We devise a novel statistical method for deconvolving multivariate geochronology and geochemistry datasets to characterize sediment sources. The approach employs a third-order constrained Tucker-1 tensor decomposition to estimate the probability distributions of multiple features in sediment samples. By integrating kernel density estimation with 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, and uses a maximum-likelihood approach to correlate individual detrital grains to these 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, determining sediment mixing, enhancing the understanding of sediment transport processes, characterizing the lithology, tectonic motion, or metallogenic potential of sediment sources. This method is adaptable to other data de-mixing problems and is available in a publicly released software package.