Non-linear dynamics of singular long-period long-lasting volcanic earthquakes observed at Mt. Asama
Abstract
On September 1, 2004, a middle-scale eruption occurred at Mt. Asama. Before the eruption, we had observed several kinds of singular events since October 2003. These singular events are classified into three types depending on these waveforms. The first type event (Type-1 event) has an impulsive ground velocity with a dominant period up to 10 sec and outgoing initial motion from the vent. The second type event (Type-2 event) is a long-period and long-lasting earthquake followed by two large high frequency earthquakes. The third type event (Type-3 event) is a tremor whose tip of the waveform is sharp, suggesting a non-linear dynamics of the source process. Takeo (2007) revealed the non-linear dynamics of Type-3 event using an embedding method of time delays and surrogate data analysis, and made clear that there existed a deterministic non-linear dynamics in the tremor excitation, which could be modeled with the system dimension between 3 to 7. In this paper, we apply the embedding method of time delays to Type-2 events and estimate geometrical and dynamical non-linear parameters of them to constrain the dynamics in the excitation. Embedding by the method of time delays has become the standard procedure in non-linear dynamical system analysis of a single time series. The first step for the nonlinear analysis of a single time series is to reconstruct a topologically equivalent attractor to the original in a relatively low-dimensional delay-coordinate space. The key questions are how the minimum embedding dimension can be determined for reconstructing the original dynamics, and how we select the delay time. We employed some reliable and robust techniques in the estimation of optimum delay time and minimum embedding dimension. Concretely speaking, we used higher-order correlations to select an optimum delay time (Albano et al., 1991). A practical method for determining minimum embedding dimension proposed by Cao (1997) was used in this paper. The waveforms of Type-2 events were similar to each other, so we selected a typical Type-2 event that occurred at 12:34 on June 12, 2004. We employed a FIR low-pass filter with a cut-off frequency of 1 Hz to omit high frequency component. The optimum time lag of 0.24 sec and the minimum embedding dimension of 7 were obtained by employing these methods. We succeed in reconstructing the attractor of the tremor using these dimension and time lag. Next, we calculated a correlation integral curve of the reconstructed attractor, founding a scaling region over one decade with the correlation dimension of 2.27 plus minus 0.27. The correlation dimension converged a certain value as increasing the embedding dimension, suggesting that the time series was not random data and the correlation dimension was estimated correctly. These results indicated that the source process of Type-2 event could be modeled on a non-linear dynamics with a system dimension between 3 to 6, which is similar dimension range with the source process of Type-3 events. Modifying a hydraulic control valve model, we simulated a long-period oscillation resembling with the long-period component of Type-2 event.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2009
- Bibcode:
- 2009AGUFMNG23B1086T
- Keywords:
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- 4410 NONLINEAR GEOPHYSICS / Bifurcations and attractors;
- 4445 NONLINEAR GEOPHYSICS / Nonlinear differential equations;
- 7280 SEISMOLOGY / Volcano seismology