Advertisement

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

Abstract

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.

Keywords

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

Notes

Acknowledgments

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).

References

  1. Abdolmaleki, M., Mokhtari, A. R., Akbar, S., Alipour-Asll, M., & Carranza, E. J. M. (2014). Catchment basin analysis of stream sediment geochemical data: Incorporation of slope effect. Journal of Geochemical Exploration, 140, 96–103.CrossRefGoogle Scholar
  2. Agterberg, F. P. (2007). Mixtures of multiplicative cascade models in geochemistry. Nonlinear Processes in Geophysics, 14(3), 201–209.CrossRefGoogle Scholar
  3. Agterberg, F. P. (2012). Multifractals and geostatistics. Journal of Geochemical Exploration, 122, 113–122.CrossRefGoogle Scholar
  4. Agterberg, F. P. (2015). Self-similarity and multiplicative cascade models. Journal of the Southern African Institute of Mining and Metallurgy, 115(1), 1–11.CrossRefGoogle Scholar
  5. Agterberg, F. P. (2017). Pareto–Lognormal modeling of known and unknown metal resources. Natural Resources Research, 26(1), 3–20.CrossRefGoogle Scholar
  6. Ahrens, L. H. (1953). A fundamental law of geochemistry. Nature, 172, 1148.CrossRefGoogle Scholar
  7. Ahrens, L. H. (1954). The lognormal distribution of the elements (2). Geochimica et Cosmochimica Acta, 6(2–3), 121–131.CrossRefGoogle Scholar
  8. Aitchison, J. (1986). The statistical analysis of compositional data (p. 416). London: Chapman & Hall.CrossRefGoogle Scholar
  9. Allegre, C. J., & Lewin, E. (1995). Scaling laws and geochemical distributions. Earth and Planetary Science Letters, 132(1–4), 1–13.CrossRefGoogle Scholar
  10. Arias, M., Gumiel, P., & Martín-Izard, A. (2012). Multifractal analysis of geochemical anomalies: A tool for assessing prospectivity at the SE border of the Ossa Morena Zone, Variscan Massif (Spain). Journal of Geochemical Exploration, 122, 101–112.CrossRefGoogle Scholar
  11. Bølviken, B., Stokke, P. R., Feder, J., & Jössang, T. (1992). The fractal nature of geochemical landscapes. Journal of Geochemical Exploration, 43(2), 91–109.CrossRefGoogle Scholar
  12. Buccianti, A. (2015). Frequency distributions of geochemical data, scaling laws, and properties of compositions. Pure and Applied Geophysics, 172(7), 1851–1863.CrossRefGoogle Scholar
  13. Buccianti, A., Lima, A., Albanese, S., & De Vivo, B. (2017). Measuring the change under compositional data analysis (CoDA): Insight on the dynamics of geochemical systems. Journal of Geochemical Exploration.  https://doi.org/10.1016/j.gexplo.2017.05.006.Google Scholar
  14. Buccianti, A., & Zuo, R. (2016). Weathering reactions and isometric log-ratio coordinates: Do they speak to each other? Applied Geochemistry, 75, 189–199.CrossRefGoogle Scholar
  15. Carranza, E. J. M. (2010a). Catchment basin modelling of stream sediment anomalies revisited: Incorporation of EDA and fractal analysis. Geochemistry: Exploration, Environment, Analysis, 10(4), 365–381.Google Scholar
  16. Carranza, E. J. M. (2010b). Mapping of anomalies in continuous and discrete fields of stream sediment geochemical landscapes. Geochemistry: Exploration, Environment, Analysis, 10(2), 171–187.Google Scholar
  17. Carranza, E. J. M. (2017). Geochemical mineral exploration: Should we use enrichment factors or log-ratios? Natural Resources Research, 26(4), 411–428.CrossRefGoogle Scholar
  18. Carranza, E. J. M., & Hale, M. (1997). A catchment basin approach to the analysis of reconnaissance geochemical-geological data from Albay Province, Philippines. Journal of Geochemical Exploration, 60(2), 157–171.CrossRefGoogle Scholar
  19. Chen, G., & Cheng, Q. (2017). Fractal density modeling of crustal heterogeneity from the KTB deep hole. Journal of Geophysical Research: Solid Earth, 122(3), 1919–1933.Google Scholar
  20. Cheng, Q. (1999). The gliding box method for multifractal modeling. Computers & Geosciences, 25(9), 1073–1079.CrossRefGoogle Scholar
  21. Cheng, Q. (2007). Mapping singularities with stream sediment geochemical data for prediction of undiscovered mineral deposits in Gejiu, Yunnan Province, China. Ore Geology Reviews, 32(1), 314–324.CrossRefGoogle Scholar
  22. Cheng, Q. (2012). Multiplicative cascade processes and information integration for predictive mapping. Nonlinear Processes in Geophysics, 19(1), 57–68.CrossRefGoogle Scholar
  23. Cheng, Q. (2014). Generalized binomial multiplicative cascade processes and asymmetrical multifractal distributions. Nonlinear Processes in Geophysics, 21(2), 477–487.CrossRefGoogle Scholar
  24. Cheng, Q. (2016). Fractal density and singularity analysis of heat flow over ocean ridges. Scientific Reports, 6, 19167.CrossRefGoogle Scholar
  25. Cheng, Q. (2017a). Singularity analysis of global zircon U–Pb age series and implication of continental crust evolution. Gondwana Research, 51, 51–63.CrossRefGoogle Scholar
  26. Cheng, Q. (2017b). Fractal density and singularity analysis of extreme geo-processes. In First complex systems digital campus world E-conference 2015 (pp. 395–405). Cham: Springer.Google Scholar
  27. Cheng, Q., & Agterberg, F. P. (2009). Singularity analysis of ore-mineral and toxic trace elements in stream sediments. Computers & Geosciences, 35(2), 234–244.CrossRefGoogle Scholar
  28. Cheng, Q., Agterberg, F. P., & Ballantyne, S. B. (1994). The separation of geochemical anomalies from background by fractal methods. Journal of Geochemical Exploration, 51(2), 109–130.CrossRefGoogle Scholar
  29. Cracknell, M. J., & de Caritat, P. (2017). Catchment-based gold prospectivity analysis combining geochemical, geophysical and geological data across northern Australia. Geochemistry: Exploration, Environment, Analysis, 17(3), 204–216.Google Scholar
  30. Egozcue, J. J., & Pawlowsky-Glahn, V. (2005). Groups of parts and their balances in compositional data analysis. Mathematical Geology, 37(7), 795–828.CrossRefGoogle Scholar
  31. Egozcue, J. J., Pawlowsky-Glahn, V., Mateu-Figueras, G., & Barcelo-Vidal, C. (2003). Isometric logratio transformations for compositional data analysis. Mathematical Geology, 35(3), 279–300.CrossRefGoogle Scholar
  32. Evertsz, C. J., & Mandelbrot, B. (1992). Multifractal measures. In H.-O. Peitgen, H. Jurgens, & D. Saupe (Eds.), Chaos and fractals. New York: Springer.Google Scholar
  33. Filzmoser, P., Hron, K., & Reimann, C. (2011). Interpretation of multivariate outliers for compositional data. Computers & Geosciences, 39, 77–85.CrossRefGoogle Scholar
  34. Gao, J., Long, L., Klemd, R., Qian, Q., Liu, D., Xiong, X., et al. (2009). Tectonic evolution of the South Tianshan orogen and adjacent regions, NW China: Geochemical and age constraints of granitoid rocks. International Journal of Earth Sciences, 98(6), 1221–1238.CrossRefGoogle Scholar
  35. Govett, G. J., Goodfellow, W. D., Chapman, R. P., & Chork, C. Y. (1975). Exploration geochemistry-distribution of elements and recognition of anomalies. Mathematical Geology, 7(5), 415–446.CrossRefGoogle Scholar
  36. Groeneveld, R. A., & Meeden, G. (1984). Measuring skewness and kurtosis. The Statistician, 33, 391–399.CrossRefGoogle Scholar
  37. Halsey, T. C., Jensen, M. H., Kadanoff, L. P., Procaccia, I., & Shraiman, B. I. (1986). Fractal measures and their singularities: The characterization of strange sets. Physical Review A, 33(2), 1141–1151.CrossRefGoogle Scholar
  38. Korvin, G. (1992). Fractal models in the earth sciences. Amsterdam: Elsevier.Google Scholar
  39. Lancianese, V., & Dinelli, E. (2016). Geochemical mapping based on geological units: A case study from the Marnoso-arenacea formation (Northern Apennines, Italy). Chemie der Erde-Geochemistry, 76(2), 197–210.CrossRefGoogle Scholar
  40. Link, R. F., & Koch, G. S. (1975). Some consequences of applying lognormal theory to pseudolognormal distributions. Mathematical Geology, 7(2), 117–128.CrossRefGoogle Scholar
  41. Liu, Y., Cheng, Q., Xia, Q., & Wang, X. (2013). Application of singularity analysis for mineral potential identification using geochemical data—A case study: Nanling W-Sn–Mo polymetallic metallogenic belt, South China. Journal of Geochemical Exploration, 134, 61–72.CrossRefGoogle Scholar
  42. Liu, Y., Cheng, Q., Xia, Q., & Wang, X. (2014). Identification of REE mineralization-related geochemical anomalies using fractal/multifractal methods in the Nanling belt, South China. Environmental Earth Sciences, 72(12), 5159–5169.CrossRefGoogle Scholar
  43. Liu, Y., Cheng, Q., Zhou, K., Xia, Q., & Wang, X. (2016). Multivariate analysis for geochemical process identification using stream sediment geochemical data: A perspective from compositional data. Geochemical Journal, 50(4), 293–314.CrossRefGoogle Scholar
  44. Liu, Y., Zhou, K., & Cheng, Q. (2017). A new method for geochemical anomaly separation based on the distribution patterns of singularity indices. Computers & Geosciences, 105, 139–147.CrossRefGoogle Scholar
  45. Lovejoy, S., & Schertzer, D. (2007). Scaling and multifractal fields in the solid earth and topography. Nonlinear Processes in Geophysics, 14(4), 465–502.CrossRefGoogle Scholar
  46. Ma, T., Li, C., & Lu, Z. (2014). Estimating the average concentration of minor and trace elements in surficial sediments using fractal methods. Journal of Geochemical Exploration, 139, 207–216.CrossRefGoogle Scholar
  47. Mandelbrot, B. B. (1975). Stochastic models for the Earth’s relief, the shape and the fractal dimension of the coastlines, and the number-area rule for islands. Proceedings of the National Academy of Sciences, 72(10), 3825–3828.CrossRefGoogle Scholar
  48. Mandelbrot, B. B. (1983). The Fractal Geometry of Nature (p. 468). San Francisco: Freeman.Google Scholar
  49. Monecke, T., Monecke, J., Herzig, P. M., Gemmell, J. B., & Mönch, W. (2005). Truncated fractal frequency distribution of element abundance data: A dynamic model for the metasomatic enrichment of base and precious metals. Earth and Planetary Science Letters, 232(3), 363–378.CrossRefGoogle Scholar
  50. Nezhad, S. G., Mokhtari, A. R., & Rodsari, P. R. (2017). The true sample catchment basin approach in the analysis of stream sediment geochemical data. Ore Geology Reviews, 83, 127–134.CrossRefGoogle Scholar
  51. Oertel, A. C. (1969). Frequency distributions of element concentrations-I. Theoretical aspects. Geochimica et Cosmochimica Acta, 33(7), 821–831.CrossRefGoogle Scholar
  52. Ondrick, C. W., & Griffiths, J. C. (1969). Frequency distribution of elements in rensselaer graywacke, Troy, New York. Geological Society of America Bulletin, 80(3), 509–518.CrossRefGoogle Scholar
  53. Panahi, A., & Cheng, Q. (2004). Multifractality as a measure of spatial distribution of geochemical patterns. Mathematical Geology, 36(7), 827–846.CrossRefGoogle Scholar
  54. Pawlowsky-Glahn, V., & Buccianti, A. (2011). Compositional data analysis: Theory and applications. Hoboken: Wiley.CrossRefGoogle Scholar
  55. Rantitsch, G. (2001). The fractal properties of geochemical landscapes as an indicator of weathering and transport processes within the Eastern Alps. Journal of Geochemical Exploration, 73(1), 27–42.CrossRefGoogle Scholar
  56. Reimann, C., & Filzmoser, P. (2000). Normal and lognormal data distribution in geochemistry: Death of a myth. Consequences for the statistical treatment of geochemical and environmental data. Environmental Geology, 39(9), 1001–1014.CrossRefGoogle Scholar
  57. Sinclair, A. J. (1991). A fundamental approach to threshold estimation in exploration geochemistry; probability plots revisited. Journal of Geochemical Exploration, 41(1–2), 1–22.CrossRefGoogle Scholar
  58. Stanley, C. R. (2006). Numerical transformation of geochemical data: 1. Maximizing geochemical contrast to facilitate information extraction and improve data presentation. Geochemistry: Exploration, Environment, Analysis, 6(1), 69–78.Google Scholar
  59. Taylor, S. E. (2008). Kurtosis. In Louise-Anne McNutt (Ed.), Encyclopedia of Epidemiology. Sarah Boslaugh: Sage Publications.Google Scholar
  60. Turcotte, D. L. (1986). A fractal approach to the relationship between ore grade and tonnage. Economic Geology, 81(6), 1528–1532.CrossRefGoogle Scholar
  61. van Rooij, M. M., Nash, B. A., Rajaraman, S., & Holden, J. G. (2013). A fractal approach to dynamic inference and distribution analysis. Frontiers in Physiology, 4, 1–16.Google Scholar
  62. Xia, L., Xu, X., Xia, Z., Li, X., Ma, Z., & Wang, L. (2004). Petrogenesis of Carboniferous rift-related volcanic rocks in the Tianshan, northwestern China. Geological Society of America Bulletin, 116(3–4), 419–433.CrossRefGoogle Scholar
  63. Xiao, W., Han, C., Yuan, C., Sun, M., Lin, S., Chen, H., et al. (2008). Middle Cambrian to Permian subduction–related accretionary orogenesis of Northern Xinjiang, NW China: Implications for the tectonic evolution of central Asia. Journal of Asian Earth Sciences, 32, 102–117.CrossRefGoogle Scholar
  64. Xie, S., & Bao, Z. (2004). Fractal and multifractal properties of geochemical fields. Mathematical Geology, 36(7), 847–864.CrossRefGoogle Scholar
  65. Xie, S., Cheng, Q., Xing, X., Bao, Z., & Chen, Z. (2010). Geochemical multifractal distribution patterns in sediments from ordered streams. Geoderma, 160(1), 36–46.CrossRefGoogle Scholar
  66. Xie, X., Mu, X., & Ren, T. (1997). Geological mapping in China. Journal of Geochemical Exploration, 60, 99–113.CrossRefGoogle Scholar
  67. Yousefi, M., Carranza, E. J. M., & Kamkar-Rouhani, A. (2013). Weighted drainage catchment basin mapping of geochemical anomalies using stream sediment data for mineral potential modeling. Journal of Geochemical Exploration, 128, 88–96.CrossRefGoogle Scholar
  68. Zhang, D., Zhang, Z., Xue, C., Zhao, Z., & Liu, J. (2010). Geochronology and geochemistry of the ore-forming porphyries in the Lailisigao’er-Lamasu region of the Western Tianshan Mountains, Xinjiang, NW China: Implications for petrogenesis, metallogenesis, and tectonic setting. The Journal of Geology, 118(5), 543–563.CrossRefGoogle Scholar
  69. Zhao, X., Xue, C., Symons, D. T., Zhang, Z., & Wang, H. (2014). Microgranular enclaves in island-arc andesites: A possible link between known epithermal Au and potential porphyry Cu–Au deposits in the Tulasu ore cluster, western Tianshan, Xinjiang, China. Journal of Asian Earth Sciences, 85, 210–223.CrossRefGoogle Scholar

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

Personalised recommendations