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Lévy Flights and Wavelets Analysis of Volcano-Seismic Data

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In this work, we explore the use of Lévy flight and wavelet techniques as a tool for investigating the statistical properties of the seismic signals generated during volcanic eruptions. Using two methodologies, we discuss the statistical characterization of the whole seismic signal, from days prior to the eruption to days after the eruption. We show that the seismic energy released can be modeled using the stochastic Lévy flight model. The values of the Lévy flight exponent parameters \(\alpha\) were less than 2.0, indicating that the evolution of the released energy exhibits a long memory behavior. Furthermore, the wavelet techniques help to characterize the temporal evolution of the eruptive process. This observation is supported by our wavelet analysis, where we conclude that the proportions of total wavelet energy at lower levels of the eruption is high compared to the proportions at upper levels. The results from this study are expected to provide the basis for further analysis that might require a previous knowledge of the statistical behavior and parameters that characterize the seismic signals generated by these events.

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Data Availability

The seismicity at Bezymianny during the volcanic events were recorded by seismic stations belonging to the Bezymianny Volcano Campaign Seismic Network (PIRE). Raw seismograms from PIRE’s stations were obtained from the IRIS Data Management Center at http://www.iris.edu (last accessed September 2017).


  1. Abe, S., & Suzuki, N. (2017). Subdiffuson of volcanic earthquakes. Acta Geophysica,65, 491.

  2. Beccar-Varela, M. P., Gonzalez-Huizar, H., Mariani, M. C., Serpa, L., & Tweneboah, O. K. (2016a). Chile 2015: Lévy flight and long-range correlation analysis of earthquake magnitudes in Chile. Pure and Applied Geophysics,173, 2257–2266.

  3. Beccar-Varela, M. P., Gonzalez-Huizar, H., Mariani, M. C., & Tweneboah, O. K. (2016b). Use of wavelets techniques to discriminate between explosions and natural earthquakes. Physica A,457, 42–51.

  4. Beccar-Varela, M. P., Mariani, M. C., Tweneboah, O. K., & Florescu, L. (2017). Analysis of the Lehman Brothers collapse and the Flash Crash event by applying wavelets methodologies. Physica A,474, 162–171.

  5. Bell, A. F., Kilburn, C. R. J., & Nain, I. G. (2015). Volcanic eruptions: real-time forecasting. In M. Beer, E. Payelli, I. Kougioumtzoglou, & A.-K. Au (Eds.), Encyclopedia of earthquakes engineering. New York: Springer.

  6. Bell, A. F., Naylor, M., & Main, I. G. (2013). The limits of predictability of volcanic eruptions from accelerating rates of earthquakes. Geophysical Journal International,194(3), 1541–1553.

  7. Bogoyavlenskaya, G. E., Braitseva, O. A., Melekestsev, I. V., Kirianov, V. Y., & Miller, C. D. (1985). Catastrophic eruptions of the directed-blast type at Mount St. Helens, Bezymianny and Shiveluch volcanoes. Journal of Geodynamics,3, 189218.

  8. Buurman, H., West, M. E., & Thompson, G. (2013). The seismicity of the 2009 Redoubt eruption. Journal of Volcanology and Geothermal Research,259, 1630.

  9. Carey, S. N., & Sigurdsson, H. (1982). Influence of particle aggregation on deposition of distal tephra from the May 18, 1980 eruption of Mt. St. Helens volcano. Journal of Geophysical Research,87, 70617072.

  10. Garcia-Aristizabal, A., Marzocchi, W., & Fujita, E. (2012). A Brownian model for recurrent volcanic eruptions: An application to Miyakejima Volcano (Japan). Bulletin of Volcanology,74, 545–558.

  11. Gorshkov, G. S. (1959). Gigantic eruption of the volcano Bezymianny. Bulletin Volcanologique,20, 77–112.

  12. Ivanov, I., Koulakov, I., West, M., Jakovlev, A., Gordeev, E., Senyukov, S., et al. (2016). Magma sources beneath the Klyuchevskoy and Bezymianny volcanoes inferred from local earthquake seismic tomography. Journal of Volcanology and Geothermal Research,323, 6271.

  13. Khintchine, A. Y., & Lévy, P. (1936). Sur les lois stables (p. 202). Paris: C. R. Acad. Sci.

  14. Lévy, P. (1925). Calcul des probabilités. Paris: Gauthier-Villars.

  15. Mariani, M. C., Florescu, I., Sengupta, I., Beccar Varela, M. P., Bezdek, P., & Serpa, L. (2013). Lévy models and scale invariance properties applied to Geophysics. Physica A: Statistical Mechanics and Its Applications,392, 824–839.

  16. Mariani, M. C., Gonzalez-Huizar, H., Bhuiyan, M. A. M., & Tweneboah, O. K. (2017). Using dynamic fourier analysis to discriminate between seismic signals from natural earthquakes and mining explosions. AIMS Geosciences,3(3), 438–449.

  17. McNutt, S. R. (1996). Seismic monitoring and eruption forecasting of volcanoes: A review of the state-of-the-art and case histories. In R. Scarpa & R. Tilling (Eds.), Monitoring and mitigation of volcano hazard (pp. 99–146). New York: Springer.

  18. McNutt, S. R. (2002). Volcano seismology and monitoring for eruptions. International Handbook of Earthquake and Engineering Seismology,81A, 383–406.

  19. McNutt, S. R., & Nishimura, T. (2008). Volcanic tremor during eruptions: temporal characteristics, scaling and constraints on conduit size and processes. Journal of Volcanology and Geothermal Research,178, 10–18.

  20. Rutherford, M. J., & Devine, J. D. (1988). The May 18, 1980, eruption of Mount St. Helens. 3. Stability and chemistry of amphibole in the Magma chamber. Journal of Geophysical Research,93, 1194911959.

  21. Shimozuru, D. (1971). A seismological approach to the prediction of volcanic eruptions. The surveillance and prediction of volcanic activity (pp. 19–45). Paris: UNESCO.

  22. Shumway, R. H., & Stoffer, D. S. (2010). Time series analysis and its applications with R examples. New York: Springer.

  23. Thelen, W., West, M. E., & Senyukov, S. (2010). Seismic characterization of the fall 2007 eruptive sequence at Bezymianny Volcano, Russia. Journal of Volcanology and Geothermal Research,194, 201213.

  24. Wassermann, J. (2012). Volcano seismology, IASPEI new manual of seismological observatory practice 2. Potsdam: Deutsches GeoForschungsZentrum GFZ.

  25. West, M. E. (2013). Recent eruptions at Bezymianny volcano—A seismological comparison. Journal of Volcanology and Geothermal Research,263, 42–57.

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The authors would like to thank the reviewers for the careful reading of the manuscript and the fruitful suggestions that helped to improve this work. The authors would also like to thank Dr. Paul Glasserman for his discussions and suggestions about this topic that we implemented in this manuscript.

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Correspondence to Maria C. Mariani.

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Beccar-Varela, M.P., Gonzalez-Huizar, H., Mariani, M.C. et al. Lévy Flights and Wavelets Analysis of Volcano-Seismic Data. Pure Appl. Geophys. 177, 723–736 (2020). https://doi.org/10.1007/s00024-019-02298-x

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  • Lévy models
  • wavelets techniques
  • Bezymianny volcano
  • volcanic eruptions