HR: 0800h
AN: NG11A-0175 [Abstracts]
TI: Non-linear dynamic of singular long-period volcanic tremors observed at Mt. Asama
AU: * Takeo, M
EM: takeo@eri.u-tokyo.ac.jp
AF: Earthquake Research Institute, Univ. Tokyo, 1-1-1, Yayoi, Bunkyo, Tokyo, 113-0032, Japan
AB:
On September 1, 2004, a middle-scale eruption occurred at Mt.Asama. Before the eruption, we observed three
long-period tremors with singular waveforms, which occurred at 4:25, 11:30, and 20:30 on June 24, 2004. The
common characteristic of these tremors is that the tip of the waveform is sharp. This sharp-pointed waveform
may suggest a non-linear dynamics of the source process. In addition, these singular tremors occurred at
intervals of 7 to 9 hours on the same day, suggesting that the source process of these tremors is in common. In
this paper, the dynamical structure and characteristics of these tremors are investigated by employing some
reliable and robust techniques in the estimation of geometrical and dynamical parameters.
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. We
employed some reliable and robust techniques in the estimation of optimum delay time and minimum
embedding dimension.
To select the long-period component, we employ a FIR low-pass filter with a cut-off frequency of 0.4Hz. For the
tremor occurred at 4:25, the optimum time lag of 0.24 sec and the minimum embedding dimension of 8 were
obtained by employing these methods. We succeed in reconstructing an attractor of the tremors using these
dimension and time lag. Then, we calculated a correlation integral curve of the reconstructed attractor, founding a
scaling region over one decade with the correlation dimension of 2.04 plus minus 0.17. The correlation
dimension converges a certain value as increasing the embedding dimension. This suggests that the time
series is not random data and the correlation dimension is estimated correctly.
The optimum time lag and the minimum embedding dimension for the tremor at 11:30 were 2.0 sec and 6,
respectively. We find a certain degree of scaling region, and estimated that the correlation dimension is 2.84 plus
minus 0.32. The optimum time lag of 0.36 sec and the minimum embedding dimension of 8 were obtained for
the tremor at 20:30. In this case, a correlation integral curve of the reconstructed attractor represents a scaling
region over one decade with the correlation dimension of 1.80 plus minus 0.20.
The surrogate data analysis is a kind of statistical hypothesis testing. If testing parameters obtained from 39 sets
of surrogate data shift clearly from that of the original data, the null-hypothesis is rejected with a significance level
of 0.05. This surrogate data analyses for these three tremors indicate that the null-hypotheses are rejected with
the strong rejection level, suggesting there exists a deterministic non-linear dynamics in the tremor excitation,
which can be modeled with the system dimension ranging between 3 to 7.
DE: 4440 Fractals and multifractals
DE: 4455 Nonlinear waves, shock waves, solitons (0689, 2487, 3280, 3285, 4275, 6934, 7851, 7852)
DE: 7280 Volcano seismology (8419)
SC: Nonlinear Geophysics [NG]
MN: 2007 Fall Meeting