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Published January 1973 | public
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Constrained least-squares analysis of petrologic problems with an application to lunar sample 12040

Reid, M. J. ORCID icon
Gancarz, A. J.
Albee, A. L.
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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.

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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