Skip to main content
NCBI home page
Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1995 Jul 18;92(15):6697–6704. doi: 10.1073/pnas.92.15.6697

Scaling in geology: landforms and earthquakes.

D L Turcotte 1
PMCID: PMC41397  PMID: 11607562

Abstract

Landforms and earthquakes appear to be extremely complex; yet, there is order in the complexity. Both satisfy fractal statistics in a variety of ways. A basic question is whether the fractal behavior is due to scale invariance or is the signature of a broadly applicable class of physical processes. Both landscape evolution and regional seismicity appear to be examples of self-organized critical phenomena. A variety of statistical models have been proposed to model landforms, including diffusion-limited aggregation, self-avoiding percolation, and cellular automata. Many authors have studied the behavior of multiple slider-block models, both in terms of the rupture of a fault to generate an earthquake and in terms of the interactions between faults associated with regional seismicity. The slider-block models exhibit a remarkably rich spectrum of behavior; two slider blocks can exhibit low-order chaotic behavior. Large numbers of slider blocks clearly exhibit self-organized critical behavior.

Full text

PDF
6697

Images in this article

6700Fig. 6
on p.6700

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Bak P, Tang C, Wiesenfeld K. Self-organized criticality. Phys Rev A Gen Phys. 1988 Jul 1;38(1):364–374. doi: 10.1103/physreva.38.364. [DOI] [PubMed] [Google Scholar]
  2. Barriere B, Turcotte DL. Seismicity and self-organized criticality. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1994 Feb;49(2):1151–1160. doi: 10.1103/physreve.49.1151. [DOI] [PubMed] [Google Scholar]
  3. Carlson JM, Grannan ER, Swindle GH. Self-organizing systems at finite driving rates. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1993 Jan;47(1):93–105. doi: 10.1103/physreve.47.93. [DOI] [PubMed] [Google Scholar]
  4. Carlson JM, Langer JS, Shaw BE, Tang C. Intrinsic properties of a Burridge-Knopoff model of an earthquake fault. Phys Rev A. 1991 Jul 15;44(2):884–897. doi: 10.1103/physreva.44.884. [DOI] [PubMed] [Google Scholar]
  5. Carlson JM. Two-dimensional model of a fault. Phys Rev A. 1991 Nov 15;44(10):6226–6232. doi: 10.1103/physreva.44.6226. [DOI] [PubMed] [Google Scholar]
  6. Chen K, Bak P, Obukhov SP. Self-organized criticality in a crack-propagation model of earthquakes. Phys Rev A. 1991 Jan 15;43(2):625–630. doi: 10.1103/physreva.43.625. [DOI] [PubMed] [Google Scholar]
  7. Hill D. P., Reasenberg P. A., Michael A., Arabaz W. J., Beroza G., Brumbaugh D., Brune J. N., Castro R., Davis S., Depolo D., Ellsworth W. L., Gomberg J., Harmsen S., House L., Jackson S. M., Johnston M. J., Jones L., Keller R., Malone S., Munguia L., Nava S., Pechmann J. C., Sanford A., Simpson R. W., Smith R. B., Stark M., Stickney M., Vidal A., Walter S., Wong V., Zollweg J. Seismicity remotely triggered by the magnitude 7.3 landers, california, earthquake. Science. 1993 Jun 11;260(5114):1617–1623. doi: 10.1126/science.260.5114.1617. [DOI] [PubMed] [Google Scholar]
  8. Inaoka H, Takayasu H. Water erosion as a fractal growth process. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1993 Feb;47(2):899–910. doi: 10.1103/physreve.47.899. [DOI] [PubMed] [Google Scholar]
  9. Kramer S, Marder M. Evolution of river networks. Phys Rev Lett. 1992 Jan 13;68(2):205–208. doi: 10.1103/PhysRevLett.68.205. [DOI] [PubMed] [Google Scholar]
  10. Leheny RL, Nagel SR. Model for the evolution of river networks. Phys Rev Lett. 1993 Aug 30;71(9):1470–1473. doi: 10.1103/PhysRevLett.71.1470. [DOI] [PubMed] [Google Scholar]
  11. Mandelbrot B. B. Stochastic models for the Earth's relief, the shape and the fractal dimension of the coastlines, and the number-area rule for islands. Proc Natl Acad Sci U S A. 1975 Oct;72(10):3825–3828. doi: 10.1073/pnas.72.10.3825. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Mandelbrot B. How long is the coast of britain? Statistical self-similarity and fractional dimension. Science. 1967 May 5;156(3775):636–638. doi: 10.1126/science.156.3775.636. [DOI] [PubMed] [Google Scholar]
  13. Nakanishi H. Cellular-automaton model of earthquakes with deterministic dynamics. Phys Rev A. 1990 Jun 15;41(12):7086–7089. doi: 10.1103/physreva.41.7086. [DOI] [PubMed] [Google Scholar]
  14. Nakanishi H. Statistical properties of the cellular-automaton model for earthquakes. Phys Rev A. 1991 Jun 15;43(12):6613–6621. doi: 10.1103/physreva.43.6613. [DOI] [PubMed] [Google Scholar]
  15. Prigozhin L. Sandpiles and river networks: Extended systems with nonlocal interactions. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1994 Feb;49(2):1161–1167. doi: 10.1103/physreve.49.1161. [DOI] [PubMed] [Google Scholar]
  16. Rinaldo A, Rodriguez-Iturbe I, I, Rigon R, Ijjasz-Vasquez E, Bras RL. Self-organized fractal river networks. Phys Rev Lett. 1993 Feb 8;70(6):822–825. doi: 10.1103/PhysRevLett.70.822. [DOI] [PubMed] [Google Scholar]
  17. Vasconcelos GL, de Sousa Vieira M, Nagel SR. Implications of a conservation law for the distribution of earthquake sizes. Phys Rev A. 1991 Dec 15;44(12):R7869–R7872. doi: 10.1103/physreva.44.r7869. [DOI] [PubMed] [Google Scholar]
  18. de Sousa Vieira M Self-organized criticality in a deterministic mechanical model. Phys Rev A. 1992 Nov 15;46(10):6288–6293. doi: 10.1103/physreva.46.6288. [DOI] [PubMed] [Google Scholar]

Articles from Proceedings of the National Academy of Sciences of the United States of America are provided here courtesy of National Academy of Sciences

RESOURCES