Modeling apparent Pb loss in zircon U-Pb geochronology

The loss of radiogenic Pb from zircon is known to be a major factor that can cause inaccuracy in the U-Pb geochronological system; hence, there is a need to better characterize the distribution of Pb loss in natural samples. Treatment of zircon by chemical abrasion (CA) has become standard practice in isotope dilution-thermal ionization mass spectrometry (ID-TIMS), but CA is much less commonly employed prior to in situ analysis via laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS) or secondary ionization mass spectrometry (SIMS). Differentiating the effects of low levels of Pb loss in Phanerozoic zircon with relatively low-precision in situ U-Pb dates, where the degree of Pb loss is insufficient to cause discernible discordance, is challenging. We show that U-Pb isotopic ratios that have been perturbed by Pb loss may be modeled by convolving a Gaussian distribution that represents random variations from the true isotopic value stemming from analytical uncertainty with a distribution that characterizes Pb loss. We apply this mathematical framework to model the distribution of apparent Pb loss in 10 igneous samples that have both non-CA LA-ICP-MS or SIMS U-Pb dates and an estimate of the crystallization age, either through CA U-Pb or 40 Ar / 39 Ar geochronology. All but one sample showed negative age offsets that were unlikely to have been drawn from an unperturbed U-Pb date distribution. Modeling apparent Pb loss using the logit-normal distribution produced good fits with all 10 samples and showed two contrasting patterns in apparent Pb loss; samples where most zircon U-Pb dates undergo a bulk shift and samples where most zircon U-Pb dates exhibited a low age offset but fewer dates had more significant offset. Our modeling framework allows comparison of relative degrees of apparent Pb loss between samples of different age, with the first and second Wasserstein distances providing useful estimates of the total magnitude of apparent Pb loss. Given that the large majority of in situ U-Pb dates are acquired without the CA treatment, this study highlights a pressing need for improved characterization of apparent Pb-loss distributions in natural samples to aid in interpreting non-CA in situ U-Pb data and to guide future data collection strategies.