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, k; 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 k 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 k = 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 k 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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[1] The Bruun rule, widely used to predict transgression due to sea level rise on decade to century timescales based on a fixed nearshore profile, neglects the influence of inland topography and substrate lithology, leading to physically unreasonable predictions on longer timescales. We use a new approach, the shoreline Exner equation, to model shoreline transgression on wave-dominated coasts over timescales of decades to millennia. Our results show that interactions between nearshore processes and inland topography, neglected by Bruun-style models, drive morphologic evolution which modulates shoreline retreat. Analytical solutions suggest that while short-term shoreline retreat will sometimes follow the Bruun rule, long-term transgression will always follow the slope of the inland topography. Moreover, our results show that the slope of the inland landscape, relative to the nearshore slope, exerts a first-order control on coastal morphology, such that steep coasts tend to form cliff-backed beaches while gentle coasts tend to form barrier island-lagoon systems. However compositional variations between the inland landscape and nearshore system can alter this pattern. Sea Level Rise and Shoreline Transgression[2] Sea level rise on wave-dominated coasts drives shoreline retreat on timescales of years to tens of millennia. Models aimed at predicting short-time (up to decades) response to sea level rise typically focus on beach and nearshore processes. However with sustained sea level rise the shoreline can transgress significantly inland, suggesting that the composition and morphology of the inland coastal landscape can strongly influence coastal behavior on longer timescales (centuries to millennia). Wave-dominated coasts display wide variations in inland topography (Figure 1), from steep coasts with rugged mountains and beaches backed by cliffs, to gentle coasts with broad coastal plains and beaches backed by barrier islands and lagoons. Here we analyze the transition between short-and long-term coastal responses to sea level rise, modeling shoreline transgression and associated changes in coastal morphology.[3] If the land surface is static during transgression then shoreline retreat follows the slope of the inland topography, e.g., storm surge flooding. This passive inundation is simple to model, but shoreline retreat is usually accompanied by erosion and deposition which drive morphologic changes that impact future retreat. Predictions of shoreline response to sea level rise often account for this morphodynamic feedback using the Bruun rule [Bruun, 1962;Zhang et al., 2004].[4] The Bruun rule assumes the beach and shoreface (Figure 2a) maintain a fixed equilibrium profile during shoreline retreat, with no external sources or sinks of sediment (e.g., fluvial influx or wave-driven efflux). The Bruun rule predicts that shoreline retreat parallels the average slope S s of this equilibrium profile, independent of the inland slope S 0 . More precisely, given the cross-shore shoreline trajectory (x, z) = (s[t], z sea ...