An algorithm for U-Pb isotope dilution data reduction and uncertainty propagation
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 sourc...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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American Geophysical Union (AGU)
2012
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| Online Access: | http://hdl.handle.net/1721.1/73489 https://orcid.org/0000-0001-9722-469X |
| _version_ | 1826188134780502016 |
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| author | McLean, Noah Morgan Bowring, J. F. Bowring, Samuel A. |
| author2 | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences |
| author_facet | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences McLean, Noah Morgan Bowring, J. F. Bowring, Samuel A. |
| author_sort | McLean, Noah Morgan |
| collection | MIT |
| description | 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are increasingly important, and thus previous simplifications for data reduction and uncertainty propagation are no longer valid.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. |
| first_indexed | 2024-09-23T07:55:06Z |
| format | Article |
| id | mit-1721.1/73489 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T07:55:06Z |
| publishDate | 2012 |
| publisher | American Geophysical Union (AGU) |
| record_format | dspace |
| spelling | mit-1721.1/734892022-09-23T09:37:25Z An algorithm for U-Pb isotope dilution data reduction and uncertainty propagation McLean, Noah Morgan Bowring, J. F. Bowring, Samuel A. Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences McLean, Noah Morgan Bowring, Samuel A. 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. National Science Foundation (U.S.) (Grants EAR‐0746205) National Science Foundation (U.S.) (Grants EAR‐0930166) 2012-09-28T18:16:06Z 2012-09-28T18:16:06Z 2011-06 2011-04 Article http://purl.org/eprint/type/JournalArticle 1525-2027 http://hdl.handle.net/1721.1/73489 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 https://orcid.org/0000-0001-9722-469X en_US http://dx.doi.org/10.1029/2010gc003478 Geochemistry Geophysics Geosystems 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. application/pdf American Geophysical Union (AGU) MIT web domain |
| spellingShingle | McLean, Noah Morgan Bowring, J. F. Bowring, Samuel A. An algorithm for U-Pb isotope dilution data reduction and uncertainty propagation |
| title | An algorithm for U-Pb isotope dilution data reduction and uncertainty propagation |
| title_full | An algorithm for U-Pb isotope dilution data reduction and uncertainty propagation |
| title_fullStr | An algorithm for U-Pb isotope dilution data reduction and uncertainty propagation |
| title_full_unstemmed | An algorithm for U-Pb isotope dilution data reduction and uncertainty propagation |
| title_short | An algorithm for U-Pb isotope dilution data reduction and uncertainty propagation |
| title_sort | algorithm for u pb isotope dilution data reduction and uncertainty propagation |
| url | http://hdl.handle.net/1721.1/73489 https://orcid.org/0000-0001-9722-469X |
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