| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Research Abstract |
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
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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, 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. To verify this approach, we applied this method to Julian's non-linear tremor model, obtaining suitable embedding dimension and correlation dimension for Julian's system.
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. We analyzed two other tremors and revealed the non-linear dynamics of long-period tremors using the embedding method of time delays and the 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 (prospective dimension 3 or 4).
We also applied a non-linear prediction approach based on the theory of KM_2O-Langevin equation to evaluate a contribution from non-linearity of the system. In addition, we developed a new method for detecting and picking P- and S-wave signals automatically. Compared to methods currently in use, our method requires less assumption with properties of the data time series. We also developed a new approach for analysis of frequency structure of tremor based on the theory of KM_2O-Langevin equation. We applied the new algorithm to obtain a frequency structure form highly noisy data of deep low-frequency tremors occurred in western Shikoku, Japan, and reveal the characteristic frequency structure of deep low-frequency tremors with peaks lined up from 1 to 5Hz at intervals of 0.5Hz.
In next step, we apply the embedding method of time delays to the long-period long-lasting earthquakes 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 waveforms of the long-period long-lasting earthquakes were similar to each other, so we selected a typical event that occurred at 12:34 on June 12, 2004. We employed a FIR low-pass filter with a cut-off frequency of 1Hz 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 long-period earthquakes, and got a correlation integral curve of the reconstructed attractor, founding a scaling region over one decade with the correlation dimension of 2.04 plus minus 0.11. This result indicates that the source process of long-period long-lasting earthquake 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 long-period tremors. Another way of saying, the apparent waveform characteristics of long-period earthquakes and long-period tremors are quite different, however the both correlation dimensions calculated from the reconstructed attractors are almost same values.
Modifying a hydraulic control valve model with the system dimension of 4, we succeeded to simulate a long-period oscillation resembling with the long-period earthquakes and with the long-period tremors based on a same mathematical model. These two long-period oscillations are sharply distinguished by a discharge coefficient of vent. The remaining problem is how to excite seismic waves from the simulated valve oscillations. Less
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