Abstract
Populations of detrital zircons are shaped by geologic factors such as sediment transport, erosion mechanisms, and the zircon fertility of source areas. Zircon U-Pb age datasets are influenced both by these geologic factors and by the statistical effects of sampling. Such statistical effects introduce significant uncertainty into the inference of parent population age distributions from detrital zircon samples. This uncertainty must be accounted for in order to understand which features of sample age distributions are attributable to earth processes and which are sampling effects. Sampling effects are likely to be significant at a range of common detrital zircon sample sizes (particularly when n < 300).In order to more accurately account for the uncertainty in estimating parent population age distributions, we introduce a new method to infer probability model ensembles (PMEs) from detrital zircon samples. Each PME represents a set of the potential parent populations that are likely to have produced a given zircon age sample. PMEs form the basis of a new metric of correspondence between two detrital zircon samples, Bayesian Population Correlation (BPC), which is shown in a suite of numerical experiments to be unbiased with respect to sample size. BPC uncertainties can be directly estimated for a specific sample comparison, and BPC results conform to analytical predictions when comparing populations with known proportions of shared ages. We implement all of these features in a set of MATLAB® scripts made freely available as open-source code and as a standalone application. The robust uncertainties, lack of sample size bias, and predictability of BPC are desirable features that differentiate it from existing detrital zircon correspondence metrics. Additionally, analysis of other sample limited datasets with complex probability distributions may also benefit from our approach.
Highlights
Detrital zircon U-Pb ages can provide a robust indicator of the provenance 3 of sedimentary rocks or modern sediment through comparison with the ages 4 of potential source rocks
In order to more accurately account for the uncertainty in estimating parent population age distributions, we introduce a new method to infer probability model ensembles (PMEs) from detrital zircon samples
In order to assess the correspondence of two zircon age populations us[311] ing the robust constraints contained in PMEs, we develop a new compara[312] tive metric called Bayesian Population Correlation (BPC)
Summary
Detrital zircon U-Pb ages can provide a robust indicator of the provenance 3 of sedimentary rocks or modern sediment through comparison with the ages 4 of potential source rocks. Our method infers sets of poten[68] tial parent populations that are likely to have produced a given sample, 69 which we refer to as probability model ensembles (PMEs; Fig. 2). BPC uncertainties can be directly estimated for a specific dataset comparison and BPC results can be predicted from population characteris[83] tics using an analytical expression we derive from probability theory Such predictability permits quantitative interpretations about processes affecting parent populations (e.g., dilution in a sedimentary system). Sampling the posterior distribution P(θ|d) yields a representative set of the potential parent populations likely to have produced the observed sample, which we call a Probability Model Ensemble (PME). This information is lost when only a single kernel density estimator (KDE) curve or probability density plot is used for a given detrital zircon sample
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