FROM TURBIDITE BED THICKNESS DISTRIBUTIONS TO DEPOSITIONAL ENVIRONMENTS: METHODS AND PITFALLS OF FITTING AND INTERPRETING THE POWER-LAW AND LOGNORMAL MODELS

Turbidite bed-thickness distributions have become increasingly popular as potential predictors of depositional settings. Most recent work focuses on power-law models: it is assumed that the initial input volumes have power-law distribution and departures from this are interpreted as signs of confinement or erosion. Talling (2001) has suggested that turbidite bed-thicknesses could be better modeled as mixtures of lognormal distributions. The purpose of this paper is to briefly discuss the methods for choosing between the power-law and the lognormal model and to suggest a potential use of the results in the interpretation of the depositional setting. This is done through the analysis of two contrasting datasets: the Tarcău Sandstone of the East Carpathians, Romania, probably representing a number of channel-levee systems, and the largely unchannelized Marnoso-Arenacea Formation (data from Talling, 2001). It is suggested here that (1) log-log 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 (e.g., log-linear, cumulative probability, histogram of log-transformed values, q-q plots) and the use of a goodness-of-fit statistic other than R squared, such as the chi-squared and the Kolmogorov-Smirnov statistics; (2) a distribution described by a segmented power law on an exceedence plot is neither a power-law distribution, nor a simple mixture of two power-law distributions, and therefore the segmented power-law model should be abandoned; (3) the components of the lognormal mixture can be modeled using the expectation-maximization algorithm; (4) in addition to the examples provided by Talling (2001), bed thicknesses in the Tarcău Sandstone fit better a bimodal lognormal mixture than the power-law model; and (5) clear differences in the bed-thickness distributions of the two formations may reflect the dissimilarity in their overall depositional setting and architecture.