A novel iterative approach for mapping local singularities from geochemical data

Nonlinear Processes in Geophysics

Volumn 14, Issue 3, 2007, Pages 317-324

  Chen, Zhijun ^a   Cheng, Qiuming ^a,b   Chen, Jiaoguo ^a   Xie, Shuyun ^a  

^a CHINA UNIVERSITY OF GEOSCIENCES   (China)

^b YORK UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ANOMALY; FRACTAL ANALYSIS; GEOCHEMISTRY; GEOLOGICAL MAPPING; MINERAL EXPLORATION; QUARTZ VEIN; SPHALERITE; ZINC;

BOLIVIA; POTOSI [BOLIVIA]; PULACAYO; SOUTH AMERICA;

EID: 34547353389     PISSN: 10235809     EISSN: 16077946     Source Type: Journal    
DOI: 10.5194/npg-14-317-2007     Document Type: Article

References (39)

1. Agterberg, F. P.: Geomathematics: mathematical background and Geo-science Application, Elsevier scientific publishing company, Amsterdam, 317-324, 1974.
2. Agterberg, F. P.: Multifractal Simulation of Geochemical Map Patterns, Journal of China University of Geosciences, 12, 31-39, 2001.
3. Arneodo, A., Argoul, F., Bacry, E. Elezgaray, J., Freysz, E., Grasseau, G., Muzy, J. F., and Pouligny, B.: Wavelet transform of fractals, in: Wavelets and applications: Proceedings of the International Conference, edited by: Meyer, Y., Marseille, France, May 1989, Springer-Verlag, Paris, 287-352, 1992.
4. Arneodo, A., Bacry, E., and Muzy, J. F.: The thermodynamics of fractals revisited with wavelets, Physica A, 213, 232-275, 1995.
5. Arneodo, A., Audit, B., Bacry, E., Manneville, S., Muzy, J. F., and Roux, S. G.: Thermodynamics of fractal signals based on wavelet analysis: application to fully developed turbulence data and DNA sequences, Physica A, 254, 24-45, 1998.
6. Carr, J. R.: Statistical self-affinity, fractal dimension, and geologic interpretation, Eng. Geology, 48, 269-282, 1997.
7. Chen, Z. J., Cheng, Q., and Chen, J. G.: Significance of Fractal Measure in Local Singularity Analysis of Multifractal Model, in: Proceedings of IAMG'05: GIS and Spatial Analysis, edited by: Cheng, Q. and Bonham-Cater, G., International Association for Mathematical Geology, China University of Geosciences Printing House, Wuhan, vol. 1, 475-480, 2005.
8. Cheng, Q. and Agterberg, F. P.: Multifractal modeling and spatial statistics, Math. Geology, 28, 1-16, 1996.
9. Cheng, Q.: Multifractal modeling and spatial analysis with GIS: gold potential estimation in the Mitchell-Sulphurets area, North-western British Columbia, Ph.D. thesis, University of Ottawa, Ottawa, 268 pp, 1994.
10. Cheng, Q.: Multifractal modeling and lacunarity analysis, Math. Geology, 29, 919-932, 1997.
11. Cheng, Q.: Multifractality and spatial statistics, Comput Geosci., 25, 949-961, 1999a.
12. Cheng, Q.: Multifractal interpolation, in: Proceedings of the Firth Annual Conference of the International Association for Mathematical Geology, edited by: Lippard, S. J., Naess, A., and Sinding-Larsen, R., Trondheim, Norway, vol. 1, 245-250, 1999b.
13. Cheng, Q.: Interpolation by means of multiftractal, kriging and moving average techniques, in: CD Proceedings of GAC/MAC meeting GeoCanada2000, 29 May to 2 June, Calgary, http://www.gisworld.org/gac-gis/geo2000.htm, 2000.
14. Cheng, Q.: Singularity analysis for image processing and anomaly enhancement, in: Proceedings IAMO'01, International Association for Mathematical Geology, Cancun, Mexcico, 6-12 September, CD-ROM, 200 la.
15. Cheng, Q.: Multifractal and geostatistical methods for exploration geochemical anomaly texture and singularity analysis, Earth Science - Journal of China University of Geosciences (in Chinese with English abstract), 26, 161-166, 2001b.
16. Cheng, Q.: Quantifying the generalized self-similarity of spatial patterns for mineral resources assessment, Earth Science - Journal of China University of Geosciences (in Chinese with English abstract), 29, 733-744, 2004.
17. Cheng, Q.: A new model for incorporating spatial association and singularity in interpolation of exploratory data, in: Geostatistics Banff 2004, Quantitative Geology and Geostatistics, Springer Press, edited by: Leuangthong, O. and Deutsch, C. V., Netherlands, 14, 1017-1025, 2005.
18. Cheng, Q.: GIS based fractal/multifractal anomaly analysis for modeling and prediction of mineralization and mineral deposits, in: GIS Application in the Earth Sciences - GAC Special Paper, Geological Association of Canada Special Book, edited by: Harris, J. R., 285-296, 2006a.
19. Cheng, Q.: Singularity - generalized self-similarity - fractal specturm (3S) Model, Earth Science - Journal of China University of Geosciences (in Chinese with English abstract), 31, 337-348, 2006b.
20. Cheng, Q.: Mapping singularities with stream sediment geochemical data for prediction of undiscovered mineral deposits in Gejiu, Yunnan Province, China, Ore Geology Reviews, in press, doi:10.1016/j.oregeorev.2006.10.002, 2006c.
21. Cheng, Q.: Multifractal imaging filtering and decomposition methods in Space, Fourier Frequency, and Eigen Domains, Nonlin. Processes Geophys., 14, 293-303, 2007, http://www.nonlin-processes-geophys.net/14/293/2007/.
22. Chilès, J. P. and Delfiner, P.: Geostatistics: Modeling Spatial Uncertainty, John Wiley & Sons, Inc., New York, 694 pp., 1999.
23. de Wijs, H. J.: Statistics of ore distribution, part I: Geologie en Mijnbouw, 30, 365-375, 1951.
24. Everstz, C. J. G. and Mandelbrot, B. B.: Multifractal measures, in: Chaos and Fractals, edited by: Peitgen, H., Jürgens, H., and Saupe, D., Springer, Berlin, 921-953, 1992.
25. Falconer, K.: Fractal Geometry: Mathematical Foundations and Applications, John Wiley & Sons Ltd., Chichester, 288 pp., 1990.
26. Feder, J.: Fractals, Plenum, New York, 283 pp., 1988.
27. Frisch, U. and Parisi, G.: Fully developed turbulence and intermittency, in: Turbulence and Predictability of Geophysical Flows and Climate Dynamics, edited by: Ghil, M., Benzi, R., and Parisi, G., Amsterdam, North Holland, 84-88, 1985.
28. Goovaerts, P.: Geostatistics in soil science: state-of-the-art and perspectives, Geoderma, 89, 1-45, 1999.
29. Gringarten, E. and Deutsch, C. V.: Teacher's Aide: Variogram Interpretation and Modeling, 33, 507-534, 2001.
30. Halsey, T. C., Jensen, M. H., Kadanoff, L. P., Procaccia I., and Shraimann, B.: Fractal measures and their singularities: the characterization of strange sets, Phys. Rev., A, 33, 1141-1151, 1986.
31. Herzfeld, U. C. and Overbeck, C.: Analysis and simulation of scale-dependent fractal surfaces with application to seafloor morphology, 25, 979-1007, 1999.
32. Li, B. L.: Fractal geometry applications in description and analysis of patch patterns and patch dynamics, Ecol. Model., 132, 33-50, 2000.
33. Mallet, S. and Hwang, W. L.: Singularity detection and processing with wavelets, IEEE Trans. information Theory, 38, 617-643, 1992.
34. Mallet, S.: A wavelet Tour of Signal Processing (2nd), China Machine Press, Beijing, 637 pp, 2003.
35. Mandelbrot, B. B.: Fractals: Form, Chance, and Dimension, W H Freeman & Co. New York, 1977.
36. Mandelbrot, B. B.: The Fractal Geometry of Nature, W H Freeman & Co., New York, 468 pp., 1983.
37. Matheron, G.: Traite de Geostatistique Appliquee, Tome 1, Memoires du Bureau de Recherches Geologiques, et Minieres, no. 14, Editions Technip, Paris, 334 pp, 1962.
38. Schertzer, D. and Lovejoy, S.: Non-linear variability in geophysics, Kluwer Academic Publ., Dordrecht, 318 pp., 1991.
39. Yang, W. X., Hull, J. B., and Seymour, M. D.: Detecting the singularities in engineering signals, J. Mat. Processing Technol., 175, 439-445, 2006.