On the power law size distribution of turbidite beds
A number of studies have shown that cumulative distributions of turbidite bed thicknesses (as observed in boreholes or outcrops) follow a power law, in the sense that the number of beds whose measured thickness is greater than η is proportional to η−β. The purpose of this paper is to investigate the relationship between the distribution of measured thicknesses of turbidite sand beds and the distribution of bed volumes. The distribution of sand bed volumes has practical implications to model hydrocarbon reservoirs in 3D and quantifies how the total amount of sand within a turbidite sequence is distributed among beds of different sizes. If the cumulative distribution of bed volumes v is proportional to v−c, the few largest beds account for more and more of the total volume of sand and the sequence becomes more and more ‘punctuated’ as the exponent c decreases below 1. The relationship between the exponents of the distribution of measured bed thicknesses (β) and of bed volumes (c) can be investigated by assuming that the turbidite beds are disc-like bodies distributed in the 3D space of a basin, and that their thicknesses are sampled on a vertical line that does not in general intersect all the beds. The relationship between b and c can be shown to depend on how bed length scales with bed thickness (as noted by other authors) and on how the beds are distributed in the 3D space of the basin (which is a new result). The main conclusion is that it is not generally possible to make inferences on the distribution of turbidite bed volumes knowing only the distribution of bed thicknesses. On the other hand, if some independent information is available on the geometrical characteristics of the turbidite deposit, the observations of bed thicknesses can be converted to bed volumes, thus providing general information on the 3D characteristics of the sequence.