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\subsection{Temperature estimation using $\Delta_{47}$}  Using the clumped isotope composition of carbonate minerals as a geothermometer is a young and developing technique. Critical to it's successful application is a robust calibration between $\Delta_{47}$ and temperature. At present there exist several different calibrations (references). These are illustrated in Figure 4. There is a range in both the temperature sensitivity (gradient) and offset of the different calibrations. The differences between calibrations are laboratory dependent andthat  measurements of samples when converted to temperature only make geological sense when the local $\Delta_{47}$ - $T$ relationship is used. For this study we have used the temperature calibration determined at UEA using biogenic carbonates (bivalves and foraminifera) and travertine samples collected from sites with well characterized temperatures: \[{\Delta _{47}} = \frac{{0.0389 \times {{10}^6}}}{{{T^2}}} + 0.2139\]  where T is in Kelvins. As with most previous studies the calibration has been made over a restricted temperature range (0-56$^{\circ}$C). For the most part this range is below the temperature of most of the samples reported in this study. We have confidence, however, that the calibration can be extrapolated to higher temperatures. In Figure 4 we have plotted data obtained in our laboratory for the $\Delta_{47}$ value of a Carrara marble sample that had been crushed and experimentally re-crytallised at 600$^{\circ}$C and 1000MPa in a solid media apparatus before rapidly quenching(Bernasconi, 2014 pers. comm.) Our extrapolate calibration passes very close to the mean of these high temperature data. Also, our calibration lies very close to the theoretical calculations of the temperature dependence of heavy isotope clumping in calcite \citep{Guo:2009fy}. These observations gives us confidence in extrapolating our suggest that the UEA  calibration to cover is robust over  the range of temperatures expected in the upper crust.