On the frequency distribution of turbidite thickness

Abstract

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.

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

“…In Unit 2 this departure consists in a sudden decrease in the slope of the exceedance plot across a thickness threshold that must scale to a critical flow magnitude above which flow stripping also affected the sandy part of the turbidity currents. The exceedance plot of sandstone beds of Unit 3 are similar to published data from nonponded turbidite systems (see for example Talling, 2001). …”

“…Conversely, the sandstones beds from Unit 2 and 3 ( Fig. 11b and c, respectively) define convex-upward curves that resemble the experimental distributions of turbidites subject to flow stripping of Sinclair and Cowie (2003) as well as those reported in the literature from non-ponded, open ended turbidite systems (see for example Talling, 2001). However, a significant change of gradient of the exceedance plot for sandstone thickness in Unit 2 occurs at a thickness of c. 125 cm (i.e.…”

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

“…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). 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).…”

“…Because the thickness of a turbidite bed is determined by the shape of the bed and the distance from the source, initial sediment volume, grain size and flow type (Talling 2001), the statistical evaluation may provide information on processes controlling turbidite feeding, depositional processes, distribution and geometry (e.g. Rothman et al 1995;Malinverno 1997;Carlson & Grotzinger 2001).…”

“…Generally, four types of distribution -truncated Gaussian, exponential, lognormal and power law distributions were applied to bed thickness distributions in turbidite deposits (e.g. Ricchi Lucchi & Valmori 1980;Muto 1995;Drummond & Wilkinson 1996;Malinverno 1997;Talling 2001;Sinclair & …”