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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 21, issue 2
Nonlin. Processes Geophys., 21, 477–487, 2014
https://doi.org/10.5194/npg-21-477-2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.
Nonlin. Processes Geophys., 21, 477–487, 2014
https://doi.org/10.5194/npg-21-477-2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 04 Apr 2014

Research article | 04 Apr 2014

Generalized binomial multiplicative cascade processes and asymmetrical multifractal distributions

Q. Cheng1,2 Q. Cheng
  • 1State Key Lab of Geological Processes and Mineral Resources, China University of Geosciences, Beijing and Wuhan, China
  • 2Department of Geography, York University, Toronto, M3J1P3, Canada

Abstract. The concepts and models of multifractals have been employed in various fields in the geosciences to characterize singular fields caused by nonlinear geoprocesses. Several indices involved in multifractal models, i.e., asymmetry, multifractality, and range of singularity, are commonly used to characterize nonlinear properties of multifractal fields. An understanding of how these indices are related to the processes involved in the generation of multifractal fields is essential for multifractal modeling. In this paper, a five-parameter binomial multiplicative cascade model is proposed based on the anisotropic partition processes. Each partition divides the unit set (1-D length or 2-D area) into h equal subsets (segments or subareas) and m1 of them receive d1 (> 0) and m2 receive d2 (> 0) proportion of the mass in the previous subset, respectively, where m1+m2 ≤ h. The model is demonstrated via several examples published in the literature with asymmetrical fractal dimension spectra. This model demonstrates the various properties of asymmetrical multifractal distributions and multifractal indices with explicit functions, thus providing insight into and an understanding of the properties of asymmetrical binomial multifractal distributions.

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