Skip to main content

The fractal structure of the sequence of volcanic eruptions worldwide: Order clustering of events and episodic discharge of material

Journal of Volcanology and Seismology volume 8, pages 34–53 (2014)Cite this article

Abstract

This study of the time-dependent structure of the Earth’s volcanic activity at scales from a few months to a few centuries is based on three sequences of events: two selections from the Smithsonian catalog and a selection from the ice core-volcano index catalog (IVI). This data selection was based on carefully chosen (1) lower thresholds for event size and (2) time intervals, so as to make the resulting data subsets homogeneous. The next step was to analyze the time structure. Three types of clustering trends were revealed, as follows. (1) The rate of events in the sequence is not uniform over time, with their dates forming activity episodes. (2) The time-ordered sequence of eruption size shows that larger events form closely connected clusters. We give the name “order clustering” to this novel phenomenon. (3) The eruption rate shows episodic and spiky behavior. In each of the three cases the tendency to clustering has a multi-scale, fractal (self-similar) character: the sequences of eruptions behave as impulsive 1/f noise. These results suggest the hypothesis that there must be some global mechanism that is responsible for synchronization of bursts of activity on this planet.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

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

References

  • Aki, K., Maximum likelihood estimates of b in the formula logN = a − bM and its confidence limits, Bull. Earthquake Res. Inst. Univ. Tokyo, 1965, vol. 43, pp. 237–239.

    Google Scholar 

  • Ammann, C.M. and Naveau, P., Statistical analysis of tropical explosive volcanism occurrences over the last 6 centuries, Geophys. Res. Lett., 2003, vol. 30, pp. 14-1–14-4.

    Google Scholar 

  • Bak, P., How Nature Works. The Science of Self-Organized Criticality, New York: Copernicus, 1997.

    Google Scholar 

  • Bak P., Tang C., and Weisenfeld, K., Self-organized criticality: an explanation of 1/f noise, Phys. Rev., 1987, vol. 38, pp. 364–374.

    Article  Google Scholar 

  • Bebbington, M.S. and Lai, C.D., On nonhomogeneous models for volcanic eruptions, J. Math. Geol., 1996, vol. 28, pp. 585–600.

    Article  Google Scholar 

  • Cambray, H. and Cadet, J.-P., Synchronisme de l’activite volcanique d’arc: mythe ou realite?, C. R. Acad. Sci., 1996, Ser. IIa, vol. 322, pp. 237–244.

    Google Scholar 

  • Condit, C.D. and Connor, B.C., Recurrence rates of volcanism in basaltic volcanic fields: an example from the Springerville volcanic field, Arizona, Geol. Soc. Am. Bull., 1996, vol. 108, no. 10, pp. 1225–1241.

    Article  Google Scholar 

  • Connor, B.C. and Hill, B.E., Three non-homogeneous Poisson models for the probability of basaltic volcanism: application to the Yucca Mountain region, Nevada, J. Geophys. Res., 1995, vol. 100, no. B6, pp. 10107–10125.

    Article  Google Scholar 

  • De la Cruz-Reina, S., Poisson-distributed patterns of explosive eruptive activity, Bull. Volcanol., 1991, vol. 54, pp. 57–67.

    Article  Google Scholar 

  • Dubois, J. and Cheminee, J.-L., Fractal analysis applied to the sequence of volcanic eruptions of Piton de la Fournaise (La Reunion Island): Cantor dust model, C. R. Acad. Sci. Paris, 1988, vol. 307, no. 15, pp. 1723–1729.

    Google Scholar 

  • Dubois, J. and Cheminee, J.-L., Fractal analysis of eruptive activity of some basaltic volcanoes, J. Volcanol. Geotherm. Res., 1991, vol. 45, no. 3–4, pp. 197–208.

    Article  Google Scholar 

  • Dubois, J. and Cheminee, J.-L., Piton de la Fournaise volcano eruptive cycles: fractal analysis, attractors, deterministic aspects, Bull. Soc. Geol. France, 1993, vol. 164, pp. 3–16.

    Google Scholar 

  • Godano, C. and Civetta, L., Multifractal analysis of Vesuvius volcano eruptions, Geophys. Res. Lett., 1996, vol. 23, no. 10, pp. 1167–1170.

    Article  Google Scholar 

  • Gusev, A.A. Multi-scale order clustering in the sequence of terrestrial earthquakes, Fizika Zemli, 2005, no. 10, pp. 30–45.

    Google Scholar 

  • Gusev, A. A., Ponomareva, V.V., Braitseva, O. A., Melekestsev, I. V., and Sulerzhitsky, L. D., Great explosive eruptions on Kamchatka during the last 10,000 years: Selfsimilar irregularity of the output of volcanic products, J. Geophys. Res., 2003, vol. 108, no. B2, 2126. doi:10.1029/2001JB000312, 2003.

    Article  Google Scholar 

  • Guttorp, P. and Thompson, M.L., Estimating second-order parameters of volcanicity from historical data, J. Am. Stat. Assoc., 1991, vol. 86, pp. 578–583.

    Article  Google Scholar 

  • Ho, C.-H., Non-homogeneous Poisson model for volcanic eruptions, Math. Geol., 1991, vol. 23, pp. 91–98.

    Article  Google Scholar 

  • Ho, C.-H., Smith, E.I., Feuerbach, D.L., and Naumann, T.R., Eruptive probability calculation for the Yucca Mountain site, USA: statistical estimation of recurrence rates, Bull. Volcanol., 1991, vol. 54, pp. 50–56.

    Article  Google Scholar 

  • Jaquet, O. and Carniel, R., Stochastic modelling at Stromboli: a volcano with remarkable memory, J. Volcanol. Geotherm. Res., 2001, vol. 105, pp. 249–262.

    Article  Google Scholar 

  • Jones, G., Chester, D.K., and Shooshtarian, F., Statistical analyses of the frequency of eruptions at Furnas Volcano, Sao Miguel, Azores, J. Volcanol. Geotherm. Res., 1999, vol. 92, pp. 31–38.

    Article  Google Scholar 

  • Kennett, J.P., McBirney, A.R., and Thunell, R.C., Episodes of Cenozoic volcanism in the circum-Pacific region, J. Volcanol. Geotherm. Res., 1977, vol. 2, pp. 145–163.

    Article  Google Scholar 

  • Makarenko, G.F., Bursts of trap volcanism during Mesozoic and Cenozoic time, Vulkanol. Seismol., 1982, no. 4, pp. 65–77.

    Google Scholar 

  • Mandelbrot, B.B., The Fractal Geometry of Nature, New York: W.H. Freeman, 1982.

    Google Scholar 

  • Mandelbrot, B.B., Multifractals and 1/f Noise: Wild Self-Affinity in Physics (1963–1976), Springer, 1999.

    Book  Google Scholar 

  • Mason, B.G., Pyle, D., Dade, B., and Jupp, T., Seasonality of volcanic eruptions, J. Geophys. Res., 2004, vol. 109, no. B4, B04206.

    Google Scholar 

  • Milotti, E., 1/f noise: a pedagogical review, 2002, URL: http://arxiv.org/abs/physics/0204033.

    Google Scholar 

  • Ogata, Y. and Abe, K., Some statistical features of the longterm variation of the global and regional seismic activity, Int. Stat. Rev., 1991, vol. 59, no. 2, pp. 139–161.

    Article  Google Scholar 

  • Pelletier, J.D., Statistical self-similarity of magmatism and volcanism, J. Geophys. Res., 1999, vol. 104, no. B7, pp. 15 425–15 438.

    Article  Google Scholar 

  • Pisarenko, V.F. and Pisarenko, D.V., Spectral properties of multifractal measures, Phys. Lett. A, 1991, vol. 153, no. 4–5, pp. 169–172.

    Article  Google Scholar 

  • Prueher, L.M. and Rea, D.K., Tephrochronology of the Kamchatka-Kurile and Aleutian arcs: evidence for volcanic episodicity, J. Volcanol. Geotherm. Res., 2001, vol. 106, pp. 67–87.

    Article  Google Scholar 

  • Rea, D.K. and Scheidegger, K.F., Eastern Pacific spreading rate fluctuation and its relation to Pacific area volcanic episodes, J. Volcanol. Geotherm. Res., 1979, vol. 5, pp. 135–148.

    Article  Google Scholar 

  • Robock, A., Volcanic eruptions and climate, Rev. Geophys., 2000, vol. 38, pp. 191–219.

    Article  Google Scholar 

  • Robock, A. and Free, M.P., The volcanic record in ice cores for the past 2000 years, in Climatic Variations and Forcing Mechanisms of the Last 2000 Years, Jones, P.D., Bradley, R.S., and Jouzel, J., Eds., Springer-Verlag, 1996, pp. 533–546.

    Chapter  Google Scholar 

  • Siebert, L. and Simkin, T., Volcanoes of the World, 2002: http://www.volcano.si.edu/gvp/world/

    Google Scholar 

  • Sigurdsson, H., Ed., Encyclopedia of Volcanoes, San Diego, California: Academic Press, 2000.

    Google Scholar 

  • Simkin, T., Terrestrial volcanism in space and time, Ann. Rev. Earth Planet. Sci., 1993, vol. 21, pp. 427–452.

    Article  Google Scholar 

  • Simkin, T. and Siebert, L., Volcanoes of the World, 2nd ed., Tucson, Arizona: Geoscience Press, 1994.

    Google Scholar 

  • Telesca, L., Cuomoa, V., Lapenna, V., and Macchiato, M., Time-clustering analysis of volcanic occurrence sequences, Phys. Earth Planet. Inter., 2002, vol. 131, pp. 47–62.

    Article  Google Scholar 

  • Turcotte, D.L., Fractals and Chaos in Geology and Geophysics, Cambridge University Press, 1992.

    Google Scholar 

  • Wickman, F.E., Repose patterns of volcanoes. I. Volcanic eruptions regarded as random phenomena, Arkansas Miner. Geol., 1966, vol. 4, pp. 291–301.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Volcanology and Seismology, Far East Branch, Russian Academy of Sciences, 9 Piip boulevard, Petropavlovsk-Kamchatskii, 683006, Russia

    A. A. Gusev

  2. Kamchatka Branch, Geophysical Service, Russian Academy of Sciences, 9 Piip boulevard, Petropavlovsk-Kamchatskii, 683006, Russia

    A. A. Gusev

Authors
  1. A. A. Gusev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. A. Gusev.

Additional information

Original Russian Text © A.A. Gusev, 2014, published in Vulkanologiya i Seismologiya, 2014, No. 1, pp. 38–60.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Gusev, A.A. The fractal structure of the sequence of volcanic eruptions worldwide: Order clustering of events and episodic discharge of material. J. Volcanolog. Seismol. 8, 34–53 (2014). https://doi.org/10.1134/S0742046314010023

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0742046314010023

Keywords

  • Volcanic Eruption
  • Fractal Structure
  • Time Structure
  • Surrogate Data
  • Time Dependent Behavior