Abstract
The use of principal component analysis in studying chemical trends in volcanic rock suites is described. It is suggested that eigenvectors generated from a correlation matrix, rather than a covariance matrix, could be used in this context. In the latter situation many elements are swamped by silicon's numerical size and range. In the former situation the alkalies and titanium begin to show their true importance.
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References
Anderson, T. W., 1958, An introduction to multivariate statistical analysis: John Wiley & Sons, New York, 374 p.
Cattell, R. B., 1965, Factor analysis: an introduction to essentials: Biometrics, v. 21, p. 190–215.
Chayes, F., 1964, A petrographic distinction between Cenozoic volcanoes in and around the open ocean: Jour. Geophys. Res., v. 69, no. 8, p. 1573–1588.
Colley, H., 1968, The geology of Erromango, New Hebrides: unpubl. doctoral dissertation, Sheffield Univ., 250 p.
Cooley, W. W., and Lohnes, P. R., 1962, Multivariate procedures for the behavioral sciences: John Wiley & Sons, New York, 211 p.
Cundari, A., and Le Maitre, R. W., 1970, Petrogeny of the leucite-bearing rocks of the Roman and Birunga volcanic regions: Jour. Petrology, v. 11, no. 1, p. 33–47.
Greenstadt, J., 1960, The determination of the characteristic roots of a matrix by the Jacobi method,in Mathematical methods for digital computers, v. 1: John Wiley & Sons, New York, 293 p.
Harman, H. H., 1960, Modern factor analysis: Univ. Chicago Press, Chicago, Illinois, 460 p.
Hotelling, H., 1933, Analysis of a complex of statistical variables into principal components: Jour. Educ. Psychology, v. 24, p. 417–441.
Howarth, R. J., 1970, Principal component analysis of the geochemistry and mineralogy of the Portaskaig tillite and Kilty fanned schist (Dalradian) of Co. Donegal, Eire: Math Geology, v. 2, no. 3, p. 285–301.
Le Maitre, R. W., 1968, Chemical variation within and between volcanic rock series—a statistical approach: Jour. Petrology, v. 9, no. 2, p. 220–252.
Matalas, N. C., and Reiher, B. J., 1967, Some comments on the use of factor analysis: Water Res. Research, v. 3, no. 1, p. 213–223.
McCammon, R. B., 1966, Principal component analysis and its applications in large-scale correlation studies: Jour. Geology v. 74, no. 5, pt. 2, p. 721–733.
Overall, J. E., and Klett, C. J., 1972, Applied multivariate analysis: McGraw Hill Book Co., New York, 500 p.
Spearman, C., 1904, General intelligence, objectively determined and measured: Am. Jour. Psychology, v. 15, p. 201–293.
Spencer, D. W., 1966, Factors affecting element distribution in a Silurian graptolite band: Chemical Geology, v. 1, no. 3, p. 221–249.
Vistelius, A. B., Ivanov, D. N., Kuroda, Y., and Ruiz Fuller, C., 1970, Variations of modal composition of granitic rocks in some regions around the Pacific: Math. Geology, v. 2, no. 1, p. 63–80.
Wahlstedt, W. G., and Davis, J. C., 1968,fortran iv program for computation and display of principal components: Kansas Geol. Survey Computer Contr. 21, 27 p.
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Till, R., Colley, H. Thoughts on use of principal component analysis in petrogenetic problems. Mathematical Geology 5, 341–350 (1973). https://doi.org/10.1007/BF02111985
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DOI: https://doi.org/10.1007/BF02111985