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

• Main Authors: Q. F. Wang, L. Wan, Y. Zhang, J. Zhao, H. Liu
• Format: Article
• Language: English
• Published: Copernicus Publications 2011-07-01
• Series: Nonlinear Processes in Geophysics
• Online Access: http://www.nonlin-processes-geophys.net/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.