Error propagation in geochemical modeling of trace elements in two-component mixing

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.