so that fdep + frock = 1.
This theoretical mixing was quantified by applying a Monte Carlo
simulation, where end-member parameter values were randomly sampled from
their independently observed regional parameter distributions (obtained
for example from a literature review, see below) to create 10 000
different theoretical initial conditions (i.e., the assumed stream water
isotopic composition before MSR). A Rayleigh fractionation model was
then applied to calculate the residual fraction of sulfur concentration
after reduction (fred ). The model is based on the
initial isotopic composition of the stream water
(δ0 ; here represented by the 10 000 theoretical
predictions of δsample ) and the residual isotopic
composition in the stream water (δR ; represented
by the observed isotopic value of stream waterδstream ), according to: