The effect of variability in rock thermal conductivity on exhumation rate estimates from thermochronological data

• Variable conductivity influences exhumation rates estimates from thermochronology.
• New analytical expression corrects exhumation rates from a linear increase in conductivity.
• Conductivity variability related to variability in rock type is less important.

To infer exhumation rates from thermochronological data requires knowledge of the temperature field in the Earth's crust, which is principally determined by a balance between heat conduction and heat advection during exhumation. The rate of heat conduction is set by the thermal conductivity which is known to strongly vary among rock types and to be a function of depth, pressure and temperature, among other factors. Despite this, most methods used to extract exhumation rate from thermochronological datasets neglect the effect of the observed variability in conductivity. Here we have computed the effect of assuming a linear variation in thermal conductivity with depth, rock type and temperature on estimates of exhumation rates based on the interpretation of thermochronological data. We show how the relationship between depth and temperature is affected by variations in rock conductivity for a range of exhumation rates. Assuming that the conductivity is a linear function of depth but is not affected by rock advection leads to very large variations in apparent exhumation rate, especially in low exhuming environments. This case is to be considered where effective conductivity may be a function of pressure, or porosity or affected by pore fluid circulation. If the conductivity is a function of initial depth (a proxy for rock type) and is advected with rock motion, the perturbation caused by a linear change in conductivity is much less important. In this situation, we show that it leads to a systematic yet small over-estimation or under-estimation in exhumation rate, when the conductivity is assumed to decrease or increase with depth, respectively. We also estimated the effect of the temperature dependence of rock conductivity on thermochronologically-derived measures of exhumation rate and demonstrate that neglecting the temperature dependence of conductivity leads to an approximate 20% underestimation of the true exhumation rate.