Mathematical Geology

, Volume 26, Issue 5, pp 639–649 | Cite as

Further Comment: Spatial Continuity Measures

  • Robert F. Shurtz
Letter to the Editor


In closing, I think it not inappropriate to make clear—both toReply's authors and to the geostatistical community at large—that my purpose in pressing these issues is not mere whimsical or frivolous harassment.

My purpose is to urge the mining industry, as I have done before (1984), to insist upon reserve estimation methods that are soundly based onall applicable mathematical principles undistorted by speculative interpretation, selection, or practice. My criticism of geostatistics is not so much of what its practitioners do — and of what I first did long ago (1959)—but of the undisciplined and misleading things its pundits say about what they do.


Estimation Method Continuity Measure Mining Industry Mathematical Principle Spatial Continuity 
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  1. Arik, A., 1992, Outlier Restricted Kriging: A New Kriging Algorithm for Handling of Outlier High Grade Data in Ore Reserve Estimation,in Y. C. Kim (Ed.),Proceedings of the 23rd International APCOM Symposium: Society of Mining Engineers, Littleton, CO, p. 181–187.Google Scholar
  2. Armstrong, M., 1984, Common Problems Seen in Variograms: Math. Geol., v. 16, n. 3, p. 305–313.Google Scholar
  3. Barnes, R. J., 1991, The Variogram Sill and the Sample Variance: Math. Geol., v. 23, n. 4, p. 673–678.Google Scholar
  4. Billingsley, P., 1978,Ergodic Theory and Information: Robert E. Krieger Publishing Company, Huntington, NY, 193 p. (reprint of 1965 edition, John Wiley & Sons, New York).Google Scholar
  5. Cramér, H., 1954,Mathematical Methods of Statistics: Princeton University Press, Princeton, NJ, 575 p.Google Scholar
  6. Cressie, N., 1990, The Origins of Kriging: Math. Geol., v. 22, n. 3, p. 239–252.Google Scholar
  7. David, M., 1977,Geostatistical Ore Reserve Estimation: Elsevier Scientific Publishing Company, New York, 364 p.Google Scholar
  8. Deutsch, C. V., 1993, Kriging in a Finite Domain: Math. Geol., v. 25, p. 41–52.Google Scholar
  9. Englund, E. J., 1990, A Variance of Geostatisticians: Math. Geol., v. 22, no. 4, p. 417–455.Google Scholar
  10. Feller, W., 1968,An Introduction to Probability Theory and Its Applications (Vol. 1): John Wiley & Sons, New York, 509 p.Google Scholar
  11. Graybill, F. A., 1961,An Introduction to Linear Statistical Models (Vol. 1): McGraw-Hill Book Company, New York, 463 p.Google Scholar
  12. Isaaks, E. H., and Srivastava, R. M., 1988, Spatial Continuity Measures for Probabilistic and Deterministic Geostatistics: Math. Geol., v. 20, n. 4, p. 313–341.Google Scholar
  13. Isaaks, E. H., and Srivastava, R. M., 1989,An Introduction to Applied Geostatistics: Oxford University Press, New York, 561 p.Google Scholar
  14. Journel, A. G., 1985, The Deterministic Side of Geostatistics: Math. Geol., v. 17, n. 1, p. 1–15.Google Scholar
  15. Journel, A. G., and Huijbregts, CH. J., 1978,Mining Geostatistics: Academic Press, New York, 600 p.Google Scholar
  16. Kac, M., 1959, Statistical Independence in Probability Analysis and Number Theory: The Carus Mathematical Monographs. Number 12, The Mathematical Association of America, 94 p.Google Scholar
  17. Kendall, M. G., 1945, On the Analysis of Oscillatory Time Series: J. Roy. Stat. Soc., n. 108, p. 93.Google Scholar
  18. Kendall, M., Stuart, A., and Ord, J. K., 1983,The Advanced Theory of Statistics (Vol. 3): Macmillan Publishing Co., New York, 780 p.Google Scholar
  19. Korn, G. A., and Korn, T. M., 1968,Mathematical Handbook for Scientists and Engineers: McGraw-Hill Book Company. New York, 1130 p.Google Scholar
  20. Krige, D. G., 1979, Private communication.Google Scholar
  21. Myers, D. E., 1991, Book Review (“Estimating and Choosing” by G. Matheron) Math. Geol., v. 23, n. 3, p. 895–897.Google Scholar
  22. Shurtz, R. F., 1959, The Electronic Computer and Statistics for Predicting Ore Recovery: Mining Engineering, Oct., p. 1035–1044.Google Scholar
  23. Shurtz, R. F., 1984, Discussions APCOM '84: Institution of Mining and Metallurgy, 66 p.Google Scholar
  24. Shurtz, R. F., 1986, Sources and Application of information in Geostatistics, In R. V. Ramani (Ed.),Proceedings of the 19th International APCOM Symposium: Society of Mining Engineers, Littleton, CO, p. 31–42.Google Scholar
  25. Shurtz, R. F., 1988, Spectral Pattern Recognition in Under-Sampled Functions: Math. Geol., v. 20, n. 6, p. 731–751.Google Scholar
  26. Shurtz, R. F., 1991, Comment: A Study of “Probabilistic” and “Deterministic” Geostatistics: Math. Geol., v. 23, n. 3, p. 443–479.Google Scholar
  27. Shurtz, R. F., 1992, Pseudo-Fractal Interpolation for Risk Analysis: Math. Geol., v. 24, n. 1, p. 99–128.Google Scholar
  28. Shurtz, R. F., 1993, Personal communication, R. F. Shurtz to Michel David, March 13, 1993.Google Scholar
  29. Srivastava, R. M., and Isaaks, E. H., 1990, A Reply to “A Study of ‘Probabilistic’ and ‘Deterministic’ Geostatistics’ by Robert F. Shurtz: Math. Geol., v. 23, n. 3, p. 481–495.Google Scholar

Copyright information

© International Association for Mathematical Geology 1994

Authors and Affiliations

  • Robert F. Shurtz
    • 1
  1. 1.San Francisco

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