An algorithm for U-Pb isotope dilution data reduction and uncertainty propagation
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Author(s)
McLean, Noah Morgan
Bowring, J. F.
Bowring, Samuel A.
Date Issued
June 2011
Journal
Geochemistry Geophysics Geosystems
Publisher
American Geophysical Union (AGU)
Citation
McLean, N. M., J. F. Bowring, and S. A. Bowring. “An Algorithm for U-Pb Isotope Dilution Data Reduction and Uncertainty Propagation.” Geochemistry Geophysics Geosystems 12 (2011). ©2012 American Geophysical Union
Version
Final published version
Abstract
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are increasingly important, and thus previous simplifications for data reduction and uncertainty propagation are no longer valid.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.
MIT Department
Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1029/2010gc003478
