Compensational stacking, the tendency for sediment transport systems to preferentially fill topographic lows through deposition, is a concept widely used in the interpretation of the stratigraphic record. We propose a metric to quantify the degree of compensation by comparing observed stacking patterns in subsiding basins to what would be expected from uncorrelated random stacking. This method uses the rate of decay of spatial variability in sedimentation between picked depositional horizons with increasing vertical stratigraphic averaging distance. We present data from six sedimentary basins where this decay can be measured. The depositional environments range from river deltas to deep-water minibasins, and scales range from meters to 1.5 km in thickness. The decrease in standard deviation of sedimentation divided by subsidence with increasing vertical averaging distance is well described by a power law in each study basin. We term the exponent in this power law the compensation index, κ; its value is 0.5 for uncorrelated random stacking and 1.0 for perfect compensational stacking. Values less than 0.5 indicate anti-compensation, i.e., a tendency of depositional units to stack on top of one another. Parameters controlling the magnitude of κ include the frequency of system-scale avulsions and the temporal variability in deposition rates. Data describing the decay in the standard deviation of sedimentation/subsidence from the six studied basins collapse approximately onto a single power-law trend with κ = 0.75 when the measurement window is standardized by the mean channel depth of each system. Channel depth thus emerges as a fundamental length scale in stratigraphic architecture across environments. Although further study will likely reveal measurable variability in κ between depositional environments, the overall power-law collapse presented here suggests that a stacking behavior midway between purely random and perfect compensation is a good starting point in quantitatively estimating the stratigraphic arrangement of sedimentary deposits.

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