Mass balance calculations with end member compositional variability: applications to petrologic problems - D. Myers, J.; L. Angevine, C.; D. Frost, C. (Elsevier)
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: C"p"m = ChmX + 1 - 1XC"1 and the isotopic signature is: "p"mC"p"m = "h"mC"h"mX + 1 - 1X"1C"1 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, 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 C"p"m-C"1 concentration or "p"mC"p"m-"1C"1 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 = (C"h"m - C"2) - X(C"p"m - C"2)C"1 - C"2 and: Y = (C"h"m"h"m - C"2"2) - X(C"p"m"p"m - C"2"2)C"1"1 - C"2"2 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.
http://linkinghub.elsevier.com/retrieve/pii/0012-821X(87)90157-9
Keywords: TE-TZ; U