Multifractal Simulation of Geochemical Map Patterns

  • Frederik P. Agterberg
Part of the Computer Applications in the Earth Sciences book series (CAES)


Using a simple multifractal model based on the De Wijs model, various geochemical map patterns for element concentration values are being simulated. Each pattern is self-similar on the average in that a similar pattern can be derived by application of the multiplicative cascade model used to any small subarea on the pattern. In other experiments, the original, self-similar pattern is distorted by superimposing a 2dimensional trend pattern and by mixing it with a constant concentration value model. It is investigated how such distortions change the multifractal spectrum estimated by the 3-step method of moments.


Fractal Dimension Multifractal Spectrum Histogram Method Singularity Exponent Geochemical Pattern 
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  1. Agterberg, F.P., 1994, Fractals, multifractals, and change of support, in Dimitrakopoulos, R., ed., Geostatistics for the next century: Kluwer, Dordrecht, p. 223–234.CrossRefGoogle Scholar
  2. Agterberg, F.P., 1995, Multifractal modeling of the sizes and grades of giant and supergiant deposits: Intern. Geology Review, v. 37, no. 1, p 1–8.CrossRefGoogle Scholar
  3. Agterberg, F.P., 1999, Discussion of “Statistical Aspects of Physical and Environmental Science:” Bull. Intern. Statistical Inst., Tome 58 (Book 3), p. 213–214.Google Scholar
  4. Agterberg, F.P., Cheng, Q., and Wright, D.F., 1993, Fractal modeling of mineral deposits, in Elbrond, J. and Tang, X, eds., Proc., APCOM XXIV, Intern. Symp. Application of Computers and Operations Research in the Mineral Industries: Can. Inst. Mining Metall. (Montréal, Canada), p. 43–53.Google Scholar
  5. Cargill, S.M., Root, D.H., and Bailey, E.H., 1981, Estimating usable resources from historical industry data: Economic Geology, v. 76, no. 5, p. 1081–1095.CrossRefGoogle Scholar
  6. Cheng, Q., 1994, Multifractal modelling and spatial analysis with GIS: gold potential estimation in the Mitchell-Sulphurets area, northwestern British Columbia: unpubl. doctoral dissertation, Univ. Ottawa, 268 p.Google Scholar
  7. Cheng, Q., and Agterberg, F.P., 1996, Multifractal modeling and spatial statistics: Math. Geology, v. 28, no. 1 p. 1–16.Google Scholar
  8. Cheng, Q., Agterberg, F.P., and Ballantyne, S.B., 1994, The separation of geochemical anomalies from background by fractal methods: Jour. Geochem. Exploration, v. 51, no. 2, p. 109–130.CrossRefGoogle Scholar
  9. De Wijs, H.J., 1951, Statistics of ore distribution: Geologie en Mijnbouw, v. 13, p. 365–375.Google Scholar
  10. Drew, L.J., Schuenemeyer, J.H., and Bawiec, W.J., 1982, Estimation of the future rates of oil and gas discoveries in the western Gulf of Mexico: U.S. Geol. Survey Prof. Paper 1252, 26 p.Google Scholar
  11. Evertsz, C.J.G., and Mandelbrot, B.B., 1992, Multifractal measures (Appendix B), in Peitgen, H.-O., Jurgens, H., and Saupe, D., eds., Chaos and fractals: Springer Verlag, New York, p. 922–953.Google Scholar
  12. Feder, J., 1988, Fractals: Plenum, New York, 283 p.CrossRefGoogle Scholar
  13. Harris, D.P., 1984, Mineral Resources Appraisal: Clarendon Press, Oxford, 445 p.Google Scholar
  14. Herzfeld, U.C., 1993, Fractals in geosciences - challenges and concerns, in Davis, J.C., and Herzfeld, U.C., Computers in geology: 25 years of progress: Intern. Assoc. Math. Geology Studies in Mathematical Geology, no. 5, Oxford Univ. Press, New York, p. 176–230.Google Scholar
  15. Herzfeld, U.C., Kim, I.I., and Orcutt, J.A., 1995, Is the ocean floor a fractal?: Math. Geology, v. 27, no. 3, p. 421–442.CrossRefGoogle Scholar
  16. Herzfeld, U.C., and Overbeck, C., 1999, Analysis and simulation of scale-dependent fractal surfaces with application to seafloor morphology: Computers & Geosciences, v. 25, no. 9, p. 979–1007.CrossRefGoogle Scholar
  17. Krige, D.G., 1978, Lognormal-de Wijsian geostatistics for ore evaluation: South African Inst. Mining Metall. Johannesburg, 50 p.Google Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Frederik P. Agterberg
    • 1
  1. 1.Geological Survey of CanadaOttawaCanada

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