Extreme Environmental Events

2011 Edition
| Editors: Robert A. Meyers (Editor-in-Chief)

Fractals in Geology and Geophysics

  • Donald L. Turcotte
Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-7695-6_31

Article Outline


Definition of the Subject


Drainage Networks



Volcanic Eruptions



Self‐Affine Fractals


Earth's Magnetic Field

Future Directions



Fractal Dimension Volcanic Eruption Peak Discharge Drainage Network Flood Hazard 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Primary Literature

  1. 1.
    Kossobokov VG, Keilis-Borok VI, Turcotte DL, Malamud BD (2000) Implications of a statistical physics approach for earthquake hazard assessment and forecasting. Pure Appl Geophys 157:2323CrossRefGoogle Scholar
  2. 2.
    Malamud BD, Turcotte DL (1999) Self-affine time series: I. Generation and analyses. Adv Geophys 40:1Google Scholar
  3. 3.
    Malamud BD, Turcotte DL (2006) The applicability of power-law frequency statistics to floods. J Hydrol 332:168CrossRefGoogle Scholar
  4. 4.
    Malamud BD, Turcotte DL, Barton CC (1996) The 1993 Mississippi river flood: A one hundred or a one thousand year event? Env Eng Geosci 2:479Google Scholar
  5. 5.
    Malamud BD, Turcotte DL, Guzzetti F, Reichenbach P (2004) Landslide inventories and their statistical properties. Earth Surf Process Landf 29:687CrossRefGoogle Scholar
  6. 6.
    Malamud BD, Turcotte DL, Guzzetti F, Reichenbach P (2004) Landslides, earthquakes, and erosion. Earth Planet Sci Lett 229:45CrossRefGoogle Scholar
  7. 7.
    Mandelbrot BB (1967) How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science 156:636CrossRefGoogle Scholar
  8. 8.
    Mandelbrot BB, Van Ness JW (1968) Fractional Brownian motions, fractional noises and applications. SIAM Rev 10:422CrossRefGoogle Scholar
  9. 9.
    McClelland L et al (1989) Global Volcanism 1975-1985. Prentice-Hall, Englewood CliffsGoogle Scholar
  10. 10.
    Meybeck M (1995) Global distribution of lakes. In: Lerman A, Imboden DM, Gat JR (eds) Physics and Chemistry of Lakes, 2nd edn. Springer, Berlin, pp 1-35Google Scholar
  11. 11.
    Peckham SD (1989) New results for self‐similar trees with applications to river networks. Water Resour Res 31:1023CrossRefGoogle Scholar
  12. 12.
    Pelletier JD (1999) Paleointensity variations of Earth's magnetic field and their relationship with polarity reversals. Phys Earth Planet Int 110:115CrossRefGoogle Scholar
  13. 13.
    Pelletier JD (1999) Self‐organization and scaling relationships of evolving river networks. J Geophys Res 104:7259Google Scholar
  14. 14.
    Pelletier JD, Turcotte DL (1999) Self‐affine time series: II. Applications and models. Adv Geophys 40:91Google Scholar
  15. 15.
    Rapp RH (1989) The decay of the spectrum of the gravitational potential and the topography of the Earth. Geophys J Int 99:449CrossRefGoogle Scholar
  16. 16.
    Strahler AN (1957) Quantitative analysis of watershed geomorphology. Trans Am Geophys Un 38:913Google Scholar
  17. 17.
    Tokunaga E (1978) Consideration on the composition of drainage networks and their evolution. Geogr Rep Tokyo Metro Univ 13:1Google Scholar
  18. 18.
    Turcotte DL (1987) A fractal interpretation of topography and geoid spectra on the earth, moon, Venus, and Mars. J Geophys Res 92:E597CrossRefGoogle Scholar
  19. 19.
    Turcotte DL (1994) Fractal theory and the estimation of extreme floods. J Res Natl Inst Stand Technol 99:377Google Scholar
  20. 20.
    US Water Resources Council (1982) Guidelines for Determining Flood Flow Frequency. Bulletin 17B. US Geological Survey, RestonGoogle Scholar

Books and Reviews

  1. 21.
    Feder J (1988) Fractals. Plenum Press, New YorkGoogle Scholar
  2. 22.
    Korvin G (1992) Fractal Models in the Earth Sciences. Elsevier, AmsterdamGoogle Scholar
  3. 23.
    Mandelbrot BB (1982) The Fractal Geometry of Nature. Freeman, San FranciscoGoogle Scholar
  4. 24.
    Turcotte DL (1997) Fractals and Chaos in Geology and Geophysics, 2nd edn. Cambridge University Press, CambridgeGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Donald L. Turcotte
    • 1
  1. 1.Department of GeologyUniversity of CaliforniaDavisUSA