Reid, M. J. and Gancarz, A. J. and Albee, A. L. (1973) Constrained least-squares analysis of petrologic problems with an application to lunar sample 12040. Earth and Planetary Science Letters, 17 (2). pp. 433-445. ISSN 0012-821X. doi:10.1016/0012-821X(73)90212-4. https://resolver.caltech.edu/CaltechAUTHORS:20180313-073633736
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Abstract
Many petrologic problems, which may be expressed as a set of linear equations, have been solved by least-squares analysis. In many cases insufficient attention has been paid to the physical conditions of the model resulting in incorrect application of the method. This paper presents a systematic treatment of the application of least-squares analysis to petrologic problems including the direct utilization of physical constraints and weighting factors in the problem, and the assessment of uncertainties in the solution. As an example, least-squares analysis is used to examine, in detail, the mass balance equations for lunar rock 12040 and to determine the consistency of the available analytical data.
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| Additional Information: | © 1973 Published by Elsevier B.V. Received 22 August 1972, Revised 25 October 1972. We are grateful to D. Muhleman for a long series of discussions on various aspects of this paper and to D. Muhleman, S. Delong, and R. Dean for their comments on a preliminary draft of the paper. G.J. Wasserburg initiated the work on sample 12040 and pointed out that we do not really understand a rock unless we can explain the complete phase distribution of every element. The work was supported by NAS contract NAS-9-8074 and NSF grant GA-12867. The micro probe laboratory has been developed with the support of the Jet Propulsion Laboratory, National Science Foundation, and the Union Pacific Foundation. One of us (A.J.G.) holds a National Science Foundation Graduate Fellowship. | ||||||||||||
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| Issue or Number: | 2 | ||||||||||||
| DOI: | 10.1016/0012-821X(73)90212-4 | ||||||||||||
| Record Number: | CaltechAUTHORS:20180313-073633736 | ||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20180313-073633736 | ||||||||||||
| Official Citation: | M.J. Reid, A.J. Gancarz, A.L. Albee, Constrained least-squares analysis of petrologic problems with an application to lunar sample 12040, Earth and Planetary Science Letters, Volume 17, Issue 2, 1973, Pages 433-445, ISSN 0012-821X, https://doi.org/10.1016/0012-821X(73)90212-4. (http://www.sciencedirect.com/science/article/pii/0012821X73902124) | ||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
| ID Code: | 85262 | ||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||
| Deposited By: | Tony Diaz | ||||||||||||
| Deposited On: | 13 Mar 2018 17:44 | ||||||||||||
| Last Modified: | 15 Nov 2021 20:27 |
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