Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Strange seismic attractor?

  • 44 Accesses

  • 10 Citations


Different time series were constructed from the data set containing all the seismic events recorded by the Parkfield network between 1969 and 1987. These series were analyzed to determine whether there exists an attractor in the phase space of the dynamical system characterizing seismic activity and to tentatively establish its dimension. The study has yielded ambiguous results. For all the time series analyzed, the dimension of the attractor appears higher than 12 and the correlation function of the seismic time series is undistinguishable from that of a series of random numbers of the same length. The lack of difference between the scaling parameters of two series suggests that, for all practical purposes, the seismic time series cannot be discriminated from a random series.

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


  1. Aki, K.,A probabilistic synthesis of precursory phenomena. InEarthquake Prediction (eds., Simpson, D. W., and Richards, P. G.) (AGU, Washington, D.C. 1981), pp. 566–574.

  2. Arnéodo, A., andSornette, D. (1984),Monte-Carlo Random Walk Experiment as a Test of Chaotic Orbits of Maps of the Interval, Phys. Rev. Lett.52, 1857–1860.

  3. Beltrami, H., andMareschal, J. C. (1990),Seismic Strange Attractor?, EOS71, 1453.

  4. Burridge, R., andKnopoff, L. (1967),Model and Theoretical Seismicity, Bull. Seismol. Soc. Am.,57, 341–371.

  5. Cao, T., andAki, K. (1984),Seismicity Simulation with a Mass-spring Model and a Displacement Hardening-softening Friction Law, Pure and Appl. Geophys.122, 10–23.

  6. Essex, C., Lookman, T., andNerenberg, M. A. H. (1987),The Climatic Attractor over Short Time Scales, Nature326, 64–66.

  7. Grassberger, P., andProcaccia, I. (1983a),Characterization of Strange Attractors, Phys. Rev. Lett.50, 346–349.

  8. Grassberger, P., andProcaccia, I. (1983b),Measuring the Strangeness of Strange Attractors, Physica D9, 189–208.

  9. Horowitz, F. G. (1989),A Strange Attractor Underlying Parkfield Seismicity? EOS70, 1359.

  10. Huang, J., andTurcotte, D. L. (1990),Are Earthquakes an Example of Deterministic Chaos?, Geophys. Res. Lett.17, 223–226.

  11. Kanamori, H., andAnderson, D. L. (1975),Theoretical Basis of Some Empirical Relations in Seismology, Bull. Seismol. Soc. Am.65, 1073–1096.

  12. Keilis-Borok, V. I. (1990),The Lithosphere of the Earth as a Nonlinear System with Implications for Earthquake Prediction, Rev. Geophys.28, 19–34.

  13. Keilis-Borok, V. I. andKossobokov, V. G. (1990),Premonitory Activation of Earthquake Flow: Algorithm M8, Phys. Earth Planet. Int.61, 73–83.

  14. King, G. (1983),The Accommodation of Large Strains in the Upper Lithosphere of the Earth and Other Solids by Self-similar Fault Systems: The Geometrical Origin of b Value, Pure and appl. Geophys.121, 761–785.

  15. Lorenz, E. N. (1981),Dimension of Weather and Climate Attractors, Nature353, 241.

  16. Nerenberg, M. A. H., andEssex, C. (1990),Correlation Dimension and Systematic Geometric Effects, Phys. Rev. Lett. A42, 7065–7074.

  17. Nicolis, C., andNicolis, G. (1984),Is There a Climatic Attractor?, Nature311, 529–532.

  18. Nussbaum, J., andRuina, A. (1987),A Two degrees of Freedom Earthquake Model with Static Dynamic Friction, Pure and Appl. Geophys.125, 629–656.

  19. Provenzale, A., Smith, L. A., Vio, R., andMurante, G. (1992),Distinguishing Between Low-dimensional Dynamics and Randomness in Measured Time Series, Physica D58, 31–49.

  20. Pacheco, J. F., Scholz, C. H., andSykes, L. R. (1992),Changes in Frequency-size Relationship from Small to Large Earthonakes, Nature355, 71–73.

  21. Rundle, J. B. (1992),Derivation of the Complete Gutenberg-Richter Magnitude-frequency Relation Using the Principle of Scale Invariance, J. Geophys. Res.94, 12,337–12,342.

  22. Rundle, J. B., andJackson, D. D. (1977),Numerical Simulation of Earthquake Sequences, Bull. Seismol. Soc. Am.67, 1363–1377.

  23. Smith, L. A. (1988),Intrinsic Limits on Dimension Calculations, Phys. Lett. A133, 283.

  24. Takens, F.,Detecting strange attractors in turbulences. InProc. Warwick Symp. 1980 (eds. Rand, D., and Young, B.), Lecture Notes in Mathematics 898 (Springer-Verlag, Berlin 1981).

  25. Tsonis, A. A., andElsner, J. B. (1988),The Weather Attractor over Very Short Time Scales, Nature333, 545–547.

  26. Turcotte, D. L. (1986),A Fractal Model for Crustal Deformation, Tectonophys.132, 261–269.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Beltrami, H., Mareschal, J. Strange seismic attractor?. PAGEOPH 141, 71–81 (1993). https://doi.org/10.1007/BF00876235

Download citation

Key words

  • Earthquakes
  • deterministic chaos
  • attractor
  • time series
  • Parkfield