Ergodicity examined by the Thirumalai-Mountain metric for Taiwanese seismicity

• Autorzy: Li H.-C. , Chen C.-C.
• Języki publikacji: EN

Abstrakty

EN

Ergodicity is a behavior generally limited to equilibrium states and is here defined as the equivalence of ensemble and temporal averages. In recent years, effective ergodicity is identified in simulated earthquakes generated by numerical fault models and in real seismicity of natural fault networks by using the Thirumalai-Mountain metric. Although the effective ergodicity is already reported for Taiwanese seismicity, an immediate doubt is the unrealistic gridded sizes for discretizing the seismic data. In this study, we re-examined the effective ergodicity in Taiwanese seismicity by using reasonable gridded sizes which corresponded with the location errors in the real earthquake catalogue. Initial time and magnitude cut-off were examined for the validity of ergodic behavior. We found that several subsets extracted from Taiwanese seismicity possessed effectively ergodic intervals and all terminations of these ergodic intervals temporally coincided with the occurrences of large earthquakes (ML < 6.5). We thus confirm the ergodicity in the crustal seismicity by using the Thirumalai-Mountain metric.

Słowa kluczowe

EN

ergodicity; Thirumalai–Mountain metric; seismicity; Taiwan

• Wydawca: Instytut Geofizyki PAN ; Springer
• Czasopismo: Acta Geophysica
• Rocznik: 2012
• Tom: Vol. 60, no. 3
• Strony: 769--793
• Opis fizyczny: Bibliogr. 36 poz.

Twórcy

autor

Li H.-C.

autor

Chen C.-C.

• Department of Earth Sciences and Institute of Geophysics, National Central University, Jhongli, Taiwan,

Bibliografia

• Bak, P., C. Tang, and K. Weisenfield (1987), Self-organized criticality: An explanation of the 1/f noise, Phys. Rev. Lett. 59, 4, 381-384, DOI: 10.1103/PhysRevLett.59.381.
• Chen, C.-C., J.B. Rundle, J.R. Holliday, K.Z. Nanjo, D.L. Turcotte, S.C. Li, and K.F. Tiampo (2005), The 1999 Chi-Chi, Taiwan, earthquake as a typical example of seismic activation and quiescence, Geophys. Res. Lett. 32, L22315, DOI: 10.1029/2005GL023991.
• Chen, C.-C., J.B. Rundle, H.C. Li, J.R. Holliday, K.Z. Nanjo, D.L. Turcotte, and K.F. Tiampo (2006), From tornadoes to earthquakes: Forecast verification for binary events applied to the 1999 Chi-Chi, Taiwan, earthquake, Terr. Atmos. Ocean. Sci. 17, 503-516.
• Chen, C.-C., Y.-T. Lee, and L.-Y. Chiao (2008), Intermittent criticality in the longrange connective sandpile (LRCS) model, Phys. Lett. A 372, 24, 4340-4343, DOI: 10.1016/j.physleta.2008.04.043.
• Cohen, J., P. Cohen, S.G. West, and L.S. Aiken (2003), Applied Multiple Regression Correlation Analysis for the Behavioral Sciences, Lawrence Erlbaum Associates Inc., New Jersey.
• Dawson, B., and R.G. Trapp (2004), Basic and Clinical Biostatistics, 4th ed., Lange Medical Books, McGraw-Hill, New York.
• Ferguson, C.D., W. Klein, and J.B. Rundle (1999), Spinodals, scaling and ergodicity in a model of an earthquake fault with long-range stress transfer, Phys. Rev. E 60, 1359-1373, DOI: 10.1103/PhysRevE.60.1359.
• Fisher, D.S. (1985), Sliding charge-density waves as a dynamic critical phenomenon, Phys. Rev. B 31, 3, 1396-1427, DOI: 10.1103/PhysRevB.31.1396.
• Fisher, D.S., K. Dahmen, S. Ramanathan, and Y. Ben-Zion (1997), Statistics of earthquakes in simple models of heterogeneous faults, Phys. Rev. Lett. 78, 25, 4885-4888, DOI: 10.1103/PhysRevLett.78.4885.
• Gopal, A.D., and D.J. Durian (1995), Nonlinear bubble dynamics in a slowly driven foam, Phys. Rev. Lett. 75, 2610-2613, DOI: 10.1103/PhysRevLett.75.2610.
• Gutenberg, B., and C.F. Richter (1954), Seismicity of the Earth and Associated Phenomena, 2nd ed., Princeton University Press, New Jersey.
• Habermann, R.E. (1987), Man-made changes of seismicity rates, Bull. Seismol. Soc. Am. 77, 141-159.
• Hertz, J., A. Korgh, and R.G. Palmer (1991), Introduction to the Theory of Neural Computation, Addison Wesley, Reading, MA.
• Herz, A.V.M., and J.J. Hopfield (1995), Earthquake cycles and neural reverberations: Collective oscillations in systems with pulse-coupled threshold elements, Phys. Rev. Lett. 75, 1222-1225, DOI: 10.1103/PhysRevLett.75.1222.
• Hoel, P.G. (1966), Introduction to Mathematical Statistics, Wiley Series in Probability and Statistics, John Wiley & Sons, New York.
• Klein, W., J.B. Rundle, and C.D. Ferguson (1997), Scaling and nucleation in models of earthquake faults, Phys. Rev. Lett. 78, 19, 3793-3796, DOI: 10.1103/PhysRevLett.78.3793.
• Kvam, P.H., and B. Vidakovic (2007), Nonparametric Statistics with Applications to Science and Engineering, John Wiley & Sons, New Jersey.
• Lee, Y.-T., C.-C. Chen, Y.-F. Chang, and L.-Y. Chiao (2008), Precursory phenomena associated with large avalanches in long-range connective sandpile (LRCS) model, Physica A 387, 21, 5263-5270, DOI: 10.1016/j.physa.2008.05.004.
• Mignan, A., M.J. Werner, S. Wiemer, C.-C. Chen, and Y.-M. Wu (2011), Bayesian estimation of the spatially varying completeness magnitude of earthquake catalogs, Bull. Seismol. Soc. Am. 101, 3, 1371-1385, DOI: 10.1785/0120100223.
• Ogata, Y., and K. Katsura (1993), Analysis of temporal and spatial heterogeneity of magnitude frequency distribution inferred from earthquake catalogues, Geophys. J. Int. 113, 727-738, DOI: 10.1111/j.1365-246X.1993.tb04663.x.
• Royston, P. (1995), A remark on algorithm AS 181: the W-test for normality, J. Roy. Stat. Soc., Ser. C 44, 4, 547-551.
• Rundle, J.B., and W. Klein (1995), New ideas about the physics of earthquakes, Rev. Geophys. 33, S1, 283-286, DOI: 10.1029/95RG00106.
• Rundle, J.B., K.F. Tiampo, W. Klein, and J.S. Sá Martins (2002), Self-organization in leaky threshold systems: The influence of near-mean field dynamics and its implications for earthquakes, neurobiology, and forecasting, Proc. Nat. Acad. Sci. USA 99, Suppl. 1, 2514-2521, DOI: 10.1073/pnas.012581899.
• Scholz, C.H. (1990), The Mechanics of Earthquakes and Faulting, Cambridge University Press, Cambridge, UK.
• Shapiro, S.S., and M.B. Wilk (1965), An analysis of variance test for normality (complete samples), Biometrika 52, 3-4, 591-611.
• Telesca, L., C.-C. Chen, and Y.-T. Lee (2009), Scaling behaviour in temporal fluctuations of crustal seismicity in Taiwan, Nat. Hazards Earth Syst. Sci. 9, 2067-2071, DOI: 10.5194/nhess-9-2067-2009.
• Thirumalai, D., R.D. Mountain, and T.R. Kirkpatrick (1989), Ergodic behavior in supercooled liquids and in glasses, Phys. Rev. A 39, 7, 3563-3574, DOI: 10.1103/PhysRevA.39.3563.
• Tiampo, K.F., J.B. Rundle, S. McGinnis, S.J. Gross, and W. Klein (2002), Meanfield threshold systems and phase dynamics: An application to earthquake fault systems, Europhys. Lett. 60, 3, 481-487, DOI: 10.1209/epl/i2002-00289-y.
• Tiampo, K.F., J.B. Rundle, W. Klein, J.S. Sá Martins, and C.D. Ferguson (2003), Ergodic dynamics in a natural threshold system, Phys. Rev. Lett. 91, 238501, DOI: 10.1103/PhysRevLett.91.238501.
• Tiampo, K.F., J.B. Rundle, W. Klein, J. Holliday, J.S. Sá Martins, and C.D. Ferguson (2007), Ergodicity in natural earthquake fault networks, Phys. Rev. E 75, DOI: 10.1103/PhysRevE.75.066107.
• Tiampo, K.F., W. Klein, H.-C. Li, A. Mignan, Y. Toya, S.Z.L. Kohen-Kadosh, J.B. Rundle, and C.-C. Chen (2010), Ergodicity and earthquake catalogs: Forecast testing and resulting implications, Pure Appl. Geophys. 167, 6-7, 763-782, DOI: 10.1007/s00024-010-0076-2.
• Tsai, C.-Y., G. Ouillon, and D. Sornette (2011), New empirical tests of the multifractal Omori law for Taiwan, arXiv:1109.5017v1.
• Urbach, J.S., R.C. Madison, and J.T. Markert (1995), Interface depinning, selforganized criticality, and the Barkhausen effect, Phys. Rev. Lett. 75, 2, 276-279, DOI: 10.1103/PhysRevLett.75.276.
• Wiemer, S. (2001), A software package to analyze seismicity: ZMAP, Seismol. Res. Lett. 72, 3, 373-382, DOI: 10.1785/gssrl.72.3.373.
• Wiemer, S., and M. Wyss (2000), Minimum magnitude of completeness in earthquake catalogs: Examples from Alaska, the Western United States, and Japan, Bull. Seismol. Soc. Am. 90, 4, 859-869, DOI: 10.1785/0119990114.
• Wu, Y.-M., C.-C. Chen, L. Zhao, and C.-H. Chang (2008), Seismicity characteristics before the 2003 Chengkung, Taiwan, earthquake, Tectonophysics 457, 177-182, DOI: /10.1016/j.tecto.2008.06.007.