Singularity of mineralization processes and power-law models for mineral resources quantitative assessments

Singular physical or chemical processes may result in anomalous amounts of energy release or mass accumulation that, generally, are confined to narrow intervals in space or time. Singularity is a property of different types of non-linear natural processes including cloud formation, rainfall, hurricanes, flooding, landslides, earthquakes and mineralization. The end products of these non-linear processes have in common that they can be modeled as fractals or multifractals. Hydrothermal processes in the earth's crust can result in ore deposits characterized by high concentrations of metals with fractal or multifractal properties. Here we show that the non-linear properties of the end products of singular mineralization processes can be applied for mineral resource quantitative assessment. The framework set up in the paper enhances the theoretical foundation of mineral resource quantitative assessment that has been commonly conducted for mineral exploration in mining industry and for regional, national and global planning for mineral resource utilization. Several power-law models are proposed for characterizing non-linear properties of mineralization including non-linear anomalies in rocks and other surface media such as stream sediments caused by mineralization and the distribution of mineral deposits. A case study is introduced from the Gejiu area, Yunnan Province, China for mapping mineral potential for Sn and Cu.