Mass balance calculations with end member compositional variability: applications to petrologic problems

Details Mass balance calculations with end member compositional variability: applications to petrologic problems Mass balance calculations with end member compositional variability: applications to petrologic problems

Jan 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987e%26psl..81..212m&link_type=abstract

Earth and Planetary Science Letters, Volume 81, Issue 2-3, p. 212-220.

Mathematics

Logic

2

Scientific paper

Although end member compositional variability is quite common, most quantitative mass balance procedures cannot accommodate this variability in a systematic manner. By rearranging the traditional mass balance relations, a series of equations can be derived to account for such heterogeneity. While this approach can be applied to n-component systems, the results are difficult to represent graphically. Accordingly, the procedure is most useful for two- and three-component systems. For two components, the concentration of an element in a mixture is: Cpm = Chm/X + (1 - 1/X)C1 and the isotopic signature is: ɛpmCpm = ɛhmChm/X + (1 - 1/X)ɛ1C1 where pm, hm and 1 refer to parental magma, hybrid magma and component 1, respectively, X is the proportion of parental magma, C is concentration, ɛ is isotopic ratio, and C the concentration of the denominator isotope in the particular isotopic ratio of interest. These equations describe straight lines, termed isoproportional or IP lines, of fixed mixing proportion in the Cpm-C1 concentration or ɛpmCpm-ɛ1C1 planes. Only those IP lines intersecting the rectangle defined by observed end member compositions represent viable mixing proportions. For three-component systems, the mass balance equations are: Y = (Chm - C2) - X(Cpm - C2)/C1 - C2 and: Y = (Chmɛhm - C2ɛ2) - X(Cpmɛpm - C2ɛ2)/C1ɛ1 - C2ɛ2 where Y is now the proportion of component 1 and the proportion of component 2, Z, is simply 1 - X - Y. Using major, trace and rare earth element as well as isotopic data, a region of the X-Y plane representing possible mixing combinations can be defined. Due to the compositional variability of most magmatic end members, this new mass balance procedure should be applicable to a diverse range of petrologic problems. This procedure has been applied to three different petrologic processes: Aleutian parental magma genesis, assimilation/contamination, and crust-mantle differentiation.

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