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

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Matsumura (1986)

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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-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

Bath Law (Richter, 1958)

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

Bath Law (Richter, 1958)

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

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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)

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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)

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1891

1909

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

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i = (ti)

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

Earthquake of Mw8.7

(s)

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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

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Utsu (1970)

AftershocksNov. 1968 - Apr. 1970

…AABACBCBBBAA…

B vs C&A

… - - + - - + - ++ - +++ - - …

A

B

C

Tokachi-Oki earthquakeMay 16 1968 MJ=7.9

Count runs

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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

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(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)

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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)

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LONGITUDE

Cooler color shows quiescence relative to the HIST-ETAS model

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ProbabilityForecasting

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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

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:

47Multiple Prediction Formula(Utsu,1977,78)

Aki (1981)

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:

48Multiple Prediction Formula(Utsu,1977,78)

where

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:

49Multiple 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 )

50Multiple 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 )

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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

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Thank you very much for listening

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