地球化学图纹理的多重分形模拟

Frederik P.Agterberg

Volume 26 Issue 2

Mar. 2001

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Frederik P. Agterberg, 2001. MULTIFRACTAL SIMULATION OF GEOCHEMICAL MAP PATTERNS. Earth Science, 26(2): 142-151.

Citation:

Frederik P. Agterberg, 2001. MULTIFRACTAL SIMULATION OF GEOCHEMICAL MAP PATTERNS. Earth Science, 26(2): 142-151.

Frederik P. Agterberg, 2001. MULTIFRACTAL SIMULATION OF GEOCHEMICAL MAP PATTERNS. Earth Science, 26(2): 142-151.

Citation:

Frederik P. Agterberg, 2001. MULTIFRACTAL SIMULATION OF GEOCHEMICAL MAP PATTERNS. Earth Science, 26(2): 142-151.

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MULTIFRACTAL SIMULATION OF GEOCHEMICAL MAP PATTERNS

Frederik P. Agterberg

Geological Survey of Canada, 601 Booth Street, Ottawa, K1A 0E8, Canada

Received Date: 2001-02-18
Publish Date: 2001-04-25

Abstract

Abstract

Using a simple multifractal model based on the model De Wijs, 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 2-dimensional trend pattern and by mixing it with a constant concentration value model. It is investigated how such distortions change the multifractal spectrum estimated by means of the 3-step method of moments. Discrete and continuous frequency distribution models are derived for patterns that satisfy the model of De Wijs. These simulated patterns satisfy a discrete frequency distribution model that as upper bound has a continuous frequency distribution to which it approaches in form when the subdivisions of the multiplicative cascade model are repeated indefinitely. This limiting distribution is lognormal in the center and has Pareto tails. Potentially, this approach has important implications in mineral and oil resource evaluation.
- Fractal,
- multifractal,
- model of De Wijs,
- geochemistry,
- map pattern,
- computer simulation.

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References(25)

References

[1]	Feder J. Fractals [M ]. NewYork: Plenum, 1988.283.
[2]	Lovejoy S, Schertzer D. Multifractals, universality classes, and satellite and radar measurements of cloud and rain fields[J]. Jour Geophys Res, 1990, 95 (D3): 2021~2034. doi: 10.1029/JD095iD03p02021
[3]	Stanley H E, Meakin P. Multifractal phenomena in physics and chemistry[J]. Nature, 1998, 335 (6189): 405 ~409.
[4]	Herzfeld U C. Fractals in geosciences-challenges and concerns [A]. In: Davis J C, Herzfeld U C, eds. International Assoc Math Geol Studies in Mathematical Geology[C]. New York: Oxford Univ Press, 1993.176~230.
[5]	Herzfeld U C, Kim I I, Orcutt J A. Is the ocean floor a fractal?[J]. Mathematical Geology, 1995, 27 (3): 421~442. doi: 10.1007/BF02084611
[6]	Herzfeld U C, Overbeck C. Analysis and simulation of scale-dependent fractal surfaces with application to seafloor morphology[J]. Computers & Geosciences, 1999, 25 (9): 979~1007.
[7]	Evertsz C J G, Mandelbrot B B. Multifractal measures (Appendix B) [A]. In: Peitgen H -O, Jurgens H, Saupe D, eds. Chaos and fractals[C]. New York: Springer Verlag, 1992.922~953.
[8]	Agterberg F P. Fractals, multifractals, and change of support [A]. In: Dimitrakopoulos R, ed. Geostatistics for the next century[C]. Dordrecht: Kluwer, 1994.223~234.
[9]	De Wijs H J. Statistics of ore distribution[J]. Geologie en Mijnbouw, 1951, 13: 365~375.
[10]	Matheron G. Traité de Géostatistique Appliquée. Mémoires Bur Rech[J]. GéolMinières, 196 2, 14: 33.
[11]	Cheng Q, Agterberg F P. Multifractal modeling and spatial statistics[J]. Mathematical Geol, 1996, 28 (1): 1~16. doi: 10.1007/BF02273520
[12]	Krige D G. Lognormal-De wijsian geostatistics for ore evaluation [M ]. Johannesburg: South African Inst Mining Metall, 1978.50.
[13]	Cheng Q, Agterberg F P, Balantyne S B. The separation of geochemical anomalies from background by fractal methods[J]. Jour Geochem Exploration, 1994, 51: 109~130. doi: 10.1016/0375-6742(94)90013-2
[14]	Agterberg F P. Multifractal modeling of the sizes and grades of giant and supergiant deposits[J]. International Geology Review, 1995, 37 (1): 1~8. doi: 10.1080/00206819509465388
[15]	Harris D P. Mineral resources appraisal [M ]. Oxford: Clarendon Press, 1984.445.
[16]	Cargill S M, Root D H, Bailey E H. Estimating usable resources from historical industry data[J]. Economic Geol, 1981, 84: 10811095.
[17]	Lee P J. Statistical methods for estimating petroleum resources [M ]. Taiwan: Department of Earth Sciences, National Cheng Kung University, 1999.270.
[18]	Drew L J, Schuenemeyer J H, Bawiec W J. Estimation of the future rates of oil and gas discoveries in the western gulf of Mexico[J]. US Geol Survey Profess Paper, 1982, 1252: 26.
[19]	Meneveau C, Sreenivasan K R. Simple multifractal cascade model for fully developed turbulence[J]. Phys Review Letters, 1987, 59: 424~1427.
[20]	Schertzer D, Lovejoy S, Schmitt F, et al. Multifractal cascade dynamics and turbulent intermittency[J]. Fractals, 1997, 5 (3): 427~471. doi: 10.1142/S0218348X97000371
[21]	Cheng Q. Multifractal modelling and spatial analysis with GIS: gold potential estimation in the Mitchell-Sulphurets area, nort western British Columbia[D]. Canada: University of Ottawa, 1994.268.
[22]	Sim B B L, Agterberg F P, Beaudry Ch. Determining the cutoff between background and relative base metal smelter contamination levels using multifractals methods[J]. Computers & Geosciences, 1999, 25 (7): 1023~1041.
[23]	Switzer P, McBride S. Modeling indoor air pollution using superposition[J]. Bulletin International Statistical Institute, Tome LVIII, 1999, Book2: 501~504.
[24]	Agterberg F P. Discussion of "Statistical aspects of physical and environmental science"[J]. Bulletin International Statistical Institute, Tome 58, 1999, Book3: 213~214.
[25]	Agterberg F P, Cheng Q, Wright D F. Fractal modeling of mineral deposits [A]. In: Elbrond J, Tang X, eds. Proceedings, APCOM XXIV, international symposium on the application of computers and operations research in the mineral industries[C]. Montréal, Canada: Canad Inst Mining Metall, 1993.43~53.