Error propagation in geochemical modeling of trace elements in two-component mixing
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Abstract
This study presents error propagation equations for geochemical modeling of trace elements during mixing of two compo- nents or end-members. These equations can be used to estimate uncertainties in the concentration of an element or ratio of two elements in the mixture of two components, as a function of the initial measurement uncertainties. Several examples illustrate the use of these equations in geochemical modeling. Although as expected the element concentrations and their ratios in the mixture always lie between those of the two end-members, it is not the case with the corresponding measurement uncertainties. The %Rsd (Relative standard deviation expressed in %) of the concentration of an element in the mixture is never larger than the %Rsd of the component with larger uncertainty for that element, but can be smaller than the component with smaller uncertainty. Similarly, error propagation using actual element concentration data on basalt and sediment samples from the Cocos plate was carried out to further exemplify the use of these new equations and their importance in petrogenetic problems.
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References
ALBARÈDE, F., 1995. Introduction to Geochemical Modeling, Cambridge University Press, Cambridge, 543 p. DOI: https://doi.org/10.1017/CBO9780511622960
BEVINGTON, P. R., 1969. Data Reduction and Error Analysis for the Physical Sciences, McGraw Hill, New York, 336 p.
FAURE, G., 1986. Principles of Isotope Geology, second edition, John Wiley, New York, 589 p.
GUEDENS, W. J., J. YPERMAN, J. MULLENS, L. C. VAN POUCKE and E. J. PAUWELS, 1993. Statistical analysis of errors: a practical approach for an undergraduate Chemistry lab. Part 1. The concepts. J. Chem. Educ. 70, 776-779. DOI: https://doi.org/10.1021/ed070p776
HORWITZ, W. and R. ALBERT, 1997. The concept of uncertainty as applied to chemical measurements. Analyst, 122, 615-617. DOI: https://doi.org/10.1039/a703178e
KANE, J. S., 1997. Analytical bias: the neglected component of measurement uncertainty. Analyst, 122, 1283-1288. DOI: https://doi.org/10.1039/a704789d
MYERS, J. D., C. L. ANGEVINE, and C. D. FROST, 1987. Mass balance calculations with end member compositional variability: applications to petrologic problems. Earth Planet. Sci. Lett. 81, 212-220. DOI: https://doi.org/10.1016/0012-821X(87)90157-9
RAMSEY, M. H., 1997. Measurement uncertainty arising from sampling: implications for the objectives of geoanalysis. Analyst, 122, 1255-1260. DOI: https://doi.org/10.1039/a704995a
TAYLOR, J.R., 1982. An Introduction to Error Analysis. The Study of Uncertainties in Physical Measurements. University Science Books, New York, 269 p.
VERMA, S. P., 1998a. Error propagation in equations for geochemical modeling of radiogenic isotopes in two-component mixing. Proc. Ind. Acad. Sci. (Earth Planet. Sci.), in press.
VERMA, S. P., 1998b. Geochemistry of subducting Cocos plate and the origin of subduction-unrelated mafic volcanism at the volcanic front of central Mexican Volcanic Belt. Geol. Soc. Am. Spec. Paper, 334, on Cenozoic Volcanism and Tectonics of Mexico, in press.