Graphic and algebraic solutions of the discordant lead-uranium age problem

Geochimica et Cosmochimica Acta



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Uranium-bearing minerals that give lead-uranium and lead-lead ages that are essentially in agreement, i.e. concordant, generally are considered to have had a relatively simple geologic history and to have been unaltered since their deposition. The concordant ages obtained on such materials are, therefore, assumed to approach closely the actual age of the minerals. Many uranium-bearing samples, particularly uranium ores, give the following discordant age sequences; Pb206 U238 < Pb207 U235 ??? Pb207 Pb206 or, less frequently, Pb207 Pb206 ??? Pb207 U235 < Pb206 U238. These discordant age sequences have been attributed most often to uncertainties in the common lead correction, selective loss of radio-active daughter products, loss or gain of lead or uranium, or contamination by an older generation of radiogenic lead. The evaluation of discordant lead isotope age data may be separated into two operations. The first operation, with which this paper is concerned, is mechanical in nature and involves the calculation of the different possible concordant ages corresponding to the various processes assumed to have produced the discordant ages. The second operation is more difficult to define and requires, in part, some personal judgement. It includes a synthesis of the possible concordant age solutions with other independent geologic and isotopic evidence. The concordant age ultimately chosen as most acceptable should be consistent not only with the known events in the geologic history of the area, the age relations of the enclosing rocks, and the mineralogic and paragenetic evidence, but also with other independent age measurements and the isotopic data obtained on the lead in related or associated non-radioactive minerals. The calculation of the possible concordant ages from discordant age data has been greatly simplified by Wetherill's graphical method of plotting the mole ratios of radiogenic Pb206 U238 ( N206 N238) vs. radiogenic Pb207 U235 ( N207 N235) after correcting for the contaminating common Pb206 and Pb207. The linear relationships noted in this graphical procedure have been extended to plots of the mole ratios of total Pb206 U238 ( tN206 N238) vs. total Pb207 U235 ( tN207 N235). This modification permits the calculation of concordant ages for unaltered samples using only the Pb207 Pb206 ratio of the contaminating common lead. If isotopic data are available for two samples of the same age, x and y, from the same or related deposits or outcrops, graphs of the normalized difference ratios [ ( N206 N204)x - ( N206 N204)y ( N238 N204)x -( N238 N204)y] vs. [ ( N207 N204)x - ( N207 N204)y ( N235 N204)x -( N235 N204)y] can give concordant ages corrected for unknown amounts of a common lead with an unknown Pb207/ Pb206 ratio. (If thorium is absent the difference ratios may be normalized with the more abundant index isotope, Pb208.) Similar plots of tho normalized, difference ratios for three genetically related samples (x - y) and(x - z), will give concordant ages corrected, in addition, for either one unknown period of past alteration or initial contamination by an older generation of radiogenic lead of unknown Pb207/Pb206 ratio. Practical numerical solutions for many of tho concordant age calculations are not currently available. However, the algebraic equivalents of these new graphical methods give equations which may be programmed for computing machines. For geologically probable parameters the equations of higher order have two positive real roots that rapidly converge on the exact concordant ages corrected for original radiogenic lead and for loss or gain of lead or uranium. Modifications of these general age equations expanded only to the second degree have been derived for use with desk calculators. These graphical and algebraic methods clearly suggest both the type and minimum number of samples necessary for adequate mathematical analysis of discordant lead isotope age data. This mathematical treatment also makes it clear t

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Graphic and algebraic solutions of the discordant lead-uranium age problem
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Geochimica et Cosmochimica Acta
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Geochimica et Cosmochimica Acta
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