Investigating Complex Isochron Data Using Mixture Models

Abstract

Abstract The isochron technique for dating geological events is widely used in many fields of isotope geochemistry. However, data sets can be complex, and many samples may not behave as closed systems, resulting in excess scatter around a regression line. In certain data sets, however, excess scatter may result when geological samples are partially reset or when samples are comprised of multiple components recording different geological processes separated in time and/or initial isotope composition. Here we introduce a new approach for investigating evidence of such multicomponent mixtures within isochron space. We provide a mathematical framework to resolve the number of mixture components, without requiring any prior knowledge of this number. Crucially, the model reports the proportion of each individual sample that belongs to each mixture component, allowing the user to return to the samples and independently test model outputs with other techniques. It is important to distinguish accurate and meaningful ages and initial daughter isotope compositions from the meaningless values that are caused by mismatch between geological processes and the models that we use to describe them. First, we demonstrate our new model on a synthetic data set to show that it can successfully separate distinct isochrons in a complex mixture. We further validate our approach with a previously published data set using the 187Re‐187Os system in bitumen and 147Sm/144Nd system in magmatic rocks. We identify discrete components in these data sets and using complementary geological observations discuss the implications of treating these scattered data as recording multiple geological processes.

Keywords

• isochron
• mixture model
• discrete mixtures
• Re‐Os
• Sm‐Nd