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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 18, issue 4
Nonlin. Processes Geophys., 18, 447–454, 2011
https://doi.org/10.5194/npg-18-447-2011
© Author(s) 2011. This work is distributed under
the Creative Commons Attribution 3.0 License.
Nonlin. Processes Geophys., 18, 447–454, 2011
https://doi.org/10.5194/npg-18-447-2011
© Author(s) 2011. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 06 Jul 2011

Research article | 06 Jul 2011

Number-average size model for geological systems and its application in economic geology

Q. F. Wang1, L. Wan1,2, Y. Zhang1, J. Zhao1, and H. Liu1 Q. F. Wang et al.
  • 1State Key Laboratory of Geological Processes and Mineral Resources, China University of Geosciences, Beijing 100083, China
  • 2School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong 510006, China

Abstract. Various natural objects follow a number-size relationship in the fractal domain. In such relationship, the accumulative number of the objects beyond a given size shows a power-law relationship with the size. Yet in most cases, we also need to know the relationship between the accumulative number of the objects and their average size. A generalized number-size model and a number-average size model are constructed in this paper. In the number-average size model, the accumulative number shows a power-law relationship with the average size when the given size is much less than the maximum size of the objects. When the fractal dimension Ds of the number-size model is smaller than 1, the fractal dimension Ds of the number-average size model is almost equal to 1; and when Ds > 1, the Dm is approximately equal to Ds. In mineral deposits, according to the number-average size model, the ore tonnage may show a fractal relationship with the grade, as the cutoff changes for a single ore deposit. This is demonstrated by a study of the relationship between tonnage and grade in the Reshuitang epithermal hot-spring gold deposit, China.

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