Skip to main content
SpringerLink
Log in

Size distribution of the number of lithospheric plates

  • Published:
Izvestiya, Physics of the Solid Earth Aims and scope Submit manuscript

Abstract

To describe the cumulative distribution of the number of lithospheric plates over areas S, the dependence N(≥S) ∼ S −0.33 was proposed by Bird [2003]. Based on dimension considerations, the dependence N(≥S) ∼ (ɛ/S)1/3, where ɛ is the generation rate of kinetic energy of convection in the mantle estimated at 10−11 m2/s3, is proposed. The analogy of plate formation with developed hydrodynamic turbulence and other processes involving an energy input into the system and its dissipation is considered. Simple experiments on random partitioning of a surface into polygons gave their cumulative distributions over areas resembling those observed for lithospheric plates. This has led to the conclusion that the plate distribution pattern is characteristic of the random partitioning of surfaces.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. K. Aki, “Scaling Law of Seismic Spectrum,” J. Geophys. Res. 72, 1217–1231 (1967).

    Article  Google Scholar 

  2. G. I. Barenblatt, Similarity, Self-Similarity, and Intermediate Asymptotics (Gidrometeoizdat, Leningrad, 1978; Consultants Bureau, New York, 1979).

    Google Scholar 

  3. G. I. Barenblatt and V. A. Gorodtsov, “On the Structure of the Microstress Field in a Well-Developed Plastic Flow,” Prikl. Mat. Mekh. 28(2), 326–334 (1964).

    Google Scholar 

  4. P. Bird, “An Updated Digital Model of Plate Boundaries,” Geochem. Geophys. Geosystems 4(3), 1027 (2003).

    Article  Google Scholar 

  5. W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1966; Mir, Moscow, 1967), Vol. 2.

    Google Scholar 

  6. G. S. Golitsyn, “Simple Theoretical and Experimental Study of Convection with Some Geophysical Applications and Analogies,” J. Fluid Mech. 95, 567–608 (1979).

    Article  Google Scholar 

  7. G. S. Golitsyn, Convection Study with Geophysical Applications and Analogies (Gidrometeoizdat, Leningrad, 1980) [in Russian].

    Google Scholar 

  8. G. S. Golitsyn, “The Place of the Gutenberg-Richter Law among Other Statistical Laws of Nature,” in Computational Seismology (Moscow, 2001), Vol. 32, pp. 138–161.

    Google Scholar 

  9. G. S. Golitsyn, “Energy Cycle of Geodynamics and the Seismic Process,” Fiz. Zemli, No. 6, 3–6 (2007) [Izvestiya, Phys. Solid Earth 43, 443–446 (2007).

  10. G. S. Golitsyn and A. N. Vul’fson, “A Conservative Form of the Deep Convection Equations and the Efficiency of Heat Energy Conversion in a Polytropic Mantle Model,” Fiz. Zemli, No. 8, 7–16 (2007) [Izvestiya, Phys. Solid Earth 43, 625–634 (2007)].

  11. Y. Y. Kagan, “Observational Evidence for Earthquakes As a Nonlinear Dynamic Process,” Physica D 77, 160–172 (1994).

    Article  Google Scholar 

  12. A. B. Kazansky, “Studying the Motion Energy Dissipation Process in Highly Fractured Glaciers Using Remote Sensing Technique,” Ann. Glaciology 19, 239–248 (1987).

    Google Scholar 

  13. V. I. Keilis-Borok, “Symptoms of Instability in a system of Earthquake-Prone Faults,” Physica D 77, 193–199 (1994).

    Article  Google Scholar 

  14. M. G. Kendall and P. A. P. Moran, Geometrical Probability (Griffin, London, 1963; Fizmatlit, Moscow, 1972) [in Russian].

    Google Scholar 

  15. E. G. Mirlin, “Problem of Eddy Motions in “Solid” Shells of the Earth and Geotectonic Implications,” Geotektonika, No. 4, 43–60 (2006).

  16. A. S. Monin and A. M. Yaglom, Statistical Hydromechanics (Fizmatgiz, Moscow, 1965 and 1967), 2 vols. [in Russian].

    Google Scholar 

  17. A. M. Obukhov, “Pressure Fluctuations in a Turbulent Flow,” Dokl. Akad. Nauk SSSR 66(1), 17–20 (1949).

    Google Scholar 

  18. L. Prandtl, “Meteorologishe Anwendungen der Stromunglehre,” Beitr. Phys. Atmospher. 19(3), 189–202 (1932).

    Google Scholar 

  19. G. Schubert, D. Turcotte, and P. Olson, Mantle Convection in the Earth and Planets (Cambridge Univ. Press, New York, 2001).

    Book  Google Scholar 

  20. D. Sornette and V. F. Pisarenko, “Fractal Plate Tectonics,” Geophys. Rev. Lett. 30, 1105 (2002).

    Article  Google Scholar 

  21. Y.-h. Taguchi, “Numerical Study of Granular Turbulence and an Appearance of the k-5/3 Energy Spectrum in the Absence of Mean Flow,” Physica D 80, 61–71 (1995)

    Google Scholar 

  22. V. P. Trubitsyn, “Geodynamic Model of the Evolution of the Pacific Ocean,” Fiz. Zemli, No. 2, 3–27 (2006) [Izvestiya, Phys. Solid Earth 42, 93–113 (2006)].

Download references

Author information

Authors and Affiliations

  1. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Pyzhevskii per. 3, Moscow, 109017, Russia

    G. S. Golitsyn

Authors
  1. G. S. Golitsyn
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. S. Golitsyn.

Additional information

Original Russian Text © G.S. Golitsyn, 2008, published in Fizika Zemli, 2008, No. 3, pp. 3–8.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Golitsyn, G.S. Size distribution of the number of lithospheric plates. Izv., Phys. Solid Earth 44, 175–180 (2008). https://doi.org/10.1134/S1069351308030014

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1069351308030014

PACS numbers

Search

Navigation