Advanced Search

Indexed by SCI、CA、РЖ、PA、CSA、ZR、etc .

Volume 12 Issue 1
Mar 2001
Turn off MathJax
Article Contents
Frederik P Agterberg. Multifractal Simulation of Geochemical Map Patterns. Journal of Earth Science, 2001, 12(1): 31-39.
Citation: Frederik P Agterberg. Multifractal Simulation of Geochemical Map Patterns. Journal of Earth Science, 2001, 12(1): 31-39.

Multifractal Simulation of Geochemical Map Patterns

Funds:

the NSERC project Canada

  • Received Date: 20 Feb 2001
  • Accepted Date: 02 Mar 2001
  • Available Online: 17 Aug 2022
  • Issue Publish Date: 30 Mar 2001
  • 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.

     

  • loading
  • Agterberg F P, 1994. Fractals, Multifractals, and Change of Support. In: Dimitrakopoulos R, ed. Geostatistics for the Next Century. Dordrecht: Kluwer. 223-234
    Agterberg F P, 1995. Multifractal Modeling of the Sizes and Grades of Giant and Supergiant Deposits. Intermational Geology Review, 37(1): 1-8 doi: 10.1080/00206819509465388
    Agterberg F P, 1999. Discussion of "Statistical Aspects of Physical and Environmental Science". Bulletin International Statistical Institute, Tome 58 (Book 3): 213-214
    Agterberg F P, Cheng Q, Wright D F, 1993. Fractal Modeling of Mineral Deposits. In: EIbrond J, Tang X, eds. Proceedings, APCOM XXIV, International Symposium on the Application of Computers and Operations Research in the Mineral Industries. Montreal, Canada: Canad Inst Mining Metall. 43-53
    Cargill S M, Root D H, Bailey E H, 1981. Estimating Usable Resources from Historical Industry Data. Economic Geol, 84: 1081-1095
    Cheng Q, 1994. Multifractal Modelling and Spatial Analysis with GIS: Gold Potential Estimation in the Mitchell-Sulphurets Area, Nortwestern British Columbia: [ Dissertation. ]. Canada: University of Ottawa. 268
    Cheng Q, Agterberg F P, 1996. Multifractal Modeling and Spatial Statistics. Mathematical Geol, 28(1): 1-16 doi: 10.1007/BF02273520
    Cheng Q, Agterberg F P, Balantyne S B, 1994. The Separation of Geochemical Anomalies from Background by Fractal Methods. Jour Geochem Exploration, 51: 109-130 doi: 10.1016/0375-6742(94)90013-2
    De Wijs H J, 1951. Statistics of Ore Distribution. Geologie en Mijnbouw, 13: 365-375
    Drew LJ, Schuenemeyer J H, Bawiec W J, 1982. Estimation of the Future Rates of Oil and Gas Discoveries in the Western Gulf of Mexico. US Geol Survey Prof Paper 1252, 26
    Evertsz CJ G, Mandelbrot B B, 1992. Multifractal Measures (Appendix B). In: Peitgen HO, Jurgens H, Saupe D, eds. Chaos and Fractals. New York: Springer-Verlag. 922-953
    Feder J, 1988. Fractals. New York: Plenum. 283
    Harris D P, 1984. Mineral Resources Appraisal. Oxford, U K: Clarendon Press. 445
    Herzfeld U C, 1993. Fractals in Geosciences-Challenges and Concerns. In: Davis J C, Herzfeld U C, eds. Computers in Geology: 25 Years of Progress: International Assoc Math Geol Studies in Mathematical Geology, no. 5. New York: Oxford Univ Press. 176-230
    Herzfeld U C, Overbeck C, 1999. Analysis and Simulation of Scale-Dependent Fractal Surfaces with Application to Seafloor Morphology. Computers & Geosciences, 25(9): 979-1007
    Herzfeld U C, KimI I, OrcuttJ A, 1995. Is the Ocean Floor a Fractal? Mathematical Geology, 27(3): 421-442 doi: 10.1007/BF02084611
    Krige D G, 1978. Lognormal-De Wijsian Geostatistics for Ore Evaluation. Johannesburg: . South African Inst Mining Metall. 50
    Lee P J, 1999. Statistical Methods for Estimating Petroleum Resources. Tainan: Department of Earth Sciences, National Cheng Kung University. 270
    Lovejoy S, Schertzer D, 1990. Multifractals, Universality Classes, and Satellite and Radar Measurements of Cloud and Rain Fields. Jour Geophys Res, 95(D3): 2021-2034 doi: 10.1029/JD095iD03p02021
    Mandelbrot B B, 1983. The Fractal Geometry of Nature. Updated Edition. New York: Freeman. 486
    Matheron G, 1962. Traité de Géostatistique Appliquée. Memoires Bur Rech. Géol Minières, 14: 33
    Meneveau C, Sreenivasan K R, 1987. Simple Multifractal Cascade Model for Fully Developed Turbulence. Phys Review Letters, 59: 424-1427
    Schertzer D, Lovejoy S, Schmitt F, Chigirinskaya Y, Marsan D, 1997. Multifractal Cascade Dynamics and Turbulent Intermittency. Fractals, 5(3): 427-471 doi: 10.1142/S0218348X97000371
    Sim B B L, Agterberg F P, Beaudry Ch, 1999. Determining the Cutoff between Back ground and Relative Base Metal Smelter Contamination I evels Using Multifractals Methods. Computers & Geosciences, 25(7): 1023-1041
    Stanley H E, Meakin P, 1988. Multifractal Phenomena in Physics and Chemistry. Nature, 335(6189): 405-409 doi: 10.1038/335405a0
    Switzer P, McBride S, 1999. Modeling Indoor Air Pollution Using Superposition. Bulletin International Statistical Institute, Tome LVIII, (Book 2): 501-504
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(9)

    Article Metrics

    Article views(82) PDF downloads(1) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return