Tracking Proterozoic–Triassic sediment routing to western Laurentia via bivariate non-negative matrix factorization of detrital provenance data

Abstract

When reconstructing sediment provenance, the challenge posed by multiple univariate (i.e., age-only) detrital geochronology data sets with similar one-dimensional distributions can be mitigated by incorporation of a second variable such as Hf isotopic data. However, there is no commonly applied method of sample intercomparison, much less forward or inverse modeling of these bivariate data sets. In this paper we explore application of non-negative matrix factorization (NMF) to bivariate data sets. Factorization of univariate mixed (a.k.a., sink or daughter) data sets has been demonstrated to successfully recover both the one-dimensional endmember (a.k.a., source or parent) distributions and their mixture weightings. We show that NMF can successfully recover both the two-dimensional distributions and mixing weights in synthetic data sets. Application of the method to 24 published Neoproterozoic–Triassic samples from western Laurentia yields six two-dimensional endmember distributions that are a close match to empirical sediment sources on the southern, eastern, and northern margin of Laurentia. The results are broadly consistent with previous interpretations and confirm that the method can characterize unknown sediment sources based on data from analyzed sink samples. Correlating between factorized endmembers and empirical sources indicates that the Transcontinental Arch was not a barrier to east–west sediment transport until the late Cambrian. Quantitative comparison also shows that the closest known match for a factorized endmember with highly evolved Permo-Triassic zircons is from northern South America and suggests northward transport of this detritus following assembly of Pangea. Recognizing these empirical sources and their distribution into strata that would later be incorporated into the North American Cordillera sets the stage for interpreting sediment provenance records in the Jurassic–Paleogene Cordilleran retroarc foreland basin. Supplementary material: The open-source software ( DZnmf2D ) and a user manual is available in public repositories: https://doi.org/10.5281/zenodo.4460336 . All other supplemental files are available at https://doi.org/10.6084/m9.figshare.c.5280320 Thematic collection: This article is part of the Fold-and-thrust belts and associated basins collection available at: https://www.lyellcollection.org/cc/fold-and-thrust-belts