Russian Roulette and Coral Reefs: Towards a Quantitative Definition of Reef Frameworks

Russian Roulette is a useful analogue to the Markov property inherent in the spatial patterns of coral-dominated sedimentary systems, i.e. that events define the probability of subsequent or neighboring events. Using remotely-sensed (satellite imagery, acoustic, Lidar, etc.) classification maps, we investigate the spatial patterns of coral bioherms, biostromes, and non-frameworks in different environmental and biogeographic settings. Relationships between classes encoding different facies within a scene show that coral landscapes possess a high-order and embedded Markov property, i.e. neighborhood relations are highly probabilistic despite smaller components being fractal, expressing random processes. This information allows the use of graph theory to quantitatively express spatial and genetic relationships of facies. Digraphs, and the resulting adjacency and reachability matrices, differ between biostromal and biohermal frameworks. So what? A better understanding of spatial patterns will allow a quantification of reef frameworks and associated facies by a single or few indices rather than many words, and enhance interpretation of incomplete (i.e. core) records, which will also allow better reconstruction of the entire sedimentary environment from such incomplete records with implications for the identification of potential reservoirs in reefal frameworks or other, spatially similarly operating systems.