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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
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
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
The Omori-Utsu formula for aftershock decay rate
t : Elapsed time from the mainshock
K,c,p :constant parameters
Utsu (1961)11
Mogi (1962)
Utsu (1957)
(t > t0)
Kagan & Knopoff Models
(e.g., 1981, 1987)
(t ) = Kt -p
Utsu (1961)17
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 (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
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
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 )
54
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