Natural Resources Research

, Volume 28, Issue 1, pp 5–29 | Cite as

New Insights into Element Distribution Patterns in Geochemistry: A Perspective from Fractal Density

  • Yue Liu
  • Qiuming ChengEmail author
  • Kefa Zhou
Original Paper


Multifractal features of element concentrations in the Earth’s crust have demonstrated to be closely associated with multiple probability distributions such as normal, lognormal and power law. However, traditional understanding of geochemical distribution satisfying normal, lognormal or power-law models still faces a serious problem in adjusting theoretical statistics with the empirical distribution. Given that the differences among different geochemical distribution populations may have considerable effects on the target estimation, a new perspective from the singularity of fractal density is adopted to investigate mixed geochemical distribution patterns within frequency and space domains. In the framework of fractal geometry, ordinary density such as volume density (e.g., g/cm3 and kg/m3) described in Euclidean space can be considered as a special case of the fractal density (e.g., g/cmα and kg/mα). According to the nature of fractal density, geochemical information obtained from Euclidean geometry may not sufficiently reflect inherent geochemical features, because some information might be hidden within fractal geometry that can be only revealed by means of a set of fractional dimensions. In the present study, stream sediment geochemical data collected from west Tianshan region, Xinjiang (China), were used to explore element distribution patterns in the Earth’s crust based on a fractal density model. Four elements Cu, Zn, K and Na were selected to study the differences between minor and major elements in terms of their geochemical distribution patterns. The results strongly suggest that element distribution patterns can be well revealed and interpreted by means of a fractal density model and related statistical and multifractal parameters.


Element distribution patterns Fractal density Singularity analysis Multifractal theory West Tianshan region 



Editor-in-Chief Dr. John Carranza is warmly thanked for efficient editorial handling and his helpful review of the manuscript, and special thanks to Dr. Antonella Buccianti and an anonymous reviewer for their valuable comments. This work is jointly funded by the CAS “Light of West China” program (2015-XBQN-B-23), and the National Natural Science Foundation of China (Nos: 41702356, U1503291, 41430320).


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Copyright information

© International Association for Mathematical Geosciences 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Desert and Oasis Ecology, Xinjiang Institute of Ecology and GeographyChinese Academy of SciencesÜrümqiChina
  2. 2.Xinjiang Research Centre for Mineral ResourcesChinese Academy of SciencesÜrümqiChina
  3. 3.Xinjiang Key Laboratory of Mineral Resources and Digital GeologyÜrümqiChina
  4. 4.State Key Laboratory of Geological Processes and Mineral ResourcesChina University of GeosciencesWuhanChina
  5. 5.State Key Laboratory of Geological Processes and Mineral ResourcesChina University of GeosciencesBeijingChina
  6. 6.Department of Earth and Space Science and EngineeringYork UniversityTorontoCanada

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