Interpretation of Complex Lithologic Successions by Substitutability Analysis

  • John C. Davis
  • J. M. Cocke
Part of the Computer Applications in the Earth Sciences book series (CAES)


Many stratigraphic successions are characterized by repetitive patterns of lithologies. These patterns are most apparent if lithologies are grouped into relatively few categories, and become increasingly obscure as rock types are classified into finer subdivisions. Most cyclothems and megacyclothems, for example, are patterns composed of only four or five distinctive lithologies. Unfortunately, the gross classification necessary to reveal a cyclic pattern results in lithologic categories which yield meager environmental information.

A section through supposedly cyclic lower Pennsylvanian rocks in eastern Kansas was examined and the lithologies classified into 17 states. Although this degree of subclassification is typical of lithofacies studies, the variety of rock types conceals any cyclicity that might be present. Seemingly different lithologies appear at common positions within cyclothems, obscuring the repetitive pattern in the sequence. These lithologies “substitute” for one another in successive cycles, but may be identified by substitutability analysis, a classification procedure that groups states on the basis of their context in a sequence. States with common high conditional probabilities on subjacent and superjacent states are considered equivalent. Results suggest that lithologies must be combined into fewer than eight states before a cyclic pattern emerges. Analyses also suggest that the lower Pennsylvanian cyclothems studied represent interaction of two depositional processes rather than a single megacyclic process.


Black Shale Cyclic Pattern Flow Graph Composite State Stratigraphic Section 
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. Anderson, R. Y., 1967, Sedimentary laminations in time-series study, in Colloquium on time-series analysis: Kansas Geol. Survey Computer Contr. 18, p. 68–72.Google Scholar
  2. Anderson, R. Y., and Koopmans, L. H., 1963, Harmonic analysis of varve time series: Jour. Geophysical Res., v. 68, no. 3, p. 877–893.CrossRefGoogle Scholar
  3. Anderson, T. W., and Goodman, L. A., 1957, Statistical inference about Markov chains: Am. Math. Stat., v. 28, p. 89–110.MathSciNetCrossRefMATHGoogle Scholar
  4. Berge, C., and Ghouli-Houri, A., 1965, Programming, games and transportation networks: Methuen and Co., Ltd., London, 260 p,Google Scholar
  5. Carr, D. D., and others, 1966, Stratigraphic sections, bedding sequences, and random processes: Science, v. 154, no. 3753, p. 1162–1164.CrossRefGoogle Scholar
  6. Carss, B. W., 1967, In search of geological cycles using a technique from communications theory, in Colloquium on time-series analysis: Kansas Geol. Survey Computer Contr. 18, p. 51–56.Google Scholar
  7. Duff, P. M. D., Hallam, A., and Walton, E. K., 1967, Cyclic sedimentation: Elsevier Publ. Co., Amsterdam, 280 p.Google Scholar
  8. Krumbein, W. C., 1967, FORTRAN IV computer programs for Markov chain experiments in geology: Kansas Geol. Survey Computer Contr. 13, 38 p.Google Scholar
  9. Krumbein, W. C., and Dacey, M. F., 1969, Markov chains and embedded Markov chains in geology: Jour. Intern. Assoc. Math. Geol., v. 1, no. 1, p. 79–96.CrossRefGoogle Scholar
  10. Mann, C. J., 1967, Spectral-density analysis of stratigraphic data, in Colloquium on time-series analysis: Kansas Geol. Survey Computer Contr. 18, p. 41–45.Google Scholar
  11. Merriam, D. F., ed., 1964, Symposium on cyclic sedimentation: Kansas Geol. Survey Bull. 169, 636 p.Google Scholar
  12. Moore, R. C., 1936, Stratigraphic classification of the Pennsylvanian rocks of Kansas: Kansas Geol. Survey Bull. 22, 256 p.Google Scholar
  13. Moore, R. C., 1949, Division of the Pennsylvanian System in Kansas: Kansas Geol. Survey Bull. 83, 203 p.Google Scholar
  14. Moore, R. C., and Merriam, D. F., 1965, Upper Pennsylvanian cyclothems in the Kansas River Valley: Field Conf. Guidebook, Kansas Geol. Survey, 22 p.Google Scholar
  15. Pearn, W. C., 1964, Finding the ideal cyclothem, in Symposium on cyclic sedimentation: Kansas Geol. Survey Bull. 169, p. 399–413.Google Scholar
  16. Preston, F. W., and Henderson, J. H., 1964, Fourier series characterization of cyclic sediments for stratigraphic correlation, in Symposium on cyclic sedimentation: Kansas Geol. Survey Bull. 169, p. 415–425.Google Scholar
  17. Rosenfeld, A., Huang, H. K., and Schneider, V. H., 1968, An application of cluster detection to text and picture processing: Univ. Maryland Computer Science Center, College Park, Md., Office Naval Res. Grant Nonr 5144(00), Tech. Rept. 68–68, 64 p.Google Scholar
  18. Sackin, M. J., and Merriam, D. F., 1969, Autoassociation, a new geological tool: Jour. Intern. Assoc. Math. Geol., v. 1, no. 1, p. 7–16.CrossRefGoogle Scholar
  19. Schwarzacher, W., 1964, An application of statistical time-series analysis of a limestone-shale sequence: Jour. Geology, v. 72, no. 2, p. 195–213.CrossRefGoogle Scholar
  20. Schwarzacher, W., 1967, Some experiments to simulate the Pennsylvanian rock sequence of Kansas, in Colloquium on time-series analysis: Kansas Geol. Survey Computer Contr. 18, p. 5–14.Google Scholar
  21. Schwarzacher, W., 1969, The use of Markov chains in the study of sedimentary cycles: Jour. Intern. Assoc. Math. Geol., v. 1, no. 1, p. 17–39.CrossRefGoogle Scholar
  22. Sokal, R. R., and Sneath, P. H. A., 1963, Principles of numerical taxonomy: W. H. Freeman and Co., San Francisco, 353 p.Google Scholar
  23. Vistelius, A. B., and Feigel’son, T., 1965, The theory of formation of sedimentary beds: Doklady Akad. Nauk SSSR, v. 164, no. 1, p. 158–160.Google Scholar
  24. Weller, J. M., 1930, Cyclical sedimentation of the Pennsylvanian Period and its significance: Jour. Geology, v. 38, p. 97–135.CrossRefGoogle Scholar
  25. Weller, J. M., 1960, Stratigraphic principles and practices: Harper & Bros., New York, 725 p.Google Scholar
  26. Weller, J. M., and Wanless, H. R., 1939, Correlation of minable coals of Illinois, Indiana, and western Kentucky: Am. Assoc. Petroleum Geologists Bull., v. 23, p. 1374–1392.Google Scholar
  27. Zeller, D. E., ed., 1968, The stratigraphic succession in Kansas: Kansas Geol. Survey Bull. 189, 81 p.Google Scholar

Copyright information

© Plenum Press, New York 1972

Authors and Affiliations

  • John C. Davis
    • 1
    • 2
  • J. M. Cocke
    • 1
    • 2
  1. 1.Kansas Geological SurveyUSA
  2. 2.East Tennessee State UniversityUSA

Personalised recommendations