Quantifying the effect of recent relief changes on age-elevation relationships

The effect that recent relief changes may have on the distribution of rock ages with elevation is investigated for a range of thermochronometers. From the solution of the heat transport equation in a crustal block undergoing uplift and surface erosion, the temperature history of rock particles that are exhumed at the Earth's surface today is computed. These T-t paths are then used to calculate apparent isotopic ages for the (U-Th)/He system in apatite, characterized by a low (≈ 70°C) closure temperature. The results show that recent relief changes strongly affect the distribution of ages with elevation (notably the slope of the age-elevation relationship). The calculations presented here predict that, in most situations, regions that have undergone a steady decrease in surface relief in the recent past should be characterized by an inverted age-elevation relationship, that is older ages should be found near valley bottoms and younger ages near summit tops. It is also shown how the wavelength of the topography, the geothermal gradient, the exhumation rate and the duration of the relief reduction event affect this result.