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Measured rates of sedimentation: What exactly are we estimating, and why?
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Data on rates of sedimentation are essential in studies of sedimentation systems. These data are obtained in three main study contexts: (1) the study of sedimentation systems that are active today, (2) the source-to-sink study of sedimentation systems that no longer are active, and (3) the study of the relationship between accumulation rate and measurement timespan. The aim of this paper is to question the meaning of measured rates of sedimentation, and their interpretability, particularly in these three contexts.

Individual measurements of rate of sedimentation must always be interpreted with care. Firstly, there are different definitions, for instance with different statistical support or measurement dimension; values that are defined differently cannot be compared directly. Secondly, appropriate sampling schemes must have been used for the measurement; this minimises sampling bias. Thirdly, the inherent limitations of the data sources must be taken into account. Rates of sedimentation can usually be measured successfully in active sedimentation systems. The same is not true for systems that are no longer active; these can only be studied using the stratigraphic successions left behind. Rates of erosion can never be measured successfully in stratigraphic successions.

Rate of sedimentation is essentially a ratio – an amount of sedimentation per length of time – therefore the obvious strategy to use in determining it is first to measure the amount and the time independently, then to combine the values. The amount can be measured in terms of thickness or volume or mass per unit area. The duration of the time interval can be preset using quasi-continuous measurement techniques or site reoccupation, or it can be identified from interval-specific sedimentary structures, or it can be measured using dated horizons. An alternative strategy is to use a surrogate measurement variable. Rates of erosion in ancient systems are usually measured in this way, using cosmogenic radionuclide concentrations. These two strategies are reviewed in this paper.

Sets of measurements made in systems that are active today can certainly be used to estimate the rate of sedimentation for the system as a whole. This estimation is best carried out using geostatistical estimation techniques. The alternative is simply to average the measured rate values. This latter approach should not be used, however, because the mean sedimentation rate in a system gives information only about the net sediment movement at the system boundaries. It says nothing at all about how the system is operating or about its spatial and temporal variability.

Measurements of rates of sedimentation made for source-to-sink studies are necessarily made in stratigraphic successions. The measurements are used to estimate quantities in the sediment mass budget equation. The amount of decumulation is inherently incapable of being measured in stratigraphic successions, therefore there are always unknowns in the mass budget equation whenever the lithic surface at the start of the time interval considered cannot be recognised everywhere. This means that the mass budget equation is applicable in practice only when all the systems involved in the study are entirely non-erosional for that entire time interval — a highly unrealistic situation.

The consistently inverse relationship documented between accumulation rates and measurement timespan is taken usually to indicate that this relationship is substantially scale-invariant. This in turn is often taken as indicating that the stratigraphic record is fractal in nature. There are nevertheless grounds for doubt, all of which relate to the ways that the data are collected and used for estimation. The relationship is in fact the natural mathematical result of last-in-first-out (LIFO) operation and is produced in any type of system in which addition and removal processes both operate. It says nothing particular about sedimentation processes. The future analysis of accumulation rate data collected from stratigraphic successions will sensibly be framed in the context of estimating the parameters of a LIFO model.

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