Calculations of wallrock melting degree in AFC processes. (Abstract/Poster in atti di convegno)

Type
Label
  • Calculations of wallrock melting degree in AFC processes. (Abstract/Poster in atti di convegno) (literal)
Anno
  • 2010-01-01T00:00:00+01:00 (literal)
Alternative label
  • G. Cavazzini (2010)
    Calculations of wallrock melting degree in AFC processes.
    in 89° Congresso Società Italiana di Mineralogia e Petrologia, L'evoluzione del Sistema Terra dagli Atomi ai Vulcani., Ferrara, 13-15 Settembre 2010
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • G. Cavazzini (literal)
Pagina inizio
  • 133 (literal)
Pagina fine
  • 133 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#altreInformazioni
  • L'evoluzione del Sistema Terra dagli Atomi ai Vulcani, S1.6-O7 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#titoloVolume
  • L'evoluzione del Sistema Terra dagli Atomi ai Vulcani. (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#pagineTotali
  • 1 (literal)
Note
  • Abstract (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • G. Cavazzini, Istituto Geoscienze e Georisorse (literal)
Titolo
  • Calculations of wallrock melting degree in AFC processes. (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#curatoriVolume
  • Societa' Italiana di Mineralogia e Petrologia; Societa' Italiana di Geochimica; Associazione Italiana di Vulcanologia; Istituto Nazionale di Geofisica e Vulcanologia (literal)
Abstract
  • Analytical solutions are found of differential equations which describe isotopic and trace element concentration changes in magmatic liquids which evolve by assimilation-fractional crystallization (AFC) where the assimilated material changes its composition as the instantaneous melt in fractional melting model of Shaw [1]. These differential equations are obtained by relating melting model [1] to DePaolo's AFC model [2] through a relationship between instantaneous wallrock melting degree and residual liquid fraction in the assimilating magma. The chemical and isotopic evolution of a magmatic liquid by AFC as the concentration in the assimilated changes according to fractional melting model [1] was modeled by [3, 4], who calculated the effect of the behavior of the element in melting on concentration and isotopic paths. However, these authors did not solve any differential equation, giving only numerical results. The analytical solutions are easy to use and versatile. They are obtained by integrating with DePaolo's parameter r (the ratio between assimilation and crystallization rates) as a constant, and describe very well the concentration and the isotopic changes in a very large range of residual liquid fraction. In any case, an exact solution exists and is given, which is analytical-numerical, as it involves an hypergeometric 2F1 Gauss function. These calculations are important as they can aid in ascertaining if an isotopic and concentration data set can be interpreted in terms of a certain AFC process or not. In interpreting a data set in terms of an AFC process, we assume starting from a parental liquid characterized by certain chemical and isotopic compositions which crystallizes and assimilates melt produced by melting of a wallrock characterized by certain chemical and isotopic compositions. Moreover, we also assume a value for ratio r, and, in the model which is proposed here, an other parameter must be assumed to trace the evolution path, which is the ratio ? between the mass of the liquid when assimilation begins and the mass of the wallrock which is involved in the melting process. Parameters r and ? calculate the melting degree of the wallrock at any step, and the melting degree cannot exceed 1. Moreover, for the AFC process to be a single one - i.e. for the concentration and isotopic data-set can be interpreted as the result of the evolution of a single mass of magma - values of ? must fall in a reasonably narrow range. As an example of application, we consider Sr isotopic and concentration data of the mafic to intermediate volcanic rocks from the Long Valley caldera and Devil's Postpile National Monument, Eastern California (data from [5] and [6]), which were interpreted by [4] as the result of a single AFC process. Assuming the same concentration and isotopic parameters used by [4] for the initial uncontaminated liquid and the wallrock, and the same values for Sr distribution coefficients in crystallization and melting, both the analytical solutions show, however, that for any r value too much different values of ratio ?, which differ by a factor of two, should be input into the equations to generate paths which describe the data point distribution. We thus infer that this rock distribution cannot be actually interpreted as derived by AFC starting from a single mass of liquid in the terms proposed by [4]. [1] Shaw, D. (1970): Geoch. Cosmoch. Acta, 34, 237-243. [2] DePaolo, D. J. (1981): Earth Planet. Sci. Lett., 53, 189-202. [3] Spera, F. & Bohrson, W. (2001): Journ. Petrol., 42, 999-1018. [4] Bohrson, W. & Spera, F. (2001): Journ. Petrol., 42, 1019-1041. [5] Vogel, T.A., Woodburne, T.B., Eichelberger, J.C., Layer, P.W. (1994): Journ. Geophys. Res. 99, 19829-19842. [6] Cousens, B.L. (1996): Journ. Geophys. Res., 101, 27673-27689. (literal)
Editore
Prodotto di
Autore CNR
Insieme di parole chiave

Incoming links:


Prodotto
Autore CNR di
Editore di
Insieme di parole chiave di
data.CNR.it