Skip to main content

Fractals in Geology and Geophysics

  • Reference work entry
Extreme Environmental Events

Article Outline

Glossary

Definition of the Subject

Introduction

Drainage Networks

Fragmentation

Earthquakes

Volcanic Eruptions

Landslides

Floods

Self‐Affine Fractals

Topography

Earth's Magnetic Field

Future Directions

Bibliography

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 599.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Abbreviations

Fractal :

A collection of objects that have a power-law dependence of number on size.

Fractal dimension :

The power-law exponent in a fractal distribution.

Bibliography

Primary Literature

  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 157:2323

    Article  Google Scholar 

  2. Malamud BD, Turcotte DL (1999) Self-affine time series: I. Generation and analyses. Adv Geophys 40:1

    Google Scholar 

  3. Malamud BD, Turcotte DL (2006) The applicability of power-law frequency statistics to floods. J Hydrol 332:168

    Article  Google Scholar 

  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 2:479

    Google Scholar 

  5. Malamud BD, Turcotte DL, Guzzetti F, Reichenbach P (2004) Landslide inventories and their statistical properties. Earth Surf Process Landf 29:687

    Article  Google Scholar 

  6. Malamud BD, Turcotte DL, Guzzetti F, Reichenbach P (2004) Landslides, earthquakes, and erosion. Earth Planet Sci Lett 229:45

    Article  CAS  Google Scholar 

  7. Mandelbrot BB (1967) How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science 156:636

    Article  CAS  Google Scholar 

  8. Mandelbrot BB, Van Ness JW (1968) Fractional Brownian motions, fractional noises and applications. SIAM Rev 10:422

    Article  Google Scholar 

  9. McClelland L et al (1989) Global Volcanism 1975-1985. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  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 1-35

    Google Scholar 

  11. Peckham SD (1989) New results for self‐similar trees with applications to river networks. Water Resour Res 31:1023

    Article  Google Scholar 

  12. Pelletier JD (1999) Paleointensity variations of Earth's magnetic field and their relationship with polarity reversals. Phys Earth Planet Int 110:115

    Article  Google Scholar 

  13. Pelletier JD (1999) Self‐organization and scaling relationships of evolving river networks. J Geophys Res 104:7259

    Google Scholar 

  14. Pelletier JD, Turcotte DL (1999) Self‐affine time series: II. Applications and models. Adv Geophys 40:91

    Google Scholar 

  15. Rapp RH (1989) The decay of the spectrum of the gravitational potential and the topography of the Earth. Geophys J Int 99:449

    Article  Google Scholar 

  16. Strahler AN (1957) Quantitative analysis of watershed geomorphology. Trans Am Geophys Un 38:913

    Google Scholar 

  17. Tokunaga E (1978) Consideration on the composition of drainage networks and their evolution. Geogr Rep Tokyo Metro Univ 13:1

    Google Scholar 

  18. Turcotte DL (1987) A fractal interpretation of topography and geoid spectra on the earth, moon, Venus, and Mars. J Geophys Res 92:E597

    Article  Google Scholar 

  19. Turcotte DL (1994) Fractal theory and the estimation of extreme floods. J Res Natl Inst Stand Technol 99:377

    Google Scholar 

  20. US Water Resources Council (1982) Guidelines for Determining Flood Flow Frequency. Bulletin 17B. US Geological Survey, Reston

    Google Scholar 

Books and Reviews

  1. Feder J (1988) Fractals. Plenum Press, New York

    Google Scholar 

  2. Korvin G (1992) Fractal Models in the Earth Sciences. Elsevier, Amsterdam

    Google Scholar 

  3. Mandelbrot BB (1982) The Fractal Geometry of Nature. Freeman, San Francisco

    Google Scholar 

  4. Turcotte DL (1997) Fractals and Chaos in Geology and Geophysics, 2nd edn. Cambridge University Press, Cambridge

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

Š 2011 Springer-Verlag

About this entry

Cite this entry

Turcotte, D.L. (2011). Fractals in Geology and Geophysics. In: Meyers, R. (eds) Extreme Environmental Events. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7695-6_31

Download citation

Publish with us

Policies and ethics