Lévy Flights and Wavelets Analysis of Volcano-Seismic Data

Abstract

In this work, we explore the use of Levy 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 Levy flight model. The values of the Levy 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.