Estimating palaeorelief from detrital mineral age ranges

We propose a method that uses the increase in mineral age with elevation in some bedrock landscapes to quantify palaeotopographic relief from the age range of detrital minerals in coeval sediment. We use the rate at which mineral age changes with elevation (its age‐gradient, dt/dz) and its age range (Δt) in the sediment to invert for relief: Δz=Δt/(dt/dz). Relief inversion requires a single‐grain dating precision high enough that detrital grains originate from resolvably different elevations (e.g. laser microprobe ⁴⁰Ar/³⁹Ar fusion). The technique assumes that there is no change in mineral age during erosion and transport, that sediment is mixed well enough and (or) sampled sufficiently to capture the extrema of mineral ages, and that isochrons were horizontal during erosion. Subject to these constraints, inversion of the age range of individual grains in synorogenic sedimentary sequences allows quantitative estimation of relief development for eroded mountain ranges. This method provides the only direct quantitative measure of palaeorelief, a poorly constrained, but important aspect of many geological, geomorphological and geodynamic models.