Analysis and simulation of namurian sediments in central Scotland using a Markov-process model

  • William Alfred Read


Many difficulties inherent in analyzing cyclical successions in terms of an idealized cycle and, to a lesser extent, in terms of the modal cycle and composite sequence can be overcome by structuring data in terms of probabilities of upward transitions from one lithology to another. This enables a finite Markov-process model to be used. Transition probability matrices have been constructed from two versions of the same borehole section through paralic Namurian (Pendleian Stage, E 1 ) sediments east of Stirling. The first version does not allow, but the second allows, adjacent items to be of the same lithology. The matrix derived from the first version indicates the following preferred upward succession of lithologies: coal, mudstone, siltstone, sandstone, seatclay, silty and sandy rooty beds, coal. A version of the Chi-square test strongly rejects the hypothesis that the lithologies were deposited in random order. The second matrix is used as computer input forTestmark, Stochex, andMarchain programs, the last of which stimulates a realistic vertical succession. The transition probability data fit readily into the broad framework of deltaic cycles.


Sandstone Lithology Mudstone Siltstone Modal Cycle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Allègre, C., 1964, Vers une logique mathématique des séries sédimentaires: Soc. Geol. France Bull., ser. 7, tome 6, p. 214–218.Google Scholar
  2. Allen, J. R. L., 1965a, Fining-upwards cycles in alluvial successions: Liverpool Manchester Geol. Jour., v. 4, p. 229–246.Google Scholar
  3. Allen, J. R. L., 1965b, A review of the origin and characteristics of Recent alluvial sediments: Sedimentology, v. 5, no. 2, p. 89–191.Google Scholar
  4. Anderson, T. W., and Goodman, L. A., 1957, Statistical inference about Markov chains: Ann. Math. Stat., v. 28, p. 89–110.Google Scholar
  5. Blakely, R. F., and Potter, P. E., 1968, A program for generation of synthetic stratigraphic sections: Brigham Young Univ., Geol. Studies, v. 15, pt. 1, p. 3–12.Google Scholar
  6. Carr, D. D., Horowitz, A., Hrabar, S. V., Ridge, K. F., Rooney, R., Straw, W. T., Webb, W., and Potter, P. E., 1966, Stratigraphic sections, bedding sequences, and random processes: Science, v. 154, no. 3753, p. 1162–1164.Google Scholar
  7. Coleman, J. M., and Gagliano, S. M., 1964, Cyclic sedimentation in the Mississippi River deltaic plain: Gulf-Coast Assoc. Geol. Soc. Trans., v. 14, p. 67–80.Google Scholar
  8. Coleman, J. M. and Gagliano, S. M., 1965, Sedimentary structures: Mississippi River deltaic plain,in Primary sedimentary structures and their hydrodynamic interpretation: Soc. Econ. Paleont. Min., Sp. Publ. No. 12, p. 133–148.Google Scholar
  9. Coleman, J. M., Gagliano, S. M., and Webb, J. E., 1964, Minor sedimentary structures in a prograding distributary: Marine Geology, v. 1, no. 3, p. 240–258.Google Scholar
  10. Duff, P. McL. D., Hallam, A., and Walton, E. K., 1967. Cyclic sedimentation: Elsevier Publ. Co., Amsterdam, 280 p.Google Scholar
  11. Duff, P. McL. D., and Walton, E. K., 1962, Statistical basis for cyclothems: a quantitative study of the sedimentary succession in the East Pennine Coalfield: Sedimentology, v. 1, no. 4, p. 235–256.Google Scholar
  12. Fisk, H. N., 1955, Sand facies of Recent Mississippi delta deposits: Proc. 4th World Petroleum Cong., Section 1/C, Paper 3, p. 377–398.Google Scholar
  13. Forsyth, I. H., and Read, W. A., 1962, The correlation of the Limestone Coal Group above the Kilsyth Coking Coal in the Glasgow-Stirling Region: Great Britain Geol. Survey Bull., No. 19, p. 29–32.Google Scholar
  14. Francis, E. H., 1956, The economic geology of the Stirling and Clackmannan Coalfield, Scotland, area north of the River Forth: Great Britain Geol. Survey, Coalfield Paper No. 1, 36 p.Google Scholar
  15. Frazier, D. E., 1967, Recent deltaic deposits of the Mississippi River: their development and chronology: Gulf-Coast Assoc. Geol. Soc. Trans., v. 17, p. 287–315.Google Scholar
  16. Gingerich, P. D., 1969. Markov analysis of cyclic alluvial sediments: Jour. Sed. Pet., v. 39, no. 1, p. 330–332.Google Scholar
  17. Goodlet, G. A., 1959, Mid-Carboniferous sedimentation of the Midland Valley of Scotland: Edinburgh Geol. Soc. Trans., v. 17, pt. 3, p. 217–240.Google Scholar
  18. Griffiths, J. C., 1966, Future trends in geomathematics: Pennsylvania State Univ., Mineral Industries, v. 35, no. 5, p. 1–8.Google Scholar
  19. Harbaugh, J. W., 1966, Mathematical simulation of marine sedimentation with IBM 7090/7094 computers: Kansas Geol. Survey Computer Contr. 1, 52 p.Google Scholar
  20. Harbaugh, J. W., and Merriam, D. F., 1968, Computer applications in stratigraphic analysis: John Wiley & Sons, New York, 282 p.Google Scholar
  21. Holt, M. J., and McIntosh, A. J., 1966, The scope of mathematics: Oxford Univ. Press, London. 266 p.Google Scholar
  22. Kemeny, J. G., and Snell, J. L., 1960, Finite Markov chains: Van Nostrand & Co., Princeton, N.J., 210 p.Google Scholar
  23. Kolb, C. R., and Van Lopik, J. R., 1966, Depositional environments of the Mississippi River deltaic plain—southeastern Louisiana,in Deltas in their geologic framework: Houston Geol. Soc., Houston, Texas, p. 17–62.Google Scholar
  24. Krumbein, W. C., 1967a,fortran iv computer programs for Markov chain experiments in geology: Kansas Geol. Survey Computer Contr. 13, 38 p.Google Scholar
  25. Krumbein, W. C., 1967b, Computer simulation of transgressive and regressive deposits with a discretestate, continuous-time Markov model: Kansas Geol. Survey Computer Contr. 22, p. 11–18.Google Scholar
  26. Krumbein, W. C., 1968,fortran iv computer program for simulation of transgression and regression with continuous-time Markov models: Kansas Geol. Survey Computer Contr. 26, 38 p.Google Scholar
  27. Krumbein, W. C., and Graybill, F. A., 1965, An introduction to statistical models in geology: McGraw-Hill Book Co., New York, 475 p.Google Scholar
  28. Pearn, W. C., 1964, Finding the ideal cyclothem: Kansas Geol. Survey Bull. 169, p. 399–413.Google Scholar
  29. Potter, P. E., and Blakely, R. F., 1967, Generation of synthetic vertical profile of a fluvial sandstone body: Jour. Soc. Pet. Eng., v. 6, p. 243–251.Google Scholar
  30. Potter, P. E., and Blakely, R. F., 1968, Random processes and lithological transitions: Jour. Geology, v. 76, no. 2, p. 154–170.Google Scholar
  31. Read, W. A., 1969, Fluviatile deposits in Namurian rocks of central Scotland: Geol. Mag., v. 106, p. 331–347.Google Scholar
  32. Read, W. A., and Dean, J. M., 1967, A quantitative study of a sequence of coal-bearing cycles in the Namurian of central Scotland, 1: Sedimentology, v. 9, no. 2, p. 137–156.Google Scholar
  33. Read, W. A., and Dean, J. M., 1968, A quantitative study of a sequence of coal-bearing cycles in the Namurian of central Scotland, 2: Sedimentology, v. 10, no. 2, p. 121–136.Google Scholar
  34. Sackin, M. J., Sneath, P. H. A., and Merriam, D. F., 1965,algol program for cross-association of nonnumeric sequences using a medium-size computer: Kansas Geol. Survey Sp. Dist. Publ. 23, 36 p.Google Scholar
  35. Schwarzacher, W., 1967, Some experiments to simulate the Pennsylvanian rock sequence in Kansas: Kansas Geol. Survey Computer Contr. 18, p. 5–14.Google Scholar
  36. Selley, R. C., in press, Studies of sequence in sediments using a simple mathematical device: Geol. Soc. London Quart. Jour.Google Scholar
  37. Visher, G. S., 1965, Use of vertical profile in environmental reconstruction: Am. Assoc. Petroleum Geologists Bull., v. 49, no. 1, p. 41–61.Google Scholar
  38. Vistelius, A. B., 1949, The mechanism of formation of sedimentary beds: Doklady Akad. Nauk SSSR, v. 65, p. 191–194.Google Scholar
  39. Vistelius, A. B., and Faas, A. V., 1965a, Nature of the sequence of beds in sections of some sedimentary sequences: Doklady Akad. Nauk SSSR, v. 164, p. 629–632.Google Scholar
  40. Vistelius, A. B., and Faas, A. V., 1965b, Variations in thickness of beds in a section of Paleozoic flysch: Doklady Akad. Nauk SSSR, v. 164, p. 1115–1118.Google Scholar
  41. Vistelius, A. B., and Feigel'son, T., 1965, The theory of formation of sedimentary beds: Doklady Akad. Nauk SSSR, v. 164, p. 158–160.Google Scholar
  42. Zeller, E. J., 1964, Cycles and psychology: Kansas Geol. Survey Bull. 169, p. 631–636.Google Scholar

Copyright information

© Plenum Publishing Corporation 1969

Authors and Affiliations

  • William Alfred Read
    • 1
  1. 1.Institute of Geological SciencesUK

Personalised recommendations