Abstract
On formation of a bed and distribution of bed thickness, A. N. Kolmogorov presented a mathematical explanation that if repetitive alternations of material accumulation and erosion form a sequence of beds, the resultant bed-thickness distribution curve takes a shape truncated by the ordinate at zero thickness. In this truncated distribution curve, its continuation and extension from positive to negative thickness represents the distribution of beds with negative thickness, that is, the depth of erosion. When a distribution curve, including both positive and negative parts, is expressed by a function f(x),the ratio \(\int_0^\infty {f(x)dx to} \int_{ - \infty }^\infty {f(x)dx} \),called Kolmogorov's coefficient and designated as p,is a parameter representing the degree of accumulation in the depositional environment. On the assumption that f(x)is described by the Gaussian distribution function, the coefficient pfor Permian and Pliocene sequences in central Japan was calculated. The coefficients also were obtained from published data for different types of sediments from other areas. It was determined that they are more or less different depending on their depositional environments. The calculated results are summarized as follows:
In addition, a ratio \(q = \int_0^\infty {xf(x)dx/} \int_{ - \infty }^\infty {|x|f(x)dx} \),called Kolmogorov's ratio in this paper, is introduced for estimating a degree of total thickness actually observed in the field relative to total thickness once present in a basin. The calculated results of Kolmogorov's ratio are as follows:
The sedimentological significance of these values is discussed.
Similar content being viewed by others
References
Atkinson, D. J., 1962, Tectonic control of sedimentation and the interpretation of alternation in the Tertiary of Prince Charles Foreland, Spitzbergen: Geol. Soc. America Bull., v. 73, no. 3 p. 343–364.
Beerbower, J. R., 1964, Cyclothem and cyclic depositional mechanisms in alluvial plain sedimentation: Kansas Geol. Survey Bull., 169, p. 31–42.
Bokman. J., 1957, Suggested use of bed-thickness measurements in stratigraphic descriptions: Jour. Sed. Pet., v. 27, no. 3, p. 333–335.
Bouma, A. H., 1962, Sedimentology of some flysch deposits; a graphic approach to facies interpretations: Elsevier Publ. Co. Amsterdam, 168 p.
Chrobok, S. M., 1970. Rhythmen. Probleme und Grundlagen ihrer Typisierung für die geologische Analyse und Synthese (Teil I): Geologie, Jg. 19, s. 137–156.
Duff, P. M. D., Hallam, A., and Walton, E. K., 1967, Cyclic sedimentation: Developments in sedimentology 10, Elsevier Publ. Co. Amsterdam, 280 p.
Ingram, R., 1954, Terminology for the thickness of stratification and parting units in sedimentary rocks: Geol. Soc. America Bull., v. 65, no. 9, p. 937–938.
Kimura, T., 1966, Thickness distribution of sandstone beds and cyclic sedimentations in the turbidite sequences at two localities in Japan: Bull. Earthquake Res. Inst., Univ.Tokyo, v. 44, p. 561–607.
Kolmogorov, A. N., 1951, Solution of a problem in probability theory connected with the problem of the mechanism of stratification: Am. Math. Soc. Trans., no. 53, p. 171–177.
Kuenen, P. H., 1967, Emplacement of flysch-type sand beds: Sedimentology, v. 9, no. 3, p. 203–243.
Makiyama, J., 1963, Regional geology of central Japan (in Japanese): Asakura Book Co., Tokyo, 251 p.
McBride, E. F., 1962, Flysch and associated beds of the Martinsburg Formation (Ordovician), central Appalachians: Jour. Sed. Pet., v. 32, no. 1, p. 39–91.
McCormick, C. D., and Picard, M. D., 1969, Petrology of Gartra Formation (Triassic), Uinta Mountain Area, Utah and Colorado: Jour. Sed. Pet., v. 39, no. 4, p. 1484–1508.
McKee, E. D., and Weir, G. W., 1953, Terminology for stratification and cross-stratification in sedimentary rocks: Geol. Soc. America Bull., v. 64, no. 4, p. 381–390.
Miyamoto, M., Kikuchi, H., and Sakai, M., 1962, A consideration of the geological structure in the Kakegawa district, Shizuoka Prefecture (in Japanese): Jour. Geol. Soc. Japan, v. 68, p. 293–300.
Mizutani, S., 1957, Permian sandstones in the Mugi area, Gifu Prefecture, Japan: Jour. Earth Sci., Nagoya Univ., v. 5, p. 135–151.
Mizutani, S., 1959, Clastic plagioclase in Permian graywacke from the Mugi area, Gifu Prefecture, central Japan: Jour. Earth Sci., Nagoya Univ., v. 7, p. 108–136.
Mizutani, S., 1964, Superficial folding of the Paleozoic System of central Japan: Jour. Earth Sci., Nagoya Univ., v. 12, p. 17–83.
Pettijohn, F. J., 1957, Sedimentary rocks (2nd ed.): Harper & Brothers, New York, 718 p.
Potter, P. E., and Siever, R., 1955, A comparative study of Upper Chester and Lower Pennsylvanian stratigraphic variability: Jour. Geology, v. 63, no. 5, p. 429–451.
Simonen, A., 1953, Stratigraphy and sedimentation of the Svecofennidic, early Archean supracrustal rocks in southwestern Finland: Bull. Comm. géol. Finlande, no. 160, p. 1–64.
Simonen, A., and Kouvo., O., 1951, Archean varved schists north of Tempere in Finland: Bull. Comm. géol. Finlande, no. 154, p. 93–114.
Ujiie, H., 1962, Geology of the Sagara-Kakegawa sedimentary basin in central Japan: Sci. Rept., Tokyo Univ. Education, v. 8, p. 123–188.
Walker, R. G., 1967, Turbidite sedimentary structures and their relationship to proximal and distal depositional environments: Jour. Sed. Pet. v. 37, no. 1, p. 25–43.
Way, J.H., Jr., 1968, Bed-thickness analysis of some Carboniferous fluvial sedimentary rocks near Joggins, Nova Scotia: Jour. Sed. Pet. v. 38, no. 2, p. 424–433.
Additional references
Allen, J. R. L., 1962, Petrology, origin and deposition of the highest Lower Old Red Sandstone of Shropshire, England: Jour. Sed. Pet. v. 32, no. 4, p. 657–697.
Bokman, J., 1953, Lithology and petrology of the Stanley and Jackfork formations: Jour. Geology, v. 61, no. 2, p. 152–170.
Dott, R. H., Jr., 1963, Dynamics of subaqueous gravity depositional processes: Am. Assoc. Petroleum Geologists Bull., v. 47, no. 1, p. 104–128.
Enos, P., 1969, Anatomy of a flysch: Jour. Sed. Pet. v. 39, no. 2, p. 680–723.
Kelley, V. C., 1956, Thickness of strata: Jour. Sed. Pet. v. 26, no. 4, p. 289–300.
Kelling, G., 1969, The environmental significance of cross stratification parameters in an Upper Carboniferous fluvial basin: Jour. Sed. Pet., v. 39, no. 3, p. 857–875.
Middleton, G. V., 1962, Size and sphericity of quartz grains in two turbidite formations: Jour. Sed. Pet., v. 32, no. 4, p. 725–742.
Raam, A., 1968, Petrology and diagenesis of Broughton Sandstone (Permian), Kiama district, New South Wales: Jour. Sed. Pet. v. 38, no. 2. p. 319–331.
Schwarzacher, W., 1953, Cross-bedding and grain size in the Lower Cretaceous sands of East Anglia: Geol. Mag., v. 90, no. 5, p. 322–330.
Scott, K. M., 1966, Sedimentology and dispersal pattern of a Cretaceous flysch sequence, Patagonian Andes, southern Chile: Am. Assoc. Petroleum Geologists Bull., v. 50, no. 1, p. 72–107.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mizutani, S., Hattori, I. Stochastic analysis of bed-thickness distribution of sediments. Mathematical Geology 4, 123–146 (1972). https://doi.org/10.1007/BF02080298
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02080298