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
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
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
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
Malamud BD, Turcotte DL (1999) Self-affine time series: I. Generation and analyses. Adv Geophys 40:1
Malamud BD, Turcotte DL (2006) The applicability of power-law frequency statistics to floods. J Hydrol 332:168
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
Malamud BD, Turcotte DL, Guzzetti F, Reichenbach P (2004) Landslide inventories and their statistical properties. Earth Surf Process Landf 29:687
Malamud BD, Turcotte DL, Guzzetti F, Reichenbach P (2004) Landslides, earthquakes, and erosion. Earth Planet Sci Lett 229:45
Mandelbrot BB (1967) How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science 156:636
Mandelbrot BB, Van Ness JW (1968) Fractional Brownian motions, fractional noises and applications. SIAM Rev 10:422
McClelland L et al (1989) Global Volcanism 1975-1985. Prentice-Hall, Englewood Cliffs
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
Peckham SD (1989) New results for self‐similar trees with applications to river networks. Water Resour Res 31:1023
Pelletier JD (1999) Paleointensity variations of Earth's magnetic field and their relationship with polarity reversals. Phys Earth Planet Int 110:115
Pelletier JD (1999) Self‐organization and scaling relationships of evolving river networks. J Geophys Res 104:7259
Pelletier JD, Turcotte DL (1999) Self‐affine time series: II. Applications and models. Adv Geophys 40:91
Rapp RH (1989) The decay of the spectrum of the gravitational potential and the topography of the Earth. Geophys J Int 99:449
Strahler AN (1957) Quantitative analysis of watershed geomorphology. Trans Am Geophys Un 38:913
Tokunaga E (1978) Consideration on the composition of drainage networks and their evolution. Geogr Rep Tokyo Metro Univ 13:1
Turcotte DL (1987) A fractal interpretation of topography and geoid spectra on the earth, moon, Venus, and Mars. J Geophys Res 92:E597
Turcotte DL (1994) Fractal theory and the estimation of extreme floods. J Res Natl Inst Stand Technol 99:377
US Water Resources Council (1982) Guidelines for Determining Flood Flow Frequency. Bulletin 17B. US Geological Survey, Reston
Books and Reviews
Feder J (1988) Fractals. Plenum Press, New York
Korvin G (1992) Fractal Models in the Earth Sciences. Elsevier, Amsterdam
Mandelbrot BB (1982) The Fractal Geometry of Nature. Freeman, San Francisco
Turcotte DL (1997) Fractals and Chaos in Geology and Geophysics, 2nd edn. Cambridge University Press, Cambridge
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag
About this entry
Cite this entry
Turcotte, D.L. (2012). Fractals in Geology and Geophysics. In: Meyers, R. (eds) Mathematics of Complexity and Dynamical Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1806-1_33
Download citation
DOI: https://doi.org/10.1007/978-1-4614-1806-1_33
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-1805-4
Online ISBN: 978-1-4614-1806-1
eBook Packages: Mathematics and StatisticsReference Module Computer Science and Engineering