Multifractal structure and Gutenberg-Richter parameter associated with volcanic emissions of high energy in Colima, México (years 2013–2015)

Abstract. The evolution of multifractal structures in physical processes, for instance, climatology, seismology or volcanology, contributes to detecting changes in the corresponding phenomena. The evolution of the multifractal structure of volcanic emissions of low, moderate, and high energy (Colima, México years 2013–2015) contributes to this research to detect quite evident signs of the immediacy of possible dangerous emissions of high energy close to 8.0x10⁸ J. These signs are manifested by the evolution of six multifractal parameters: the central Hölder exponent (α₀), the maximum and minimum Hölder exponents (α_max, α_min) the multifractal amplitude (W= α_max-α_min), the multifractal asymmetry (γ = [α_max-α₀]/[α₀-α_min]) and the complexity index, CI, which is defined as the addition of normalised values of α₀, W and γ. The results of the adapted Gutenberg-Richter seismic law to volcanic emissions of energy, as well as the corresponding skewness and standard deviation of the volcanic emission data, also contribute to confirming the results obtained using multifractal analysis. The obtained results, based on multifractal structure, adaptation of Gutenberg-Richter law to volcanic emissions, and basic statistical parameters, could be assumed as relevant to prevent a forthcoming volcanic episode of high energy, which could be additionally quantified by an appropriate forecasting algorithm.