Turbidite bed thickness distributions: methods and pitfalls of analysis and modelling

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.

Quantitative approach in environmental interpretations of deep-marine sediments (Dukla Unit, Western Carpathian Flysch Zone)

“…The distribution of the turbidite beds is often ascribed to the so-called segmented power law distribution that is characterized by several straight-segment intervals on an exceedence probability plot (Winkler & Gawenda 1999;Carlson & Grotzinger 2001;Sinclair 2003). However, Sylvester (2007) argues that the segmented power law trend is not a simple mixture of the power law population. Carlson & Grotzinger (2001) assume that power law distribution may be the primary input signal for some systems.…”

“…Among these, lognormal and power law distribution seem to be most appropriate for describing the turbidite bed thickness variation (see discussion in Sylvester 2007). The power law distribution is often interpreted as a sign of the tendency of large dissipative systems to develop a state of criticality and generate events of all sizes (Sylvester 2007).…”

“…This stepped trend is equivalent to the segmented power law trend seen in cumulative plots of bed thickness. Sylvester (2007) also prefers description of turbidite bed thickness data by a lognormal mixture model and emphasizes the importance of variability of bed thicknesses (thin and thicker beds) for interpretation of deposition setting.…”

“…Among these, lognormal and power law distribution seem to be most appropriate for describing the turbidite bed thickness variation (see discussion in Sylvester 2007). The power law distribution is often interpreted as a sign of the tendency of large dissipative systems to develop a state of criticality and generate events of all sizes (Sylvester 2007). For example, it has been linked to self-organization of continental slopes to a critical state or to generation of slope failures by earthquakes (Rothman & Grotzinger 1996;Talling 2001).…”

Fill to spill stratigraphic evolution of a confined turbidite mini-basin succession, and its likely well bore expression: The Castagnola Fm, NW Italy

“…The depositional model for 'fill and spill' basins of Sinclair and Tomasso (2002) is four-fold and features i) an initial flow ponding phase during which turbidity currents are fully contained by the confining topography of an upper basin; ii) a flow stripping phase which records the partial surmounting of the confining topography by the uppermost, finer grained fraction of turbidity current depositing its load downstream of it in a lower basin; iii) a flow by-pass phase occurring as the upper basin is filled in and the barrier separating it from the lower basin is healed so to induce either by-pass or abandonment of the upper basin and, locally, incision through older deposits; iv) a late-stage blanketing phase during which infilling of the lower basin results in reduction of gradients across the whole systems and backfilling where bypass had previously occurred in association with incision. The first two of these stages are amenable to statistical analysis of the distribution of bed thicknesses (Malinverno 1997;Sylvester 2007;Bersezio et al, 2005;Felletti and Bersezio 2010). Statistical experiments confirm that in a fully ponded scenario the thickness population of turbidite beds is likely to reflect the magnitude distribution of inbound flows (i.e., all the sediment is trapped by the basin topography) whereas when flow stripping occurs (part of the larger flows reaching the sill escapes the basin) thickness statistics are considerably modified (Sinclair and Cowie, 2003;Fig 1).…”