Unmixing detrital geochronology age distributions

Despite recent advances in quantitative methods of detrital provenance analysis, there is currently no widely accepted method of unmixing detrital geochronology age distributions. We developed a model that determines mixing proportions for source samples through inverse Monte Carlo modeling, wherein mixed samples are compared to randomly generated combinations of source distributions, and a range of best mixing proportions are retained. Results may then be used to constrain a forward optimization routine to find a single best-fit mixture. Quantitative comparison is based on the Kolmogorov-Smirnov (KS) test D statistic and Kuiper test V statistic for cumulative distribution functions, and the Cross-correlation coefficient for finite mixture distributions (probability density plots or kernel density estimates). We demonstrate the capacity of this model through a series of tests on synthetic data, and published empirical data from North America mixed in known proportions; this proof-of-concept testing shows the model is capable of accurately unmixing highly complex distributions. We apply the model to two published empirical data sets mixed in unknown proportions from Colombia and central China. Neither example yields perfect model fits, which provides a cautionary note of potentially inadequate characterization of source and/or mixed samples, and highlights the importance of such characterization for accurate interpretation of sediment provenance. Sample size appears to be a major control on mixture model results; small (n<100) samples may lead to misinterpretation. The model is available as a MATLAB-based stand-alone executable (.exe file) graphical user interface.