THE DEPENDENCE OF ACCRETION AND DENUDATION RATES ON AVERAGING-TIME: DIFFERENT RELATIONSHIPS FOR ONE- AND TWO-DIMENSIONAL MEASUREMENTS

Simple mathematics show that mean measured accumulation rates of stratigraphic sections must tend to decrease as averaging-time increases. The outcome results from intervals of erosion and non-deposition, plus the way landscape change is categorized by direction (erosion, deposition, uplift, subsidence, progradation, back-stepping, etc.) and corresponding rates are measured only at places of net change in that direction. In large global compilations of accumulation rate for numerous environments, mean rates fall from time scales of minutes to millions of years. Unsteadiness and gaps can be expected at all time scales. Short-term historic rates must be expected to exceed long-term geologic rates as a result of averaging-time alone; records of climate change and recent human influence may be obscured. Gradients of the inverse relationship become less steep as time scale lengthens: vertical accretion is steadier in the long term. On alluvial flood-plains, decreasing trends for vertical erosion and deposition rates are the same, as expected in a model transfer zone with temporary storage and no net deposition. Upstream, empirical data suggest that the inverse scaling is less severe and may even be absent in rates of upland denudation that are integrated across a catchment rather than determined at a point. As measurement area increases, a wider range of processes is captured; places of activity and inactivity are integrated more appropriately. Downstream, on the continental shelf, sediment accumulates by both vertical aggradation and horizontal progradation. Global compilation of progradation rates reveals a negative dependence on averaging time that steepens at long time scales. When combined, global mean empirical vertical and horizontal components generate an expected expansion rate of cross-sectional area that is independent of averaging times from months to millions of years. This finding would be consistent with steady denudation and sediment conservation. The implied time-scale invariant global sediment flux (volume per unit width of deposit per year), trapped on the continental shelf and slope, appears to be 1-5 square meters per year. Perhaps averaging time may be ignored for global budgets. It remains to be determined at what smaller catchment size the flux would scale with time span.