Tracing Sources with Isotopes
One of the most powerful applications of isotope geochemistry is identifying and quantifying the sources of geological materials. When a basaltic magma assimilates continental crust on its way to the surface, the mixture inherits isotopic signatures from both the mantle source and the crustal contaminant. Plotting the isotope ratios of multiple samples reveals a systematic trend — a mixing line — whose end-members reveal the original sources.
Binary Mixing in Isotope Space
For two end-members A and B, the mixture M plots along a line in ratio-vs-ratio space. The position of M along the line is controlled by the mixing fraction f and the concentration ratio of the element in each end-member. When concentrations are equal, the mixing line is straight and f maps linearly to position. When concentrations differ, the line curves — a hyperbola whose curvature reveals the concentration contrast.
Ternary Mixing and Beyond
With three end-members, data plot within a triangle in isotope space. Each vertex represents a pure end-member, and any interior point can be decomposed into unique proportions of all three. Adding more isotope systems (Sr, Nd, Pb, Hf) over-constrains the problem, allowing statistical tests of whether the assumed end-members are correct. This simulation lets you visualize how mixing fraction and end-member positions control the mixture composition.
Applications in Magma Genesis
The Sr-Nd isotope diagram is the classic tool for mantle geochemistry. Depleted MORB-source mantle plots with low ⁸⁷Sr/⁸⁶Sr and high ¹⁴³Nd/¹⁴⁴Nd, while old continental crust plots in the opposite corner. Ocean island basalts scatter between several identified mantle end-members (DMM, HIMU, EM-I, EM-II), revealing the isotopic heterogeneity of the deep mantle and the recycling of crustal material through plate tectonics.