Advertisement

Fractal Density and Singularity Analysis of Extreme Geo-Processes

  • Qiuming ChengEmail author
Conference paper
Part of the Springer Proceedings in Complexity book series (SPCOM)

Abstract

Density is a fundamental physical parameter involved in most geodynamics models used for prediction in the earth sciences. A new concept of fractal density was proposed to characterize the extreme physical properties of complex geo-processes. As a generalization of the ordinary density concept, the fractal density has a unit of ratio of mass or energy over a fractal set (e.g., g/cm α and J/m α , where the singularity α can be a non-integer number). From a fractal density point of view the ordinary density becomes scale dependent with singularity which should be substituted by fractal density in dynamic models. We demonstrate that several extreme geo-processes occurred in the Earth’s crust originated from cascade earth dynamics (e.g., mantle convection) and self-organized criticality (e.g., slab breakoffs and faults as avalanches) can cause fractal density of mass accumulation or energy release. Examples shown in the paper include energy release of earthquakes and floods.

Keywords

Power-law Fractal and multifractals Extreme geo-events Mass density and energy density 

Notes

Acknowledgments

This research has been supported by an NSERC Discovery Research “Research and development of multifractal methods and GIS technology for mineral exploration and environmental assessments” (ERC-OGP0183993).

References

  1. 1.
    Mandelbrot BB (1989) Multifractal measures, especially for the geophysicist. Pure Appl Geophys 131:5–42ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    Cheng Q (2016) Fractal density and singularity analysis of heat flow in oceanic ridges. Sci Rep. doi: 10.1038/srep19167
  3. 3.
    Cheng Q (2015) Multifractal interpolation method for spatial data with singularity. J South Afr Inst Min Metal 115:1–6CrossRefGoogle Scholar
  4. 4.
    Cheng Q (2007) Mapping singularities with stream sediment geochemical data for prediction of undiscovered mineral deposits in Gejiu, Yunnan Province, China. Ore Geol Rev 32:314–324CrossRefGoogle Scholar
  5. 5.
    Cheng Q, Agterberg FP (2009) Singularity analysis of ore-mineral and toxic trace elements in stream sediments. Comput Geosci 35:234–244ADSCrossRefGoogle Scholar
  6. 6.
    Cheng Q (2012) Singularity theory and methods for mapping geochemical anomalies caused by buried sources and for predicting undiscovered mineral deposits in covered areas. J Geochem Explor 122:55–70CrossRefGoogle Scholar
  7. 7.
    Cheng Q, Li L, Wang L (2009) Characterization of peak flow events with local singularity method. Nonlinear Process Geophys 16:503–513ADSCrossRefGoogle Scholar
  8. 8.
    HYDAT CD-ROM User’s Manual: Surface Water and Sediment Data, Atmospheric Environment Program, Version 96 – 1.04 User’s Manual, Environment Canada, p 95 (1996)Google Scholar
  9. 9.
    Kenny FM (1997) A chromostereo enhanced digital elevation model of the Oak Ridges Moraine Area, Southern Ontario and Lake Ontario Bathymetry. Geological Survey of Canada. Open file 3423, scale 1:200 000Google Scholar
  10. 10.
    Gutenberg B, Richter CF (1944) Frequency of earthquakes in California. Bull Seismol Soc Am 4:185–188Google Scholar
  11. 11.
    Apostol BF (2006) A model of seismic focus and related statistical distributions of earthquakes. Phys Lett A 357:462–466ADSCrossRefzbMATHGoogle Scholar
  12. 12.
    Turcotte DL (1997) Fractals and chaos in geology and geophysics, 2nd edn. Cambridge University Press, Cambridge, 398 ppGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Department of Earth and Space Science and EngineeringYork UniversityTorontoCanada
  2. 2.Department of GeographyYork UniversityTorontoCanada
  3. 3.State Key Lab of Geological Processes and Mineral ResourcesChina University of GeosciencesBeijing, WuhanChina

Personalised recommendations