Advertisement

A stochastic model for strike-slip faulting

  • G. Ranalli
Article

Abstract

The frequency of length of strike-slip faults in continental crust follows a lognormal probability distribution, and a nonlinear positive correlation exists between length and offset. These results appear to be scale-independent. An explanation of the observations is presented in terms of a stochastic model which treats the occurrence of faulting as a Kolmogorov-type process obeying the law of proportionate effect. This model accounts for the length distribution of faults. Tentatively, the correlation between length and offset is ascribed to an allometric law relating the relative growth rates of these two parameters. The possibility of the application of the concepts of continuum damage mechanics to the problem is also briefly explored as a way to introduce time-space averages of tectonic stress and strain-rate into the model.

Key words

stochastic process structural geology continuum mechanics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Agterberg, F. P., 1974, Geomathematics: Amsterdam: Elsevier.Google Scholar
  2. Aitchison, J. and Brown, J. A. C., 1957, The lognormal distribution: Cambridge, University Press.Google Scholar
  3. Caputo, M., 1977, A mechanical model for the statistics of earthquakes, magnitude, moment, and fault distribution: Bull. Seism. Soc. Amer., v. 67, p. 849–861.Google Scholar
  4. Hult, J., 1979, CDM—Capabilities, limitations, and promises,in Easterling, K. E., ed., Mechanisms of deformation and fracture: Oxford, Pergamon Press, p. 233–247.Google Scholar
  5. Huxley, J. S., 1932, Problems of relative growth: New York, Dial Press.Google Scholar
  6. Kanamori, H. and Anderson, D. L., 1975, Theoretical basis of some empirical relations in seismology: Bull Seism. Soc. Amer., v. 65, p. 1073–1095.Google Scholar
  7. Kapteyn, J. C., 1903, Skew frequency curves in biology and statistics: Groningen, Noordhoff.Google Scholar
  8. King, G. C. P., 1978, Geological faults: fracture, creep and strain: Proc. Roy. Soc. London, A-288, p. 197–212.Google Scholar
  9. Kolmogorov, A. N., 1941, Über das logarithmisch normale Verteilungsgesetz der Dimensionen der Teilchen bei Zerstückelung: C. R. Acad. Sci. U.R.S.S. v. 31, p. 99–101.Google Scholar
  10. Ranalli, G., 1976, Length distribution of strike-slip faults and the process of breakage in continental crust: Can. Jour. Earth Sci., v. 13, p. 704–707.Google Scholar
  11. Ranalli, G., 1977, Correlation between length and offset in strike-slip faults: Tectonophysics, v. 37, T1-T7.Google Scholar
  12. Smart, J. S., 1979, Determinism and randomness in fluvial geomorphology: EOS, Trans. Amer. Geophys. Union, v. 60, 651–655.Google Scholar
  13. Sole Sugrañes, L., 1978, Alineaciones y fracturas en el sistema Catalan segun las imagenes LANDSAT-1: Tecniterrae, v. 22, p. 1–11.Google Scholar
  14. Tchalenko, J. S., 1970, Similarities between shear zones of different magnitudes: Bull. Geol. Soc. Amer., v. 81, p. 1625–1640.Google Scholar
  15. Vistelius, A. B., 1960, The skew frequency distribution and the fundamental law of the geochemical processes: Jour. Geol., v. 68, p. 1–22.Google Scholar

Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • G. Ranalli
    • 1
    • 2
  1. 1.Department of GeologyCarleton UniversityOttawaCanada
  2. 2.Institut für Meteorologie und GeophysikGoethe-UniversitätFrankfurt a. MainBRD

Personalised recommendations