The power-law attributes of stratigraphic layering and their possible significance

Abstract

Abstract Conventional stratigraphic logging is biased towards human-scale units and is correspondingly suspect as a basis for statistical analysis of spatial layering relationships. AR analysis uses lithological sample series to define layers in terms of the ‘first returns’ of each sample value, yielding objective layer thickness inventories (LTI) covering several orders of magnitude. Bilogarithmic LTI plots, relating the return thicknesses to their numerical frequency in the section, reveal power-law relationships with non-integer exponents. Over two orders of magnitude, the geometric layering relationships are thus shown to be self-similar (fractal). The power-law exponents also relate to Hurst exponents that describe the variability in the data series and the negative long range dependence in the sampled records. Kilometre-scale gamma ray logs of continental, paralic, shallow marine and pelagic facies yield similar power-law exponents, regardless of the interpreted processes and rates of accumulation. This suggests that a ‘universal’ power law describes the self-similar layering of the stratigraphic record. This is inferred to mean that the power-law behaviours are the outcome of the threshold interactions between a sediment-transporting fluid and its bed. They suggest that the erosional operations that generate the record are characterized by self-organized criticality and involve a strange attractor.