GEOMETRIC CONSTRAINTS ON COMPOSITION OF SEDIMENT DERIVED FROM EROSIONAL LANDSCAPES

Although unroofing sequences are well known in the stratigraphic recor d, there is no general theory for estimating relevant basic quantities such as the time history of sediment production from a particular uni t or the degree-of mixing between successive units. Here we investigat e the production of sediment from layered source rocks that are milled off by steady-state erosional topography. The shape of the sediment-p roduction function for milling off a thin horizontal layer is given by the derivative of the hypsometric function, in the form of area conta ined 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 fun ction for a sharp transition from one unit to another is given directl y 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 corr ections to the mixing time. Finite layer thickness also has the effect of smoothing the production function although most natural hypsometri c functions are smooth enough that this effect is relatively weak. The quality of an unroofing sequence can be measured in terms of the 'sha rpness' of separation of successive peaks in sediment production produ ced by milling off a sequence of geometrically similar layers. This pe ak sharpness can be parameterized by a ratio of the interval between s uccessive 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 th e dip angle. The dip angle in concert with topographic mixing exerts a strong control on the degree of signal segregation; in particular, pr oduction of cleanly segregated signals for dip angles greater than abo ut 15 degrees requires very high ratios of layer thickness to relief. Hence identification of distinct unroofing sequences may place signifi cant and useful constraints on the attitude and/or thickness of units in the eroding stratigraphy.