Size-Frequency Distributions of Carbonate Build-Ups in the Maldives Archipelago

The Maldives archipelago is well poised for the study of scales of accumulation of carbonates. It is one of the largest assemblages of reefs and carbonate platforms in the world, lies far from continental siliciclastics and has monsoon climate with less windward-leeward asymmetry than the trade-wind belts. Reef development has proceeded uninterruptedly since the Oligocene with a constant theme of deposition: a stiff rim of reefs holding a fill of loose sediment. This pattern of growth, the “bucket structure”, repeats across scale. It is as characteristic for individual lagoonal patch reefs as for the morphology of the entire archipelago. The Maldivian reef features were digitized from Landsat imagery covering eight orders of magnitude in area and analyzed for their area-frequency distribution. Trends were then sought that give an adequate mathematical representation of the data. In contrast to the power-law distributions reported for contiguous facies mosaics, we show the trends within the Maldivian dataset to vary with scale. Reefs that comprise the left tail of the size spectrum, from 10^3 - 10^5.5 sq. m, are clearly not a power-law but close to an exponential size-frequency distribution. Units in this size range correspond to the smallest instances of lagoonal and atoll rim patch reefs that can be resolved from Landsat. The central portion of the dataset (10^5.5 - 10^8 sq. m) is represented by larger lagoonal and atoll rim reefs and follows a power-law. Reef units exceeding 100 sq. km, the atolls comprising the archipelago itself, are separated from the central portion by a discontinuity. The atolls also follow a power-law distribution, albeit with a different scaling exponent. The results of the study, that the area-frequency relationship of the Maldivian reefs systematically changes with size, has important implications for the notion of predictability in scale of reefal carbonate deposition. We frame the results against the ecology of reef growth and hydrodynamic set-up of the archipelago in an effort to append real-world process information to the observed switches in trend with scale.

AAPG Search and Discovery Article #90142 © 2012 AAPG Annual Convention and Exhibition, April 22-25, 2012, Long Beach, California