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

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

Ogata, Yosihiko

The Institute of Statistical Mathematics ， Tokyoand

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-Mc)2] / E[M-Mc]2

6

Bath Law (Richter, 1958)

o

D1 := Mmain-M1

= 1.2

Magnitude Frequency:

Utsu (1957)

D1 = 1.4~

Median based on 90 Japanese Mmain>6.5Shallow earthquakes

=

7


o

D1=Mmain-M1

= 1.2

Utsu (1961, 1969)

Mainshock Magnitude

Mag

nit

ud

e d

iffe

ren

ce

Magnitude Frequency: 8

o

D1=Mmain-M1

= 1.2


Utsu (1961, 1969)

D1 = 5.0 – 0.5Mmain~

Mainshock Magnitude

for 6 < Mmain< 8

D1 = 2.0~ for Mmain<6

= = Mag

nit

ud

e d

iffe

ren

ce

Magnitude Frequency: 9

Aftershocks

10

The Omori-Utsu formula for aftershock decay rate

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 > t0)(t ) = Kt -p

t > t0 = 1.0 day15

Mogi (1962)

Utsu (1957)

(t > t0)(t ) = Kt -p

Utsu (1961)16

Mogi (1962)

Utsu (1957)

(t > t0)

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

1891

1909

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

20

i = (ti)

Ogata & Shimazaki (1984, BSSA)Aftershocks of the1965 Rat Islands

Earthquake of Mw8.7

(s)

21

Utsu (1969)Utsu & Seki (1954)

log S = M – 3.9

log L = 0.5M – 1.8

log S = 1.02M – 4.01

22

Utsu (1970)

AftershocksNov. 1968 - Apr. 1970

…AABACBCBBBAA…

B vs C&A

… - - + - - + - ++ - +++ - - …

A

B

C

Tokachi-Oki earthquakeMay 16 1968 MJ=7.9

Count runs

23

Utsu (1970)Standard aftershock activity:Occurrence rate of aftershock of Ms 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 < t < 100 days (M0>=5.5), where

cf., Reasenberg and Jones (1989)24

Utsu (1970) Secondary Aftershocks

25

Omori-Utsu formula:

).,,,,( are parameters and rate; background is

event; th of magnitude is

event; th of timeoccurrence is

00 pcK

jM

jt

j

j

26

(Ogata, 1986, 1988)

Omori-Utsu formula:

Kagan & Knopoff model (1987)

= 0, t < 10a+1.5Mj (t ) = Kt –3/2

, t > 10a+1.5Mj =

(Ogata, 1986, 1988)

27

Omori-Utsu formula:

Kagan & Knopoff model (1987)

= 0, t < tM

(M).(t ) = 10(2/3)(M-Mc) Kt –3/2, t > t

M

=

(Ogata, 1986, 1988)

27

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29

30

31

32

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

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

35

36

37

38

39

Asperities Yamanaka & Kikuchi (2001)

40

41

42

43

LONGITUDE

Cooler color shows quiescence relative to the HIST-ETAS model

44

ProbabilityForecasting

45

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:

46





47Multiple Prediction Formula(Utsu,1977,78)

Aki (1981)






where






logit Prob{ F | location, magnitude, time, space }

= …

F := { Ongoing events will be FORESHOCKS }

Utsu (1978), Ogata, Utsu & Katsura (1995, 96, GJI )

50Multiple Prediction Formula


= logit Prob{ F | location of the first event }

Multiple Prediction Formula



+ …

51





+ logit Prob{ F | magnitude sequential feature }


+ … Utsu(1978)

52





+ logit Prob{ F | temporal feature of a cluster }



+ …

53





+ logit Prob{ F | temporal feature of a cluster }

+ logit Prob{ F | spatial feature of a cluster }


- 3 x logit Prob{ F }


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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 devicesand Manuals

57

Thank you very much for listening

58

Documents

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