The model of entropy for the Upper Carboniferous coal-bearing formations in the Upper Silesian Coal Basin and an attempt of its geological interpretation


  • Marek DOKTOR Akademia Górniczo-Hutnicza, Wydział Geologii, Geofizyki i Ochrony Środowiska; al. Mickiewicza 30, 30-059 Kraków
  • Andrzej J. KRAWCZYK Akademia Górniczo-Hutnicza, Wydział Geologii, Geofizyki i Ochrony Środowiska; al. Mickiewicza 30, 30-059 Kraków



entropy, coal-bearing successions, Upper Carboniferous, Upper Silesian Coal Basin


The paper presents the model of entropy for the coal-bearing formations of the Upper Silesian Coal Basin. The coal-bearing formations include exclusively continental (fluvial) sediments in their upper parts and paralic sediments in the lower parts, the latter composed of partly continental, partly near-shore deposits laid down in broadly understood sea coast environment (shoreline, sand bars, beaches, etc.). For studies 18 boreholes were selected in which both the continental and the paralic successions were represented. For all lithofacies distinguished in all successions the normalized, pre- and post-depositional entropies were calculated. Then, successions were categorized on the basis of these calculations. The dendrogram shows three groups of successions from which the first corresponds almost exclusively to the Paralic Series and the second one - to the Mudstone Series. The third group differs distinctly from the first two groups and represents the sediments of the Krakow Sandstone Series.


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Allegre C., 1964. Vers une logique mathematique des series sedimentaires. Bulletin de la Societe Geologique de France, 7, 6, 214–218.

Carr T.R., Horowitz A., Hrabar S.V., Ridge K.F., Rooney R., Straw W.T., Webb W. & Potter P.E., 1966. Stratigraphic sections, bedding sequences and random processes. Science, 154, 1162–1164.

Dembowski Z. & Unrug R., 1970. Analiza statystyczna sedymentacji cyklicznej w warstwach łaziskich (Górnośląskie Zagłębie Węglowe). Rocznik Polskiego Towarzystwa Geologicznego, 40, 63–110.

Doktor M. & Gradziński R., 1985. Środowisko depozycji aluwialnych utworów węglonośnych serii mułowcowej (górny karbon Zagłębia Górnośląskiego). Studia Geologia Polonica, 82, 5–67.

Doktor M., Gradziński R. & Słomka T., 1997. Cyclicity in Upper Carboniferous coal-bearing fluvial sediments: example from the Upper Silesia, Poland. Prace Państwowego Instytutu Geologicznego, 157, 2, 53–61.

Doktor M. & Gradziński R., 1999. Środowiska depozycyjne rozpoznane w serii paralicznej Górnośląskiego Zagłębia Węglowego. The 4th Czech-Polish Conference about Carboniferous Sedimentology, Ostrava, Documenta Geonica 1999, 35–40.

Doktor M., 2007. Conditions of accumulation and sedimentary architecture of the Cracow Sandstone Series (upper Westphalian) Upper Silesia Coal Basin, Poland. Annales Societatis Geologorum Poloniae, 77, 219–268

Duff P.McL.D., Hallam A. & Walton E.K., 1967. Cyclic sedimentation. Elsevier, Amsterdam.

Gingerich P.D., 1969. Markov analysis of cyclic alluvial sediments. Journal of Sedimentary Petrology, 39, 1, 330–332.

Gradziński R., Doktor M. & Słomka T., 1995. Depositional environments of the coal-bearing Cracow Sandstone Series (upper Westphalian), Upper Silesia, Poland. Studia Geologica Polonica, 108, 149–170.

Hattori I., 1976. Entropy in Markov chains and discrimination of cyclic patterns in lithologic successions. Mathematical Geology, 8, 4, 477–497.

Hiscott R.N., 1981. Chi-square tests for Markov chain analysis. Mathematical Geology, 13, 1, 69–80.

Hota R.N. & Maejima W., 2004. Comparative study of cyclicity of lithofacies in lower Gondwana formations of Talchir basin, Orissa, India: a statistical analysis of subsurface logs. Gondwana Research, 7, 2, 353–362.

Khan Z.A. & Casshyap S.M., 1981. Entropy in Markov analysis of late Paleozoic cyclical coal measures of east Bokaro basin, Bihar, India. Mathematical Geology, 13, 2, 153–162.

Kotas A., 1985. Structural evolution of the Upper Silesian Coal Basin (Poland). Compte Rendu 10th International Congress of Carboniferous Stratigraphy and Geology (Madrid), 3, 459–469.

Krumbein W.C., 1967. FORTRAN IV computer programs for Markov chain experiments in geology. Kansas Geological Survey Computer Contributions, 13, 1–38.

Potter P.E. & Blakely R.G., 1967. Generation of a synthetic vertical profile of a fluvial sandstone body. Society of Petroleum Engineers Journal, 7, 243–251.

Potter P.E. & Blakely R.G., 1968. Random processes and lithologic transitions. Journal of Geology, 76, 2, 154–170.

Powers D.W. & Easterling R.G., 1982. Improved methodology for using embedded Markov chains to describe cyclical sediments. Journal of Sedimentary Petrology, 52, 3, 913–923.

Radomski A. & Gradziński R., 1981. Facies sequences in the Upper Carboniferous alluvial coal-bearing deposits, Upper Silesia, Poland. Studia Geologica Polonica, 68, 29–41.

Read W.A., 1969. Analysis and simulation of Namurian sediments in central Scotland using a Markov-process model. Mathematical Geology, 1, 2, 199–219.

Schwarzacher W., 1969. The use of Markov chains in the study of sedimentary cycles. Mathematical Geology, 1, 1, 17–39.

Tewari R.Ch., Singh D.P. & Khan Z.A., 2009. Application of Markov chain and entropy analysis to lithologic succession – an example from the early Permian Barakar Formation, Bellampalli coalfield, Andhra Pradesh, India. Journal of Earth System Science, 118, 5, 583–596.

Turk G., 1979. Transition analysis of structural sequences: Discussion. Geological Society of America Bulletin, 90, 10, 989–991.

Vistelius A.B. & Faas A.V., 1965. The mode of alteration of strata in certain sedimentary rock sections. Doklady Akademii Nauk SSSR [English trans.], 164, 40–42.

Vistelius A.B. & Feygelson T.S., 1965. Stratification theory. Doklady Akademii Nauk SSSR [English trans.], 164, 20–22.

Ward J.H., Jr., 1963. Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association, 58, 301, 236–244.

Yu J., 1984. Tests for quasi-independence of embedded Markov chains. Mathematical Geology, 16, 3, 267–282.




How to Cite

DOKTOR, M., & KRAWCZYK, A. J. (2010). The model of entropy for the Upper Carboniferous coal-bearing formations in the Upper Silesian Coal Basin and an attempt of its geological interpretation. Geology, Geophysics and Environment, 36(1), 37.