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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 1

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Utsu (1975) 2

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

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

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Matsumura (1986) 5

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

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Bath Law (Richter, 1958) o D 1 := M main -M 1 = 1.2 Magnitude Frequency: Utsu (1957) D 1 = 1.4 ~ Median based on 90 Japanese M main >6.5 Shallow earthquakes = 7

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Bath Law (Richter, 1958) o D 1 =M main -M 1 = 1.2 Utsu (1961, 1969) Mainshock Magnitude Magnitude difference Magnitude Frequency: 8

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o D 1 =M main -M 1 = 1.2 Bath Law (Richter, 1958) Utsu (1961, 1969) D 1 = 5.0 – 0.5M main ~ Mainshock Magnitude for 6 < M main < 8 D 1 = 2.0 ~ for M main <6 == Magnitude difference Magnitude Frequency: 9

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Aftershocks 10

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

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

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Mogi (1962) 13

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Mogi (1967) 14

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Mogi (1962) Utsu (1957) (t > t 0 ) (t ) = Kt -p t > t 0 = 1.0 day 15

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Mogi (1962) Utsu (1957) (t > t 0 ) (t ) = Kt -p Utsu (1961) 16

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Mogi (1962) Utsu (1957) (t > t 0 ) Kagan & Knopoff Models (e.g., 1981, 1987) (t ) = Kt -p Utsu (1961) 17

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

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Ogata (1983, J. Phys. Earth) 19

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

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i = (t i ) Ogata & Shimazaki (1984, BSSA) Aftershocks of the1965 Rat Islands Earthquake of M w 8.7 (s) 21

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

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

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Utsu (1970) Standard aftershock activity: Occurrence rate of aftershock of M s is 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 during 1 =5.5), where cf., Reasenberg and Jones (1989) 24

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Utsu (1970) Secondary Aftershocks 25

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

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

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

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

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

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Asperities Yamanaka & Kikuchi (2001) 40

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

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Probability Forecastin g 45

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Multiple Prediction Formula(Utsu,1977,78) P 0 : Empirical occurrence probability of a large earthquake. P m : 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: 46

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P 0 : Empirical occurrence probability of a large earthquake. P m : 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: 47 Multiple Prediction Formula(Utsu,1977,78)

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Aki (1981) P 0 : Empirical occurrence probability of a large earthquake. P m : 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 Multiple Prediction Formula(Utsu,1977,78)

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where P 0 : Empirical occurrence probability of a large earthquake. P m : 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 Multiple Prediction Formula(Utsu,1977,78)

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logit Prob{ F | location, magnitude, time, space } = … F := { Ongoing events will be FORESHOCKS } Utsu (1978), Ogata, Utsu & Katsura (1995, 96, GJI ) 50 Multiple Prediction Formula

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logit Prob{ F | location, magnitude, time, space } = logit Prob{ F | location of the first event } Multiple Prediction Formula F := { Ongoing events will be FORESHOCKS } Utsu (1978), Ogata, Utsu & Katsura (1995, 96, GJI ) + …+ … 51

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logit Prob{ F | location, magnitude, time, space } = logit Prob{ F | location of the first event } Multiple Prediction Formula F := { Ongoing events will be FORESHOCKS } + logit Prob{ F | magnitude sequential feature } Utsu (1978), Ogata, Utsu & Katsura (1995, 96, GJI ) + …+ … Utsu(1978) 52

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logit Prob{ F | location, magnitude, time, space } = logit Prob{ F | location of the first event } Multiple Prediction Formula F := { Ongoing events will be FORESHOCKS } + logit Prob{ F | temporal feature of a cluster } + logit Prob{ F | magnitude sequential feature } Utsu (1978), Ogata, Utsu & Katsura (1995, 96, GJI ) + …+ … 53

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logit Prob{ F | location, magnitude, time, space } = logit Prob{ F | location of the first event } Multiple Prediction Formula F := { Ongoing events will be FORESHOCKS } + logit Prob{ F | temporal feature of a cluster } + logit Prob{ F | spatial feature of a cluster } + logit Prob{ F | magnitude sequential feature } - 3 x logit Prob{ F } Utsu (1978), Ogata, Utsu & Katsura (1995, 96, GJI ) 54

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TIMSAC84-SASE version 2 (Statistical Analysis of Series of Events) SASeis Windows Visual Basic SASeis 2006 SASeis DOS version with R graphical devices and Manuals 57

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Thank you very much for listening 58

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