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)![le](/content/k152q87984407605/xxlarge8804.gif) ![gamma](/content/k152q87984407605/xxlarge947.gif) D– min. where D is the Euclidean dimension. For D– max![le](/content/k152q87984407605/xxlarge8804.gif) ![gamma](/content/k152q87984407605/xxlarge947.gif) D– (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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