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released from processing plants into the river system. Pb input from the Mesozoic
rocks was apparently minor as the isotopic signature was masked by large inputs
from the other two sources.
One of the significant advantages of using Pb isotopes as tracers is that accu-
rate estimates of the relative contributions of Pb can be determined when the data
plot along a mixing line (and other sources of Pb are assumed to be negligible)
(Kristensen et al. 2014 ). Since the trend is linear, the estimated contributions are
typically calculated using a simple binary model (Monna et al. 1997 ; Bird et al.
2010a , b ; 2011 ) that takes the form of:
20x Pb
20y Pb
20x Pb
20y Pb
(
/
) S (
/
) A
=
% A
(4.8)
20x Pb
20y Pb
20x Pb
20y Pb
(
/
) B (
/
) A
where% A is the contribution of sourceA in a sample and 20x Pb/ 20y Pb S , 20x Pb/ 20y Pb A
and 20x Pb/ 20y Pb B are the average ratios in the sample (S) and the two end-member
sources, A and B, respectively. In the case of the Rio Pilcomayo, Miller et al. ( 2007 )
were able to use the equation to estimate the relative contribution of Pb from the
upstream mining operations to the channel bed at selected locations along the river.
The estimates for samples collected in 2000 ranged from
99 to about 56% of the
total Pb present (these estimates were recalculated from Miller et al. ( 2002 )onthe
basis of a more recent and accurate understanding of the isotopic signatures of the
ore deposits).
In addition to the spatial (downstream) variations in the contribution of Pb from
the mines to the Rio Pilcomayo, Miller et al. ( 2007 ) found that the Pb isotopic ratios
>
Fig. 4.7 Sites from which to determine background (geogenic) Pb isotopic ratios (modified from
Miller et al. 2007 )
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