Comparison between two types of multifractal modeling |
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| Authors: | Qiuming Cheng and F P Agterberg |
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| Institution: | (1) Department of Earth and Atmospheric Science, York University, M3J 1P3 North York, Ontario, Canada;(2) Geological Survey of Canada, 601 Booth Street, K1A 0E8, Ontario, Canada |
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| Abstract: | The interrelationships between two previously developed multifractal models are discussed. These are the Evertsz-Mandelbrot model developed on the basis of the multifractal spectrum f( ), and the Schertzer-Lovejoy model based on the codimension function C( ) where and represent Hölder exponent and field order, respectively. It is shown how these two models are interrelated: they are identical for values of within the range D–(0) D–min. where D is the Euclidean dimension. For D–maxD–(0), however, f() remains a continuous function of whereas C() assumes constant value. In this respect, the fractal spectrum f() can provide more information about the multifractal measure than the codimension function C(). The properties of the two models are illustrated by application to the binomial multiplicative cascade model. |
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| Keywords: | multifractal measure fractal spectrum codimension binomial multiplicative cascade model |
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