Determination of Geo-dependent Bioavailable ⁸⁷Sr/⁸⁶Sr Isotopic Ratios for Archaeological Sites from the Inn Valley (Austria): A Model Calculation

Abstract

In this chapter, we show how to assess local bioavailable ⁸⁷Sr/⁸⁶Sr isotopic ratios of archaeological strata by analysis of water, leached soil samples and vegetation from selected archaeological sites. We present a detailed description and instruction of how to calculate the data. In this pilot study, calculation of cut-off values between local and non-local stable strontium isotopic ratios was performed for five locations in the Austrian Inn Valley. These cut-off values, determined as ⁸⁷Sr/⁸⁶Sr(fauna) ± 0.001, agree within acceptable limits with the measured isotopic signature of excavated animal bone material from the chosen archaeological sites. This way, the vertebrate consumer can clearly be classified as a local or non-local individual. Our model calculation, which leads to a reliable geo-dependent bioavailable ⁸⁷Sr/⁸⁶Sr isotopic ratio, reveals a high dependence on the isotopic signal from groundwater rather than from soil.

Appendix

Table 2 Model calculation of bioavailable geo-dependent Sr isotopic ratio

f(atm, aq-f):

Abundance of the atmospheric water (=rainwater) component in the drinking water

f(atm, aq-v):

Abundance of the atmospheric water (=rainwater) component in the vegetation water

f(aq-v, veg):

Abundance of the vegetation water component in the vegetation

f(aq-f, fauna):

Abundance of the drinking water component in the fauna

⁸⁷Sr/⁸⁶Sr (atm):

Sr isotopic ratio in the atmosphere (ocean water, rainwater, taken from the literature)

⁸⁷Sr/⁸⁶Sr (wat):

Sr isotopic ratio in the groundwater (sampled water from wells or groundwater horizon)

⁸⁷Sr/⁸⁶Sr (aq-f):

Sr isotopic composition of drinking water (mixture of rain and groundwater ) incorporated into the fauna

⁸⁷Sr/⁸⁶Sr (aq-v):

Sr isotopic composition of vegetable water (mixture of rain and groundwater )

⁸⁷Sr/⁸⁶Sr (veg):

Sr isotopic ratio in the vegetation (wood , measured)

⁸⁷Sr/⁸⁶Sr (fauna):

Sr isotopic composition of the fauna (localised Sr isotopic ratio, human and animal, calculated)

⁸⁷Sr/⁸⁶Sr (wea):

Sr isotopic composition of weathered soil , bioavailable component (gained by leaching of sampled soil with 1 N HCl; for details see methods section)

Sr (atm) (ppm):

Sr content of the atmospheric or rainwater (taken from the literature)

Sr (wat) (ppm):

Sr content of the groundwater (taken from the literature)

Sr (aq-v) (ppm):

Sr content in vegetation water, mixture of ground and rainwater

Sr (aq-f) (ppm):

Sr content in drinking water , mixture of ground and rain water

Sr (veg) (ppm):

Sr content of the vegetation (wood , time-dependent assimilated, calculated)

Sr (fauna) (ppm):

Sr content incorporated into the fauna, time-dependent assimilated (human and animal, calculated)

Sr (wea) (ppm):

Sr content of the weathered soil (taken from literature)

X(…):

correlation of ⁸⁷Sr/⁸⁶Sr and Sr content for the special case

Equation of the mixing hyperbola in coordinates of the ⁸⁷Sr/⁸⁶Sr ratio and the Sr concentration (Sr) (Faure and Mensing 2005)

( ⁸⁷Sr/⁸⁶Sr ) _M  = a/(Sr ) _M  + b, with

$$ \begin{array}{c}\hfill a=\frac{{\mathrm{Sr}}_A{\mathrm{Sr}}_B{\left(\frac{87\mathrm{S}\mathrm{r}}{86\mathrm{S}\mathrm{r}}\right)}_B-{\mathrm{Sr}}_B{\left(\frac{87\mathrm{S}\mathrm{r}}{86\mathrm{S}\mathrm{r}}\right)}_A}{{\mathrm{Sr}}_A-{\mathrm{Sr}}_B};\hfill \\ {}\hfill b=\frac{{\mathrm{Sr}}_A{\left(\frac{87\mathrm{S}\mathrm{r}}{86\mathrm{S}\mathrm{r}}\right)}_A-{\mathrm{Sr}}_B{\left(\frac{87\mathrm{S}\mathrm{r}}{86\mathrm{S}\mathrm{r}}\right)}_B}{{\mathrm{Sr}}_A-{\mathrm{Sr}}_B};\hfill \end{array} $$

The numerical values of a and b entirely depend on the ⁸⁷Sr/⁸⁶Sr ratios and Sr concentrations of the components A and B in the mixture M.

$$ {\mathrm{Sr}}_M={\mathrm{Sr}}_A\times {f}_A+{\mathrm{Sr}}_B\times \left(1-{f}_A\right); $$

f _A is the abundance of A in the mixture M