Fractal dimension used as a proxy to understand the spatial distribution for carlin-type gold deposits
Hao Liu, Bappa Mukherjee, Yujun Zuo, Paresh Nath Singha Roy, Zhonghu Wu, Wenjibin Sun, Lulin Zheng, Chao Pan, Jianyun Lin
Abstract
The spatial distribution of ore-forming element grades typically exhibits strong nonlinear characteristics as a result of continuous geological processes. The trend of change in ore grade sequences is a crucial indicator of the degree of enrichment of an ore deposit. Therefore, quantitative evaluation of the spatial distribution of ore-forming elements holds great significance for understanding ore-forming processes as well as for ore exploration. In this work, based on the principles of fractal theory, a MATLAB-based program to calculate fractal dimensions was developed, and fractal analysis was conducted on the gold concentration values (g/t) of 25 drill holes in the Lannigou Gold Mining Area, Guizhou, China. Rescaled range analysis and the fractal correlation integral were utilized to obtain the spatial distribution of gold concentrations in the drill holes. Rescaled range analysis revealed that the Hurst exponent (HR/S) values vary in the range of 0.58–0.97, which reflected the persistent behavior of vertical variation in gold tonnage at the studied wells. Furthermore, the relationship between gold grade distribution and associated fluctuations in the fractal dimension derived from the correlation dimension (DC) was discussed. The DC value was found to vary between 1.01 and 1.59, indicating that high-grade gold deposits were distributed along steep fractal gradients and that fractal dimension values could be used as a reliable proxy to efficiently understand the migration pathways of auriferous fluid. Studies have shown that the Hurst exponent of the Au grade sequence exhibited a strong dependence on the grade of mineralization, with gold mineralized veins persisting throughout the studied drill holes. Thus, fractal dimension gradients can serve as an important proxy for identifying the locations of potential economic gold deposits in unexplored areas. Moreover, this approach can be employed to map the distribution patterns of other types of ore deposits.