Stratigraphy is often interpreted within hierarchical, or scale-dependent, frameworks that subdivide deposits based on distinct jumps in characteristics such as duration of deposition or scale. While the interpretation is logically valid, few studies quantitatively demonstrate that the jumps exist. Rather, recent work has quantitatively shown some characteristics of stratigraphy to be fractal, or scale invariant. Compensational stacking, the tendency for sediment-transport systems to preferentially fill topographic lows, is a concept widely used in stratigraphic interpretation. Here we use the compensation index, a metric that quantifies the strength of compensational stacking in sedimentary deposits, to describe the architecture of stratigraphy exposed in outcrops of submarine-fan strata in the Carboniferous Ross Sandstone representing contrasting architectural styles: (1) predominantly lobe elements and (2) predominantly channel elements. In both datasets, the stratigraphic architecture is classified into hierarchical classes of beds, stories, and elements. Results are the following. First, at both sites we document statistically significant increases in the strength of compensation across larger hierarchical levels supporting the use of hierarchical interpretations of stratigraphy. It is therefore plausible for some characteristics of sedimentary systems to be hierarchical and others to be fractal. Second, we document that lobe elements stack more compensationally than channel elements. We interpret this pattern to document that compensation increases along a longitudinal transect through this distributive submarine fan.

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