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Lévy Flights and Wavelets Analysis of Volcano-Seismic Data

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Abstract

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).

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Acknowledgements

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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Keywords

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