Maximal Lyapunov exponent variations of volcanic tremor recorded during explosive and effusive activity at Mt Semeru volcano, Indonesia

Abstract

Abstract. We analyze 25 episodes of volcanic tremor recorded from 22 November until 31 December 2009 at Mt Semeru volcano in order to investigate their spectral and dynamical properties. The overtone frequencies for most of the tremor events indicate a pattern of period-doubling, which is one possible route that can lead a system to chaotic behavior. Exponential divergence of the phase space orbits is a strong indicator of chaos and was quantified by estimating the maximal Lyapunov exponent (MLE) for all tremor events. MLEs were found to vary linearly with the number of frequency overtones present in the tremor signals. This implies that the tremor source at Semeru fluctuates between a quasi-periodic state with few overtone frequencies (2-3) and small MLEs (~0.013), and a chaotic one with more overtones (up to 8) and larger MLEs (up to 0.039). These results agree well with the tremor generation model suggested previously by Julian (1994), which describes wall oscillations of a crack excited by unsteady fluid flow. In this model, as fluid pressure increases, a period-doubling cascade leads to numerous new frequencies and a chaotic tremor signal. The temporal variation of MLEs exhibited significant fluctuations from 23 until 31 December when the eruptive activity shifted from explosive to effusive. Such a situation may reflect variable fluid pressure conditions inside the conduit, where at first magma is accumulated and subsequently is erupted, releasing the buildup of pressure. Our results give further evidence for the role of nonlinear deterministic processes in generating volcanic tremor and call for similar investigations to be conducted in other volcanoes.

On data reduction methods for volcanic tremor characterization: the 2012 eruption of Copahue volcano, Southern Andes

“…For each 20-min segment, the permutation entropy for the vertical component, filtered in the frequency range 0.5-10 Hz, was calculated. The use of this parameter to detect volcanic tremor is supported by numerous studies that associate its source mechanism to a lowdimensional nature (e.g., Konstantinou et al 2013). The dimension of a time series is a measure of its complexity, which is generally extracted in the reconstructed phase space by computing the fractal dimension, Lyapunov exponents, or Kolmogorov-Sinai entropy, among others (see Abarbanel et al 1993, for a review).…”

The Characteristics of Volcanic Eruption in Indonesia

“…The type of eruption of the Semeru is Strombolian, because it involves the fragmentation of low viscosity basaltic magma by volatile degassing [9]. Other volcanological studies have suggested that the Semeru eruption type is vulcanian with VEI ranging between 2 and 3, because it has generated eruption columns, lava dome growth, and small pyroclastic flow [11], has produced basaltic incandescent lavas; and was accompanied by hot clouds. The greatest eruption occurred in 1944.…”

Identifikasi dinamika sumber tremor vulkanik Gunungapi Raung berdasarkan analisis fraktal

“…Penentuan dimensi fraktal merupakan analisis non linier untuk mengidentifikasi dinamika dari sumber tremor vulkanik suatu gunungapi bersifat kaotik atau tidak (Konstantinou et al, 2013). Beberapa penelitian mengenai analisis fraktal yang sudah dilakukan di beberapa gunungapi antara lain analisis fraktal tremor vulkanik yang terekam di gunung Semeru (Maryanto & Mulyana, 2008) (Konstantinou et al, 2013) dan analisis fraktal tremor vulkanik yang terekam di gunung Sakurajima (Maryanto, Santosa, Mulyana, & Hendrasto, 2011 ( 1) dimana px(i) merupakan probability distribution dari Xi dan py(j) merupakan probability distribution dari Yj (j=α,α+1,…, α+M) . Gambar 1 merupakan delay time tremor vulkanik gunung Raung didapatkan 0,08 sekon (timelag dikalikan dengan sampling rate) (Fraser & Swinney, 1986).…”