Abstract
During the last decade most of the computer applications in petrology have been concerned with data bases, petrological mixing models, the use of multivariate statistical techniques and, more recently, the modeling of igneous differentiation trends.
The characteristics of three of the major data bases, that is RKNFSYS (approximately 16,000 analyses), CLAIR (approximately 26,000 analyses), and PETROS (approximately 35,000 analyses) are compared. As a result of the experience gained in building these bases, a new international igneous data base (IGBA) is being organized, which will supercede eventually the others due to the inclusion of mineralogical and more textural information.
Recent developments in petrological mixing models include a better understanding of the principles behind the various models, in particular the fact that for constant sum major element data, a constrained model should be used. A completely generalized model capable of dealing with metamorphic reactions of the type A + B + C +.. =D+E+F+G.. also has been developed.
The use of principal-components analysis, factor analysis, and discriminant analysis in the interpretation of the chemistry of igneous rocks and mineral groups has become increasingly popular, but unfortunately, either through ignorance or the use of statistical packages, some of the interpretations have been incorrect. In particular, principal-component analysis based on the correlation matrix seems difficult to justify for major element geochemical data.
The modeling of igneous differentiation trends has been approached in two different ways. One mainly empirical method predicts the path of crystallization of any given anhydrous liquid composition at 1 atmosphere pressure. The inclusion of H2Oand pressure into the method is only a question of time. The other method is based on Rayleigh’s Law of fractional crystallization.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Albarede, F., and Provost, A., 1971, Petrological and geochemical mass-balance equations: an algorithm for least-squares fitting and general error analysis: Computers & Geosciences, v. 3, no. 2, p. 309–326.
Allegre, C.J., Treuil, M., Minster, J.F., Minster, B., and Albarede, F., 1977, Systematic use of trace elements in igneous process. Part 1: Fractional crystallisation processes in volcanic suites: Contrib. Mineral. Petrol., v. 60, no. 1, p. 57–75.
Barr, D.L., Mutschier, F.E., and Lavin, O.P., 1977, KEYBAM: a system of interactive computer programs for use with the PETROS petrochemical data bank: Computers & Geosciences, v. 3, no. 3, p. 489–496.
Bryan, W.B., 1969, Materials balance in igneous rock suites: Ann. Rept. Dir. Geophys. Lab. Carnegie Inst. Washington, v. 67, p. 241–243.
Bryan, W.B., Finger, L.W., and Chayes, F., 1969a, A least-squares approximation for estimating the composition of a mixture: Ann. Rept. Dir. Geophys. Lab. Carnegie Inst. Washington, v. 67, p. 243–244.
Bryan, W.B., Finger, L.W., and Chayes, F., 1969b, Estimating proportions in petrographic mixing equations by least-squares approximation: Science, v. 163, no. 3870, p. 926–927.
Chayes, F., 1964, A petrographic distinction between Cenozoic volcanics in and around the open oceans: Jour. Geophys. Res., v. 69, no. 8, p. 1573–1588.
Chayes, F., 1968, On locating field boundaries in simple phase diagrams by means of discriminant functions: Am. Mineral., v. 53, nos. 3 and 4, p. 359–371.
Chayes, F., 1971, Electronic storage, retrieval, and reduction of data about the chemical composition of common rock: Ann. Rept. Dir. Geophys. Lab. Carnegie Inst. Washington, v. 70, p. 197–201.
Chayes, F., 1975, On distinguishing alkaline from other basalts: Ann. Rept. Dir. Geophys. Lab. Carnegie Inst. Washington, v. 74, p. 546–547.
Chayes, F., 1976, Characterizing the consistency of current usage of rock names by means of discriminant functions: Ann. Rept. Dir. Geophys. Lab. Carnegie Inst. Washington, v. 75, p. 782–784.
Chayes, F., 1979, Partitioning by discriminant analysis: a measure of consistency in the nomenclature and classification of volcanic rocks, in The evolution of igneous rocks: Princeton Univ. Press, Princeton, New Jersey, p. 521–532.
Chayes, F., and Le Maitre, R.W., 1972, The number of published analyses of igneous rocks: Ann. Rept. Dir. Geophys. Lab. Carnegie Inst. Washington, v. 71, p. 493–495.
Gleadow, A.J.W., Le Maitre, R.W., Sewell, D.K.B., and Lovering, J.F., 1974, Chemical discrimination of petrographically defined clast groups in Apollo 14 and 15 lunar breccias: Chem. Geology, v. 14, no. 1, p. 39–61.
Joreskog, K.G., Klovan, J.E., and Reyment, R.A., 1976, Geological factor analysis, in Methods in Geomathematics 1: Elsevier Sci. Publ. Co., Amsterdam, 178 p.
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.
Le Maitre, R.W., 1973, Experiences with CLAIR: a computerised library of analysed igneous rocks: Chem. Geology, v. 12, no. 4, p. 301–308.
Le Maitre, R.W., 1976a, Chemical variability of some common igneous rocks: Jour. Petrology, v. 17, no. 4, p. 589–637.
Le Maitre, R.W., 1976b, Some problems of the projection of chemical data into mineralogical classifications: Contrib. Mineral. Petrol, v. 56, no. 2, p. 181–189.
Le Maitre, R.W., 1976c, A new approach to the classification of igneous rocks using the basalt-andesite-dacite-rhyolite suite as an example: Contrib. Mineral. Petrol, v. 56, no. 2, p. 191–203.
Le Maitre, R.W., 1978, Numerical petrology: Trans. Leicester Lit. Phil. Soc., v. 72, in press.
Le Maitre, R.W., 1979, A new generalised petrological mixing model: Contrib. Mineral. Petrol, v. 71, no. 2, p. 133–137.
Le Maitre, R.W., and Ferguson, A.K., 1978, The CLAIR data system: Computers & Geosciences, v. 4, no. 1, p. 65–76.
Maaloe, S., 1976, Quantitative aspects of fractional crystallisation of major elements: Jour. Geology, v. 84, no. 1, p. 81–96.
Middleton, G.V., 1964, Statistical studies on scapolites: Can. Jour. Earth Sci., v. 1, no. 1, p. 23–34.
Miesch, A.T., 1976, Q-mode factor analysis of geochemical and petrologic data matrices with constant row-sums: U.S. Geol. Survey Prof. Paper 574-G, p. 1–47.
Minster, J.F., Minster, J.B., Treuil, M., and Allegre, C.J., 1977, Systematic use of trace elements in igneous processes: Part II. Inverse problem the fractional crystallisation process in volcanic suites: Contrib. Mineral. Petrol., v. 61, no. 1, p. 49–77.
Mottana, A., Sutterlin, P.G., and May, R.W., 1971, Factor analysis of garnets and omphacites: a contribution to the geochemical classification of eclogites: Contrib. Mineral. Petrol, v. 31, no. 3, p. 238–250.
Mutschler, F.E., Rougon, D.J., and Lavin, O.P., 1976, PETROS — a data bank of major-element chemical analyses of igneous rocks for research and teaching: Computers & Geosciences, v. 2, no. 1, p. 51–57.
Mutschler, F.E., Rougon, D.J., Lavin, O.P., and Hughes, R.D., 1978, PETROS a data bank of major element chemical analyses of igneous rocks: U.S. Dept. Commerce, Nat. Oceanic Atmos. Admin., Envir. Data Serv., Pamphlet 1978(W), 4 p.
Nathan, H.D., and Van Kirk, C.K., 1978, A model of magma-tic crystallisation: Jour. Petrology, v. 19, no. 1, p. 66–94.
Saxena, S.K., and Walter, L.S., 1974, A statistical-chemical and thermodynamic approach to the study of lunar mineralogy: Geochim. Cosmochim. Acta, v. 38, no. 1, p. 79–95.
Shaw, D.M., 1974, R-mode factor analysis on enstatite chondrite analyses: Geochim. Cosmochim. Acta, v. 38, no. 10, p. 1607–1613.
Stormer, J.C., and Nicholls, J., 1978, XLFRAC: a program for the interactive testing of magmatic differentiation models: Computers & Geosciences, v. 4, no. 2, p. 143–159.
Streckeisen, A., and Le Maitre, R.W., 1979, A chemical approximation to the modal OAPF classification of the the igneous rocks: Neues Jahrb. Mineral. Abh. Band 136, Heft 2, p. 169–206.
Taimre, T., 1977, Theoretical modelling of liquidus relation in silicate systems: unpubl. honours project, Univ. Melbourne, 132 p.
Till, R., and Colley, H., 1973, Thoughts on the use of principal component analysis in petrogenetic problems: Jour. Math. Geology, v. 5, no. 4, p. 341–350.
Wright, T.L., and Doherty, P.C., 1970, A linear programming and least squares computer method for solving petrologic mixing problems: Geol. Soc. America Bull., v. 81, no. 7, p. 1995–2008.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1981 Plenum Press, New York
About this chapter
Cite this chapter
Le Maitre, R.W. (1981). Some Developments in Computer Applications in Petrology. In: Merriam, D.F. (eds) Computer Applications in the Earth Sciences. Computer Applications in the Earth Sciences. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-7732-0_11
Download citation
DOI: https://doi.org/10.1007/978-1-4684-7732-0_11
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-7734-4
Online ISBN: 978-1-4684-7732-0
eBook Packages: Springer Book Archive