Self-organizing models of shallow-water carbonate accumulation

The stratigraphic record of shallow water carbonate accumulation is remarkably complex. The combination of a wide variety of facies elements, the great abundances of individual elements that constitute even relatively short stratigraphic sections, and the possibilities of both high- and low-frequency organization of those facies into hierarchical stratigraphic units has made shallow-water carbonates one of the most closely studied and hotly debated of all sedimentary systems. Carbonate stratigraphy has until now been analyzed largely through a combination of field observations and simple one- and two-dimensional forward models of deposition. Herein we demonstrate the use of a cellular model of carbonate accumulation that displays emergent self-organizational behavior. The utility of such a model resides in its ability to generate stratigraphic patterns both vertically and spatially that are mathematically and geometrically similar to those encountered in natural systems, Importantly, these cellular models reproduce significant components of natural stratigraphic complexity through the use of a single simple numerical algorithm. It is the application of that linking algorithm across a cellular grid that produces emergent stratigraphic organization. Specifically, simulations consisting of two modeled lithologies produce vertical records of facies composition that exhibit thickness-frequency distributions similar to the negative exponential forms reported from numerous stratigraphic sections. Likewise, area-frequency distributions across simulated depositional surfaces are similar to those found to describe facies mosaics (buildups, patch reefs, mud banks) on modern carbonate platforms. As such, this stochastically driven cellular model produces successful simulations of shallow-water carbonate stratigraphy and strongly indicates that the application of this and similar models potentially provides both a novel and an important avenue of investigation into the complex and dynamic carbonate depositional environment.