Changes of scaling relationships in an evolving population: The example of “sedimentary” stylolites

Abstract

Bed-parallel (“sedimentary”) stylolites are used as an example of a population that evolves by the addition of new components, their growth and their merger. It is shown that this style of growth controls the changes in the scaling relationships of the population. Stylolites tend to evolve in carbonate rocks through time, for example by compaction during progressive burial. The evolution of a population of stylolites, and their likely effects on porosity, are demonstrated using simple numerical models. Starting with a power-law distribution, the adding of new stylolites, the increase in their amplitudes and their merger decrease the slope of magnitude versus cumulative frequency of the population. The population changes to a non-power-law distribution as smaller stylolites merge to form larger stylolites. The results suggest that other populations can be forward- or backward-modelled, such as fault lengths, which also evolve by the addition of components, their growth and merger. Consideration of the ways in which populations change improves understanding of scaling relationships and vice versa, and would assist in the management of geofluid reservoirs.