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Contributions of Prof. Tokuji Utsu to Statistical Seismology and Recent Developments

1. Contributions of Prof. Tokuji Utsu to Statistical Seismology and Recent Developments. Ogata, Yosihiko The Institute of Statistical Mathematics ， Tokyo and Graduate University for Advanced Studies. Utsu (1975). 2. Ogata et al. (1982,86). 3.

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Contributions of Prof. Tokuji Utsu to Statistical Seismology and Recent Developments

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  1. 1 Contributions of Prof. Tokuji Utsuto Statistical Seismology and Recent Developments Ogata, Yosihiko The Institute of Statistical Mathematics，Tokyo and Graduate University for Advanced Studies

  2. Utsu (1975) 2

  3. Ogata et al. (1982,86) 3 Seismicity rate=Trend+Clustering+Exogeneous effect deep Intermediate Shallow Shallow seismicity Intermediate + deep seismicity

  4. Seismicity rate = trend + seasonality + cluster effect Ma Li & Vere-Jones (1997) SEASONALITY CLUSTERING 4

  5. 5 Matsumura (1986)

  6. 6 Magnitude Frequency: Utsu (1965) b-value estimation Aki (1965) MLE & Error assesment Utsu (1967) b-value test Utsu (1971, 1978) modified G-R Law Utsu (1978) h-value estimation h = E[(M-Mc)2] / E[M-Mc]2

  7. Magnitude Frequency: 7 o Bath Law (Richter, 1958) Utsu (1957) ~ D1 = 1.4 D1 := Mmain-M1 = 1.2 Median based on 90 Japanese Mmain>6.5 Shallow earthquakes =

  8. Magnitude Frequency: 8 o Bath Law (Richter, 1958) D1=Mmain-M1 = 1.2 Magnitude difference Utsu (1961, 1969) Mainshock Magnitude

  9. Magnitude Frequency: 9 o Bath Law (Richter, 1958) D1=Mmain-M1 = 1.2 Magnitude difference Utsu (1961, 1969) ~ D1 = 5.0 – 0.5Mmain for 6 < Mmain< 8 = = ~ for Mmain<6 D1 = 2.0 Mainshock Magnitude

  10. 10 Aftershocks

  11. 11 Utsu (1961) The Omori-Utsu formula for aftershock decay rate ｔ : Elapsed time from the mainshock Ｋ，ｃ，ｐ : constant parameters

  12. 12 Utsu (1961, 1969) 1981 Nobi (M8) Aftershock freq. Data from Omori (1895)

  13. Mogi (1962) 13

  14. Mogi (1967) 14

  15. 15 Mogi (1962) t > t0 = 1.0 day Utsu (1957) l (t) = Kt-p (t > t0)

  16. 16 Mogi (1962) Utsu (1961) Utsu (1957) l (t) = Kt-p (t > t0)

  17. 17 Mogi (1962) Utsu (1961) Utsu (1957) l (t) = Kt-p (t > t0) Kagan & Knopoff Models (e.g., 1981, 1987)

  18. 18 Utsu (1962, BSSA) 1958 Central Araska 1958 Southeastern Araska 1957 Aleutian

  19. 19 Ogata (1983, J. Phys. Earth)

  20. 20 Relative Quiescence in the Nobi aftershocks preceding the 1909 Anegawa earthquake of Ms7.0 1891 1909

  21. 21 Ogata & Shimazaki (1984, BSSA) Aftershocks of the1965 Rat Islands Earthquake of Mw8.7 l(s) ti = L(ti)

  22. Utsu & Seki (1954) 22 Utsu (1969) log S = 1.02M – 4.01 log S = M – 3.9 log L = 0.5M – 1.8

  23. 23 Tokachi-Oki earthquake May 16 1968 MJ=7.9 Utsu (1970) Aftershocks Nov. 1968 - Apr. 1970 …AABACBCBBBAA… A B vs C&A …--+--+-++-+++--… B Count runs C

  24. 24 Utsu (1970) cf., Reasenberg and Jones (1989) Standard aftershock activity: Occurrence rate of aftershock of Ms is during 1 < t < 100 days (M0>=5.5), where p=1.3, c=0.3 and b=0.85 are median estimates. The constant 1.83 is the best fit to 66 aftershock sequences in Japan during 1926-1968

  25. 25 Utsu (1970) Secondary Aftershocks

  26. 26 Omori-Utsu formula: (Ogata, 1986, 1988)

  27. 27 Omori-Utsu formula: (Ogata, 1986, 1988) Kagan & Knopoff model (1987) n (t)=Kt–3/2, t > 10a+1.5Mj = = 0,t < 10a+1.5Mj

  28. 27 Omori-Utsu formula: (Ogata, 1986, 1988) Kagan & Knopoff model (1987) y(M).n (t)=10(2/3)(M-Mc) Kt–3/2, t > tM = = 0,t < tM

  29. 28

  30. 29

  31. 30

  32. 31

  33. 32

  34. 1926 – 1995, M >= 5.0, depth < 100km 33

  35. 1926 – 1995, M >= 5.0, depth < 100km 34

  36. 35

  37. 36

  38. 37

  39. 38

  40. 39

  41. 40 Asperities Yamanaka & Kikuchi (2001)

  42. 41

  43. 42

  44. 43

  45. 44 LONGITUDE Cooler color shows quiescence relative to the HIST-ETAS model

  46. 45 Probability Forecasting

  47. 46 Multiple Prediction Formula(Utsu,1977,78) P0: Empirical occurrence probability of a large earthquake. Pm: Occurrence probability conditional on a precursory anomaly m; m = 1, 2, …, M, where probabilities are assumed mutually independent. Then, the occurrence probability based on all precursory anomalies is:

  48. 47 Multiple Prediction Formula(Utsu,1977,78) P0: Empirical occurrence probability of a large earthquake. Pm: Occurrence probability conditional on a precursory anomaly m; m = 1, 2, …, M, where probabilities are assumed mutually independent. Then, the occurrence probability based on all precursory anomalies is:

  49. 48 Multiple Prediction Formula(Utsu,1977,78) P0: Empirical occurrence probability of a large earthquake. Pm: Occurrence probability conditional on a precursory anomaly m; m = 1, 2, …, M, where probabilities are assumed mutually independent. Then, the occurrence probability based on all precursory anomalies is: Aki (1981)

  50. 49 Multiple Prediction Formula(Utsu,1977,78) P0: Empirical occurrence probability of a large earthquake. Pm: Occurrence probability conditional on a precursory anomaly m; m = 1, 2, …, M, where probabilities are assumed mutually independent. Then, the occurrence probability based on all precursory anomalies is: where

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