Theoretical study of statistical fractal model with applications to mineral resource prediction

  • Authors:

  • Shen Wei;Zhao Pengda

  • Affiliations:

  • Institute of Geochemistry, Chinese Academy of Sciences, Guiyang, People's Republic of China and Institute of High and New Techniques applied to Land Resources, China University of Geosciences, Bei ...;Institute of High and New Techniques applied to Land Resources, China University of Geosciences, Xueyuan Road 29, Beijing 100083, People's Republic of China

  • Venue:
  • Computers & Geosciences
  • Year:
  • 2002

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Abstract

The statistical estimation of fractal dimensions is an important topic of investigation. Current solutions emphsize visual straight-line fitting, but nonlinear statistical modeling has the potential of making valuable contributions in this field. In this paper, we present the concepts of generalized fractal models and generalized fractal dimension and conclude that many geological models are special cases of the generalized models. We show that the power-function distribution possesses the fractal property of scaling invariance under upper truncation, which may help in lead statistical fractal modeling. A new method is developed on the basis of nonlinear regression to estimate fractal parameters. This method has advantages with respect to the traditional method based on linear regression for estimating the fractal dimension. Finally, the new method is illustrated by means of application to a real data set.