Mathematics – Logic
Scientific paper
Jul 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981gecoa..45.1087c&link_type=abstract
Geochimica et Cosmochimica Acta, vol. 45, Issue 7, pp.1087-1097
Mathematics
Logic
7
Scientific paper
Rb-Sr isotopic data for large, relatively homogeneous, whole-rock samples of Uivak 1 gneiss from the Saglek-Hebron area of northern Labrador exhibit a scatter which exceeds that predicted by experimental error. Isotopic analyses of adjacent compositionally-different layers of Uivak gneiss, 1-2 cm in width, define secondary isochrons, with slopes corresponding to an age of ca . 1800 Ma. As field evidence combined with previous isotopic dating demonstrates that the compositional layering did not form at this time, the secondary isochrons are interpreted as resulting from localized Sr-isotopic homogenization along 87 Sr abundance gradients generated by ageing in the previously-layered gneisses. The geological scatter in the larger gneiss specimens is therefore attributed to the same phenomenon on a reduced scale, viz. Sr isotopic equilibration at 1800 Ma between adjacent volumes of gneiss. However regional differences in mean 87 Sr / 86 Sr and mean 87 Rb / 86 Sr are assumed to be unchanged. This interpretation has led us to the development of a weighted least squares regression technique that utilizes the geologically-induced error structure in the whole-rock Rb-Sr data. The method encompasses three models. In the first, the ` Local Isotopic Equilibrium ` or ` Free-line ' model, it is assumed that the error structure in the whole-rock samples is the same as that in the layered gneisses except for an unknown scaling factor, common to both 87 Rb / 86 Sr and 87 Sr / 86 Sr . In the other two models, the initial strontium isotopic composition is constrained to values greater than primordial Sr and corresponding to that expected for the contemporary `Bulk Earth' by forcing the least squares fit for the data to pass through a fixed-point that corresponds to the present-day 87 Rb / 86 Sr and 87 Sr / 86 Sr composition of the Bulk Earth viz. approximately 0.085 and 0.7047 respectively. In the first of these models, ` Bulk Earth Model 1 ', no assumptions are made about the error structure of the primary data. An estimate of the age can be obtained but no estimate of its uncertainty. In the second, ` Bulk Earth Model 2' , the first two methods are combined and estimates for both the age and its 95% confidence limits may be found. In developing the method, nineteen whole-rock samples plus the means of the slabbed gneisses yielded the following results for the age and initial 87 Sr / 86 Sr , respectively, of the Uivak 1 gneisses: 1. (1) Free-line Model: 3621 -410 +686 Ma, 0.70006 -565 +354 2. (2) Bulk Earth Model 1: 3606 Ma, 0.70020 3. (3) Bulk Earth Model 2: 3606 -175 +213 Ma, 0.70020 -27 +22
Cameron Maryellen
Collerson Kenneth D.
Compston William
Morton Roger
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