| There are many calculations of geology or geochemistry involving compositionaldata, for example, the ratio content of major and minor elements of rocks or minerals.When Lange’s plagioclase-liquid equilibrium thermodynamic model is used as a hy-grometer, the ratio content of water is a function of temperature, pressure and themagmatic-liquid components as well as the crystalline-plagioclase components, whereboth liquid and plagioclase components are those compositional data with the sum ofall liquid components equating100%and that of all crystalline-plagioclase compo-nents equating1. Those ratio data or compositional data is spuriously related to eachother due to the data-sum constraint, and if we utilize these ratio data directly for cal-culation, it will necessarily bring some error of the calculation results. This paper uti-lizes compositional data analysis or log contrast method to remove that spurious rela-tions among ratio data. Meanwhile, in Lange’s hygrometer model, the relation be-tween water and liquid components and that between water and plagioclase compo-nents are both oversimplified to the linear relations; these components measured bye.g. electron probe, where there are measurement errors; it is well known that a leastquadratic analysis can only decrease the measurement errors. In this paper, the newmodel, based on a quadratic log-contrast method for experiment with mixture, refinesLange’s hygrometer according to the two aspects mentioned above and calculates thestandard error of estimate of water content that is±0.156%H O, and all liquid andplagioclase compositions are fitted equally well. When the new model is used as athermometer, all measured temperature are recovered equally well within an averagedeviation of±10.6°C. This research also develops the new programs of thermometerand hygrometer based on the modified model, and then applies this thermometer tothe calculation of diagenetic temperature of Dapai lead-zinc deposit. |
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