A First-Order Model for Sediment Deposition in Basins

The record of surface processes preserved in the stratigraphy of a depositional basin is incomplete because the net accumulation of sediment is an unsteady process. Unsteady sedimentation produces a time-dependent trend in the thickness of sedimentary bodies, and hence rates of deposition averaged over different time intervals are not directly comparable. The nature of this time dependence has been determined empirically using field data from terrigenous shelf deposits and consists of two regimes: a power-law relationship between vertical thickness (aggradation) and measurement time interval at durations less than 10,000 yr, and a near-linear trend at durations greater than 100,000 yr. Horizontal thickness (progradation) co-varies with vertical thickness such that the total volume of deposited sediment depends primarily on tectonic subsidence rate over the entire range of measurements. Here we show that a noisy diffusion model is capable of quantitatively reproducing these observations. The model predicts two asymptotic scaling regimes: small-scale fluctuations in sedimentation dominate aggradation at shorter intervals of time, while at longer intervals the aggradation balances tectonic subsidence. Our model shows this transition in temporal scaling is due to the finite spatial extent of sedimentary basins, and allows us to convert time to space through a dynamic scaling relation. The transition time from field data translates to a spatial scale of order 100 km, suggesting that the break in sedimentation scaling coincides with the total width of the continental shelf. Attempts to interpret transient environmental signals from preserved outcrop at time scales smaller than the steady-state time (~100,000 yr) are prone to substantial error because these signals must be deconvolved from the transient 'noise' produced by the internally-generated variability of the depositional system. Unfortunately, the time scales of interest for climatic interpretation often fall within the range in which fluctuations dominate the record. Similar complications arise for net-erosional systems. In order to better resolve the record of environmental change imprinted on landscapes, we must better understand the nature of internally-generated variability in evolving landscapes.