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

Abstract

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 D s of the number-size model is smaller than 1, the fractal dimension D m of the number-average size model is almost equal to 1; and when D s > 1, the D m is approximately equal to D s . In mineral deposits, according to the numberaverage 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 hotspring gold deposit, China.

Identifying geochemical anomalies associated with Cu mineralization in stream sediment samples in Gharachaman area, northwest of Iran

“…For determining geochemical anomalies, geochemical data could be divided into a number of classes by different methods. Mandelbrot (1983) introduced fractal models and several researchers applied them to geoscience studies (Zuo and Xia, 2009;Carranza, 2010;Deng et al, 2010;Wang et al, 2011;Paravarzar et al, 2014). The concentration-area model was developed by Bold numbers refer to elements that have significant impacts on their factor.…”

Application of a Multifractal Model for Identification of Lithology and Hydrothermal Alteration in the Dasuji Porphyry Mo Deposit in Inner Mongolia, China

“…A multifractal is a spatially interwoven fractal with a continuous spectrum of fractal dimensions (continuous multifractals) or discrete spectra (discrete multifractals) [42][43][44]. Fractal/multifractal models, such as the Number-Size (N-Z) model [45,46], the Concentration-Area (C-A) model [47], the Spectrum-Area (S-A) model [48,49], the Concentration-Distance (C-D) model [50], the Concentration-Volume model [51,52], and the Singularity Index [53][54][55], have been frequently proved robust for separating geological anomalies, such as geochemical, geophysical and remote sensing anomalies from a complicated background. As an efficient classification method, the Concentration-Area (C-A) fractal model was proved to be useful in determining the anomaly threshold in geological exploration.…”