Quantitative evidence for the fractal nature of the stratigraphie record: results and implications

Stratal successions are the outputs of a complex dynamical system characterized by interactions and feedbacks on a wide range of temporal and spatial scales. These outputs have fractal-like properties, showing a similar geometry on all scales. A simple method has been devised which generates an inventory of objectively defined and non-hierarchical layers from borehole log data, thus allowing a statistical test of this view. Logarithmic plots of frequency versus size, for layer-thickness inventories covering intervals from 500 ft to 5000 ft in thickness and differing in age and facies, show linear trends with negative slopes. The power laws indicated support the idea of the fractal character of stratigraphie layering. The non-integer slopes of such plots, which are related to their fractal dimension, are similar in all cases, suggesting that a very general law applies. The fractal character of its layering supports the idea that the stratigraphie record is the output of a system that operates in a condition of self-organized criticality, as does the power-law relationship between rates of accumulation and the time spans over which they are measured. These findings have important theoretical and practical implications for stratigraphy, notably in its bearing on chronostratigraphic and sequence stratigraphie methods and on the search for periodicity in the record.