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Systematic use of trace elements in igneous processes

Part III: Inverse problem of batch partial melting in volcanic suites

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Abstract

This paper develops an application of the inverse method proposed by Allégre et al. (1977) and Minster et al. (1977). Using a set of trace element data in a suite of “primary” lavas, it is possible to statistically test whether the data can be described by batch partial melting. Once this is achieved, one can inverse the problem and calculate the parameters which govern the process, that is: the degrees of melting corresponding to each lava, the initial source concentrations and partition coefficients for each element. This is a non-linear, strongly underdetermined problem, but when the set of trace elements is restricted to REE, taking advantage of the fact that their properties are smoothly related, the problem can be overconstrained by assuming a set of poorly constrained model parameters. Information contained in the data and in the external constraints can then be estimated and used to build a strategy of data acquisition. From a table of mineral-liquid partition coefficients, the mineralogies of the source and of the material entering the liquid can be calculated. The method has been tested on synthetic data sets representing natural cases, and proved to converge towards the “real” solution even when a very poor definition of the external constraints is introduced.

The calculations have been applied to REE data on Grenada basanitoids (Shimizu and Arculus, 1976). It is confirmed that these lavas can be derived by 4 to 17% batch partial melting of a garnet lherzolite source (7% gt, 23% cpx) that is relatively enriched in light REE. This result is discussed in relation with Nd and Sr isotopic composition data.

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Authors and Affiliations

  1. Laboratoire de Géochimie et Cosmochimie, LA 196, Institut de Physique du Globe, Université Paris VI, France

    J. F. Minster & C. J. Allègre

  2. Département des Sciences de la Terre, Université Paris VII, 4 Place Jussieu, F-75005, Paris V, France

    J. F. Minster & C. J. Allègre

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  1. J. F. Minster
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  2. C. J. Allègre
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Minster, J.F., Allègre, C.J. Systematic use of trace elements in igneous processes. Contr. Mineral. and Petrol. 68, 37–52 (1978). https://doi.org/10.1007/BF00375445

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