Phân tích độ Entropy của chuỗi dữ liệu động đất theo thứ tự nguyên và phân số

Springer Science and Business Media LLC - Tập 84 - Trang 79-90 - 2015
António M. Lopes1, J. A. Tenreiro Machado2
1Institute of Mechanical Engineering, Faculty of Engineering, University of Porto, Porto, Portugal
2Institute of Engineering, Polytechnic of Porto, Porto, Portugal

Tóm tắt

Bài báo này nghiên cứu phân phối thống kê của các trận động đất trên toàn cầu từ năm 1963 đến năm 2012. Một lưới Đề-các, chia Trái Đất thành các vùng địa lý, được xem xét. Entropy và độ sai khác Jensen–Shannon được sử dụng để phân tích và so sánh dữ liệu thực tế. Kỹ thuật phân cụm phân cấp và định hình đa chiều được áp dụng để trực quan hóa dữ liệu. Các chỉ số dựa trên entropy có lợi thế dẫn đến một tham số đơn lẻ biểu thị các mối quan hệ giữa dữ liệu động đất. Entropy cổ điển và entropy tổng quát (phân số) cũng như độ sai khác Jensen–Shannon được thử nghiệm. Các biện pháp tổng quát dẫn đến việc xác định rõ các mô hình ẩn chứa trong dữ liệu và góp phần hiểu rõ hơn về phân phối động đất.

Từ khóa

#động đất #phân phối thống kê #độ Entropy #độ sai khác Jensen-Shannon #phân cụm phân cấp

Tài liệu tham khảo

Aggarwal, C.C., Hinneburg, A., Keim, D.A.: On the Surprising Behavior of Distance Metrics in High Dimensional Space. Springer, New York (2001) Ashtari Jafari, M.: Statistical prediction of the next great earthquake around Tehran, Iran. J. Geodyn. 49(1), 14–18 (2010) Balasis, G., Daglis, I.A., Papadimitriou, C., Anastasiadis, A., Sandberg, I., Eftaxias, K.: Quantifying dynamical complexity of magnetic storms and solar flares via nonextensive Tsallis entropy. Entropy 13(10), 1865–1881 (2011) Baleanu, D., Diethelm, K., Scalas, E., Trujillo, J.J.: Fractional Calculus. World Scientific, Singapore (2012) Bhattacharya, P., Chakrabarti, B.K., et al.: A fractal model of earthquake occurrence: theory, simulations and comparisons with the aftershock data. In: Journal of Physics: conference series, vol. 319, pp. 012004. IOP Publishing (2011) Carlson, J.M., Langer, J.S., Shaw, B.E.: Dynamics of earthquake faults. Rev. Mod. Phys. 66(2), 657 (1994) Clauset, A., Young, M., Gleditsch, K.S.: On the frequency of severe terrorist events. J. Confl. Resolut. 51(1), 58–87 (2007) Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley, New York (2012) Cox, T.F., Cox, M.A.: Multidimensional Scaling. CRC Press, Boca Raton (2000) Das, R., Wason, H., Sharma, M.: Magnitude conversion to unified moment magnitude using orthogonal regression relation. J. Asian Earth Sci. 50, 44–51 (2012) De Rubeis, V., Hallgass, R., Loreto, V., Paladin, G., Pietronero, L., Tosi, P.: Self-affine asperity model for earthquakes. Phys. Rev. Lett. 76(14), 2599 (1996) De Santis, A., Cianchini, G., Favali, P., Beranzoli, L., Boschi, E.: The Gutenberg–Richter law and entropy of earthquakes: two case studies in Central Italy. Bull. Seismol. Soc. Am. 101(3), 1386–1395 (2011) Ekström, G., Nettles, M., Abers, G.A.: Glacial earthquakes. Science 302(5645), 622–624 (2003) Geller, R.J.: Earthquake prediction: a critical review. Geophys. J. Int. 131(3), 425–450 (1997) Goltz, C., Böse, M.: Configurational entropy of critical earthquake populations. Geophys. Res. Lett. 29(20), 51 (2002) Gutenberg, B., Richter, C.F.: Frequency of earthquakes in California. Bull. Seismol. Soc. Am. 34(4), 185–188 (1944) Hallgass, R., Loreto, V., Mazzella, O., Paladin, G., Pietronero, L.: Earthquake statistics and fractal faults. Phys. Rev. E 56(2), 1346 (1997) Hartigan, J.A.: Clustering Algorithms. Wiley, New York (1975) Hartigan, J.A., Wong, M.A.: Algorithm as 136: A K-means clustering algorithm. Appl. Stat. 28(1), 100–108 (1979) Hussein, H., Elenean, K.A., Marzouk, I., Peresan, A., Korrat, I., El-Nader, E.A., Panza, G., El-Gabry, M.: Integration and magnitude homogenization of the egyptian earthquake catalogue. Nat. Hazards 47(3), 525–546 (2008) International Seismological Centre: On-line Bulletin. International Seismological Centre, Thatcham, United Kingdom (2012). http://www.isc.ac.uk Ionescu, C.M.: The Human Respiratory System; An Analysis of the Interplay between Anatomy, Structure, Breathing and Fractal Dynamics. Springer, New York (2013) Jain, A.K.: Data clustering: 50 years beyond k-means. Pattern Recognit. Lett. 31(8), 651–666 (2010) Kagan, Y.Y.: Seismic moment distribution revisited: I. Statistical results. Geophys. J. Int. 148(3), 520–541 (2002) Kagan, Y.Y., Jackson, D.D.: Probabilistic forecasting of earthquakes. Geophys. J. Int. 143(2), 438–453 (2000) Kanamori, H., Brodsky, E.E.: The physics of earthquakes. Rep. Prog. Phys. 67(8), 1429 (2004) Keilis-Borok, V.: The lithosphere of the earth as a nonlinear system with implications for earthquake prediction. Rev. Geophys. 28(1), 19–34 (1990) Khinchin, A.I.: Mathematical Foundations of Information Theory, vol. 434. Courier Dover Publications, New York (1957) Levada, A.: Learning from complex systems: on the roles of entropy and Fisher information in pairwise isotropic gaussian Markov random fields. Entropy 16(2), 1002–1036 (2014) Lopes, A.M., Tenreiro Machado, J.A., Pinto, C., Galhano, A.: Multidimensional scaling visualization of earthquake phenomena. J. Seismol. 18(1), 163–179 (2014) Lopes, A.M., Tenreiro Machado, J.A., Pinto, C., Galhano, A.: Fractional dynamics and MDS visualization of earthquake phenomena. Comput. Math. Appl. 66(5), 647–658 (2013) Machado, J.T.: Fractional order generalized information. Entropy 16(4), 2350–2361 (2014) Martínez-Torres, M.R., García, F.B., Marín, S.T., Vázquez, S.G.: A digital signal processing teaching methodology using concept-mapping techniques. IEEE Trans. Educ. 48(3), 422–429 (2005) Mega, M.S., Allegrini, P., Grigolini, P., Latora, V., Palatella, L., Rapisarda, A., Vinciguerra, S.: Power-law time distribution of large earthquakes. Phys. Rev. Lett. 90(18), 188,501 (2003) Mignan, A., Woessner, J.: Estimating the magnitude of completeness for earthquake catalogs. Community Online Resour. Stat. Seism. Anal. (2012). doi:10.5078/corssa-00180805 Nicholson, T., Sambridge, M., Gudmundsson, O.: On entropy and clustering in earthquake hypocentre distributions. Geophys. J. Int. 142(1), 37–51 (2000) Ōmori, F.: On the After-Shocks of Earthquakes, vol. 7. The University, Tokyo (1894) Peng, Z., Gomberg, J.: An integrated perspective of the continuum between earthquakes and slow-slip phenomena. Nature Geosci 3(9), 599–607 (2010) Pinto, C., Mendes Lopes, A., Tenreiro Machado, J.A.: A review of power laws in real life phenomena. Commun. Nonlinear Sci. Numer. Simul. 17(9), 3558–3578 (2012) Rousseeuw, P.J.: Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math. 20, 53–65 (1987) Sarlis, N., Christopoulos, S.R.: Natural time analysis of the centennial earthquake catalog. Chaos Interdiscip. J. Nonlinear Sci. 22(2), 023,123 (2012) Scordilis, E.: Empirical global relations converting \(m_s\) and \(m_b\) to moment magnitude. J. Seismol. 10(2), 225–236 (2006) Seely, A.J., Newman, K.D., Herry, C.L.: Fractal structure and entropy production within the central nervous system. Entropy 16(8), 4497–4520 (2014) Sokal, R.R., Rohlf, F.J.: The comparison of dendrograms by objective methods. Taxon. 11(2), 33–40 (1962) Sornette, A., Sornette, D.: Earthquake rupture as a critical point: Consequences for telluric precursors. Tectonophysics 179(3), 327–334 (1990) Sornette, D.: Earthquakes: from chemical alteration to mechanical rupture. Phys. Rep. 313(5), 237–292 (1999) Sotolongo-Costa, O., Posadas, A.: Fragment-asperity interaction model for earthquakes. Physical Rev. Lett. 92(4), 048,501 (2004) Stadler, G., Gurnis, M., Burstedde, C., Wilcox, L.C., Alisic, L., Ghattas, O.: The dynamics of plate tectonics and mantle flow: from local to global scales. Science 329(5995), 1033–1038 (2010) Stein, S., Liu, M., Calais, E., Li, Q.: Mid-continent earthquakes as a complex system. Seismol. Res. Lett. 80(4), 551–553 (2009) Stucchi, M., Albini, P., Mirto, M., Rebez, A.: Assessing the completeness of italian historical earthquake data. Ann. Geophys. 47(2–3), 659–673 (2004) Tenreiro Machado, J.A., Lopes, A.M.: Analysis and visualization of seismic data using mutual information. Entropy 15(9), 3892–3909 (2013) Turcotte, D.L., Malamud, B.D.: Earthquakes as a complex system. Int. Geophys. 81, 209-IV (2002) Utsu, T., Ogata, Y., Matsu’ura, R.S.: The centenary of the Omori formula for a decay law of aftershock activity. J. Phys. Earth 43(1), 1–33 (1995) Valério, D., Trujillo, J.J., Rivero, M., Tenreiro Machado, J.A., Baleanu, D.: Fractional calculus: a survey of useful formulas. Eur. Phys. J. Spec. Top. 222, 1827–1846 (2013) Wiemer, S.: A software package to analyze seismicity: Zmap. Seismol. Res. Lett. 72(3), 373–382 (2001)