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

Utsu (1975) 2

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

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

Matsumura (1986) 5

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

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

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

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

Aftershocks 10

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

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

Mogi (1962) 13

Mogi (1967) 14

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

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

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

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

Ogata (1983, J. Phys. Earth) 19

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

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

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

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

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 during 1 =5.5), where cf., Reasenberg and Jones (1989) 24

Utsu (1970) Secondary Aftershocks 25

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

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

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

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

Probability Forecastin g 45

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

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)

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)

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)

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

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

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

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

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

Thank you very much for listening 58