週遭噪訊是因地球上大氣擾動和人類活動交互作用下所產生的。其本質為非線性、隨機的而且非恆定的。我們提出一個新的方法，希望能利用排列熵(permutation entropy, PE)監測這些隨機的噪訊以即時預測火山噴發。排列熵(permutation entropy, PE)是由噪訊中的隨機性所得到的非線性的統計量數。我們研究了從1996年9月29日到 10月13日在冰島Gjálp爆發的火山。波形是以暫時的HOTSPOT震測的網絡系統所記錄。Bárðarbunga地震噴發時的震度為5.6，且造成火山口的環斷層破裂。位於120公里外的監測站，在地震的8.57天前和噴發前10.76天，可從排列熵(PE)可看到噪訊波場的隨機性變化。我們也計算了噪訊的主要頻率(dominant frequency, DF)和中心頻率(centroid frequency, CF)，而其結果顯示噪訊是源於自然。主要頻率大約是2Hz，在Bárðarbunga地震發生的六天前，中心頻率的範圍從0.2~4.8Hz不等，而地震後中心頻率的數值和主要頻率相近。偏振分析指出，超長週期(very long period)的震顫並非隨機性變化的原因。隨機性變化的原因很可能是因高壓地殼在上地幔隆起降低散射的結果。中心頻率和主要頻率的地殼異質性變化一致，而較高頻率的散射也降低。因此，我們認為，在所有火山的環境噪聲中PE的變化，很可能是在特定的高壓地區，導致其地殼散射特性的改變。未來，此方法應用於即時監測與預測火山爆發有很大的潛力。

Ambient seismic noise is generated by the interaction of atmospheric disturbances and human activities with the solid Earth. Its properties are nonlinear, stochastic and non-stationary. We propose a new approach to real – time forecasting of volcanic eruptions by monitoring the stochastic properties of ambient noise using permutation entropy (PE), which is a nonlinear statistical measure of the stochasticity contained within the noise. We studied the 1996 Gjálp eruption in Iceland, which lasted from 29th Sept - 13th Oct 1996. Waveforms recorded by the temporary HOTSPOT seismic network were used. The eruption commenced with the Mw = 5.6 Bárðarbunga earthquake that initiated a ring fault failure along the Bárðarbunga caldera. PE captured changes in the stochasticity of the noise wavefield (at stations located up to 120 km away) 8.57 days before the Bárðarbunga earthquake and 10.76 days before the onset of the eruption. We also calculated the dominant frequency (DF) and centroid frequency (CF) of the ambient noise, whose results suggested that the noise was due to natural sources. DF was ~ 0.2 Hz while the CF ranged between ~ 0.2 to 4.8 Hz up until ~ 6 days before the Bárðarbunga earthquake, thereafter it became similar to DF. Polarization analysis determined that very long period tremor (< 1 Hz) was not the cause of the changes in the stochasticity. Changes in the stochasticity were most likely the result of reduced scattering brought on by the strongly pressurized crust due to doming in the upper mantle. CF coincides with DF as the crustal heterogeneity changes and the higher frequency scattering is reduced. Therefore, we argue that PE variations in the ambient noise, for any given volcanic regime, are likely localized to the areas undergoing strong pressurization, which alters the scattering properties of the crust. This methodology has great potential in future applications of real-time monitoring and forecasting of volcanic eruptions.

Aki, K., & Richards, P. G. (2002). Quantitative seismology, 2nd Edition. University Science Books. 700pp.
Allen, R. M., Nolet, G., Morgan, W. J., Vogfjörd, K., Bergsson, B. H., Erlendsson, P., . . . Stefánsson, R. (2002). Imaging the mantle beneath Iceland using integrated seismological techniques. Journal of Geophysical Research: Solid Earth, 107(B12). doi:10.1029/2001jb000595
Aster, R., Kyle, P., McIntosh, W., Dunbar, N., Johnson, J., Ruiz, M., & McNamara, S. (2003). Very long period oscillations of Mount Erebus Volcano. Journal of Geophysical Research, 108(B11). doi:10.1029/2002jb002101
Bandt, C., & Pompe, B. (2002). Permutation Entropy: A Natural Complexity Measure for Time Series. Physical Review Letters, 88(17). doi:10.1103/physrevlett.88.174102
Bjarnason, I. T., & Schmeling, H. (2009). The lithosphere and asthenosphere of the Iceland hotspot from surface waves. Geophysical Journal International, 178(1), 394-418. doi:10.1111/j.1365-246x.2009.04155.x
Björnsson, H. (1988). Hydrology of ice caps in volcanic regions. Reykjavík: Societas Scientarium Islandica, University of Iceland.
Bonnefoy-Claudet, S., Cotton, F., & Bard, P. (2006). The nature of noise wavefield and its applications for site effects studies. Earth-Science Reviews, 79(3-4), 205-227. doi:10.1016/j.earscirev.2006.07.004
Brenguier, F., Shapiro, N. M., Campillo, M., Ferrazzini, V., Duputel, Z., Coutant, O., & Nercessian, A. (2008). Towards forecasting volcanic eruptions using seismic noise. Nature Geoscience, 1(2), 126-130. doi:10.1038/ngeo104
Campillo, M., & Paul, A. (2003). Long-Range Correlations in the Diffuse Seismic Coda. Science, 299(5606), 547-549. doi:10.1126/science.1078551
Campillo, M. (2006). Phase and Correlation in Random Seismic Fields and the Reconstruction of the Green Function. Pure and Applied Geophysics, 163(2-3), 475-502. doi:10.1007/s00024-005-0032-8
Cao, Y., Tung, W., Gao, J. B., Protopopescu, V. A., & Hively, L. M. (2004). Detecting dynamical changes in time series using the permutation entropy. Physical Review E, 70(4). doi:10.1103/physreve.70.046217
Carniel, R., Tárraga, M., Jaquet, O., Ortiz, R., & García, A. (2008a). The seismic noise at Las Cañadas volcanic caldera, Tenerife, Spain: Persistence characterization, and possible relationship with regional tectonic events. Journal of Volcanology and Geothermal Research, 173(1-2), 157-164. doi:10.1016/j.jvolgeores.2007.12.044
Carniel, R., Tárraga, M., Barazza, F., & García, A. (2008b). Possible interaction between tectonic events and seismic noise at Las Cañadas Volcanic Caldera, Tenerife, Spain. Bulletin of Volcanology, 70(9), 1113-1121. doi:10.1007/s00445-007-0193-7
Correig, A. M., & Urquizú, M. (2002). Some dynamical characteristics of microseism time-series. Geophysical Journal International, 149(3), 589-598. doi:10.1046/j.1365-246x.2002.01602.x
De Lauro, E., De Martino, S., Falanga, M., Palo, M., & Scarpa, R. (2005). Evidence of VLP volcanic tremor in the band [0.2-0.5] Hz at Stromboli volcano, Italy. Geophysical Research Letters, 32(17). doi:10.1029/2005gl023466
De Lauro, E., De Martino, S., Falanga, M., & Palo, M. (2006). Statistical analysis of Stromboli VLP tremor in the band [0.1-0.5] Hz: Some consequences for vibrating structures. Nonlinear Processes in Geophysics, 13(4), 393-400. doi:10.5194/npg-13-393-2006
Fichtner, A., & Tkalčić, H. (2010). Insights into the kinematics of a volcanic caldera drop: Probabilistic finite-source inversion of the 1996 Bárdarbunga, Iceland, earthquake. Earth and Planetary Science Letters, 297(3-4), 607-615. doi:10.1016/j.epsl.2010.07.013
Gudmundsson, A., Marti, J., & Turon, E. (1997). Stress fields generating ring faults in volcanoes. Geophysical Research Letters, 24(13), 1559-1562. doi:10.1029/97gl01494
Gudmundsson, A. (2007). Conceptual and numerical models of ring-fault formation. Journal of Volcanology and Geothermal Research, 164(3), 142-160. doi:10.1016/j.jvolgeores.2007.04.018
Gudmundsson, M., Björnsson, H., & Pálsson, F. (1995). Changes in jökulhlaup sizes in Grímsvötn, Vatnajökull, Iceland, 1934-91, deduced from in-situ measurements of subglacial lake volume. Journal of Glaciology, 41(138), 263-272.
Gudmundsson, M. T., Sigmundsson, F., Björnsson, H., & Högnadóttir, T. (2004). The 1996 eruption at Gjálp, Vatnajökull ice cap, Iceland: Efficiency of heat transfer, ice deformation and subglacial water pressure. Bulletin of Volcanology, 66(1), 46-65. doi:10.1007/s00445-003-0295-9
Gudmundsson, M. T., & Högnadóttir, T. (2007). Volcanic systems and calderas in the Vatnajökull region, central Iceland: Constraints on crustal structure from gravity data. Journal of Geodynamics, 43(1), 153-169. doi:10.1016/j.jog.2006.09.015
Horgan, J. (1995). From Complexity to Perplexity. Scientific American, 272(6), 104-109. doi:10.1038/scientificamerican0695-104
Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., . . . Liu, H. H. (1998). The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 454(1971), 903-995. doi:10.1098/rspa.1998.0193
Huang, N. E., & Wu, Z. (2008). A review on Hilbert-Huang transform: Method and its applications to geophysical studies. Reviews of Geophysics, 46(2), 1-23. doi:10.1029/2007rg000228
Jurkevics, A. (1988). Polarization analysis of three-component array data. Bulletin of the Seismological Society of America, 78(5), 1725-1743.
Kauffman, S. A. (1995). At home in the universe: The search for laws of self-organization and complexity. New York: Oxford University Press.
Konstantinou, K. I., Nolet, G., Morgan, W. J., Allen, R. M., & Pritchard, M. J. (2000). Seismic phenomena associated with the 1996 Vatnajökull eruption, central Iceland. Journal of Volcanology and Geothermal Research, 102(1-2), 169-187. doi:10.1016/s0377-0273(00)00187-6
Langton, C. G. (1989). Artificial life. Redwood City, Calif. u.a.: Addison-Wesley.
Langton, C. G. (1992). Artificial life II: Proceedings of the Workshop on Artificial Life: Held February 1990 in Santa Fe, New Mexico. Redwood City, CA: Addison-Wesley.
Larose, E., Margerin, L., Derode, A., Tiggelen, B. V., Campillo, M., Shapiro, N., . . . Tanter, M. (2006). Correlation of random wavefields: An interdisciplinary review. Geophysics, 71(4), S111-S121. doi:10.1190/1.2213356
Larsen, G. (2002). A brief overview of eruptions from ice-covered and ice-capped volcanic systems in Iceland during the past 11 centuries: Frequency, periodicity and implications. Geological Society, London, Special Publications, 202(1), 81-90. doi:10.1144/gsl.sp.2002.202.01.05
Lei, Y., Lin, J., He, Z., & Zuo, M. J. (2013). A review on empirical mode decomposition in fault diagnosis of rotating machinery. Mechanical Systems and Signal Processing, 35(1-2), 108-126. doi:10.1016/j.ymssp.2012.09.015
Longuet-Higgins, M. S. (1950). A Theory of the Origin of Microseisms. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 243(857), 1-35. doi:10.1098/rsta.1950.0012
Nettles, M., & Ekström, G. (1998). Faulting mechanism of anomalous earthquakes near Bárdarbunga Volcano, Iceland. Journal of Geophysical Research: Solid Earth, 103(B8), 17973-17983. doi:10.1029/98jb01392
Oskarsson, N., Steinthorsson, S., & Sigvaldason, G. E. (1985). Iceland geochemical anomaly: Origin, volcanotectonics, chemical fractionation and isotope evolution of the crust. Journal of Geophysical Research, 90(B12), 10011. doi:10.1029/jb090ib12p10011
Palo, M., & Cusano, P. (2013). Wavefield decomposition and phase space dynamics of the seismic noise at Volcàn de Colima, Mexico: Evidence of a two-state source process. Nonlinear Processes in Geophysics, 20(1), 71-84. doi:10.5194/npg-20-71-2013
Pritchard, M. J. (2000). A seismological study of the mantle beneath Iceland (Unpublished Ph.D thesis). Thesis (Ph). Retrieved from http://etheses.dur.ac.uk/4609/1/4609_2073.PDF?UkUDh:CyT
Ryabov, V. B., Correig, A., Urquizu, M., & Zaikin, A. (2003). Microseism oscillations: From deterministic to noise-driven models. Chaos, Solitons and Fractals, 16(2), 195-210. doi:10.1016/s0960-0779(02)00165-0
Sabra, K. G., Gerstoft, P., Roux, P., & Kuperman, W. A. (2005). Extracting time-domain Green's function estimates from ambient seismic noise. Geophysical Research Letters, 32(3). doi:10.1029/2004gl021862
Shapiro, N. M., & Campillo, M. (2004). Emergence of broadband Rayleigh waves from correlations of the ambient seismic noise. Geophysical Research Letters, 31(7). doi:10.1029/2004gl019491
Smithsonian Institution. (2013). Global Volcanism Program Bardarbunga (373030) in Volcanoes of the World, v. 4.4.3. Venzke, E (ed.). Retrieved from http://volcano.si.edu/volcano.cfm?vn=373030
Stehly, L., Campillo, M., & Shapiro, N. M. (2006). A study of the seismic noise from its long-range correlation properties. Journal of Geophysical Research, 111(B10). doi:10.1029/2005jb004237
Theiler, J., Eubank, S., Longtin, A., Galdrikian, B., & Farmer, J. D. (1992). Testing for nonlinearity in time series: The method of surrogate data. Physica D: Nonlinear Phenomena, 58(1-4), 77-94. doi:10.1016/0167-2789(92)90102-s
Thordarson, T., & Larsen, G. (2007). Volcanism in Iceland in historical time: Volcano types, eruption styles and eruptive history. Journal of Geodynamics, 43(1), 118-152. doi:10.1016/j.jog.2006.09.005
Trauth, M. H. (2007). Matlab recipes for earth sciences (2nd ed.). New York: Springer.
Trégourès, N. P., & Tiggelen, B. A. (2002). Quasi-two-dimensional transfer of elastic waves. Physical Review E , 66(3). doi:10.1103/physreve.66.036601
Tárraga, M., Carniel, R., Ortiz, R., Marrero, J. M., & García, A. (2006). On the predictability of volcano-tectonic events by low frequency seismic noise analysis at Teide-Pico Viejo volcanic complex, Canary Islands. Natural Hazards and Earth System Science, 6(3), 365-376. doi:10.5194/nhess-6-365-2006
Vink, G. E. (1984). A hotspot model for Iceland and the Vøring Plateau. Journal of Geophysical Research: Solid Earth, 89(B12), 9949-9959. doi:10.1029/jb089ib12p09949
Weaver, R. L., & Lobkis, O. I. (2001). Ultrasonics without a Source: Thermal Fluctuation Correlations at MHz Frequencies. Physical Review Letters, 87(13). doi:10.1103/physrevlett.87.134301
Wilkinson, M. H. (1997). Nonlinear Dynamics, Chaos-theory, and the Sciences of Complexity: Their Relevance to the Study of the Interaction between Host and Microflora. Old Herborn University Seminar Monograph 10: New Antimicrobial Strategies, 113-130.
Wolfe, C. J., Bjarnason, I. T., Vandecar, J. C., & Solomon, S. C. (1997). Seismic structure of the Iceland mantle plume. Nature, 385(6613), 245-247. doi:10.1038/385245a0
HHT (EMD/EEMD) MATLAB Software. (2015, August 17). Retrieved June 08, 2016, from http://rcada.ncu.edu.tw/research1.htm