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On the frequency distribution of turbidite thickness



The frequency distribution of turbidite thickness records information on flow hydrodynamics, initial sediment volumes and source migration and is an important component of petroleum reservoir models. However, the nature of this thickness distribution is currently uncertain, with log-normal or negative-exponential frequency distributions and power-law cumulative frequency distributions having been proposed by different authors. A detailed analysis of the Miocene Marnoso Arenacea Formation of the Italian Apennines shows that turbidite bed thickness and sand-interval thickness within each bed have a frequency distribution comprising the sum of a series of log-normal frequency distributions. These strata were deposited predominantly in a basin-plain setting, and bed amalgamation is relatively rare. Beds or sand intervals truncated by erosion were excluded from this analysis. Each log-normal frequency distribution characterizes bed or sand-interval thickness for a given basal grain-size or basal Bouma division. Measurements from the Silurian Aberystwyth Grits in Wales, the Cretaceous Great Valley Sequence in California and the Permian Karoo Basin in South Africa show that this conclusion holds for sequences of disparate age and variable location. The median thickness of these log-normal distributions is positively correlated with basal grain-size. The power-law exponent relating the basal grain-size and median thickness is different for turbidites with a basal A or B division and those with only C, D and E divisions. These two types of turbidite have been termed ‘thin bedded’ and ‘thick bedded’ by previous workers. A change in the power-law exponent is proposed to be related to: (i) a transition from viscous to inertial settling of sediment grains; and (ii) hindered settling at high sediment concentrations. The bimodal thickness distribution of ‘thin-bedded’ and ‘thick-bedded’ turbidites noted by previous workers is explained as the result of a change in the power-law exponent. This analysis supports the view that A and B divisions were deposited from high-concentration flow components and that distinct grain-size modes undergo different depositional processes. Summation of log-normal frequency distributions for thin- and thick-bedded turbidites produces a cumulative frequency distribution of thickness with a segmented power-law trend. Thus, the occurrence of both log-normal and segmented power-law frequency distributions can be explained in a holistic fashion. Power-law frequency distributions of turbidite thickness have previously been linked to power-law distributions of earthquake magnitude or volumes of submarine slope failure. The log-normal distribution for a given grain-size class observed in this study suggests an alternative view, that turbidite thickness is determined by the multiplicative addition of several randomly distributed parameters, in addition to the settling velocity of the grain-sizes present.