Thematic Set: Scaling in stratigraphic data series: implications for practical stratigraphy

Sedimentary layers are planiform, lenticular, generally composite, three-dimensional bodies, distinguished by their lithologies. They are mostly defined and logged in terms of their thickness. This parameter relates non-linearly to time, since it is the outcome of both deposition (at various instantaneous rates) and erosion, which jointly influence the net rate of accumulation. The Layer Thickness Inventory method investigates the distribution of thicknesses in borehole sections over a wide range of scale. The thickness distributions obey power laws, suggesting that, regardless of age and sedimentary facies, stratigraphic layering is geometrically fractal. There is also a relationship between rate of accumulation and the time span over which it is estimated, which expresses the fractal scale and distribution of hiatuses in the record. Such spatial and temporal relationships suggest that conventional hierarchical and cyclical stratigraphic patterns are properties subjectively imposed on the record. The spatially and temporally fractal aspects of the stratigraphic record also suggest that it is the output of a global system that operates in a condition of self-organized criticality. This has important implications for stratigraphic prediction and forward modelling, and reservoir modelling. It also underlines the need for a reassessment of hierarchical stratigraphies, including sequence stratigraphies and cyclostratigraphies.