamination (crustal or mantle; anthropogenic), alteration/mineralization (carbonatization, silicification, alkali depletion, metal associations and enrichments, etc.), and weathering processes (bedrock-saprolite-laterite; soil weathering). A method of principal components analysis known as simultaneous RQ-mode principal components analysis (Zhou et al., 1983) has the advantage of presenting the component scores of the observations and the elements in the component space using the same scale. Thus, scatter plots of component scores show the relationships of the observations with respect to each other and the elements with respect to each other. The interpretation of the results of principal components is usually oriented on placing a geological/geochemical interpretation on the linear combinations of elements (loadings) that comprise the components.

2 Maps of the principal component scores of the observations can be useful in understanding geochemical processes. If a component expresses underlying lithologies, then a map of that component will clearly outline the major lithological variation of the area. Other components that outline other processes such as mineralization or alteration can also be clearly expressed on maps that display the component scores (e.g., Grunsky, 1986a). RQ-mode PCA was applied to the data which yielded patterns that are illustrated in Figure 1. This figure shows a plot of the first two principal component scores. The locations of the elements (plotted as the element/oxide names) and the samples (plotted as black circles) illustrate the relative relationships. Elements that plot close to each other are more highly correlated than those that do not. Also, the first two principal components account for 37% (PC1 24%, PC2 13%) of the overall variability of the data. The positive quadrant of the first component shows close associations of elements that comprise mafic minerals (Ni, Co, Mg, Ni, Fe), while the second quadrant (negative C1, positive C2) shows an affinity of rare earth elements that are probably associated with pegmatitic and highly fractionated materials. The third quadrant (negative C1, negative C2) reveals associations of elements that occur in granitoid and carbonate materials, and the fourth quadrant (positive C1, negative C2) shows elements that are transitional between the mafic and felsic environments. Maps of these components are shown in Figures 2 and 3. Figure 2 shows that an area with relative enrichment in mafic materials exists within the Glennie Domain and Figure 3 shows isolated relative enrichment of REE throughout the map area. Negative C2 scores which indicate relative enrichment in Pb, W, Ba, Nb, Ga, and Ti occur as isolated locations throughout the map area also. Figure 4 shows a plot PC1 versus PC3. The third component, which accounts for 11% of the data variation, shows a clear distinction between relative Ca-Sr-Na enrichment along the positive C3 axis and a relative enrichment of REE, Li and Zn along the negative C3 axis. When viewed together with the associations of the elements along the C1 axis, it can be seen that most of the variability of C3 is associated with the felsic materials, with an inverse association with the mafic materials along the positive C1 axis. Figure 5 shows a map of the 3 rd component where relative enrichment of Ca-Sr-Na occurs in the south eastern part of the Glennie domain and isolated REE enrichment occurs in the western and northern parts of the Glennie domain Figure 6 shows a plot of PC1 versus PC7 where there is a relative enrichment in U and Cu along the negative C7 axis. Positive C7 scores represent isolated enrichment of Te, Bi, Se and may be associated with mineral occurrences. This is expressed in the map of Figure 7 where blue/purple areas represent relative U and Cu enrichment in the western and northern parts of the Glennie domain. The isolated enrichment of Te, Bi and Se occur in the northern part of the area and two isolated occurrences along the southern shield margin. Figure 8 shows a plot of PC1 versus PC8, where there is a clear enrichment trend of mafic enrichment along the positive C8 axis and ad Cu U enrichment along the negative part of the C8 axis. Relative Cu enrichment has an affinity with the mafic suite of elements (positive C1 axis) and the relative U enrichment has an affinity with the felsic suite of elements (negative C1 axis). Figure 9 shows the map of C8, where the mafic pattern is clearly depicted along the western part of the Glennie domain. Negative C8 scores occur in the northern part of the Glennie domain. References Aitchison, J., The statistical analysis of compositional data. Methuen, New York. 416p. Aitchison J., 1997: The one-hour course in compositional data analysis or compositional data analysis is 2

3 simple. In: Proceedings of IAMG '97, the Third annual conference of the International Association for Mathematical Geology. Pawlowsky-Glahn-Vera (editor) Proceedings of the Annual Conference of the International Association for Mathematical Geology (3), Aitchison, J., Logratios and natural laws in compositional data analysis. Mathematical Geology 31 (5), Aitchison, J., Barceló-Vidal, C., Martín-Fernández, J.A. and Pawlowsky-Glahn, V., 2000: Logratio analysis and compositional distance. Mathematical Geology, 32, (3), Aitchison, J. and Egozcue, J.J., Compositional Data Analysis: Where Are We and Where Should We Be Heading?, Mathematical Geology 37 (7), Aitchison, J., Mateu-Figueras, G. and Ng, K.W., 2003: Characterization of distributional forms for compositional data and associated distributional tests. Mathematical Geology, 35, (6), Buccianti, A. and Pawlowsky-Glahn, V., New Perspectives on Water Chemistry and Compositional Data Analysis, Mathematical Geology 37 (7), Chayes, F., 1960: On correlation between variables of constant sum, Journal of Geophysical Research, (65), Chayes, F., 1966: Alkaline and subalkaline basalts, American Journal of Science, (264), Chayes, F., 1970: Ratio Correlation, University of Chicago Press, Chicago, 99 p. Egozcue, J.J., Pawlowsky-Glahn, V., Mateu-Figueras G and Barceló-Vidal, C., 2003: Isometric logratio transformations for compositional data analysis. Mathematical Geology, 35, (3), von Eynatten, H., Pawlowsky-Glahn, V., and Egozcue, J,.2002: Understanding perturbation on the simplex: A simple method to better visualize and interpret compositional data in ternary diagrams. Mathematical Geology, 34, (3), von Eynatten, H., Barceló-Vidal, C. and Pawlowsky-Glahn, V. 2003: Modelling compositional change: The example of chemical weathering of granitoid rocks. Mathematical Geology, 35, (3), , Grunsky, E.C., in press. The evaluation of geochemical survey data using data/statistical methods and geographic information systems, in Geographic Information Systems in the Earth Sciences, Geological Association of Canada Special Volume 44, J.R. Harris, editor,.pp Lee, L. and Helsel, D., Statistical analysis of water-quality data containing multiple detection limits: S-language software for regression on order statistics, Computers & Geosciences, 31, (10), Pawlowsky-Glahn, V., and Olea, R.A., 2004: Geostatistical Analysis of compositional data, International Association for Mathematical Geology Studies in Mathematical Geology No. 7, Oxford University Press, New York, 181p. Sanford, R.F, Pierson, C.T., and Crovelli, R.A., 1993, An Objective Replacement Method for Censored Geochemical Data, Mathematical Geology, 25, (1),

4 Tolosana-Delgado, R., Otero, N. and Pawlowsky-Glahn, V Some Basic concepts of Compositional Geometry, Mathematical Geology 37 (7), Figure 1. PC1 vs. PC2. log-centered till geochemistry. See text for explanation. 4

5 Figure 2. Map of the first principal component. Red areas are associated with mafic minerals; blue/purple areas are associated with felsic minerals. See Figure 1 for the element associations along the first principal component axis. Domain boundaries are shown. 5

6 Figure 3. Map of the second principal component. Red areas are those with relative enrichment of REE and blue areas show relative enrichment with Ba, W, Pb, Ga, Nb and TiO 2. See Figure 1 for the association of elements along the second principal component axis. 6

7 Figure 4. PC1 vs. PC3. See text for detailed explanation. 7

8 Figure 5. Map of the 3 rd principal component scores. The positive values (in red/orange) area associated with relative Ca-Sr-Na in the eastern part of the Glennie Domain. The negative C3 scores that show relative REE, Li and Zn enrichment are shown in blue/purple, particularly in the west and northern part of the Glennie Domain. 8

9 Figure 6. PC1 vs. PC7. See text for detailed explanation. 9

10 Figure 7. Map of the 7th principal component scores. See text for explanation. 10

11 Figure 8. PC1 vs. PC8. See text for detailed explanation. 11

12 Figure 9. Map of the 8th principal component scores. See text for explanation. 12

Geochemical Data Evaluation and Interpretation

Geochemical Data Evaluation and Interpretation Eric Grunsky Geological Survey of Canada Workshop 2: Exploration Geochemistry Basic Principles & Concepts Exploration 07 8-Sep-2007 Outline What is geochemical