메뉴 건너뛰기




Volumn 180, Issue 3, 2010, Pages 1313-1328

Statistical distributions of earthquake numbers: Consequence of branching process

Author keywords

Earthquake interaction, forecasting, and prediction; North America; Probabilistic forecasting; Probability distributions; Statistical seismology; Theoretical seismology

Indexed keywords

EARTHQUAKE CATALOGUE; EARTHQUAKE MAGNITUDE; EARTHQUAKE PREDICTION; FREQUENCY-MAGNITUDE DISTRIBUTION; NUMERICAL MODEL; PARAMETERIZATION; POISSON RATIO; POWER LAW DISTRIBUTION; PROBABILITY; SEISMOLOGY; TECTONIC SETTING; THRESHOLD; UNCERTAINTY ANALYSIS;

EID: 77950140914     PISSN: 0956540X     EISSN: 1365246X     Source Type: Journal    
DOI: 10.1111/j.1365-246X.2009.04487.x     Document Type: Article
Times cited : (71)

References (56)
  • 1
    • 0037763184 scopus 로고
    • Estimation for the negative binomial distribution based on the conditional likelihood
    • Anraku K, Yanagimoto T. Estimation for the negative binomial distribution based on the conditional likelihood. Commun. Stat.-Simulat. Comput. 1990, 19(3):771-786.
    • (1990) Commun. Stat.-Simulat. Comput. , vol.19 , Issue.3 , pp. 771-786
    • Anraku, K.1    Yanagimoto, T.2
  • 2
    • 78651007076 scopus 로고
    • Sampling theory of the negative binomial and logarithmic series distributions
    • Anscombe FJ. Sampling theory of the negative binomial and logarithmic series distributions. Biometrika 1950, 37(3/4):358-382.
    • (1950) Biometrika , vol.37 , Issue.3-4 , pp. 358-382
    • Anscombe, F.J.1
  • 4
    • 14344261878 scopus 로고    scopus 로고
    • Plate-tectonic analysis of shallow seismicity: apparent boundary width, beta, corner magnitude, coupled lithosphere thickness, and coupling in seven tectonic settings
    • and electronic supplement
    • Bird P, Kagan YY. Plate-tectonic analysis of shallow seismicity: apparent boundary width, beta, corner magnitude, coupled lithosphere thickness, and coupling in seven tectonic settings. Bull. seism. Soc. Am. 2004, 94(6):2380-2399. and electronic supplement
    • (2004) Bull. seism. Soc. Am. , vol.94 , Issue.6 , pp. 2380-2399
    • Bird, P.1    Kagan, Y.Y.2
  • 5
    • 0035533779 scopus 로고    scopus 로고
    • Hawkes branching point processes without ancestors
    • Bremaud P, Massoulie L. Hawkes branching point processes without ancestors. J. appl. Probab. 2001, 38(1):122-135.
    • (2001) J. appl. Probab. , vol.38 , Issue.1 , pp. 122-135
    • Bremaud, P.1    Massoulie, L.2
  • 6
    • 65549085067 scopus 로고    scopus 로고
    • Power-law distributions in empirical data
    • Clauset A, Shalizi CR, Newman MEJ. Power-law distributions in empirical data. SIAM Rev. 2009, 51:661-703.
    • (2009) SIAM Rev. , vol.51 , pp. 661-703
    • Clauset, A.1    Shalizi, C.R.2    Newman, M.E.J.3
  • 8
    • 0000153123 scopus 로고
    • Engineering seismic risk analysis
    • Cornell CA. Engineering seismic risk analysis. Bull. seism. Soc. Am. 1968, 58:1583-1606.
    • (1968) Bull. seism. Soc. Am. , vol.58 , pp. 1583-1606
    • Cornell, C.A.1
  • 9
    • 0026613453 scopus 로고
    • Poissonian and negative binomial modelling of earthquake time series in the Aegean area
    • Dionysiou DD, Papadopoulos GA. Poissonian and negative binomial modelling of earthquake time series in the Aegean area. Phys. Earth planet. Inter. 1992, 71(3-4):154-165.
    • (1992) Phys. Earth planet. Inter. , vol.71 , Issue.3-4 , pp. 154-165
    • Dionysiou, D.D.1    Papadopoulos, G.A.2
  • 10
    • 0007178056 scopus 로고    scopus 로고
    • Paleoseismicity: seismicity evidence for past large earthquakes
    • Ebel JE, Bonjer K-P, Oncescu MC. Paleoseismicity: seismicity evidence for past large earthquakes. Seismol. Res. Lett. 2000, 71(2):283-294.
    • (2000) Seismol. Res. Lett. , vol.71 , Issue.2 , pp. 283-294
    • Ebel, J.E.1    Bonjer, K.-.P.2    Oncescu, M.C.3
  • 12
    • 67649909558 scopus 로고    scopus 로고
    • Omori-Utsu law c-values associated with recent moderate earthquakes in Japan
    • Enescu B, Mori J, Miyazawa M, Kano Y. Omori-Utsu law c-values associated with recent moderate earthquakes in Japan. Bull. seism. Soc. Am. 2009, 99(2A):884-891.
    • (2009) Bull. seism. Soc. Am. , vol.2-99 , pp. 884-891
    • Enescu, B.1    Mori, J.2    Miyazawa, M.3    Kano, Y.4
  • 13
    • 0000724858 scopus 로고
    • Experimental evidence concerning contagious distributions in ecology
    • Evans DA. Experimental evidence concerning contagious distributions in ecology. Biometrika 1953, 40(1-2):186-211.
    • (1953) Biometrika , vol.40 , Issue.1-2 , pp. 186-211
    • Evans, D.A.1
  • 16
    • 34248673702 scopus 로고    scopus 로고
    • Overview of the working group for the development of regional earthquake likelihood models (RELM)
    • Field EH. Overview of the working group for the development of regional earthquake likelihood models (RELM). Seism. Res. Lett. 2007, 78(1):7-16.
    • (2007) Seism. Res. Lett. , vol.78 , Issue.1 , pp. 7-16
    • Field, E.H.1
  • 18
    • 0002920216 scopus 로고
    • Point spectra of some mutually exciting point processes
    • Hawkes AG. Point spectra of some mutually exciting point processes. J. Roy. Statist. Soc. 1971, B33:438-443.
    • (1971) J. Roy. Statist. Soc. , vol.B33 , pp. 438-443
    • Hawkes, A.G.1
  • 21
    • 0027526792 scopus 로고
    • Local magnitudes and apparent variations in seismicity rates in Southern California
    • Hutton LK, Jones LM. Local magnitudes and apparent variations in seismicity rates in Southern California. Bull. seism. Soc. Am. 1993, 83:313-329.
    • (1993) Bull. seism. Soc. Am. , vol.83 , pp. 313-329
    • Hutton, L.K.1    Jones, L.M.2
  • 23
    • 0000363656 scopus 로고    scopus 로고
    • Testable earthquake forecasts for 1999
    • Jackson DD, Kagan YY. Testable earthquake forecasts for 1999. Seism. Res. Lett. 1999, 70(4):393-403.
    • (1999) Seism. Res. Lett. , vol.70 , Issue.4 , pp. 393-403
    • Jackson, D.D.1    Kagan, Y.Y.2
  • 25
    • 0007246778 scopus 로고
    • A probabilistic description of the seismic regime
    • (English translation). Scanned versions of the Russian and English text are available at
    • Kagan YY. A probabilistic description of the seismic regime. Izv. Acad. Sci. USSR, Phys. Solid Earth 1973a, 213-219. http://eq.ess.ucla.edu/~kagan/pse_1973_index.html, (English translation). Scanned versions of the Russian and English text are available at
    • (1973) Izv. Acad. Sci. USSR, Phys. Solid Earth , pp. 213-219
    • Kagan, Y.Y.1
  • 26
    • 0000765575 scopus 로고
    • Statistical methods in the study of the seismic process (with discussion: comments by M.S. Bartlett, A.G. Hawkes, & J.W. Tukey)
    • Scanned version of text is available at
    • Kagan YY. Statistical methods in the study of the seismic process (with discussion: comments by M.S. Bartlett, A.G. Hawkes, & J.W. Tukey). Bull. Int. Statist. Inst. 1973b, 45(3):437-453. http://moho.ess.ucla.edu/~kagan/Kagan_1973b.pdf, Scanned version of text is available at
    • (1973) Bull. Int. Statist. Inst. , vol.45 , Issue.3 , pp. 437-453
    • Kagan, Y.Y.1
  • 27
    • 0026082280 scopus 로고
    • Likelihood analysis of earthquake catalogues
    • Kagan YY. Likelihood analysis of earthquake catalogues. Geophys. J. Int. 1991, 106(1):135-148.
    • (1991) Geophys. J. Int. , vol.106 , Issue.1 , pp. 135-148
    • Kagan, Y.Y.1
  • 28
    • 21344443233 scopus 로고    scopus 로고
    • Comment on " The Gutenberg-Richter or characteristic earthquake distribution, which is it?" by Steven G. Wesnousky
    • Kagan YY. Comment on " The Gutenberg-Richter or characteristic earthquake distribution, which is it?" by Steven G. Wesnousky. Bull. seism. Soc. Am. 1996, 86(1a):274-285.
    • (1996) Bull. seism. Soc. Am. , vol.86 , Issue.1 A , pp. 274-285
    • Kagan, Y.Y.1
  • 29
    • 0036507545 scopus 로고    scopus 로고
    • Aftershock zone scaling
    • Kagan YY. Aftershock zone scaling. Bull. seism. Soc. Am. 2002, 92(2):641-655.
    • (2002) Bull. seism. Soc. Am. , vol.92 , Issue.2 , pp. 641-655
    • Kagan, Y.Y.1
  • 30
    • 0037465143 scopus 로고    scopus 로고
    • Accuracy of modern global earthquake catalogs
    • Kagan YY. Accuracy of modern global earthquake catalogs. Phys. Earth planet. Inter. 2003, 135(2-3):173-209.
    • (2003) Phys. Earth planet. Inter. , vol.135 , Issue.2-3 , pp. 173-209
    • Kagan, Y.Y.1
  • 31
    • 7244247255 scopus 로고    scopus 로고
    • Short-term properties of earthquake catalogs and models of earthquake source
    • Kagan YY. Short-term properties of earthquake catalogs and models of earthquake source. Bull. seism. Soc. Am. 2004, 94(4):1207-1228.
    • (2004) Bull. seism. Soc. Am. , vol.94 , Issue.4 , pp. 1207-1228
    • Kagan, Y.Y.1
  • 33
    • 0026051038 scopus 로고
    • Long-term earthquake clustering
    • Kagan YY, Jackson DD. Long-term earthquake clustering. Geophys. J. Int. 1991, 104(1):117-133.
    • (1991) Geophys. J. Int. , vol.104 , Issue.1 , pp. 117-133
    • Kagan, Y.Y.1    Jackson, D.D.2
  • 34
    • 0033732689 scopus 로고    scopus 로고
    • Probabilistic forecasting of earthquakes
    • Kagan YY, Jackson DD. Probabilistic forecasting of earthquakes. Geophys. J. Int. 2000, 143(2):438-453.
    • (2000) Geophys. J. Int. , vol.143 , Issue.2 , pp. 438-453
    • Kagan, Y.Y.1    Jackson, D.D.2
  • 35
    • 0023471638 scopus 로고
    • Statistical short-term earthquake prediction
    • Kagan YY, Knopoff L. Statistical short-term earthquake prediction. Science 1987, 236(4808):1563-1567.
    • (1987) Science , vol.236 , Issue.4808 , pp. 1563-1567
    • Kagan, Y.Y.1    Knopoff, L.2
  • 36
    • 77950125351 scopus 로고    scopus 로고
    • Earthquake Patterns in Diverse Tectonic Zones of the Globe
    • Kagan YY, Bird P, Jackson DD. Earthquake Patterns in Diverse Tectonic Zones of the Globe. Pure appl. Geophys. 2010, 167(6/7). http://scec.ess.ucla.edu/~ykagan/globe_index.html
    • (2010) Pure appl. Geophys. , vol.167 , Issue.6-7
    • Kagan, Y.Y.1    Bird, P.2    Jackson, D.D.3
  • 38
    • 34347216751 scopus 로고    scopus 로고
    • Evidence of clustering and nonstationarity in the time distribution of large worldwide earthquakes
    • doi
    • Lombardi AM, Marzocchi W. Evidence of clustering and nonstationarity in the time distribution of large worldwide earthquakes. J. geophys. Res. 2007, 112:B02303. 10.1029/2006JB004568, doi
    • (2007) J. geophys. Res. , vol.112
    • Lombardi, A.M.1    Marzocchi, W.2
  • 39
    • 0012346731 scopus 로고
    • Statistical models for earthquake occurrence and residual analysis for point processes
    • Ogata Y. Statistical models for earthquake occurrence and residual analysis for point processes. J. Am. Statist. Assoc. 1988, 83:9-27.
    • (1988) J. Am. Statist. Assoc. , vol.83 , pp. 9-27
    • Ogata, Y.1
  • 40
    • 0001663614 scopus 로고    scopus 로고
    • Space-time point-process models for earthquake occurrences
    • Ogata Y. Space-time point-process models for earthquake occurrences. Ann. Inst. Statist. Math. 1998, 50(2):379-402.
    • (1998) Ann. Inst. Statist. Math. , vol.50 , Issue.2 , pp. 379-402
    • Ogata, Y.1
  • 41
    • 4344607023 scopus 로고
    • Some methods of estimation for logarithmic series distribution
    • Patil GP. Some methods of estimation for logarithmic series distribution. Biometrics 1962, 18(1):68-75.
    • (1962) Biometrics , vol.18 , Issue.1 , pp. 68-75
    • Patil, G.P.1
  • 42
    • 84983262751 scopus 로고
    • Maximum likelihood estimation for the complete and truncated logarithmic series distributions
    • Patil GP, Wani JK. Maximum likelihood estimation for the complete and truncated logarithmic series distributions. Sankhya 1965, 27A(2/4):281-292.
    • (1965) Sankhya , vol.27 A , Issue.2-4 , pp. 281-292
    • Patil, G.P.1    Wani, J.K.2
  • 43
    • 77954311548 scopus 로고    scopus 로고
    • U.S. Geological Survey, U.S. Dep. of Inter., Natl. Earthquake Inf. Cent.
    • Preliminary determinations of epicenters (PDE), and
    • U.S. Geological Survey, U.S. Dep. of Inter., Natl. Earthquake Inf. Cent. 2008, http://neic.usgs.gov/neis/epic/epic.html, http://neic.usgs.gov/neis/epic/code_catalog.html, Preliminary determinations of epicenters (PDE), and
    • (2008)
  • 44
    • 20344387201 scopus 로고    scopus 로고
    • Anomalous scaling of offspring and generation numbers in branching processes
    • Saichev A, Helmstetter A, Sornette D. Anomalous scaling of offspring and generation numbers in branching processes. Pure appl. Geophys. 2005, 162:1113-1134.
    • (2005) Pure appl. Geophys. , vol.162 , pp. 1113-1134
    • Saichev, A.1    Helmstetter, A.2    Sornette, D.3
  • 45
    • 33846521137 scopus 로고    scopus 로고
    • Power law distribution of seismic rates
    • doi
    • Saichev A, Sornette D. Power law distribution of seismic rates. Tectonophysics 2007, 431:7-13. 10.1016/j.tecto.2006.05.026, doi
    • (2007) Tectonophysics , vol.431 , pp. 7-13
    • Saichev, A.1    Sornette, D.2
  • 49
    • 77950185498 scopus 로고
    • Comments on estimation for the negative binomial distribution
    • G. P. Patil, Stat. Publ. Soc., Calcutta
    • Shenton LR, Myers R. Comments on estimation for the negative binomial distribution. Classical and Contagious Discrete Distributions 1963, 241-262. in, pp, ed., G. P. Patil, Stat. Publ. Soc., Calcutta
    • (1963) Classical and Contagious Discrete Distributions , pp. 241-262
    • Shenton, L.R.1    Myers, R.2
  • 50
    • 0014894509 scopus 로고
    • A clustering model for earthquake occurrences.
    • Shlien S, Toksöz MN. A clustering model for earthquake occurrences. Bull. seism. Soc. Am. 1970, 60(6):1765-1788.
    • (1970) Bull. seism. Soc. Am. , vol.60 , Issue.6 , pp. 1765-1788
    • Shlien, S.1    Toksöz, M.N.2
  • 51
    • 27744464116 scopus 로고    scopus 로고
    • Apparent clustering and apparent background earthquakes biased by undetected seismicity
    • doi
    • Sornette D, Werner MJ. Apparent clustering and apparent background earthquakes biased by undetected seismicity. J. geophys. Res. 2005, 110(9):B09303. 10.1029/2005JB003621, doi
    • (2005) J. geophys. Res. , vol.110 , Issue.9
    • Sornette, D.1    Werner, M.J.2
  • 52
    • 0348102523 scopus 로고    scopus 로고
    • Negative binomial distribution
    • Kotz S, Balakrishnan N, Read C, Vidakovic B. 2nd edn, Wiley-Interscience, Hoboken, NJ
    • Tripathi RC. Negative binomial distribution. Encyclopedia of Statistical Sciences 2006, Vol. 8:5413-20. Kotz SBalakrishnan NRead CVidakovic B. in, pp, eds, 2nd edn, Wiley-Interscience, Hoboken, NJ
    • (2006) Encyclopedia of Statistical Sciences , vol.8 , pp. 5413-5420
    • Tripathi, R.C.1
  • 53
    • 0000994312 scopus 로고
    • Stochastic models for earthquake occurrence (with discussion)
    • Vere-Jones D. Stochastic models for earthquake occurrence (with discussion). J. Roy. Stat. Soc. 1970, B32(1):1-62.
    • (1970) J. Roy. Stat. Soc. , vol.B32 , Issue.1 , pp. 1-62
    • Vere-Jones, D.1
  • 55
    • 20344369041 scopus 로고    scopus 로고
    • Approximating the distribution of Pareto sums
    • Zaliapin IV, Kagan YY, Schoenberg F. Approximating the distribution of Pareto sums. Pure appl. Geophys. 2005, 162(6-7):1187-1228.
    • (2005) Pure appl. Geophys. , vol.162 , Issue.6-7 , pp. 1187-1228
    • Zaliapin, I.V.1    Kagan, Y.Y.2    Schoenberg, F.3
  • 56
    • 4644316414 scopus 로고    scopus 로고
    • Analyzing earthquake clustering features by using stochastic reconstruction
    • doi
    • Zhuang JC, Ogata Y, Vere-Jones D. Analyzing earthquake clustering features by using stochastic reconstruction. J. geophys. Res. 2004, 109(B5):B05301. 10.1029/2003JB002879, doi
    • (2004) J. geophys. Res. , vol.109 , Issue.B5
    • Zhuang, J.C.1    Ogata, Y.2    Vere-Jones, D.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.