An algorithm for U‐Pb isotope dilution data reduction and uncertainty propagation
By N. McLean, James Frederick Bowring, S. Bowring. 2011
350 citations recorded by the source corpus.
High‐precision U‐Pb geochronology by isotope dilution‐thermal ionization mass spectrometry is integral to a variety of Earth science disciplines, but its ultimate resolving power is quantified by the uncertainties of calculated U‐Pb dates. As analytical techniques have advanced, formerly small sources of uncertainty are increasingly important, and thus previous simplifications for data reduction and uncertainty propagation are no longer valid. Although notable previous efforts have treated propagation of correlated uncertainties for the U‐Pb system, the equations, uncertainties, and correlations have been limited in number and subject to simplification during propagation through intermediary calculations. We derive and present a transparent U‐Pb data reduction algorithm that transforms raw isotopic data and measured or assumed laboratory parameters into the isotopic ratios and dates geochronologists interpret without making assumptions about the relative size of sample components. To propagate uncertainties and their correlations, we describe, in detail, a linear algebraic algorithm that incorporates all input uncertainties and correlations without limiting or simplifying covariance terms to propagate them though intermediate calculations. Finally, a weighted mean algorithm is presented that utilizes matrix elements from the uncertainty propagation algorithm to propagate random and systematic uncertainties for data comparison between other U‐Pb labs and other geochronometers. The linear uncertainty propagation algorithms are verified with Monte Carlo simulations of several typical analyses. We propose that our algorithms be considered by the community for implementation to improve the collaborative science envisioned by the EARTHTIME initiative.
Subfields: Astronomy and Astrophysics, Global and Planetary Change, Inorganic Chemistry
View Paper: https://www.semanticscholar.org/paper/c0631bf1c552166a03340273a56cb559abaf9fc6
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Citations in the corpus
- IsoplotR: A free and open toolbox for geochronology (2018, methodology): “In the meanwhile, the user is advised to apply the disequilibrium correction before entering their data into IsoplotR (McLean et al., 2011).”
- Engineering cyber infrastructure for U‐Pb geochronology: Tripoli and U‐Pb_Redux (2011, methodology): “Details of how these are calculated appear in the study by McLean et al. [2011]. Also shown are the MSWD and the count of fractions used to calculate it.”
- Evaluating uncertainties in the calibration of isotopic reference materials and multi-element isotopic tracers (EARTHTIME Tracer Calibration Part II) (2015, methodology): “The only published U–Pb uncertainty propagation algorithm to include the required covariance terms is (McLean et al., 2011), which permits uncertainty correlations between all tracer parameters.”
- High-precision timeline for Earth’s most severe extinction (2014, methodology): “Data acquisition and reduction were done using the Tripoli and U-Pb Redux software packages (24, 25).”
- U–Th–Pb zircon geochronology by ID-TIMS, SIMS, and laser ablation ICP-MS: Recipes, interpretations, and opportunities (2015, methodology): “The corrected uncertainty ellipses contain 50% uncertainty of the Th/Usource, 1693 propagated onto the final date after McLean et al. (2011).”