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研究生:瑪麗莎
研究生(外文):Maria R.P. Sudibyo
論文名稱(外文):Nonlinear
指導教授:柯士達柯士達引用關係
指導教授(外文):K.I. Konstantinou
學位類別:碩士
校院名稱:國立中央大學
系所名稱:地球科學學系
學門:自然科學學門
學類:地球科學學類
論文種類:學術論文
論文出版年:2016
畢業學年度:104
語文別:英文
論文頁數:73
中文關鍵詞:火山震顫非線性的決定性系統地震學埃里伯斯火山
外文關鍵詞:volcanotremornonlinear deterministic systemseismologyErebus
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火山震顫的複雜特性被認為可代表一個非線性的決定性系統,而其動態演化可以少量的參數進行模擬。我們以此種方法分析南極洲上的埃里伯斯火山震顫的動力學。我們分析了從2002年5月17日至2002年7月31日的120筆數據。從波譜分析中我們可以得知,在埃里伯斯火山的動態震顫可分為諧波震顫、寬帶震顫和混合震顫。諧波震顫和混合震顫,可得到1到23的泛音,他們的基本頻率在五月至六月中旬期間出現擾動,但隨後穩定在1赫茲左右。諧波震顫和混合震顫的頻率都顯示出滑升和滑降,其中上揚的幅度可高達200%,而下降的幅度則為90%。為了分析這個火山震顫的動態演化現象,藉由Takens(1981)的延遲嵌入理論,我們從原始地震波形重建了描述相位空間。在給定4-12(0.04秒-0.12秒)的延遲時間範圍內,所運用的延遲時間是依據自相關函數和平交互信息(AMI)而來。使用嵌入維假近鄰法,所得到的數值在5-8之間。在埃里伯斯火山的震顫中有很大量的噪訊,所以我們在描述相空間內以流形維度3-5使用一個非線性的過濾器。此吸子的指數歧異度就是混亂狀態標誌,可以利用最大Lyapunov指數(MLE)來量化。MLEs的值由0.003-0.023。根據Julian的模型來說,低壓的狀態下會產生諧波震顫及一些泛音。在壓力提高的狀況之下,會產生更多的泛音,導致系統更加的混亂及造成更高的MLE。在埃里伯斯火山的MLE變化並不大,顯示系統內的流體壓力並不顯著。因此,此系統被歸類於簡單型(極限環)和混亂狀態之間。此震顫的來源可能是連接兩個岩漿庫的噴嘴,其中一個正好位於熔岩湖下方。岩漿從底部通過此狹窄的噴嘴噴發到上方。此流體被認為是氣態的二氧化碳,而其低黏度的特性和振盪的現象就如Julian的模型所述。
Ria Sudibyo·Friday, July 15, 2016
The complex behavior of volcanic tremor can be represented as a nonlinear deterministic system, where its dynamic evolution can be modeled mathematically with a small number of parameters. This approach is applied to analyze the dynamics of tremor at Mt. Erebus, Antarctica. We identified 120 episodes of tremor from 17 May to 31 July 2002. Based on the spectral analysis, tremor at Erebus can be categorized into harmonic, mixed episodes of harmonic and broadband, and broadband tremor. The harmonic and mixed episodes exhibit various numbers of overtones from 1 to 23, and their fundamental frequencies seem to fluctuate during May to mid-June but stabilize around 1 Hz afterwards. Both harmonic and mixed episodes reveal frequency gliding up and gliding down, where the percentage of gliding up may reach up into 200%, while the percentage of gliding down is up to 90%. To analyze the dynamical evolution of tremor, we reconstructed phase space from the original seismograms using the delay embedding theorem suggested by Takens. The delay time was selected using the autocorrelation function and Average Mutual Information (AMI), giving delay times in the range 4 to 12 (0.04 to 0.12 s). The sufficient embedding dimension was obtained using the false nearest neighbors method giving values in the range 5 to 8. As tremor at Erebus contains a high amount of noise, we applied a nonlinear projective filter in phase space using manifold dimension from 3 to 5. The exponential divergence of the attractor is the indicator of the chaotic behavior and is estimated as the maximal Lyapunov exponent (MLE). MLEs were found to vary from 0.003 to 0.023. According to Julian’s model, small pressure will create harmonic tremor with a small number of overtones. As the pressure is increasing, it will generate more overtones, leading the system to become more chaotic and resulting in higher MLE. The MLEs variation at Erebus is considered small, implying that the fluid pressure working in the system does not exhibit large variations. Therefore, the system can be categorized in the borderline between simple (limit cycle) and chaotic behavior. The source of tremor is likely a nozzle connecting two magma chambers, with one chamber located just beneath the lava lake. The nozzle works as a constricted channel that transports the fluid from the deeper to the shallower chamber. The fluid is expected to be CO2 gas which has low viscosity and can generate the kind of oscillations describe in Julian’s model.
摘要……………………………………………………………………………………….i

ABSTRACT……………………………..………………………………………………..ii

ACKNOWLEDGEMENTS………………………………………………………..........iii

TABLE OF CONTENTS…………………………………………………………..........iv

LIST OF FIGURES……………………………………………………………………...vi

LIST OF TABLES…………….…………………………………………………………viii

CHAPTER 1

INTRODUCTION ……………………………………………………………………….1

Nonlinear dynamics………………………………………………………….….1

Volcanic tremor……………………………………………………………........2

Mt. Erebus volcano……………………………………………………………...3

Aim and structure of this thesis………………………………….…...…………4

CHAPTER 2

DATA AND SPECTRA ANALYSIS ………………………………………………......14

2.1 Seismic network………………………………………………………………..14

2.2 Data preprocessing……………………………………………………………..14

2.3 Spectral analysis………………………………………………………………..15

CHAPTER 3

NONLINEAR TIME SERIES ANALYSIS ……………………………………………26

3.1 Estimation of embedding parameters…………………………………………..26

3.1.1 Estimation of delay time (τ)……………………………………………...26

3.1.2 Estimation of embedding dimension ………………………………….....27

3.2 Filtering in phase space ………………………………………………………...28

3.3 Estimation of Maximal Lyapunov Exponent …………………………………..29





CHAPTER 4

DISCUSSION AND CONCLUSIONS

4.1 Nonlinear dynamics of tremor …………….…………………………………...40

4.2 Source model for Erebus tremor ……………………………………………....41

4.3 Conclusions …………………………………………………………………....42

REFERENCES ………………………………………………………………………....48

APPENDIX A …………………………………………………………………………..51

APPENDIX B …………………………………………………………………………...56
Abarbanel, H. D. I., 1996. Analysis of observed chaotic data. New York: Springer.

Aster, R., MacIntosh, W., Kyle, P., Esser, R., Bartel, B., Dunbar, N., Johnson, J., Kartsens, R., Kurnik, C., McGowan, M., McNamara, S., Meertens, C., Pauly, B., Richmond, M., Ruiz, M., 2004. Real-time data received from Mount Erebus Volcano, Antarctica. Earth and Space Science News, Transactions American Geophysical Union, 85(10), 97-104.

Aster, R., Mah, S., Kyle, P., MacIntosh, W., Dunbar, N., Johnsohn, J., Ruiz, M., McNamara, S., 2003. Very long period oscillations of Mount Erebus Volcano. Journal of Geophysical Research, 108, 2522, doi:10.1029/2002JB002101.

Behrendt, J., 1999. Crustal and listospheric structure of the West Antarctica Rift System from geophysical investigation : A review. Global Planet. Change, 23, 25-44.

Csatho, B., Schenk, T., Kyle, P., Wilson, T., & Krabill, W., 2008. Airborne laser swath mapping of the summit of Erebus volcano, Antarctica : Applicatins to geological mapping of a volcano. Journal of Volcanology and Geothermal Research, 177, 531-548.

Dibble, R., Kienle, J., Kyle, P., & Shibuya, K., 1984. Geophysical studies of Erebus volcano, Antarctica, from 1974 December to 1982 January. New Zealand Journal of Geology and Geophysics, 27, 425-455.

Fraser, A. M., & Swinney, H. L., 1986. Independent Coordinates for Strange Attractors from Mutual Information. Phys. Rev. A, 87, 1134-1140.

Grassberger, P., Hegger, R., Kantz, H., Schaffrath, C., & Schreiber, T., 1993. On noise reduction methods for chaotic data. CHAOS, 3, 127.

Grassberger, P., Schreiber, T., & Schaffrath, C., 1991. Non-linear time sequence analysis. Int. J. Bifurcation and Chaos, 1, 521.

Hegger, R., Kantz, H., & Schreiber, T., 1999. Practical implementation of nonlinear time series methods: The TISEAN package. CHAOS, 9, 413.

Hotovec, A. J., Prejean, S. G., Vidale, J., & Gomberg, J., 2013. Strongly gliding harmonic tremor during the 2009 eruption of Redoubt Volcano. Journal of Volcanology and Geothermal Research, 259, 89-99.

Jellinek, A. M., & Bercovici, D., 2011. Seismic tremors and magma wagging during explosive volcanism. Nature, 470, 522-526.

Julian, B. R., 1994. Volcanic tremor : Nonlinear excitation by fluid flow. Journal of Geophysical Research, 99, 11859-11877.

Julian, B. R., 2000. Period doubling and other nonlinear phenomena in volcanic earthquakes and tremor. Journal of Volcanology and Geothermal Research, 101, 19-26.

Kantz, H., & Schreiber, T. 1997. Nonlinear Time Series Analysis. Cambridge: Cambridge University Press.

Kennel, M., Brown, R., & Abarbanel, H., 1992. Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev. A,, 45, 3403.

Konstantinou, K. I., 2002. Deterministic nonlinear source processes of volcanic tremor signals accompanying the 1996 Vatnajökull eruption, central Iceland. Geophysis. J. Int, 148, 663-675.

Konstantinou, K.I. & Lin, C.H., 2004. Nonlinear time series analysis of volcanic tremor events recorded at Sangay Volcano, Ecuador. Pure Appl. Geophysx., (161), pp. 145-63.

Konstantinou, K.I., Perwita, C., Maryanto, S., Surono, B. A., & Hendrasto, M., 2013. Maximal Lyapunov exponent variations of volcanic tremor recorded during explosive and effusive activity at Mt Semeru volcano. Nonlin. Processes Geophys., 20, 1137-1145, doi: 10.5194/npg-20-1137-2013.

Konstantinou, K. I., & Schlindwein, V., 2003. Nature, wavefield properties and source mechanism of volcanic tremor : a review. Journal of Volcanology and Geothermal Research, 119, 161-187.

Kyle, P., 1986. Volcanic activity of Mount Erebus, Antarctica : 1972-1984. International Volcanological Congress, Auckland-Hamilton-Rotorua, February 1-9, 1986, Abstract, 250.

Kyle, P., Moore, J., & M.F., T., 1992. Petrologic evolution of anorthoclase phonolite lavas at Mt. Erebus, Ross Island, Antarctica. Journal of Petrology, 33(4), 849-875.

Kyle, P., Sybeldon, L., McIntosh, W., Meeker, K., & Symonds, R., 1994. Sulphur dioxide emission rates from Mount Erebus, Antarctica, in P. Kyle (ed.) Volcanological and Environmental Studies of Mount Erebus, Antarctica. Antarctica Research Series, American Geophysical Union, 66, 69-82.

MacAyeal, D. R., Okal, E. A., Aster, R., & Bassis, J. N., 2008. Seismic and hydroacoustic tremor generated by collding icebergs. Journal of Geophysical Research : Earth Surface, 113, doi: 10.1029/2008JF001005.

Moussallam, Y., Oppenheimer, C., Scaillet, B., Gaillard, F., Kyle, P., Peters, N., Hartley, M., Berlo, K., Donovan, A., 2014. Tracking the changing oxidation state of Erebus magmas, from mantle to surface, driven by magma ascent and degassing. Earth and Planetary Science Letters, 393, 200-209.

McNutt, S., 2005. Volcanic seismology. Annu. Rev. Earth Planet. Sci., 33, 461-491.

McNutt, S., & Nishimura, T., 2008. Volcanic tremor during eruptions: temporal characteristics, scaling and constraints on conduit size and processes. Journal of Volcanology and Geothermal Research, 178, 10-28.

Neuberg, J., 2000. Characteristics and causes of shallow seismicity in andesite volcanoes. Phil. Trans. Math. Phys. Engin. Sci., 358, 1533-1546.

Oppenheimer, C., Morreti, R., Kyle, P. R., Eschenbacher, A., Lowenstern, J. B., Hervig, R. L., & Dunbar, N. W., 2011. Mantle to surface degassing of alkalic magmas at Erebus volcano, Antarctica. Earth and Planetary Science Letters, 306, 261-271.

Procaccia, I., 1988. Universal properties of dynamically complex systems : the organization of chaos. Nature, 333, 618-623.

Romero, M., 2004. Analysis of tremor activity at Mt. Erebus Volcano, Antarctica. Master Thesis, retrieved from http://erebus.nmt.edu/index.php/publications/theses/122-mario-ruiz-romero.

Rosenstein, M., Collins, J., & De Luca, C., 1993. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D, 65, 117.

Sauer, T., Yorke, J., & Casdagli, M., 1991. Embedology. J. Stat. Phys., 65, 579.

Takens, F., 1981. Detecting Strange Attractors in Turbulence. In F. Takens, Lecture Notes in Math. Vol. 898. New York: Springer.

Talandier, J., Hyvernaud, O., E., O., & F., P. P., 2002. Long-range detection of hydroacoustic signals from large icebergs in the Ross Sea, Antartctica. Earth Planet. Sci. Lett., 203, 519-534.

Wardell, J., 2002. Volcanic carbon dioxide and trace metal emissions from Mt. Erebus, Antarctica and White Island, New Zealand: Contribution and implications to global atmospheric budgets. PhD Thesis. Earth and Environmental Sciences, New Mexico Tech, 140 p

Wolf, A., Swift, J., Swinney, H., & Vastano, J., 1985. Determining Lyapunov exponents from a time series. Physica D,16, 285.
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