Abstract
A novel statistical method is devised for deconvolving multivariate geogchronology and geochemistry datasets into their constituent sources in order to identify provenance. The approach is based on a third-order constrained Tucker-1 tensor decomposition that estimates the probability distributions over multiple features of sediment samples. By coupling a kernel density estimation technique with a matrix-tensor factorization, the model quantitatively determines the distributions and mixing proportions of sediment sources. The methodology introduces a numerical test for rank estimation to define the number of latent sources. Additionally, a maximum-likelihood approach correlates the individual detrital grains to latent sources based on an arbitrary number of features. The method's efficacy is validated through a numerical experiment with detrital zircon data that captures natural variability associated with temporal changes in crustal thickness in the Andes. The findings hold potential implications for resolving sediment sources, determine sediment mixing, enhancing the understanding of sediment transport processes, characterizing the lithology, tectonic motion, or metallogenic potential of sediment sources. The resulting method is portable to other data dimixing problems and is implemented in a publicly available software package.