Multifractal modeling and spatial statistics |
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Authors: | Qiuming Cheng and Frederik P. Agterberg |
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Affiliation: | (1) Ottawa-Carleton Geoscience Centre, University of Ottawa, K1N 6N5 Ottawa, Canada;(2) Geological Survey of Canada, 601 Booth Street, K1A 0E8 Ottawa, Canada |
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Abstract: | In general, the multifractal model provides more information about measurements on spatial objects than a fractal model. It also results in mathematical equations for the covariance function and semivariogram in spatial statistics which are determined primarily by the second-order mass exponent. However, these equations can be approximated by power-law relations which are comparable directly to equations based on fractal modeling. The multifractal approach is used to describe the underlying spatial structure of De Wijs 's example of zinc values from a sphalerite-bearing quartz vein near Pulacayo, Bolivia. It is shown that these data are multifractal instead of fractal, and that the second-order mass exponent (=0.979±0.011 for the example) can be used in spatial statistical analysis. |
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Keywords: | autocorrelation fractals mass exponents multifractal spectrum semivariogram spatial covariance |
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