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Keywords:

  • bed thickness;
  • turbidites;
  • power law distribution;
  • lognormal distribution;
  • log–log plots;
  • lognormal mixture;
  • Tarcău Sandstone;
  • Marnoso-Arenacea Formation

Abstract

Turbidite bed thickness distributions are often interpreted in terms of power laws, even when there are significant departures from a single straight line on a log–log exceedence probability plot. Alternatively, these distributions have been described by a lognormal mixture model. Statistical methods used to analyse and distinguish the two models (power law and lognormal mixture) are presented here. In addition, the shortcomings of some frequently applied techniques are discussed, using a new data set from the Tarcău Sandstone of the East Carpathians, Romania, and published data from the Marnoso-Arenacea Formation of Italy. Log–log exceedence plots and least squares fitting by themselves are inappropriate tools for the analysis of bed thickness distributions; they must be accompanied by the assessment of other types of diagrams (cumulative probability, histogram of log-transformed values, q–q plots) and the use of a measure of goodness-of-fit other than R2, such as the chi-square or the Kolmogorov–Smirnov statistics. When interpreting data that do not follow a single straight line on a log–log exceedence plot, it is important to take into account that ‘segmented’ power laws are not simple mixtures of power law populations with arbitrary parameters. Although a simple model of flow confinement does result in segmented plots at the centre of a basin, the segmented shape of the exceedence curve breaks down as the sampling location moves away from the basin centre. The lognormal mixture model is a sedimentologically intuitive alternative to the power law distribution. The expectation–maximization algorithm can be used to estimate the parameters and thus to model lognormal bed thickness mixtures. Taking into account these observations, the bed thickness data from the Tarcău Sandstone are best described by a lognormal mixture model with two components. Compared with the Marnoso-Arenacea Formation, in which bed thicknesses of thin beds have a larger variability than thicknesses of the thicker beds, the thinner-bedded population of the Tarcău Sandstone has a lower variability than the thicker-bedded population. Such differences might reflect contrasting depositional settings, such as the difference between channel levées and basin plains.