NPG Nonlinear Processes in Geophysics NPG Nonlin. Processes Geophys. 1607-7946 Copernicus Publications Göttingen, Germany 10.5194/npg-18-447-2011 Number-average size model for geological systems and its application in economic geology Wang Q. F. 1 Wan L. 1 2 Zhang Y. 1 Zhao J. 1 Liu H. 1 State Key Laboratory of Geological Processes and Mineral Resources, China University of Geosciences, Beijing 100083, China School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong 510006, China 06 07 2011 18 4 447 454 Copyright: © 2011 Q. F. Wang et al. 2011 This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/ This article is available from https://npg.copernicus.org/articles/18/447/2011/npg-18-447-2011.html The full text article is available as a PDF file from https://npg.copernicus.org/articles/18/447/2011/npg-18-447-2011.pdf

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 <i>D</i><sub>s</sub> of the number-size model is smaller than 1, the fractal dimension <i>D</i><sub>s</sub> of the number-average size model is almost equal to 1; and when <i>D</i><sub>s</sub> > 1, the <i>D</i><sub>m</sub> is approximately equal to <i>D</i><sub>s</sub>. 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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