The Kolmogorov model of bed‐thickness distribution: an assessment based on numerical simulation and field‐data analysis

Kolmogorov's model of the distribution of bed thicknesses is assessed by numerical simulations of a sedimentation process, assumed to be a random time‐series of alternating depositional and erosional episodes conformable with a stationary Markov process in a state of equilibrium. The study supports the validity of the main point of the model. The random time‐series process generates a succession of beds with ‘positive’ (preserved) and ‘negative’ (eroded) thicknesses, the frequency distribution of which, f(x), spans the range of positive to negative x ‐values. The beds with negative thicknesses are absent in the stratigraphic record, whereby the measured bed thicknesses show a frequency distribution, f*( x | x > 0), that is left‐side truncated, cut off at the zero thickness value. The numerical simulations further indicate that f( x ) is a ‘composite’ geometrical distribution, whose actual form changes progressively with p d , the probability of sediment deposition relative to erosion. The distribution f( x ) invariably has a maximum at x ≤0, such that the truncated distribution f*( x ) for p d ≥0.5 is a simple geometrical distribution regardless of p d value. The f*( x ) distribution will appear to be a negative exponential distribution when based on the bed‐thickness data measured in a conventional metric scale. Data sets from four different turbidite successions in the Cenozoic of Japan, each comprising a few thousand beds, show this type of distribution. However, the sandstone‐capping shales in one of the turbidite successions show a truncated Gaussian distribution, attributed to a significant component of non‐turbiditic mud. No universal form of bed‐thickness distribution can be assumed for the Kolmogorov model. The form of bed‐thickness distribution may vary with the type of the depositional process and the character of the sedimentary environment.