Interpreting mixing relationships in energetic melts to estimate vapor contribution and composition

Energetic events such as meteorite impacts or nuclear explosions in silicate-rich environments produce compositionally heterogeneous melts/vapors that quench to glasses such as tektites and fallout. These glassy byproducts constitute a compositional record of an unknown vapor combined with melted, compositionally heterogeneous environmental materials. The energetic formation process often results in incomplete mixing in the melt, being preserved as a glass. While this chemical heterogeneity can theoretically be interpreted to understand the starting conditions of the system, individual source materials may have overlapping element abundances and chemical behaviors that complicate interpretation using tools such as bivariate analysis. This paper develops and compares multivariate linear-least squares approaches to understand major element relationships in compositionally heterogeneous glasses. We compare classical least squares (CLS) and principal component analysis (PCA) with two multivariate curve resolution-alternating least squares (MCR-ALS) optimization techniques that are novel in application. These approaches are tested using synthetic data to understand sensitivities to the resulting determination of the abundances and compositions of the precursor components. We explore the impact of incomplete a priori knowledge of the system prior to an energetic glass formation event on the resulting confidence and accuracy of the modeled solution (i.e., the number, composition, and abundances of the precursor materials). We conclude that a closure and equality constrained MCR-ALS approach is the most robust means of identifying precursor components, and is a suitable alternative to CLS-style approaches when the investigator has incomplete knowledge of the starting precursor chemical compositions. The MCR-ALS approach is then applied to measurements of fallout glass reported in the literature, demonstrating how multivariate approaches can be applied to objectively establish pre-event source term compositions and contributions.