The effect of palaeoclimate on heat flow data
One common method to determine heat flow in a well is to use a Bullard plot, which graphs thermal resistance (m$^2$K W$^{-1}$) against temperature. The gradient of this line is heat flow, and the uncertainty determined from the error of linear regression.
Thermal resistance is calculated by:
$$ R = \sum_{i=0}^{n} \left( \frac{\Delta z_i}{k_i} \right) $$which is the cumulative summation of resistors down the length of a borehole. The uncertainty on $R$ should increase as the individual errors on $k$ accumulate.
Climate correction
The present-day temperature perturbation, $\Delta T(z, t=0)$, in a semi-infinite solid with an instantaneous change of surface temperature $\Delta T$ at time $t$ before the present is:
$$ \Delta T(z,t=0) = \Delta T \; \mathrm{erfc} \left(\frac{z}{2 \sqrt{\kappa t}} \right) $$The effect of more than one event, $k_1, k_2, \ldots, k_n$, is found by summation - i.e. if $T(z=0,t) = T_k$ for $t_{k-1} < t < t_k$:
$$ \Delta T(z,t=0) = \sum_{k=1}^{n} T_k \left[ \mathrm{erfc}\left(\frac{z}{2 \sqrt{\kappa t_k}} \right) - \mathrm{erfc}\left(\frac{z}{2 \sqrt{\kappa t_{k-1}}} \right) \right] $$This formula can be used if the temperature has remained constant over a period of time in the past. For an application of this, check out our latest paper.
I am an ARC Industry Research Fellow in the School of Geography, Earth and Atmospheric Sciences at The University of Melbourne. I am an expert in fusing Earth evolution models with data to understand how groundwater moves critical minerals through the landscape. Related research interests include the cycling of volatiles within the Earth, probabilistic thermal models of the lithosphere to unravel past tectonic and climatic events, and understanding the how enigmatic volcanoes form.
I am a vocal advocate for the integral role of geoscience in responding to challenges we face in transitioning to the carbon-neutral economy. As an expert in my field, I have been interviewed in national and international print media, TV, and radio on a wide variety of subjects including earthquakes, volcanoes, groundwater, and critical minerals.