印尼Semeru火山地區之火山顫動非線性動態性質分析

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柯莉娜(Cholisina Anik Perwita) 查詢紙本館藏

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地球科學學系

論文名稱

印尼Semeru火山地區之火山顫動非線性動態性質分析
(Analysis of Nonlinear Dynamical Properties of Volcanic Tremor Recorded at Semeru Volcano, Indonesia)

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摘要(中)

隨著爆發性噴發造成的火山震顫是無所不在的，而在印尼東爪哇 Semeru 火山也發現一樣的訊號。為了探究顫動的非線性動力學性質分，本研究使用非線性動力學方法分析從2009 年11 月 22 日到 12 月 31 日的二十五筆火山地震數據。由 Takens 的延遲嵌入理論說明了原始地震波形的非線性系統的行為演變描述相空間被重新建構。在給定 7 – 11 秒的延遲時間範圍內，重建的延遲時間被選擇用來檢查相關函數和平均相互信息。假近鄰法應用於時間數據設置，在 5 – 7秒之間產生足夠的嵌入維度。在鄰近軌道的那些混亂狀態標誌的指數歧異度可以利用最大 Lyapunov 指數（ MLE ）被量化。 MLE 被用來檢測在震顫信號上數量的泛音及時間的函數變化。這意味著，震顫源在幾個泛音頻率的準週期狀態及小的 MLEs (~ 0.013) 和一個有著更多泛音的混亂的狀態及較大的 MLEs (up to 0.039) 之間波動著。吸引維度的估計是使用由 Grassberg Procaccia 所提出的相關演算法來完成的。相關維度的事件等於或小於 2 時，有可能作為在相空間中的吸引環面，然而對於相關維度事件大於 2 的情況中，軌跡不會靠近圓環，因此，對於一些沿著圓環的隨意較大的資料數據，就可以探究較大面積的相空間。實體觀測說明微震源涉及氣體從噴泉堵塞物從一個或多個裂隙中溢出。在測定震顫特徵上，堵塞物的性質扮演了一個非常重要的角色。

摘要(英)

Volcanic tremor that follows explosive eruptions is an ubiquitous signal found in several volcanoes and also found at Semeru volcano, East Java, Indonesia. Twenty five episodes of volcanic tremor data from 22 November – 31 December 2009 have been analyzed using methods from the discipline of nonlinear dynamics in order to investigate their nonlinear dynamical properties. The phase space which describes the evolution of the behavior of nonlinear system was reconstructed from the original tremor seismograms using the delay embedding theorem suggest by Takens. The delay time used for reconstruction was selected after examining the autocorrelation function and average mutual information giving delay time in the range of 7-11. The false nearest neighbor method was applied to time data set yielding sufficient embedding dimension between 5-7. Exponential divergence of nearby orbits is the hallmark of chaotic behavior and was quantified by the maximal Lyapunov exponent (MLE). MLEs were found to vary as a function of the number of overtones in tremor signal and as a function of time. This implies that the tremor source fluctuates between a quasi-periodic state with few overtone frequencies and small MLEs (~0.013) and a chaotic one with more overtones and larger MLEs (up to 0.039). Estimation of attractor dimension was done using the correlation algorithm suggested by Grassberg and Procaccia. The events with the correlation dimension equal to or less than 2 likely have a torus as an attractor in the phase space. For events that have correlation dimension larger than 2, the trajectory is not bounded close to the torus and therefore it can explore a larger area of the phase space. No correlation dimension for some events can be explained due to dynamical correlations that persist for arbitrarily large data sets along a torus. Physical observations indicate that the tremor source involved gas escaping from the plug of conduit through one or more fractures. The properties of the plug probably played a very important role in determining the characteristics of the tremor signal.

關鍵字(中)

★ 震顫
★ 非線性
★ Semeru volcano

關鍵字(英)

★ Tremor
★ Nonlinear
★ Semeru volcano

論文目次

摘要 I
ABSTRACT II
ACKNOWLEDGEMENTS III
TABLE OF CONTENTS IV
LIST OF FIGURES V
LIST OF TABLES VI
CHAPTER 1
INTRODUCTION 1
1.1 NONLINEAR DYNAMICS AND CHAOS 1
1.2 VOLCANIC TREMOR 2
1.3 SEMERU VOLCANO 3
1.4 STRUCTURE OF THIS THESIS 4
CHAPTER 2
ESTIMATION OF EMBEDDING PARAMETERS 13
2.1 DATA SELECTION AND SPECTRAL ANALYSIS 13
2.2 PHASE SPACE RECONSTRUCTION 14
2.3 ESTIMATION OF DELAY TIME (Τ) 15
2.4 ESTIMATION OF EMBEDDING DIMENSION (M) 16
CHAPTER 3
MAXIMAL LYAPUNOV EXPONENT AND CORRELATION DIMENSION 28
3.1 MAXIMAL LYAPUNOV EXPONENT 28
3.1.1 APPLICATION TO TREMOR DATA 29
3.2 CORRELATION DIMENSION 29
3.1.1 APPLICATION TO TREMOR DATA 31
3.3 TEMPORAL VARIATION OF DYNAMICAL PROPERTIES 32
CHAPTER 4
DISCUSSION AND CONCLUSIONS 45
4.1 ERUPTION CHRONOLOGY AND VISUAL OBSERVATIONS 45
4.2 PHYSICAL MECHANISM OF TREMOR AND ITS NONLINEAR DYNAMICS 46
4.3 CONCLUSIONS 47
REFERENCES 57

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指導教授

柯士達(Konstantinos I. Konstantinou)

審核日期

2013-7-30

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