TRACING SEDIMENTARY ORIGINS IN MULTIVARIATE GEOCHRONOLOGYVIA CONSTRAINED TENSOR FACTORIZATION

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.