Mathematical Geology

, Volume 21, Issue 2, pp 233–254 | Cite as

Measures of variability for geological data

  • D. F. Watson
  • G. M. Philip


Diverse global and local measures of variability appear in the geological literature and, along with methods used to apply them, have been subject to some debate. Measures of variability for three data types—replicate, locational, and compositional—are considered; the source and nature of the variability determine the appropriate type of measure. To illustrate the effects of these measures and expose their inadequacy when improperly applied, the variability of a three-column data set is interpreted under three different suppositions. Geologists need to be aware of the confusion and misleading results that can develop from the use of variance as a measure of variability for locational or compositional data.

Key words

Compositional data locational data replicate data statistics taxonomy topography variance 


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  1. Agterberg, F. P., 1964, Methods of Trend Surface Analysis: Colorado School Mines Q., v. 59, p. 111–130.Google Scholar
  2. Agterberg, F. P., 1974, Geomathematics: Elsevier, Amsterdam, 596 p.Google Scholar
  3. Aitchison, John, 1984, The Statistical Analysis of Geochemical Compositions: Math. Geol., v. 16, p. 531–564.Google Scholar
  4. Chayes, Felix, 1964, Variance-Covariance Relations in Some Published Harker Diagrams of Volcanic Suites: J. Petrol., v. 5, p. 219–237.Google Scholar
  5. Davis, John C., 1975, Contouring Algorithms: p. 352– B. T. Aangeenburg (ed.), Proceedings, Second International Symposium on Computer Assisted Cartography: American Congress on Surveying and Mapping.Google Scholar
  6. Davis, John C., 1986, Statistics and Data Analysis in Geology, 2nd ed.: John Wiley & Sons, New York, 646 p.Google Scholar
  7. Fisher, R. A., 1953, Disperion on a Sphere: Proc. R. Soc. Lond., Ser. A, v. 217, p. 295–305.Google Scholar
  8. Imbrie, J., and Purdy, E. G., 1962, Classification of Modern Bahamian Carbonate Sediments: Am. Assoc. Petrol. Geol., Mem. 1, p. 253–272.Google Scholar
  9. Koch, George S. Jr., and Link, Richard F., 1970, Statistical Analysis of Geological Data, v. 1: John Wiley & Sons, New York, 375 p.Google Scholar
  10. Koch, George S., Jr., and Link, Richard F., 1971, Statistical Analysis of Geological Data, v. 2: John Wiley & Sons, New York, 438 p.Google Scholar
  11. Krumbein, W. C., 1956, Regional and Local Components in Facies Maps: Bull. Amer. Assoc. Petrol. Geol., v. 40, p. 2163–2194.Google Scholar
  12. Matheron, G., 1963, Principles of Geostatistics: Econ. Geol., v. 58, p. 1246–1266.Google Scholar
  13. Matheron, G., 1970, Random Functions and Their Application in Geology: p. 79–87in Daniel F. Merriam, (ed.), Geostatistics a Colloquium: Plenum Press, New York.Google Scholar
  14. Matheron, G., 1986, Philipian/Watsonian High (Flying) Philosophy: Math. Geol., v. 18, p. 503–504.Google Scholar
  15. Matheron, G., 1987, A Simple Answer to an Elementary Question: Math. Geol., v. 19, p. 455–457.Google Scholar
  16. Philip, G. M., and Watson, D. F., 1986, A Method for Assessing Local Variation Among Scattered Measurements: Math. Geol., v. 18, p. 759–764.Google Scholar
  17. Philip, G. M., and Watson, D. F., 1987a, Neighborhood Discontinuities in Bivariate Interpolation of Scattered Observations: Math. Geol., v. 19, p. 69–74.Google Scholar
  18. Philip, G. M., and Watson, D. F., 1987b, How Ore Reserves Can Be Overestimated Through Computational Methods: Resources and Reserves Symposium, Sydney, Nov. 1987: Australasian Institute of Mining and Metallurgy, p. 49–58.Google Scholar
  19. Philip, G. M., and Watson, D. F., 1987c, Probabilism in Geological Data Analysis: Geol. Mag., v. 124, p. 577–583.Google Scholar
  20. Philip, G. M., and Watson, D. F., 1988a, Determining the Representative Composition of a Set of Sandstone Samples: Geol. Mag., v. 125, p. 267–272.Google Scholar
  21. Philip, G. M., and Watson, D. F., 1988b, Angles Measure Compositional Differences: Geology, v. 16, p. 976–979.Google Scholar
  22. Philip, G. M., and Watson, D. F., 1988c, Some Geometric Aspects of the Ternary Diagram: J. Geol. Education, to appear.Google Scholar
  23. Philip, G. M., Skilbeck, C. Gregory, and Watson, D. F., 1987, Algebraic Dispersion Fields on Ternary Diagrams: Math. Geol., v. 19, p. 171–181.Google Scholar
  24. Srivastava, R. M., 1987, Minimum Variance or Maximum Profitability? CIM Bull., v. 80, p. 63–68.Google Scholar
  25. Watson, D. F., 1985, Natural Neighbor Sorting: Aust. Comput. J., v. 17, p. 189–193.Google Scholar
  26. Watson, D. F., 1988a, Natural Neighbor Sorting on then-Dimensional Sphere: Pattern Recognition, v. 21, p. 63–67.Google Scholar
  27. Watson, D. F., 1988b, Practicaln-Dimensional Convex Hulls: in press.Google Scholar
  28. Watson, D. F., and Philip, G. M., 1984, Triangle Based Interpolation: Math. Geol., v. 16, p. 779–795.Google Scholar
  29. Watson, D. F., and Philip, G. M., 1987, Neighborhood Based Interpolation: Geobyte, v. 2, n. 2, p. 12–16.Google Scholar
  30. Watson, D. F., and Philip, G. M., 1988, Discrete Sample Density Description Using Natural Neighbour Relationships: in press.Google Scholar
  31. Watson, Geoffrey S., 1966, The Statistics of Orientation Data: J. Geol., v. 74, p. 786–797.Google Scholar
  32. Whitten, E. H. T., Bornhorst, T. J., Li, G., Hicks, D. L., and Beckwith, J. P., 1987, Suites, Subdivision of Batholiths, and Igneous-Rock Classification: Geological and Mathematical Conceptualization: Amer. J. Sci., v. 287, p. 332–352.Google Scholar
  33. Woronow, Alex, 1987, Book Review: The Statistical Analysis of Compositional Data by J. Aitchison, Math. Geol., v. 19, p. 579–581.Google Scholar
  34. Yates, S. R., Warrick, A. W., and Myers, D. E., 1986, A Disjunctive Kriging Program for Two Dimensions: Comput. Geosci., v. 12, p. 281–313.Google Scholar
  35. Young, G. S., Pielke, R. A., and Kessler, R. C., 1984, A comparison of the terrain height variance spectra of the Front Range with that of a hypothetical mountain: J. Atmos. Sci., v. 41, p. 1249–1250.Google Scholar

Copyright information

© International Association for Mathematical Geology 1989

Authors and Affiliations

  • D. F. Watson
    • 1
  • G. M. Philip
    • 2
  1. 1.The Earth Resources FoundationThe University of SydneySydneyAustralia
  2. 2.GlebeAustralia

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