Nonlinear Dynamics of Harmonic Tremor Time Series Recorded at Semeru Volcano (Indonesia)
Speaker:Cholisina Anik Perwita
Date: 2013/04/11Abstract
Harmonic tremor that follows explosive eruption is ubiquitous found in several volcanoes around the world. This kind of tremor also occurs in Semeru volcano located in East Java, Indonesia. Using the Lyapunov exponent, we try to obtain indication of nonlinear process that might be involved in generating harmonic tremor. We select 24 episodes of harmonic tremor during December 2009 that are characterized by number of harmonics as shown in the spectrogram. To reconstruct the phase space of the system, we used the embedding theorem suggested by Takens. The delay time for reconstruction was chosen from the first minimum of Average Mutual Information (AMI). Embedding dimension was estimated using false nearest neighbors and yielded result in a range between 5-7. Largest Lyapunov exponent calculated after a plot of stretching factor versus number of point yielded a curve with linear increase at the beginning and almost flat region in the end. A least square fit for the slope of the line corresponds to the largest Lyapunov exponent. Lyapunov exponent describes the rate of expansion or contraction of nearby orbits in the phase space. Value of Lyapunov exponent in our data set ranges between 0.013-0.039. Increasing value of Lyapunov exponent correlates with the number of harmonics in each tremor episode. We consider some models of source mechanism to explain Semeru tremor : (a) harmonic tremor may be modeled as a pressure cooker mechanism with a lava dome in the crater acting as a plug (Less and Bolton, 1998); (b) fluid flow induced oscillations can explain the occurrence of harmonic tremor in the Semeru volcano if the fluid is gas (Julian, 1994); (c) oscillation or wagging magma column model (Jellinek and Bercovici, 2011) even though this model is simplified to include only linear effect. Physical observation during our data set shows the lava dome completely solidified therefore the pressure cooker model may best describe the source of Semeru tremor.