Interpreting SrÅNd isotopic data from magmatic and metamorphic ...
Interpreting SrÅNd isotopic data from magmatic and metamorphic ...
Interpreting SrÅNd isotopic data from magmatic and metamorphic ...
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Vojtěch Janoušek:<br />
<strong>Interpreting</strong> Sr–Nd <strong>isotopic</strong> <strong>data</strong>: numerical recipes<br />
It is apparent <strong>from</strong> [2.1] <strong>and</strong> Fig. 3–1 that a corresponds to the initial ratio of the whole cogenetic suite<br />
<strong>and</strong> the slope b of the isochron is expressed as:<br />
Giving a formula for isochron age:<br />
The isochrons are usually fitted using<br />
software given in Tab. 3–1. The<br />
algorithm utilizes weighted linear<br />
regression <strong>and</strong> follows York (1969).<br />
λt<br />
( e −1)<br />
b = tgα =<br />
[3.2]<br />
1<br />
t = ln b +<br />
λ<br />
( 1)<br />
Isochron<br />
Provost (1990) France Pascal<br />
IsoPlot Ludwig (1993) USA QuickBasic<br />
[3.3]<br />
Exercise 3-1<br />
Table 3-1: Software used for geochronological calculations<br />
[ISOCHRON.EXE]<br />
The Rb–Sr <strong>isotopic</strong> composition of the Serra do Acari granite <strong>from</strong> Pará, Brazil, was determined by Xafi da<br />
Silva et al. (1985). We will use this granite as a case study showing how isochrons are plotted, as well as how<br />
isochron ages <strong>and</strong> initial ratios are obtained.<br />
Calculate the age <strong>and</strong> Sr initial ratio for the Acari granite using simple linear<br />
regression (MS Excel). Then calculate the same parameters using weighted linear<br />
regression implemented by Provost (1990) <strong>and</strong> produce both conventional <strong>and</strong><br />
improved isochron plots. Compare results obtained in both cases. Which sample controls the<br />
regression <strong>and</strong> why<br />
Sample<br />
87 Rb/ 86 Sr 1σ<br />
87 Sr/ 86 Sr 1σ<br />
AT-R-173 5.743 0.062 0.858993 0.000034<br />
AT-R-167 22.290 0.280 1.290200 0.000050<br />
AT-R-157 42.170 0.530 1.760370 0.000069<br />
AT-R-165 61.230 0.980 2.248950 0.000140<br />
AT-R-158 99.000 1.800 3.182530 0.000170<br />
AT-R-169 232.000 3.300 6.548880 0.000470<br />
[acari.xls, acari.sr]<br />
Hints:<br />
! Plot a diagram analogous to Figure 3–1a (if you dare, you can even plot error bars),<br />
! Fit the <strong>data</strong> by linear regression,<br />
! Intercept of the regression line equals to the sought initial ratio,<br />
! Age can be calculated <strong>from</strong> the slope using eq. [3.3],<br />
! Start ISOCHRON.EXE, import the <strong>data</strong> file provided on the floppy (acari.sr),<br />
! Note the format of the *.SR <strong>data</strong> file: first line is ignored <strong>and</strong> is intended for<br />
comments, the following lines contain: sample_number, 87 Rb/ 86 Sr, 1σ, 87 Sr/ 86 Sr <strong>and</strong><br />
1σ with several spaces in between,<br />
! If in doubt, just press ENTER to accept the defaults offered by the program.<br />
– 6 –
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