Advertisement

A Simple Quantitative Technique for Comparing Cyclically Deposited Successions

  • William A. Read
  • Daniel F. Merriam
Chapter
Part of the Computer Applications in the Earth Sciences book series (CAES)

Abstract

This paper introduces a technique for comparing cyclically deposited sedimentary sequences. Each section is coded into a limited number of lithological states and a first-order transition probability matrix is constructed. The elements of this matrix then are rearranged to form a vector. Sections are compared by calculating product-moment correlation coefficients for the appropriate vectors. Single- and unweighted average-linkage cluster analysis are used to cluster the sections on the basis of these correlation coefficients.

The method has been used to classify two different sets of succession data and in each situation the results are readily interpretable in terms of depositional environments. One data set is derived from cored borehole sections through the same uniform paralic-facies succession in the upper part of the Limestone Coal Group (Namurian, E1) and located in the small Kincardine Basin, east of Stirling in central Scotland. The other data set, which is coded in less detail, is derived from a varied series of sections in the Carboniferous of Britain and the USA.

Keywords

Coal Measure Succession Data Delta Lobe Cyclic Sedimentation Linkage Cluster Analysis 
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.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Allen, J. R. L., 1964, Sedimentation in the modern delta of the River Niger, West Africa, in Deltaic and shallow marine deposits: Elsevier Publ. Co., Amsterdam, p. 26–34.CrossRefGoogle 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, Late Quartenary Niger Delta and adjacent areas: Am. Assoc. Petroleum Geologists Bull., v. 49, no. 5, p. 547–600.Google Scholar
  4. Allen, J. R. L., 1970, Sediments of the Niger Delta: a summary and review, in Deltaic sedimentation modern and ancient: Soc. Econ. Paleontologists Mineralogists Sp. Publ., no. 15, p. 138 –151.Google Scholar
  5. Chayes, F., 1960, On correlation between variables of constant sum: Jour. Geophysical Res., v. 65, no. 12, p. 4185–4193.CrossRefGoogle Scholar
  6. Coleman, J. M., and Gagliano, S. M., 1964, Cyclic sedimentation in the Mississippi River deltaic plain: Gulf-Coast Assoc. Geol. Socs. Trans., v. 14, p. 67–80.Google Scholar
  7. Coleman, J. M., and Gagliano, S. M., 1965, Sedimentary structures: Mississippi River deltaic plain, in Primary sedimentary structures and their hydrodynamic interpretation: Soc. Econ. Paleontologists Mineralogists Sp. Publ. No. 12, p. 133–148.Google Scholar
  8. Doveton, J. H., 1971, An application of Markov chain analysis to the Ayrshire Coal Measures succession: Scottish Jour. Geology, v. 7, pt. 1, p. 11–27.CrossRefGoogle Scholar
  9. Duff, P. McL. D., Hallam, A., and Walton, E. K., 1967, Cyclical sedimentation: Elsevier Publ. Co., Amsterdam, 280 p.Google Scholar
  10. 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. 235–255.Google Scholar
  11. Elliott, R. E., 1968, Facies, sedimentation successions and cyclothems in Productive Coal Measures in the East Midlands, Great Britain: Mercian Geologist, v. 2, p. 351–372.Google Scholar
  12. Elliott, R. E., 1969, Deltaic processes and episodes: the interpretation of Productive Coal Measures occurring in the East Midlands, Great Britain:, Mercian Geologist, v. 3, p. 111–135.Google Scholar
  13. Ferm, J. C., 1970, Allegheny deltaic deposits, in Deltaic sedimentation, modern and ancient: Soc. Econ. Paleontologists Mineralogists Sp. Publ. No. 15, p. 246–255.Google Scholar
  14. Ferm. J. C., and Cavaroc, V. V., 1968, A non-marine model for the Allegheny of West Virginia, in Late Paleozoic and Mesozoic continental sedimentation, northeastern North America: Geol. Soc. America Sp. Paper No. 106, p. 1–19.Google Scholar
  15. Ferm. J. C., and Cavaroc, V. V., 1969, A field guide to Allegheny deltaic deposits in the upper Ohio Valley: Ohio Geol. Soc. and Pittsburgh Geol. Soc. Field Guide, 21 p.Google Scholar
  16. Fisher, W. L., Brown, L. F., Scott, A. J., and McGowen, J. H., 1969, Delta systems in the exploration for oil and gas: Bur. Econ. Geol., Univ. Texas at Austin, 212 p.Google Scholar
  17. Fisher, W. L., and McGowen, J. H., 1967, Depositional systems in the Wilcox Group of Texas and their relationships to occurrence of oil and gas: Gulf-Coast Assoc. Geol. Socs. Trans., v. 17, p. 105–125.Google Scholar
  18. Fisher, W. L., and McGowen, J. H., 1969, Depositional systems in the Wilcox Group (Eocene) of Texas and their relationship to occurrence of oil and gas: Am. Assoc. Petroleum Geologists Bull., v. 53, no. 1, p. 30–54.Google Scholar
  19. 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
  20. Fisk, H. N., 1960, Recent Mississippi River sedimentation and peat accumulation: Congres. Avanc. Etud. Stratigr. Carb., p. 187–199.Google Scholar
  21. Fisk, H. N., McFarlan, E., Kolb, C. R., and Wilbert, L. J., 1954, The sedimentary framework of the modern Mississippi delta: Jour. Sed. Pet., v. 24, no. 1, p. 76–99.Google Scholar
  22. Francis, E. H., Forsyth, I. H., Read, W. A., and Armstrong, A., 1970, The geology of the Stirling district: Geol. Surv. U.K., Mem., 357 p.Google Scholar
  23. Frazier, D. E., 1967, Recent deltaic deposits of the Mississippi River: their development and chronology: Gulf-Coast Assoc. Geol. Socs. Trans., v. 17, p. 287–315.Google Scholar
  24. Goodlet, G. A., 1959, Mid-Carboniferous sedimentation in the Midland Valley of Scotland: Edinburgh Geol. Soc. Trans., v. 17, pt. 3, p. 217–240.Google Scholar
  25. Harbaugh, J. W., and Merriam, D. F., 1968, Computer applications in stratigraphic analysis: John Wiley & Sons, New York, 282 p.Google Scholar
  26. Kanes, W. H., 1970, Facies and development of the Colorado River Delta in Texas: in Deltaic sedimentation modern and ancient: Soc. Econ. Paleontologists Mineralogists Sp. Publ. No. 15, p. 78–106.Google Scholar
  27. Krumbein, W. C., 1962, Open and closed number systems in stratigraphic mapping: Am. Assoc. Petroleum Geologists Bull., v. 46, no. 12, p. 2229–2245.Google Scholar
  28. Krumbein, W. C., 1967, FORTRAN IV computer programs for Markov chain experiments in geology: Kansas Geol. Survey Computer Contr. 13, 38 p.Google Scholar
  29. Krumbein, W. C., and Scherer, W., 1970, Structuring of observational data for Markov and semi-Markov models in geology: Office Naval Res. Tech. Rep. 15, 59 p.Google Scholar
  30. Merriam, D. F., 1970, Comparison of British and American Carboniferous cyclic rock sequences: Jour. Intern. Assoc. Math. Geology v. 2, no. 3, p. 241–264.CrossRefGoogle Scholar
  31. Merriam, D. F., and Sneath, P. H. A., 1967, Comparison of cyclic rock sequences using cross-association, in Essays in paleontology and stratigraphy: Kansas Univ. Dept. Geol. Sp. Publ. 2, p. 521–538.Google Scholar
  32. Mitchell, G. H., and Stubblefield, C. J., 1948, The geology of the Leicestershire and South Derbyshire Coalfield: Geol. Survey of Gt. Britain Wartime Pamphlet, No. 22, 2nd ed., 46 p.Google Scholar
  33. Moore, D., 1958, The Yoredale Series of upper Wensleydale and adjacent parts of northwest Yorkshire: Yorkshire Geol. Soc. Proc., v. 31, pt. 2, no. 5, p. 91–148.Google Scholar
  34. Moore, D., 1959, Role of deltas in the formation of some British Lower Carboniferous cyclothems: Jour. Geology, v. 67, no. 5, p. 522–539.CrossRefGoogle Scholar
  35. Morris, D. A., 1967, Lower Conemaugh (Pennsylvanian) depositional environments and paleogeography in the Appalachian Coal Basin: Unpubl. doctoral dissertation, Kansas Univ., 521 p.Google Scholar
  36. Oomkens, E., 1967, Depositional sequences and sand distribution in a deltaic complex: Geologie Mijnb., v. 46, p. 265–278.Google Scholar
  37. Oomkens, E., 1970, Depositional sequences and sand distribution in the postglacial Rhone Delta complex, in Deltaic sedimentation modern and ancient: Soc. Econ. Paleontologists Mineralogists Sp. Publ. No. 15, p. 198–212.Google Scholar
  38. Parks, J. M., 1966, Cluster analysis applied to multivariate geologic problems: Jour. Geology, v$174, no. 5, pt. 2, p. 703–715.Google Scholar
  39. Potter, P. E., and Blakely, R. F., 1968, Random processes and lithological transitions: Jour. Geology, v. 76, no. 2, p. 154–170.Google Scholar
  40. Read, W. A., 1961, Aberrant cyclic sedimentation in the Limestone Coal Group of the Stirling Coalfield: Edinburgh Geol. Soc. Trans., v. 18, p. 271–292.MathSciNetGoogle Scholar
  41. Read, W. A., 1965, Shoreward facies changes and their relation to cyclical sedimentation in part of the Namurian east of Stirling, Scotland: Scottish Jour. Geology, v. 1, pt. 1, p. 69–92.CrossRefGoogle Scholar
  42. Read, W. A., 1969a, Fluviatile deposits in Namurian rocks of central Scotland: Geol. Mag., v. 106, p. 331–347.Google Scholar
  43. Read, W. A., 1969b, Analysis and simulation of Namurian sediments in central Scotland using a Markov-process model: Jour. Intern. Assoc. Math. Geology, v. 1, no. 2, p. 199–219.MathSciNetCrossRefGoogle Scholar
  44. Read, W. A., 1970, Cyclically-deposited Namurian sediments east of Stirling, Scotland: Unpubl. doctoral dissertation, Univ. London, 273 p.Google Scholar
  45. 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
  46. 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
  47. Read, W. A., Dean, J. M., and Cole, A. J., 1971, Some Namurian (E2) paralic sediments in central Scotland: an investigation of depositional environment and facies changes using iterativefit trend-surface analysis: Geol. Soc. London Jour., v. 127, pt. 2, p. 137–176.CrossRefGoogle Scholar
  48. Read, W. A., and Sackin, M. J., in press, A quantitative comparison using cross-association of vertical sections of Namurian (E1) paralic deposits in the Kincardine Basin, east of Stirling, Scotland: Inst. Geol. Sei., Rept. No. 71/14, 21 p.Google Scholar
  49. Robertson, T., 1948, Rhythm in sedimentation and its interpretation with particular reference to the Carboniferous sequences: Edinburgh Geol. Soc. Trans., v. 14, p. 141–175.Google Scholar
  50. 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
  51. Schwarzacher, W., 1967, Some experiments to simulate the Pennsylvanian rock sequence of Kansas: Kansas Geol. Survey Computer Contr. 18, p. 5–14.Google Scholar
  52. Schwarzacher, W., 1969, The use of Markov chains in the study of sedimentary cycles: Jour. Intern. Assoc. Math. Geology, v. 1, no. 1, p. 17–39.CrossRefGoogle Scholar
  53. Selley, R. C., 1970, Studies of sequence in sediments using a simple mathematical device: Geol. Soc. London Quart. Jour., v. 125, p. 557–575.CrossRefGoogle Scholar
  54. Sokal, R. R., and Sneath, P. H. A., 1963, Principles of numerical taxonomy: W.H. Freeman and Co., San Francisco, 359 p.Google Scholar
  55. Wanless, H. R., and others, 1970, Late Paleozoic deltas in the central and eastern United States, in Deltaic sedimentation modern and ancient: Soc. Econ. Paleontologists Mineralogists Sp. Publ., No. 15, p. 215–245.Google Scholar
  56. Weller, J. M., 1958, Cyclothems and larger sedimentary cycles of the Pennsylvanian: Jour. Geology, v. 66, no. 2, p. 195–207.CrossRefGoogle Scholar
  57. Williams, E. G., and Ferm, J. C., 1964, Sedimentary facies in the Lower Allegheny rocks of western Pennsylvania: Jour. Sed. Pet., v. 34, no. 3, p. 610–614.Google Scholar

Copyright information

© Plenum Press, New York 1972

Authors and Affiliations

  • William A. Read
    • 1
    • 2
  • Daniel F. Merriam
    • 1
    • 2
  1. 1.Kansas Geological SurveyUSA
  2. 2.Syracuse UniversityUSA

Personalised recommendations