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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
Utsu (1975)
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Ogata et al. (1982,86)
Seismicity rate = Trend + Clustering + Exogeneous effect
deep
Intermediate
Shallow
Shallow
seismicity
Intermediate
+ deep
seismicity
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Seismicity rate = trend + seasonality + cluster effect
Ma Li & Vere-Jones
(1997)
SEASONALITY
CLUSTERING
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5
Matsumura (1986)
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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
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Magnitude Frequency:
o
Bath Law
(Richter, 1958)
D1 := Mmain-M1
= 1.2
Utsu (1957)
~
D1 = 1.4
Median based on
90 Japanese Mmain=
>6.5
Shallow earthquakes
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Magnitude Frequency:
Bath Law
(Richter, 1958)
D1=Mmain-M1
= 1.2
Utsu (1961, 1969)
Magnitude difference
o
Mainshock Magnitude
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Magnitude Frequency:
Bath Law
(Richter, 1958)
D1=Mmain-M1
= 1.2
Utsu (1961, 1969)
~
D1 = 5.0 – 0.5Mmain
for 6 =
< Mmain=
<8
~
D1 = 2.0 for Mmain<6
Magnitude difference
o
Mainshock Magnitude
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Aftershocks
Utsu (1961)
The Omori-Utsu formula
for aftershock decay rate
ｔ : Elapsed time from the mainshock
Ｋ，ｃ，ｐ : constant parameters
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Utsu (1961, 1969)
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1981 Nobi (M8) Aftershock freq.
Data from Omori (1895)
Mogi (1962)
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Mogi (1967)
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Mogi (1962)
t > t0 = 1.0 day
Utsu (1957)
-p
(t
)
=
Kt
(t > t0)
l
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Mogi (1962)
Utsu (1961)
Utsu (1957)
-p
(t
)
=
Kt
(t > t0)
l
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Mogi (1962)
Utsu (1961)
Utsu (1957)
-p
(t
)
=
Kt
(t > t0)
l
Kagan & Knopoff
Models
(e.g., 1981, 1987)
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Utsu (1962, BSSA)
1957
Aleutian
1958
Central
Araska
1958
Southeastern
Araska
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Ogata (1983, J. Phys. Earth)
Relative Quiescence in the Nobi
aftershocks preceding the 1909
Anegawa earthquake of Ms7.0
1891
1909
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Ogata & Shimazaki (1984, BSSA)
Aftershocks of the1965 Rat Islands
Earthquake of Mw8.7
l(s)
ti = L(ti)
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Utsu & Seki (1954)
Utsu (1969)
log S = 1.02M – 4.01
log S = M – 3.9
log L = 0.5M – 1.8
Utsu (1970)
Tokachi-Oki earthquake
May 16 1968 MJ=7.9
Aftershocks
Nov. 1968 - Apr. 1970
…AABACBCBBBAA…
B vs C&A
A
… - - + -- + - ++ - +++ -- …
B
Count runs
C
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cf., Reasenberg and Jones (1989)
Utsu (1970)
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
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Utsu (1970)
Secondary Aftershocks
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Omori-Utsu formula:
(Ogata, 1986, 1988)
t j is occurrence time of jth event;
M j is magnitude of jth event;
l0 is background rate; and parameters are (l0 , K , c,  , p ).
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Omori-Utsu formula:
(Ogata, 1986, 1988)
Kagan & Knopoff model (1987)
n (t ) =
–3/2
Kt ,
= 0,
t=
> 10
a+1.5Mj
t < 10
a+1.5Mj
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Omori-Utsu formula:
(Ogata, 1986, 1988)
Kagan & Knopoff model (1987)
–3/2
(2/3)(M-Mc)
.
y(M) n (t ) = 10
Kt ,
=
0,
t > tM
=
t < tM
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1926 – 1995, M >= 5.0, depth < 100km
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1926 – 1995, M >= 5.0, depth < 100km
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37
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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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Probability
Forecasting
Multiple Prediction Formula(Utsu,1977,78)
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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:
Multiple Prediction Formula(Utsu,1977,78)
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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:
Multiple Prediction Formula(Utsu,1977,78)
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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)
Multiple Prediction Formula(Utsu,1977,78)
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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
Multiple Prediction Formula
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F := { Ongoing events will be FORESHOCKS }
logit Prob{ F | location, magnitude, time, space }
= …
Utsu (1978), Ogata, Utsu & Katsura (1995, 96, GJI )
Multiple Prediction Formula
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F := { Ongoing events will be FORESHOCKS }
logit Prob{ F | location, magnitude, time, space }
= logit Prob{ F | location of the first event }
+…
Utsu (1978), Ogata, Utsu & Katsura (1995, 96, GJI )
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Multiple Prediction Formula
F := { Ongoing events will be FORESHOCKS }
logit Prob{ F | location, magnitude, time, space }
= logit Prob{ F | location of the first event }
+ logit Prob{ F | magnitude sequential feature }
+…
Utsu(1978)
Utsu (1978), Ogata, Utsu & Katsura (1995, 96, GJI )
Multiple Prediction Formula
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F := { Ongoing events will be FORESHOCKS }
logit Prob{ F | location, magnitude, time, space }
= logit Prob{ F | location of the first event }
+ logit Prob{ F | magnitude sequential feature }
+ logit Prob{ F | temporal feature of a cluster }
+…
Utsu (1978), Ogata, Utsu & Katsura (1995, 96, GJI )
Multiple Prediction Formula
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F := { Ongoing events will be FORESHOCKS }
logit Prob{ F | location, magnitude, time, space }
= logit Prob{ F | location of the first event }
+ logit Prob{ F | magnitude sequential feature }
+ logit Prob{ F | temporal feature of a cluster }
+ logit Prob{ F | spatial feature of a cluster }
- 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 DOS version
SASeis Windows Visual Basic
SASeis 2006
with R graphical devices
and Manuals
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Thank you very much
for listening