Advertisement

A mathematical model for orientation data from macroscopic conical folds

  • D. Kelker
  • C. W. Langenberg
Article

Abstract

Statistical techniques are developed to classify folds into one of three classes: cylindrical, conical, or neither. A translated version of Bingham's distribution on the sphere is applied to orientation data fron conical folds. Iterative least-squares techniques are used to determine the best-fitting small circle (or cone), and confidence intervals for the cone axis and half apical angle are developed. Examples of a cylindrical and a conical fold are given. Another fold is neither cylindrical nor conical and is classified as pseudoconical. Relationships between the Bingham and Fisher distributions are presented.

Key words

Conical folds orientation data Bingham distribution Fisher distribution statistical inference 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Charlesworth, H. A. K., Langenberg, C. W., and Ramsden, J., 1976, Determining axes, axial planes and sections of macroscopic folds: Can. Jour. Earth Sci., v. 13, no. 1, p. 54–65.Google Scholar
  2. Cruden, D. M. and Charlesworth, H. A. K., 1972, Observations on the numerical determination of axes of cylindrical and conical folds: Geol. Soc. Amer. Bull., v. 83, no. 7, p. 2019–2024.Google Scholar
  3. Cruden, D. M. and Kelker, D., 1978, Simple graphical methods for estimating the confidence region about the orientation of the intersection of two planes: Can. Jour. Earth Sci., v. 15, no. 10, p. 1598–1604.Google Scholar
  4. Fisher, R., 1953, Dispersion on a Sphere: Proc. R. Soc. A., v. 217, p. 295–305.Google Scholar
  5. Gray, N. H., Geiser, P. A., and Geiser, J. R., 1980, On the least-squares fit of small and great circles to spherically projected orientation data: Math. Geol., v. 12, no. 3, p. 173–184.Google Scholar
  6. Haman, P. J., 1961, Manual of stereographic projection: West Canadian Research Publications, Series 1, no. 1, 67 p.Google Scholar
  7. Kelker, D. and Langenberg, C. W., 1976, A mathematical model for orientation data from macroscopic cylindrical folds: Math. Geol. v. 8, no. 5.Google Scholar
  8. Kelley, J. C., 1968, Least squares analysis of tectonite fabric data: Geol. Soc. Amer. Bull., v. 79, no. 2, p. 223–240.Google Scholar
  9. Kendall, M. G. and Stuart, A., 1973, The advanced theory of statistics, Vol. 2: Hafner Publishing Co., New York, p. 723.Google Scholar
  10. Langenberg, C. W., Rondeel, H. E., and Charlesworth, H. A. K., 1977, A structural study in the Belgian Ardennes with sections constructed using computer-based methods: Geol. Mijnbouw, v. 56, no. 2, p. 145–154.Google Scholar
  11. Mardia, K. V., 1972, Statistics of directional data: Academic Press, London/New York, 357 p.Google Scholar
  12. McFadden, P. L., 1980a, The best estimate of Fisher's precision parameter K: Geophy. Jour. Roy. Astr. Soc., v. 60, no. 3, p. 397–407.Google Scholar
  13. McFadden, P. L., 1980b, Simple graphical methods for estimating the confidence region about the orientation of the intersection of two planes: Discussion: Can. Jour. Earth Sci., v. 17, no. 8, p. 1111–1113.Google Scholar
  14. Stauffer, M. R., 1964, The geometry of conical folds: New Zealand Jour. Geol. Geophy., v. 7, p. 340–347.Google Scholar
  15. Stauffer, M. R., 1967, The problem of conical folding around the Barrack Creek Adamellite, Queanbeyan, New South Wales: Jour. Geol. Soc. Australia, v. 14, no. 1, p. 45–56.Google Scholar
  16. Stockmal, G. S., 1979, Structural geology of the northern termination of the Lewis thrust, Front Ranges, Southern Canadian Rocky Mountains: unpublished M.Sc., thesis, University of Calgary.Google Scholar
  17. Watson, G. S., 1965, Equatorial distributions on a sphere: Biometrika, v. 52, p. 193–201.Google Scholar
  18. Woodford, A. O. and McIntyre, D. B., 1976, Curvature of the San Andreas fault, California: Geology, v. 4, p. 573–575.Google Scholar

Copyright information

© Plenum Publishing Corporation 1982

Authors and Affiliations

  • D. Kelker
    • 1
  • C. W. Langenberg
    • 2
  1. 1.Department of Statistics and Applied ProbabilityUniversity of AlbertaEdmontonCanada
  2. 2.Geological Survey DepartmentAlberta Research CouncilEdmontonCanada

Personalised recommendations