Geometric constraints on composition of sediment derived from erosional landscapes

Although unroofing sequences are well known in the stratigraphic record, there is no general theory for estimating relevant basic quantities such as the time history of sediment production from a particular unit or the degree of mixing between successive units. Here we investigate the production of sediment from layered source rocks that are milled off by steady-state erosional topography. The shape of the sediment-production function for milling off a thin horizontal layer is given by the derivative of the hypsometric function, in the form of area contained within contours as a function of contour altitude. The time-scale for the production function, the 'topographic mixing time', is set by the topographic relief divided by the uplift rate. The production function for a sharp transition from one unit to another is given directly by the hypsometric function. The effects of stratal dip parallel to the mean slope of the erosional topography and finite layer thickness can be accounted for to a first approximation by simple geometric corrections to the mixing time. Finite layer thickness also has the effect of smoothing the production function although most natural hyposometric functions are smooth enough that this effect is relatively weak. The quality of an unroofing sequence can be measured in terms of the 'sharpness' of separation of successive peeaks in sediment production produced by milling off a sequence of geometrically similar layers. This peak sharpness can be parameterized by a ratio of the interval between successive peaks in sediment production to topographic mixing time. By this measure, the quality of unroofing sequences is controlled by two parameters: the ratio of layer thickness to topographic relief, and the dip angle. The dip angle is concert with topographic mixing exerts a strong control on the degree of signal segregation; in particular, production of cleanly segregated signals for dip angles greater than about 15° requires very high ratios of layer thickness to relief. Hence identification of distinct unroofing sequences may place significant and useful constraints on the attitude and/or thickness of units in the eroding stratigraphy.