Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-04T18:04:30.013Z Has data issue: false hasContentIssue false

Non-linear dynamics, chaos, complexity and enclaves in granitoid magmas

Published online by Cambridge University Press:  03 November 2011

James Flinders
Affiliation:
James Flinders, Department of Earth Sciences, The University of Manchester, Oxford Road, Manchester M13 9PL, U.K.
John D. Clemens
Affiliation:
John D. Clemens, School of Geological Sciences, Kingston University, Penrhyn Road, Kingston-upon-Thames, Surrey KT1 2EE, U.K.

Abstract:

Most natural systems display non-linear dynamic behaviour. This should be true for magma mingling and mixing processes, which may be chaotic. The equations that most nearly represent how a chaotic natural system behaves are insoluble, so modelling involves linearisation. The difference between the solution of the linearised and ‘true’ equation is assumed to be small because the discarded terms are assumed to be unimportant. This may be very misleading because the importance of such terms is both unknown and unknowable. Linearised equations are generally poor descriptors of nature and are incapable of either predicting or retrodicting the evolution of most natural systems. Viewed in two dimensions, the mixing of two or more visually contrasting fluids produces patterns by folding and stretching. This increases the interfacial area and reduces striation thickness. This provides visual analogues of the deterministic chaos within a dynamic magma system, in which an enclave magma is mingling and mixing with a host magma. Here, two initially adjacent enclave blobs may be driven arbitrarily and exponentially far apart, while undergoing independent (and possibly dissimilar) changes in their composition. Examples are given of the wildly different morphologies, chemical characteristics and Nd isotope systematics of microgranitoid enclaves within individual felsic magmas, and it is concluded that these contrasts represent different stages in the temporal evolution of a complex magma system driven by nonlinear dynamics. If this is true, there are major implications for the interpretation of the parts played by enclaves in the genesis and evolution of granitoid magmas.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Chayes, F. 1962. Numerical correlation and petrographic variation. J GEOL 70, 440–52.CrossRefGoogle Scholar
Chen, Y., Price, R. C..White, A. J. R.&Chappell, B. W. 1990. Mafic inclusions from the Glenbog and Blue Gum granite suites, southeastern Australia. J GEOPHYS RES B95, 17757–85.CrossRefGoogle Scholar
Cocirta, C.&Orsini, J.-B. 1986. Signification de la diversité de composition des enclaves ≪microgrenuesg≫ sombre en contexte plutonique. L'example des plutons calco-alcalin de Bono et Budduso (Sardaigne septentrionale). C ACAD SCI PARIS SER (II)302, 331–6.Google Scholar
Lesher, C. E. 1990. Decoupling of chemical and isotopic exchange during magma mixing. NATURE 344, 235–7.CrossRefGoogle Scholar
Metcalf, R. V., Smith, E. I.. Walker, J. D.Reed, R. C.&Gonzales, D. A. 1995. Isotopic disequilibrium among co-mingled hybrid magmas: evidence for a two-stage magma mixing–co-mingling process in the Mt Perkins pluton. Arizona. J GEOL 103, 509–27.CrossRefGoogle Scholar
O'Hara, M. J.&Mathews, R. E. 1981. Geochemical evolution in an advancing, periodically replenished, periodically tapped, continuously fractionated magma chamber. J GEOL SOC LONDON 138, 237–77.CrossRefGoogle Scholar
Ottino, J. M. 1989. The mixing of fluids. SCI AM 260, 40–9.CrossRefGoogle Scholar
Ottino, J. M., Leong, C. W..Rising, H.&Swanson, P. D. 1988. Morphological structures produced by mixing in chaotic flows. NATURE 333, 419–25.CrossRefGoogle Scholar
Petford, N., Byron, D., Atherton, M. P.&Hunter, R. H. 1993. Fractal analysis in granitoid petrology: a means of quantifying irregular grain morphologies. EUR MINERAL 5, 593–8.CrossRefGoogle Scholar
Roberts, M. P.&Clemens, J. C. 1995. Feasibility of AFC models for the petrogenesis of calc-alkaline magma series. CONTRIB MINERAL PETROL 121, 139–47.CrossRefGoogle Scholar
Rollinson, H. R. 1993. Using geochemical data: evaluation, presentation, interpretation. Harlow: Longman Scientific & Technical.Google Scholar
Ruelle, D. 1994. Where can one hope to profitably apply the ideas of chaos? PHYS TODAY 47, 2430.CrossRefGoogle Scholar
Srogi, L.&Lutz, T. M. 1990. Three-dimensional morphologies of metasedimentary and mafic enclaves from Ascutney Mountain, Vermont. J GEOPHYS RES 95, (B11), 17 829–40.CrossRefGoogle Scholar
Stewart, I. 1993. Chaos. In: Howe, L.&Wain, A. (eds) Predicting the future, 2451. Cambridge: Cambridge University Press.Google Scholar
Wall, V. J., Clemens, J. D.&Clarke, D. B. 1987. Models for granitoid evolution and source compositions. J GEOL 95, 731–50.CrossRefGoogle Scholar