Mixtures of multiplicative cascade models in geochemistry

Nonlinear Processes in Geophysics

Volumn 14, Issue 3, 2007, Pages 201-209

  Agterberg, F P ^a  

^a GEOLOGICAL SURVEY OF CANADA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; FRACTAL ANALYSIS; FREQUENCY-MAGNITUDE DISTRIBUTION; GEOCHEMICAL METHOD; MAPPING; NUMERICAL MODEL; ROCK;

EID: 34249680309     PISSN: 10235809     EISSN: 16077946     Source Type: Journal    
DOI: 10.5194/npg-14-201-2007     Document Type: Article

References (35)

1. Agterberg, F. P.: Multifractal modeling of the sizes and grades of giant and supergiant deposits, Int. Geol. Rev., 37, 1-8, 1995.
2. Agterberg, F. P.: Multifractal simulation of geochemical map patterns, in: Geologic modeling and simulation: Sedimentary Systems, edited by: Merriam, D. F. and Davis, J. C., Kluwer, New York, 327-346, 2001a.
3. Agterberg, F. P.: Aspects of multifractal modeling: Proceedings of IAMG Annual Meeting, Cancun, September, CD-Rom, 2001b.
4. Agterberg, F. P.: New applications of the model of de Wijs in regional geochemistry, Math. Geol., Preprint, 2007.
5. Ahrens, L. H.: A fundamental law of geochemistry, Nature, 712, 1148, 1953.
6. Aitchison, J. and Brown, J. A. C.: The lognormal distribution, Cambridge Univ. Press, 1957.
7. Allègre, C. J. U. and Lewin, E.: Scaling laws and geochemical distributions, Earth Planet. Sci. Lett., 132, 1-13, 1995.
8. Brinck, J. W.: 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, Proc. Ser. STI/PUB/374, 21-32, 1974.
9. Cheng, Q.: Multifractal modeling and spatial analysis with GIS: gold potential estimation in the Mitchell-Sulphurets Area, north-western British Columbia, University of Ottawa, Canada, doctoral thesis, 1994.
10. Cheng, Q.: Multifractality and spatial statistics, Computers & Geosci., 25, 949-961, 1999.
11. Cheng, Q.: GeoData Analysis System (GeoDAS) for Mineral Exploration and Environmental Assessment, User's Guide, York University, Toronto, Canada, 2003.
12. Cheng, Q.: Multifractal distribution of eigenvalues and eigenvectors from 2D multiplicative cascade multifractal fields, Math. Geol., 37, 915-927, 2005.
13. Cheng, Q.: Mapping singularities with stream sediment geochemical data for prediction of undiscovered mineral deposits in Gejiu, Yunnan Province, China, Ore Geol. Rev., in press, 2007.
14. Cheng, Q. and Agterberg, F.P.: Multifractal modeling and spatial statistics, Math. Geol., 28(1), 1-16, 1996.
15. Cheng, Q. and Agterberg, F. P.: Singularity analysis of ore-mineral and toxic trace elements in stream sediments, Computers & Geosci., accepted, 2007.
16. Cheng, Q., Agterberg, F. P., and Ballantyne, S. B.: The separation of geochemical anomalies from background by fractal methods, J. Geochem. Explor., 51(2), 109-130, 1994.
17. De Wijs, H. -J.: Statistics of ore distribution, part I, Geologie en Mijnbouw, 13, 365-375, 1951.
18. Evertsz, C. J. G. and Mandelbrot, B. B.: Multifractal measures, Appendix B, in: Chaos and Fractals, edited by: Peitgen, H.-O., Jurgens, H., and Saupe, D., Springer-Verlag, New York, 922-953, 1992.
19. Falconer, K.: Fractal geometry - mathematical foundations and applications (2nd ed.), Wiley, New York, 2003.
20. Feder, F.: Fractals, Plenum, New York, 1988.
21. Garrett, R. G.: Geochemical abundance models: an update, 1975 to 1987, U.S. Geological Survey Circular 980, 207-220, 1986.
22. Harris, D. P.: Mineral resources appraisal, Clarendon Press, Oxford, 1984.
23. 6 m, in: Non-linear variability in geophysics, edited by: Schertzer, D. and Lovejoy, S., Kluwer, Dordrecht, 111-144, 1991.
24. Mandelbrot, B. B.: The fractal geometry of nature (updated and augmented edition), W.H. Freeman and Company, New York, 1983.
25. Mandelbrot, B. B.: Multifractal measures, especially for the geophysicist, Pure Appl. Geophys., 131, 5-42, 1989.
26. Over, T. M. and Gupta, V. K.: A space-time theory of mesoscale rainfall using random cascades, J. Geophys. Res., 101, 26 319-26 331, 1996.
27. Schertzer, D. and Lovejoy, S.: The dimension and intermittency of atmospheric dynamics Multifractal cascade dynamics and turbulent intermittency, in: Turbulent Shear Flow 4, edited by: Launder, B., Springer-Verlag, New York, pp. 7-33, 1985.
28. Schertzer, D. and Lovejoy, S.: Physical modeling and analysis of rain and clouds by anisotropic scaling of multiplicative processes, J. Geophys. Res., 92, 9693-9714, 1987.
29. Schertzer, D., Lovejoy, S., Schmitt, F., Chigirinskaya, Y., and Marsan, D.: Multifractal cascade dynamics and turbulent intermittency, Fractals, 5, 427-471, 1997.
30. Sinclair, A. J.: A fundamental approach to threshold estimation in exploration geochemistry: probability plots revisited, J. Geochem. Explor., 41(1), 1-22, 1991.
31. Turcotte, D. L.: Fractals and chaos in geology and geophysics (2nd ed.), Cambridge Univ. Press, 1997.
32. Turcotte, D. L.: Fractals in petrology, Lithos, 65(3-4), 261-271, 2002.
33. Veneziano, D. and Furcolo, P.: Marginal distribution of stationary multifractal measures and their Haar wavelet coefficients, Fractals, 11(3), 253-270, 2003.
34. Veneziano, D. and Langousis, A.: The maximum of multifractal cascades: exact distribution and approximations, Fractals, 13(4), 311-324, 2005.
35. Vistelius, A. B.: The skew frequency distributions and the fundamental law of geochemistry, J. Geol., 69, 703-728, 1960.