Abstract
This paper is concerned with the lognormal, and its logbinomial approximation, in connection with a three-parameter version of the model of de Wijs. The three parameters are: overall average element concentration value (ξ), dispersion index (d), and apparent number of subdivisions of the environment (N). Multifractal theory produces new methods for estimating the parameters of this model. In practical applications, the frequency distribution of element concentration values for small rock samples is related to self-similar spatial variability patterns of the element in large regions or segments of the Earth's crust. The approach is illustrated by application to spatial variability of gold and arsenic in glacial till samples from southern Saskatchewan. It is shown that for these two elements the model of de Wijs is satisfied on a regional scale but degree of dispersion decreases rapidly toward the local, sample-size scale. Thus the apparent number of subdivisions (N) is considerably less than would be expected if degree of dispersion were to extend from regional to local scale. A random-cut variant of the model of de Wijs produces an empirical frequency distribution of relative element concentration values that can be related to random dispersion index
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References
Agterberg, F. P., 1984, Use of spatial analysis in mineral resource evaluation: Math. Geol., v. 16, no. 6, p. 565–589.
Agterberg, F. P., 1994, Fractals, multifractals, and change of support, in Dimitrakopoulos, R., ed., Geostatistics for the next century: Kluwer, Dordrecht, p. 223–234.
Agterberg, F. P., 2001a, Multifractal simulation of geochemical map patterns, in Merriam, D. F. and Davis, J. C., Geologic modeling and simulation: Sedimentary Systems: Kluwer, New York, p. 327–346.
Agterberg, F. P., 2001b, Aspects of multifractal modelling: Proceedings of IAMG Annual Meeting, Cancun, September, 2001, CD Rom.
Agterberg, 2005, Application of a three-parameter version of the model of de Wijs in regional geochemistry: Proceedings of IAMG' 05 held in Toronto, Canada, August 21–26, 2005, China University of Geosciences Printing House, Wuhan, China, v. 1, p. 291–296.
Ahrens, L. H., 1953, A fundamental law of geochemistry: Nature, v. 172, p. 1148.
Aitchison, J., and Brown, J. A. C., 1957, The lognormal distribution: Cambridge University Press, Cambridge, 176 p.
Allègre, C. J. U., and Lewin, E., 1995, Scaling laws and geochemical distributions: Earth Planet. Sci. Lett., v. 132, p. 1–13.
Brinck, J. W., 1974, The geochemical distribution of uranium as a primary criterion for the formation of ore deposits, in: Chemical and physical mechanisms in the formation of uranium mineralization, geochronology, isotope geology and mineralization: International Atomic Energy Agency Proceedings Series, no. STI/PUB/374, p. 21–32.
Cheng, Q., 1994, Multifractal modelling and spatial analysis with GIS: gold potential estimation in the Mitchell-Sulphurets Area, northwestern British Columbia: Unpublished doctoral thesis, University of Ottawa, Canada, 268 p.
Cheng, Q., 2001, Selection of multifractal scaling breaks and separation of geochemical and geophysical anomaly: Jour. China Univ. of Geosc., v. 12, p. 54–59.
Cheng, Q., and Agterberg, F. P., 1996, Multifractal modeling and spatial statistics: Math. Geol., v. 28, no. 1, p. 1–16.
Cheng, Q., Agterberg, F. P., and Ballantyne, S. B., 1994, The separation of geochemical anomalies from background by fractal methods: J. Geochem. Explor., v. 51, no. 2, p. 109–130.
De Wijs, H. J., 1951, Statistics of ore distribution, part I: Geologie en Mijnbouw, v. 13, p. 365–375.
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.
Falconer, K., 2003, Fractal geometry—mathematical foundations and applications (2nd ed.): Wiley, New York, 337 p.
Feder, J., 1988, Fractals: Plenum, New York, 283 p.
Garrett, R. G., 1986, Geochemical abundance models: an update, 1975 to 1987: U.S. Geological Survey Circular 980, p. 207–220.
Garrett, R. G., and Thorleifson, L. H., 1995, Kimberlite indicator mineral and till geochemical reconnaissance, southern Saskatchewan: Geological Survey of Canada Open File 3119, p. 227–253.
Gonçalves, M. A., 2001, Characterization of geochemical distributions using multifractal models: Math. Geol., v. 33, no. 1, p. 41–61.
Grunsky, E. C., 2005, Assessment of geochemical data—Strategies for evaluation and interpretation: Proceedings of IAMG' 05 held in Toronto, Canada, August 21–26, 2005, China University of Geosciences Printing House, Wuhan, China, v. 1, p. 1–14.
Harris, DeVerle P., 1984, Mineral Resources Appraisal: Clarendon Press, Oxford, 445 p.
Krige, D. G., 1966, A study of gold and uranium distribution patterns in the Klerksdorp gold field: Geoexploration, v. 4, p. 43–53.
Lovejoy, S., and Schertzer, D., 1991, Multifractal analysis techniques and the rain and cloud fields from 10-3 to 106 m, in Schertzer, D. and Lovejoy, S., eds., Non-linear variability in geophysics: Kluwer, Dordrecht, p. 111–144.
Mandelbrot, B. B., 1983, The fractal geometry of nature (updated and augmented edition): W. H. Freeman and Company, New York, 468 p.
Matheron, G., 1962, Traité de géostatistique appliquée: Mém. Bur. Rech. Géol. Minières, v. 14, p. 1–333.
Matheron, G., 1974, Les functions de transfert des petites panneaux: Note Géostatistique 127, Centre de Morphologie Mathématique, Fontainebleau, France.
Ruzicka, V., 1976, Uranium resources evaluation model as an exploration tool—exploration for uranium deposits: International Agency for Atomic Energy Proceedings Series, no. 434, p. 673–682.
Schertzer, D., Lovejoy, S., Schmitt, F., Chigirinskaya, Y., and Marsan, D., 1997, Multifractal cascade dynamics and turbulent intermittency: Fractals, v. 5, no. 3, p. 427–471.
Sinclair, A. J., 1991, A fundamental approach to threshold estimation in exploration geochemistry: probability plots revisited: J. Geochem. Explor., v. 41, no. 1, p. 1–22.
Turcotte, D. L., 2002, Fractals in petrology: Lithos, v. 65, nos. 3–4, p. 261–271.
Vistelius, A. B., 1960, The skew frequency distributions and the fundamental law of geochemical processes: J. Geology, v. 68, no. 1, p. 1–22.
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Agterberg, F. New Applications of the Model of de Wijs in Regional Geochemistry. Math Geol 39, 1–25 (2007). https://doi.org/10.1007/s11004-006-9063-7
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DOI: https://doi.org/10.1007/s11004-006-9063-7