Error propagation in equations for geochemical modeling of radiogenic isotopes in two-component mixing

Abstract

This paper presents error propagation equations for modeling of radiogenic isotopes during mixing of two components or end-members. These equations can be used to estimate errors on an isotopic ratio in the mixture of two components, as a function of the analytical errors or the total errors of geological field sampling and analytical errors. Two typical cases ('Small errors' and 'Large errors') are illustrated for mixing of Sr isotopes. Similar examples can be formulated for the other radiogenic isotopic ratios. Actual isotopic data for sediment and basalt samples from the Cocos plate are also included to further illustrate the use of these equations. The isotopic compositions of the predicted mixtures can be used to constrain the origin of magmas in the central part of the Mexican Volcanic Belt. These examples show the need of high quality experimental data for them to be useful in geochemical modeling of magmatic processes.