CHARACTERIZATION OF SEDIMENT SOURCE PETROCHRONOLOGY VIA NON-NEGATIVE MATRIX FACTORIZATION OF BIVARIATE DETRITAL DATA SETS

Non-negative matrix factorization (NMF) has been used to reconstruct radiometric age distributions of unknown sediment sources based on analyses of derivative samples (a.k.a., sinks). Despite the power of NMF to characterize age distributions, multiple sources may share similar age distributions. Such non-uniqueness can be mitigated by incorporation of petrogenetic isotopic or geochemical information; however, NMF is currently limited to univariate (i.e., one-dimensional) data sets. We present a novel application of NMF to bivariate (two-dimensional) detrital petrochronological data sets. Applied to sink data sets numerically mixed from known sources, bivariate NMF successfully recovers the known sources. Breakpoint analysis of the factorized data sets yields an optimum factorization rank that matches the known number of source samples. Factorized mixture weights also closely correlate with known mixing weights (R² > 0.7).

Following this preliminary proof-of-concept testing, we apply bivariate NMF to a data set which includes U-Pb and Hf isotopic ratios at the time of U-Pb crystallization (εHf_T values) of detrital zircons from Neoproterozoic–Triassic strata from the western margin of Laurentia. Breakpoint analysis shows that the optimum factorization rank is six sources, which best match empirical samples from NE Canada, a group of sources from the Appalachian foreland, and the Mojave. Significantly, factorized sources yield εHf_T values that discriminate between potential sources where univariate data sets have been equivocal. For example, factorized sources with late Neoproterozoic–Paleozoic age modes have εHf_T values that are more negative than those documented from the Franklinian Basin in the Canadian Arctic. Rather, they are most consistent with age and εHf_T values from the Appalachian foreland basin or Ordovician granites from Scotland. Similarly, εHf_T values and age modes from factorized sources with Paleoproterozoic age modes (1600–1800 Ma) point to both juvenile and evolved sources, which are most consistent with Mojave and NE Canadian sources, respectively. These results support previous hypotheses that late Paleozoic transcontinental rivers brought sediment from eastern to western Laurentia, transecting or bypassing the transcontinental arch. Bivariate NMF of these data sets coupled with statistical comparison to potential sources provides a means to quantitatively query complex data sets that are opaque to other forms of investigation.