Regression models for estimating mineral resources from geological map data

  • C. F. Chung
  • F. P. Agterberg
Article

Abstract

Several regression models can be used for explaining discovered occurrences and estimating undiscovered occurrences of mineral deposits of a given type from geological data quantified for equal-area cells. All the models are based on the assumption that the occurrences of mineral deposits in an area are estimable as a function of the mapable geological attributes in the area. Depending upon further assumptions made with respect to the dependent variable, that is, the occurrence of mineral deposits, different regression techniques such as logistic and Poisson regression analysis can be employed. In this paper, a jackknife method was used to estimate the variances of the regression coefficient and the occurrences. The effect of undiscovered deposits on the regression models was considered by treating the known deposits separately (Separate Event Method).

As an illustrative example, the occurrence of volcanogenic massive sulfide deposits has been expressed in terms of the geological framework in parts of the island of Newfoundland. Each of the models provides a similar and relatively stable pattern that explains the occurrence of the known deposits in a study area of 6000 km2.The methods presented for calculating the variances of the estimated values are meaningful because they can be used to test whether or not an estimated probability or frequency value for any one cell is significantly greater than zero. The logistic model is used to indicate cells outside the study area where undiscovered deposits are likely to occur.

Key words

regression geological map data mineral resources logistic model Poisson regression jackknife method 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Agterberg, F. P., 1974, Geomathematics: Elsevier, Amsterdam, 596 p.Google Scholar
  2. Agterberg, F. P. and David, M., 1979, Statistical exploration,in Weiss, A., ed., Computer methods for the '80s: AIME, New York, pp. 90–115.Google Scholar
  3. Agterberg, F. P. and Robinson, S. C., 1972, Mathematical problems of geology: Bulletin 44, Book 1, International Statistical Institute, pp. 567–595.Google Scholar
  4. Chung, C. F., 1979, A system of interactive graphic programs for multivariate statistical analysis for geological data, Proceeding of the 12th Symposium on Interface: Comp. Sci. Stat., pp. 455–460.Google Scholar
  5. Cox, D. R., 1970, Analysis of binary data: Methuen, London, 142 p.Google Scholar
  6. Goldberger, A. S., 1964, Econometric theory: Wiley, New York, pp. 248–255.Google Scholar
  7. Jorgenson, D. W., 1961, Multiple regression analysis of a Poisson process: Jour. Amer. Stat. Assoc., v. 56, pp. 253–255.Google Scholar
  8. Lachenbruch, P. A., 1974, Discriminant analysis when the initial samples are misclassified; II: Non-random misclassification models: Technometrics, v. 16, pp. 419–424.Google Scholar
  9. Lachenbruch, P. A., 1979, Note on initial misclassification effects on the quadratic discriminant function: Technometrics, 21, no. 1, pp. 129–132.Google Scholar
  10. Leech, G. B., 1975, Project Appalachia, Geol. Sur. Can. Paper 75-1c, p. 121–122.Google Scholar
  11. Miller, R. G., 1974a, An unbalanced jackknife: Ann. Stat., v. 2, no. 2, pp. 880–891.Google Scholar
  12. Miller, R. G., 1974b, The jackknife—a review, Biometrika, v. 61, no. 1, pp. 1–15.Google Scholar
  13. Rao, C. R., 1973, Linear statistical inference and its applications, 2nd ed.: Wiley, New York, pp. 366–374.Google Scholar

Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • C. F. Chung
    • 1
  • F. P. Agterberg
    • 1
  1. 1.Geological Survey of CanadaOttawaCanada

Personalised recommendations