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Earthquake prediction: an empirical approach
Tectonopby~&~,148 (1988) 195-210 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
195
Research Papers
Earthquake prediction: an empirical approach T. RIKITAKE L)epmtment of Earth Sciences, College ~~~~u~ities
and Sciences, N&on Uni~er~i~, Setagaya-ku, Tdcyo {Japan)
(Received June 4,1987; revised version accepted September 28,1987)
Abstract Rikitake, T., 1988. Earthquake prediction: an empirical approach. Tectonophysics, 148: 195-210 Earthquake precursor data so far accumulated in Japan have shown that the larger the main shock magnitude, the larger the distance between the epicenter and an observation point where a precursor is observed. It is possible to empirically establish an approximate relationship between maximnm detectable distance, D_, and main shock magnitude, M, the relationship being different from discipline to discipline of precursor. When a number of precursors are observed, we may draw circles with a radius equal to D,,,, peculiar to each precursor discipline, centered at the respective observation points on the condition that M takes on a certain value. In that case the epicenter of a future earthquake should be located in the area which is common to all of the circles. If M is too small, some of the circles do not overlap. If it is too large, an epicentral area which is too wide to be realistic must be assumed. In this way an approximate epicenter location and a rough value of the main shock magnitude can be assessed. Applying the procedttre to the precursors of the Izu-Oshima Kinkai (M = 7.0, 1978) and the Niigata (M = 7.5, 1964), Japan, earthquakes, remarkable success is achieved. Probabilities of an earthquake occurring in a specified time interval can be evaluated as a function of time when a precursor is observed. For such an evaluation, we rely either on the log T-M relationship, with a prescribed value of M, or on the frequency distribution of log T which is empirically obtained depending on precursor disciplines, T being the precursor time. When a number of precnrsors are observed one by one, changes in synthetic probab~ty of earthquake occurrence can be estimated according to the existing formula (Utsu, 1977). As an example, such probability changes with time are estimated making use of the precursor data for the Izu-Oshima Kinkai earthquake. It turns out that the synthetic probability generally increases as time goes on. When a long-term precursor happens to be observed, however, the probability drops discontinuously, being followed by a gradual rise again. The temporal change in probability therefore shows considerable fluctuations. This is especially so when a short interval for probabi~ty evaluation is specified. Because of uncertain preliminary probab~ty involved in the evaluation and an unknown rate of false precursor signals against true ones, the absolute value of probability thus evaluated may not be perfectly reliable. Even so, the temporal change in probability may provide some clues for the actual publication of earthquake prediction.
1. Introduction A large number of earthquake precursor data have been accumulated in Japan in recent years, mostly under the nationwide programme on earthquake prediction launched in 1965. Although not conclusive, much of the empirical law that seems to govern the nature of precursors of various 0040-1951/88/$03.50
0 1988 Else&r Science Publishers B.V.
disciplines has now been brought to light, as summarized by R&take (1987). It is intended in this paper to present a practical way of predicting an earthquake, based only on the empirical nature of precursors thus disclosed, although debate about the physical mechanism that gives rise to a precursor will be put aside.
196
In Section detectable function
2 will be shown
distance, of main
approximately
O,,,,, shock
of a precursor magnitude,
determined
from
the
obtained
precursor-like
is observed
servation
point,
the epicenter located
by drawing
with a radius cursor
of a future
discipline,
a circle centered provided
assigned to M. On the condition precursors observed points, we are able
The
When
peculiar
be
at that point to that prevalue is
The disciplines
we have a number
of
at different observation to find an area which is
and numbers
for which the distance observation For
of main
activity
epicenter.
data,
epicenter
and
are shown in Table
it is meaningless
of the definition
the seismic
of precursor
D between
point is known,
foreshocks,
because shock
that
detectable distance as a function
a
at an ob-
that a certain
Maximum
shock magnitude
is different
should
magnitude
be
an area in which
earthquake
equal to D,,
data.
of precursor.
we can define
as a
M, can
relationship thus M-D,, from discipline to discipline phenomenon
2. Prediction of epicenter location and main shock
that the maximum
to define
of foreshock,
1. D
which
is
in an area close to the main Discipline
m,
or
microearth-
quake, in Table 1 denotes the foreshock activity of microearthquakes that occur in an area significantly distant from the main shock epicenter. Figures 1A and B are the M-log D plots for the precursors given in Table 1. D is measured in
common to all the circles. When the assumed magnitude is too small, some of the circles do not overlap. In this way, it is possible to say some-
kilometers.
thing about the epicenter magnitude in favourable
location and main shock cases. The method will
plines are indicated with the abbreviations given in Table 1. A straight line, which approximately
be applied to the precursors of the Izu-Oshima Kinkai (M = 7.0, 1978) and the Niigata (it4 = 7.5, 1964), Japan, earthquakes, with remarkable success. Temporal change in earthquake occurrence
detectable disrepresents D,,,,, , the maximum tance, is drawn in each plot. When the number of data is small, the straight lines are not quite
probability in association with the appearance of a precursor can be estimated by analyzing the precursor time vs. main shock magnitude relationship, or the frequency distribution of precursor time, depending on disciplines of precursor.
TABLE
Evaluation of such changes in probability will be made for a number of precursor disciplines in Section 3. When a series of precursors are observed one by one, temporal change in synthetic probability of earthquake occurrence fluctuates, reflecting the characteristics of each precursor. Taking the series of precursors preceding the Izu-Oshima Kinkai earthquake as an example, temporal changes in the probability of the main shock occurring in a specified time interval will be estimated in Section 4. Such probability clues for forecasting main shock.
changes may provide some the occurrence time of the
In these
figures
the precursor
1
Precursor
data
between
epicenter
of various
disciplines
and observation
Discipline
Geodetic
for which
the distance
point is known Abbre-
Number
viation
of data
1,k
21
survey and tide-gauge
observation I Microearthquake
m
10
Tilt (~ndulum)
t
46
Tilt (water-tube)
T
11
Strain (extensometer)
h
17
Strain (borehole
H
25
Geomagnetic
strainmeter)
field
g
5
Earth currents
e
70
Resistivity
(variometer)
r
30
Resistivity
(long-distance R
9
w
7
electrodes) Electromagnetic Radon
disci-
radiation
and other geochemical
elements Underground springs There are a number for different
i
15
U
10
water/hot
of data that give the same distance
observations.
value
197
accurate. However, the integrated M-log D plot for all precursors becomes as shown in Fig. 2, in which we clearly see that the overall detectability limit is confirmed fairly definitely as a function of
As a matter of fact, an attempt is made to draw the lines for each discipline with an inclination which is as close as possible to that of the line shown in Fig. 2. M.
M 80 0
6
v 0
5 I
?-
I
/
00
6-
0
50
0””
4-
/ /
/
3O
0
1
2
3
log
3’
D
2
I
0
(I)+(k)
3
log
D
CT)
M
I M
a-
8
?-
I-
5-
3
1
3O
ICY
D
(HI
M 8
(h)
(t) Fig. 1. A. M-log observation
D relationships
(k); microearthquake
(H); and strain by extensometer resistivity geochemical
by variometer elements
(r);
for the following
disciplines:
(m); tilt by pendulum (h). B. M-log resistivity
(i); and underground
D relationships
by long-distance
land deformation
tiltmeter
for the following electrodes
water and hot springs
as revealed
(t), tilt by water-tube
(u).
(R);
by geodetic
tiltmeter
disciplines:
electromagnetic
survey (1) and tide-gauge
(T); strain
geomagnetic radiation
by volume
strainmeter
field (g); earth currents (w) and
radon
and
(e); other
198
I
3.
1
3
log
0
3
log
D
M 8-
8’ 0 5.
3.
1
3
log
D
M
8
50
0
4-
,,/..li
3.
1
,2
I
3O
2
1
(u)
Fig. 1 (continued).
/O
3
log
D
199 TOTAL
0
-0.87t2.61os
I
36
/
1
Fig. 2. M-log
I
I
2
3
D
log
D
D plots for all the available precursor data.
The maximum detectable distance for each precursor discipline can be read off from the lines shown in Figs. 1A and B, as given in Table 2 for various M’s. The reason why the M-log D relationship is different from discipline to discipline is not fully understood. It is known, however, that these precursors seem to be characterized by a sensitivity for detection peculiar to each discipline (Rikitake, 1987). TABLE
DATA
Epicentral area and magnitude of main shock
When a precursor of a particular discipline is observed at an observation point, we can draw a circle centered at that point with a radius equal to D -9 which is given in Table 2, on the condition that M takes on a certain value. In that case the epicenter of a future earthquake should be located within the circular area. On the assumption that
2
Maximum distance of precursor detection for various disciplines (D,,,,) Discipline
%,
(W
M= 5.0
M = 5.5
M = 6.0
M = 6.5
M = 7.0
M= 7.5
M = 8.0
Geodetic survey and 10
17
27
46
69
117
190
69
81
93
112
138
166
204
Tilt (pendulum)
37
60
93
144
234
363
501
Tilt (water-tube)
43
60
85
131
182
257
363
102
138
190
282
398
589
813
89
126
174
257
398
589
813
tide-gauge observation Microearthquake
Strain (extensometer) Strain (borehole strainmeter) Geomagnetic field Earth currents Resistivity (variometer) Resistivity (long-distance electrodes) Electromagnetic
radiation
Radon and other geochemical elements Underground water/hot springs
25
30
55
100
182
25
4.6
39
60
98
144
234
346
158
245
380
562
912
1380
2040
13
22
37
63
107
182
269
398
616
4.4
8.7
7.6
60
85
132
117
174
257
380
562
812
1150
21
39
72
151
282
589
1050
200
there are a number
of observation
observe
of various
precursors
have a number epicenter
of circles with different
should
common
points where we
disciplines,
be located
tion at N, and N, and volume
we may
are so large that
radii. The
in an area which
is
of the circles thus drawn
to all the circles. Kinkai earthquake
A considerable
number
of precursors
istered prior to the 1978 Izu-Oshima southwest
that
of Tokyo,
observation
points
occurred as shown
were reg-
Kinkai
150 km
in Table
3. The
The cross and the rectangle
the epicentral
N,, N,, N,, O,, O,, S and T are the observation precursory I-earth at Oz.
signals currents
at the respective at N,; S-anomalous
points.
points
and
small.
cerned.
given in Table
land uplift centered
0,
do not that
the circles
overlap
with
the prescribed
On the other
hand,
1979)
centered one
at
another,
magnitude
the assumption
is too that
M = 7.5 leads to an epicentral area that seems too extensive for an earthquake of that magnitude. It is also hard to think of an earthquake of such a large magnitude occurring in the Izu area con-
water at N,;
These
Kinkai
the actual epicenter
I-underground
of
area thus determined.
area of the Izu-Oshima represent
projection
are located in the epicentral
suggesting
curred in the Tokyo Bay area. Assuming M = 7.0, D,, circles are drawn as shown in Fig. 3. The Dmax’s for radon concentra-
area represents
to note that the
and the horizontal
If M = 6.5 is assumed,
A, I, N,, N,, N,, Or, O,, S and
Fig. 3. The shaded
epicenter
and Somerville,
N,
T are shown in Fig. 3. T is the mean location of a number of microearthquake epicenters that oc-
M = 7.0 is assumed.
be
the source model (Shimazaki earth-
about
at A and I
is shown by the shaded
one in the figure. It is interesting
(I) Izu-Oshima
(M = 7.0)
strain
for them cannot
shown in the figure. An area that is covered by all
actual
quake
the circles
considerations
earthquake
and the horizontal
3. Circles
&-geomagnetic
as determined projection
1 to 8 are drawn
level at S; 2-the
same
lead to the conclu-
by the D_
with D,,,,‘s
at 0,;
for the following
3-microearthquake
field at N,; 7-resistivity
method.
of the source fault. A, I, at T;
at N,; B-resistivity
201
sion that the magnitude should be close to 7.0. In this way the D_ method leads to remarkable success in assessing the epicenter and magnitude of the Izu-Oshima Kinkai earthquake, although the precursor data were compiled well after the earthquake.
(2) Niigata earthquake Prior to the 1964 Niigata earthquake (M = 7.5), anomalous uplift at a number of benchmarks on a national highway running along the Japan Sea coast was observed, as shown in Fig. 4 (Dambara, 1973). Kasahara (1973) reported on a precursor-
NI IGATA EARTHocw(E ,(M=7.5)
Fig. 4. Anomalous
land uplift precursory
to the 1964 Niigata earthquake.
202
like ground tilt observed at a crustal movement observatory near Niigata City. Fujita (1965) also reported on geomagnetic precursors at a number of magnetic stations in the earthquake area. Assuming M = 7.5, the Dmaxmethod applied to the seven benchmarks leads to an epicentral area shown in Fig. 5 with thin shading. The circle for
the tilt precursor at the observatory denoted by M is too large to be shown in the figure. If we further take the geoma~etic precursors at nine magnetic stations into account, the epicentrai area becomes narrower, as also shown in the figure with hatching. Meanwhile, the actual epicenter and the horizontal projection of the source model are ob-
Fig. 5. The outer shaded area is the epicentraf area of the Niigata earthquake as obtained by the D,,,_ method centered at the seven Ievefhng benchmarks (solid circles) on the assumption that M= 7.5. If the anomaly in the geomagnetic
field at the nine magnetic
stations (open circles) is taken into account, the epicentral area becomes the one which is shown with the inner hatched area. The rectangle and cross show the projection of source model and epicenter, respectively. where a water-tube tiltmeter has been in operation.
M-the
Maza crustal movement observatory,
203
TABLE
3
Geoscientific No.
precursors
to the Izu-Oshima
Discipline
Kinkai
earthquake Precursor
Abbreviation
time
Epicentral distance
(day)
Observation
1
Land upheaval
1
ca. 1100
30
Nakaizu
2
Resistivity
R
300
15
Izu Oshima
distance
(long-
point
(km) (Nr) Is. (0,)
electrodes)
3
Underground
4
Radon
5
Resistivity -period
water (short-
U
285
35
Shuzenji (S)
i
195
29
Nakaizu
(Na)
90
30
Nakaizu
(N,)
Nakaizu (N3)
R
geomagnetic
variation) 6
Radon
i
82
25
7
Earth currents
e
65
30
Nakaizu (N,)
8
Geomagnetic
60
30
Nakaizu (Nl)
9
Volume strain
g H
42
41
Irozaki (I)
10
Volume strain
H
26
34
Ajiro (A)
m
38
100
U
18
90
Gmaezaki Nakaizu
field
10a
Microearthquake
11
Underground
12
Radon
i
5
25
13
Volume strain
H
4
41
14
Foreshock
f
0.65
Near the epicenter
15
Foreshock
f
0.17
Near the epicenter
water
Tokyo Bay (T)
Iro&i
(0,) (Ns)
(I)
of main shock of main shock
tained by Abe (1975), as shown in the figure. Although the accuracy of the magnetic survey at that time is not as high as it is today, it is interesting to see that the epicentral area as deduced from the precursor analysis roughly agrees with the real one. If we assume that M = 7.0, some of the D,, circles tend not to overlap. On the other hand, the epicentral area due to the present method seems TABLE
3. Prediction of occurrence time Probabiliry of earthquake occurrence cursors of the 1st and quasi-1st kin&
due to pre-
4
Parameters, cursors
too wide if M = 8.0 is assumed. It also seems unlikely that an earthquake with a magnitude as large as 8.0 will occur in the area in question. It is therefore concluded that the main shock magnitude takes on a value around 7.5.
data
numbers
and
standard
deviations
for pre-
of the 1st kind
logT=a+bM n
b
11
-0.260
0.475 0.367
7
-0.460
0.484 0.352
T
5
-1.23
0.567 0.378
Strain (extensometer)
h
17
-1.28
0.491 0.412
b-value
b
14
-0.524
0.446 0.724
Seismic wave velocity
v
17
-1.78
0.727 0.411
Anomalous
a
12
-1.60
0.754 0.142
Seismic quiescence
q
10
Geomagnetic
g
4
Discipline
Abbre-
Dam
viation
number
1 k
Tilt (water-tube)
Geodetic
survey
Tide-gauge
observation
seismicity field
Rikitake (1975, 1979) showed that a relation:
%
0.936 0.269 0.784 -2.08
0.781 0.585
(1)
approximately holds good between precursor time T and main shock magnitude M for precursors of some kinds, where a and b are parameters peculiar to a precursor discipline. When T is measured in days, he obtained a = - 1.01 and b = 0.60 for a then-available data set of precursors. It is also demonstrated by Rikitake (1987) that a relation such as eqn. (1) holds for each individual discipline of precursors of some sort: those disciplines are land deformation by geodetic survey
204
(I), land deformation by tide-gauge observation (k), ground tilt by a water-tube tiltmeter (T), strain by an extensometer (h), b-value of seismic activity (b), change in seismic wave velocity (v), anomalous seismic activity (a), seismic gap/quiescence (q) and change in geomagnetic field (g). These precursors are called precursors of the 1st kind. In Table 4 are shown the parameters determined for these precursors. Putting
while [i and t2 correspond to t, and f,, respectively. Making use of error function G(x), defined by:
E = log T
Q(X) = $iX
for the ith precursor, is given by: P,(ti,
t2) = $iC2
e-h:(c-to)2 d.$
(3)
1
as discussed by Rikitake (1969) where: h, = l/fi,
(2)
the standard deviation Us of E - &,, where co is the mean value of log T as determined by eqn (l), for each discipline is also included in the table. As can be seen in the table, the available data are scarce for some of the disciplines, probably resulting in an inaccurate estimate of a, b and Us. Such a defect certainly influences the probability evaluation in the later part of this section. This point could be improved in the future when a larger data set is compiled. For precursor disciplines such as earth currents (e), resistivity with long-distance electrodes (R), radon and other geochemical elements (i) and underground water/hot springs (u), it has been shown by Rikitake (1987) that the log T-M relationship leads to a value of T which is significantly smaller than those for precursors of the 1st kind, although a relationship similar to eqn. (1) holds. Precursors belonging to these disciplines are called precursors of the quasi-1st kind, and the parameters and their standard deviations are given in Table 5. Assuming that 6 - &, is governed by a Gaussian distribution, the probab~ity of an earthquake occurring between t, and t, (ti < tz), as evaluated
(4)
e-“‘du
(5)
eqn. (3) can be rewritten as:
(6) Subscript i to be attached to some of the quantities in eqns. (3), (4) and (6) is ignored for the sake of simplicity. On the condition that no earthquake occurs during a period between t = 0 and t = t,, the probability of an earthquake occurring between t, and f2 becomes: Pi(&, t2) = Pitt,? t,)/[l
- Pz(O, &>I
(7)
Using u(‘s given in Tables 4 and 5, temporal changes in the probability of an earthquake occurring within a prescribed period, 1 day say, from a specified date when a precursor of the 1st or quasi-1st kind is observed are estimated as shown in Figs. 6, 7 and 8. M = 7 is assumed in the estimate. No probability curve for discipline a (anomalous seismicity) is presented here because the probability for the time-span covered by these figures is extremely low. It is apparent from the probability curves thus
TABLE 5 Parameters, data numbers and standard deviations for precursors of the quasi-1st kind Discipline
Abbreviation
Data number
LI
h
mt
Earth currents Resistivity (long-distance electrodes) Radon and other geochemical elements Underground water/hot springs
e R i ”
3 9 14 9
.- 0.542 -2.00 - 0.468 -- 4.10
0.348 0.627 0.278 0.794
0.306 0.579 0.656 0.577
205
2.5
TIME
Fig. 6. Probabilities when
precursors
(days)
of an earthquake of disciplines
occurring
g, k,
within
1 day
I and v are observed.
M = 7 is assumed.
Fig. 8. Probabilities when
precursors
Probability of earthquake occurrence
due to pre-
cursors of the 2nd and 3rd kinds
Rikitake (1979) named the precursor of discipline r (resist&y observed using a variometer) as
in0
200
300 T
Fig. 7. Probabilities when
precursors
M = 7 is assumed.
within
1 day
u are observed.
a precursor of the 2nd kind. The precursor time for this kind of shock takes a value which ranges from 2 to 3 hours, regardless of the main shock magnitude. The precursor time for foreshocks (f) ranges from a few minutes to thousands of days, no indication of magnitude dependence being known. Such a precursor is called a precursor of the 3rd kind. Disciplines such as microearthquake (m), change in seismicity pattern (p), tilt by a pendulum tilt meter (t), volume strain (H) and the like seem to belong to this kind of precursor. The frequency distributions of logarithmic precursor time, log T, in units of days for the foreshock (f) and the volume strain (H), are shown in Figs. 9 and 10. Let us assume that logarithmic precursor time is governed by a Weibull distribution such as: A(s) =Ks”
log
VA<
occurring
e, i, R and
M = 7 is assumed.
obtained that the probability value and its temporal change are different from discipline to discipline of precursor. For disciplines i and u, the peak probability takes place within several days after the precursor appearance, with a peak value around 0.03. Precursors of these disciplines may be useful for short-term prediction. In contrast, for disciplines 1. v, g and the like, it takes several hundred days until the probability reaches its maximum, which is of the order of 10p4. These are regarded as long-term precursors. The differences in temporal change between precursor disciplines seriously affect the synthetic probability to be evaluated in the following section.
OO
of an earthquake of disciplines
400
500
600
700
800
I ME (days)
of an earthquake of disciplines
occurring
within
1 day
b, h, q and T are observed.
T+c)
(s=log
(8)
FREQUENCY ____*_---*----*--__*____*____*_--
1
-3.0
-
-2.6
-2.5
-
-2.1
n
-2.0
-
-1.6
W
-1.5
-
-1.1
m
-1.0
-
-0.6
-
-0.5
-
-0.1
-
14
0.0
-
0.4
0.5
-
0.9
-
14
1.0
-
1.4
1.5
-
1.9
2.0
-
2.4
-
2.5
-
2.9
I
3.0
-
3.4
3.5
-
3.9
Fig.
9. Histogram
measured
in days.
0 1 3 5 10 28 25 -
10 10 2 0 0
of log T for discipline
f (foreshock).
T is
206
log -3.@
-
-2.6
-2.5
-
-2.1
-2.0
-
-1.6
I
1
-1.5
-
-1.1
n
1
0 0
-1.0
-
-0.6
m
-0.5
-
-0.1
I
0.0
-
0.4
-
0.5
-
0.9
m
4 2 11 3
1.4
l
1.5
-
1.9
I
2.0
-
2.4
0
2.5
-
2.9
0
3.0
-
3.4
u
3.5
-
3.9
0
1.0
Fig. 10. Histogram is measured
FREQUENCY _---*----*----*--
T
1 2
of log T for discipline
H (volume strain).
T
in days.
Fig. 11. Plots of In In (l/R) fitting
for discipline
straight where X is the probability for log T to fall in an interval between s and s + As, where As is much smaller than s. c is a constant which may be chosen in such a way as to make actual calculation easy: ‘a value of c = 3 is assumed here. Denoting a cumulative probability for s to take on a value between 0 and s by P(s), we define a function: R(s)
= 1 -P(s)
As R(s) R(s)
(9)
is given by:
= exp[ -KY+r/(m
+ l)]
eqn. (11) can be drawn
respectively. Making use of the parameters
%I
=
[PA%)
It is also possible
+ l)] + (m + 1) In s
thus determined,
the cumulative probability P,(s) of an earthquake occurring in a period between 0 and s for the i th precursor can readily be calculated. On the condition that no earthquake occurs for a period between 0 and sr, the probability of an earthquake occurring between sr and s2 is obtained as: P;(S,,
= ln[ K/(m
line representing
by means of the least-squares method. In this way parameters K/(m + 1) and m + 1 are obtained from actual data. The parameters thus determined are given in Table 6 for disciplines f, t, r and H,
(IO)
we obtain: In ln(l/R)
vs. In s and a Weibull distribution
f (foreshock).
-P,h)l/[l-
to estimate
phdl (12) the mean value of
(IO). Since P can be calculated from the frequency distribution such as shown in Figs. 9 and 10 for an
s and consequently that of T as denoted by To using the parameters, although no formula for estimation is shown here. To’s are also given in Table 6. Judging from the mean precursor time thus obtained, it is clear that the precursor disciplines in Table 6 provide extremely short-term
appropriate As, we can have In ln(l/R) vs. In s plots for actual data as shown in Figs. 11 and 12, respectively, for disciplines f and H. In that case, a
ones. With the parameters given in Table 6, temporal changes in the probability p, of an earthquake
(11) by taking
TABLE
double
logarithms
of both sides of eqn.
6
Parameters,
data numbers
and mean precursor
times for precursors
of the 2nd and 3rd kinds
Discipline
Abbreviation
Data number
V(m+f)
l?t+1
Foreshock
f
122
0.0159
3.17
Tilt (pendulum)
t
46
0.00000359
8.30
Resistivity
(variometer)
Strain (volume)
G (day) 2.00 18.6
r
30
0.0254
5.24
0.0708
H
25
0.0142
3.65
0.776
207
p is given by: p=l/
[
1+
i
~~~(l/Pi-l))/(l/P~-l).-l
1
03)
Fig. 12. Plots of In In (l/R) fitting
for discipline
vs. In s and a Weibull distribution
H (volume
strain).
occurring within a prescribed period, 1 day say, are calculated as shown in Fig. 13 for disciplines r, H, f and t, respectively. 4. Temporal change in synthetic probability of
earthquake occurrence in association successive appearances of precursors
with
Utsu (1977, 1979, 1982, 1983), Aki (1981), Hamada (1983) and others have developed theories for evaluating the synthetic probability of earthquake occurrence when multiple precursors are observed. Following Utsu (1977), a formula for the probability of success of an earthquake prediction is used in the following to evaluate the synthetic probability of earthquake occurrence when a number of precursors of various disciplines are observed one by one. According to Utsu (1977), synthetic probability
I\f‘.. t“i Ii
---__
u
-
10
Fig. 13. Probabilities when precursors
20
TIME
30
of an earthquake
of disciplines
40
50
(days) occurring
within
r, H, f and t are observed.
1 day
on the condition that n independent precursors are observed and that the probabilities of respective precursors are given by pl, p2, . . . , p,,. p. is the probability of success when a prediction is made at random. The evaluation of p. is a matter of dispute, although it is customary to estimate p. from the seisrnicity in the area to be treated. As for pl, p2, . . . . p,, which are functions of time, we may rely on the probabilities for various disciplines evaluated in the last section. An example of estimating the synthetic probability will be given in the following, based on the reported precursors prior to the Izu-Oshima Kinkai earthquake (M = 7.0, 1978). The precursors are already given in Table 3. As assumed by Utsu (1979) we presume that the preliminary probability p. is given by: p. = T/( 100 x 365.25)
04)
on the assumption that an A4 > 6.5 earthquake occurs once in a lOO-yr period in the Izu Peninsula area concerned, where 7 denotes the time interval during which an earthquake is expected to occur. pi can be obtained using eqns. (7) and (12) and 7 is equal to t, - t,. When 7 is assumed as 3 h, 1, 3, 10 and 100 days, we have p. = 0.00000342, 0.0000274, 0.0000822, O.ooO274 and 0.00274, respectively. It is highly likely that precursor signals contain much noise. In other words, the probability that a precursor-like signal is false is very high. Sato and Inouchi (1977) pointed out that only 9 instances out of 56 anomalous land uplifts in Japan culminated in the occurrence of an earthquake. Therefore, the true probability of earthquake occurrence should be equal to aipi instead of pi, where pi’s are the probabilities for various precursor disciplines which can be calculated using the parameters given in Tables 4, 5 and 6, and (Y~‘S are the factors indicating the rate of appearance of the true precursor. In the case of land uplift revealed by geodetic surveys, the above data leads to (pi = 0.16, the subscript being written as 1 with
reference to the precursor numbers in Table 3, Mogi (1963), who examined about 1500 earthquakes of magnitude equal to or greater than 4 in Japan, concluded that only 4% of the earthquakes are accompanied by foreshocks. He also showed, however, that the rate of earthquakes with foreshocks amounts to 20% in the vicinity of the Izu Peninsula. We therefore assume that cy14and ty,, are equal to 0.2 for discipline f (foreshock-precursors 14 and 15) in the following probability evaluation. At the present stage of investigation, however, no exact value of LY;is available for other disciplines because of scarcity of data. In the circumstances, it can be assumed rather arbitrarily that (Y,= l/20 (i = 2, 3, . . . , 13) for precursor disciplines in Table 3 except 1 and f. Such a procedure is certainly unsatisfactory for the act& evaluation of probabihty~ but no other means that leads to a better result can be found at the moment. It is hoped that the accurate evaluation of (Y~will, in future, be achieved as more and more precursor data are accumulated. Replacing pi in eqn. (13) by arpi and using appropriate values of pay temporal changes in synthetic probability are calculated as shown in Figs. 14-18 respectively for r = 3 h, 1, 3, 10 and 100 days. It is assumed that precursor 1 (the land upfift at Nakaizu) was observed at d = 0. In Figs.
z
3
5678
9-m
III/
IllHI M.
$
s.
Ii ii
2
3
I I
1-P
I
.8
il 800
850
900 TIME
1100 (days)
Fig. IS. Changes in synthetic probability for 1‘= 1 day.
14-18, only the changes in probability after t = 800 days are shown. Up to that point, the probability is so small that it is virtually coincident with the zero line. The precursor appearances are indicated by the bars at the top of each figure; it can be seen that discontinuous increases in probability curves take place when short-term precursors such as numbers 3 (underground water, u), 4 (radon, i), 6 (radon, i} and so on are observed. On the other hand, whenever we have long-term precursors such as numbers 7 (earth currents, e) and 8 (geomagnetic field, g), the probability tends to drop to some extent. Such a tendency is observed more markedly for probability curves for a smaller value of 7. It is observed, however, that when a large value is assigned to T the probability increases successively with no marked fluctuations as precursors appear one by one. Assuming 7 = 100 days, for instance, the probability reaches 0.95 at around
I I
I
~
0 800
i’ 1 IA,, ti
l-
850
900 TIME
950
1000
1050
1100
(days)
Fig. 14. Changes in synthetic probability of earthquake occurrence for ‘I = 3 h. The occurrence times of respective precmsors are shown by vertical bars at the top, while the occurrence time of the main shock of the fzu-Oshima Kin&i earthquake is indicated by an arrow. The abscissa denotes the time (in days) after the appearance of precursor 1.
Fig. 16. Changes in synthetic probability for T = 3 days.
209
a
I
II
I I
II
III II NJ%
1-P .a .6 .4
0
800
850
900 950 T 1ME (days)
1000
1050
1100
Fig. 17. Changes in synthetic probability for 7 = 10 days. t = 1020
days. If one were to issue a prediction at about that date that an earthquake would occur within a period of 100 days, the prediction would be successful because the main shock occurred about 80 days later. For an extremely short-term or imminent prediction, the actual publication of the prediction seems to be no easy matter because of the fluctuations of synthetic probability as shown in Figs. 14-17. It might be better for such a prediction to rely only on short-term signals such as volume strain (H), underground water (u), radon (i), foreshock (f) and the like, assuming that signals belonging to long-term precursors observed at that stage are all false. 5. Conclusions Analyzing the data set of earthquake precursors so far collected in Japan, it is shown that we can define D,_ , the maximum detectable distance of 4
ii
1000
T I ME (days)
1050
1100
Fig. 18. Changes in synthetic probability for 7 = 100 days.
a precursor, as a function of main shock magnitude M. D,,,, is different from discipline to discipline of precursor. When a number of precursors are observed, we may draw circles with a radius peculiar to the precursor discipline, centered at respective observation points. In the procedure we assume a suitable value of M. In that case the epicenter of a future earthquake should be located in the area which is common to all the circles. If the assumed magnitude is too small, some of the circles do not overlap with one another. If it is too large, the area becomes too wide to be regarded as an actual epicentral area. In such a way we may infer the approximate location of the epicenter and the rough value of the earthquake magnitude at the same time. Applying the above-mentioned procedure to the reported precursors of the 1978 Izu-Oshima Kinkai (M = 7.0) and the 1964 Niigata (M = 7.5) earthquakes, remarkable success is achieved in assessing the main shock epicenter and magnitude. When a number of precursor-like signals are observed in series, it is also possible to evaluate changes in the synthetic probability of earthquake occurrence within a specified time interval 7, based on the empirically obtained probability of earthquake occurrence for precursors of various disciplines. The main shock magnitude involved in the evaluation has to be assessed in some way. An approach as discussed in the earlier half of this paper may be useful for that purpose. As an example, temporal changes in synthetic probability are estimated on the basis of the data taken before the Izu-Oshima Kinkai earthquake, for which a considerable number of precursor-like signals have been observed, as shown in Table 3. It turns out that the probability of earthquake occurrence in a time interval 7 generally increases as precursors are observed one by one. Such an increase is considerable for a short-term precursor. When a long-term precursor happens to appear, however, the probability drops discontinuously, although it tends to increase again as time goes on. Such a fluctuation is more considerable for smaller values of 7, so that a short-term earthquake prediction is more difficult than a long-term one.
210
The difficulties involved in the above evaluation of probability are twofold: the first is that the preliminary probabi~ty involved is not known very well, and the second is that the accurate probability of a signal representing a true precursor is hard to evaluate for most precursor disciplines. In the circumstances, it appears that no accurate estimate of the absolute value of probabi~ty is possible at the present stage of investigation. Even so, temporal changes in probability as presented in this paper may provide some clues for issuing earthquake predictions, which are strongly demanded by the public at large. The precursor-like phenomena analyzed here are identified as precursors after occurrence of the earthquake. In order to prove the validity of the approach proposed here, it is necessary to apply the method to actual precursors observed before an earthquake. It is hopefully expected that we will be able to monitor precursors for the Tokai earthquake which, it is feared, will occur in Central Japan in the near future, using a well equipped observation network. In that eventuality, the present approach could be tested. Judging from the speed of accumulation of precursor data under the nationwide programme of earthquake prediction in Japan, the empirical nature of precursors of various disciplines will be brought to light more clearly in the foreseeable future. In that case a more accurate evaluation of the synthetic probability of earthquake occurrence will certainly be accomplished.
Aki, K., 1981. A probabilistic mena.
In:
D.W.
Earthquake
synthesis
Simpson
Prediction,
and
of precursory
P.G.
Richards
an International
Review.
Ewing Series, Vol. IV. Am. Geophys.
Union,
T., 1973. Crustal
Niigata
earthquake.
dict., 9: 93-96 Fujita,
movements
Rep. Coord.
N., 1965. The magnetic
Niigata
before, at and after the Comm.
earthquake.
disturbances
J. Geod.
Hamada,
K., 1983. A probability
tion. Earthquake Kasahara,
Predict.
Sot.
tevellings.
Mogi,
Niigata
earthquake.
J. Phys. Earth,
model
23: 349-366.
for the
8-25
J.
model for earthquake
observation
Geod.
Sot.
K., 1963. Some discussions
and
earthquake
(in
predic-
in complement Jpn.,
19:
with
93-99
on aftershocks,
swarms-the
fracture
(in
foreshocks
of a semi-infinite
body caused by an inner stress origin and its relation earthquake
phenomena
Inst., Univ. Tokyo, Rikitake, and
(3rd Paper).
to the
Bull. Earthquake
Res.
41: 615-658.
T., 1969. An approach occurrence
to prediction
time of earthquakes.
of ma~tude
Tectonophysics,
8:
Bull. Seismol.
Sot.
81-95. Rikitake,
T., 1975. Earthquake
precursors.
Am., 65: 1133-1162. Rikitake,
T.. 1979.
Classification
Tectonophysics, Rikitake, Sato,
T., 1987. Earthquake
H. and
ground
of earthquake
Inouchi,
uplifts
precursors
N., 1977.
of the Izu-Oshima,
between
the
Proc. of Symp. Earth-
Res., 1976. Subcomm.
K. and Somerville,
precursor
136: 265-282.
On relations
Seismol. Sot. Jpn., pp. 138-144 parameters
in Japan:
Tectonophysics,
and the earthquakes.
quake Predict. Shimazaki,
precursors.
54: 293-309.
time and detectability.
Earthquake
Predict./
(in Japanese).
P., 1979, Static
and dynamic
Japan, earthquake
of January
14, 1978. Bull. Seismol. Sot. Am., 69: 1343-1378. Utsu, T., 1977. Probabilities
in earthquake
prediction.
prediction
earthquake
of 1978). Rep. Coord.
dict., 21: 164-166 Utsu,
T.. 1982.
second
of success of an
(in the case of Izu-O&ma
Kinkai
Comm.
Earthquake
Pre-
in earthquake
prediction
(the
(in Japanese).
Probabilities
paper).
Zisin (J.
(in Japanese).
of the probability
earthquake
105-114. of the fault
the
11:
Japanese).
tion and
K., 1975. Re-examination
accompanying Jpn.,
Res., 2: 227-234.
K., 1973. Tiltmeter
precise
57: 499-524
Abe,
Pre-
Japanese).
Bull. Earthquake
Res. Inst.,
Univ. Tokyo,
(in Japanese).
Utsu, T.. 1983. Probabilities
References
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(in Japanese).
Utsu, T., 1979. Calculation
The author is grateful to Professor M. Bath who reviewed the manuscript and suggested a number of improvements.
Maurice
Washington,
D.C., pp. 566-574. Dambara,
Seismol. Sot. Jpn.), Ser. 2, 30: 179-185
Acknowledgment
pheno(Editors),
associated
their relationships.
with earthquake
Earthquake
Predict.
predicRes., 2:
195
Research Papers
Earthquake prediction: an empirical approach T. RIKITAKE L)epmtment of Earth Sciences, College ~~~~u~ities
and Sciences, N&on Uni~er~i~, Setagaya-ku, Tdcyo {Japan)
(Received June 4,1987; revised version accepted September 28,1987)
Abstract Rikitake, T., 1988. Earthquake prediction: an empirical approach. Tectonophysics, 148: 195-210 Earthquake precursor data so far accumulated in Japan have shown that the larger the main shock magnitude, the larger the distance between the epicenter and an observation point where a precursor is observed. It is possible to empirically establish an approximate relationship between maximnm detectable distance, D_, and main shock magnitude, M, the relationship being different from discipline to discipline of precursor. When a number of precursors are observed, we may draw circles with a radius equal to D,,,, peculiar to each precursor discipline, centered at the respective observation points on the condition that M takes on a certain value. In that case the epicenter of a future earthquake should be located in the area which is common to all of the circles. If M is too small, some of the circles do not overlap. If it is too large, an epicentral area which is too wide to be realistic must be assumed. In this way an approximate epicenter location and a rough value of the main shock magnitude can be assessed. Applying the procedttre to the precursors of the Izu-Oshima Kinkai (M = 7.0, 1978) and the Niigata (M = 7.5, 1964), Japan, earthquakes, remarkable success is achieved. Probabilities of an earthquake occurring in a specified time interval can be evaluated as a function of time when a precursor is observed. For such an evaluation, we rely either on the log T-M relationship, with a prescribed value of M, or on the frequency distribution of log T which is empirically obtained depending on precursor disciplines, T being the precursor time. When a number of precnrsors are observed one by one, changes in synthetic probab~ty of earthquake occurrence can be estimated according to the existing formula (Utsu, 1977). As an example, such probability changes with time are estimated making use of the precursor data for the Izu-Oshima Kinkai earthquake. It turns out that the synthetic probability generally increases as time goes on. When a long-term precursor happens to be observed, however, the probability drops discontinuously, being followed by a gradual rise again. The temporal change in probability therefore shows considerable fluctuations. This is especially so when a short interval for probabi~ty evaluation is specified. Because of uncertain preliminary probab~ty involved in the evaluation and an unknown rate of false precursor signals against true ones, the absolute value of probability thus evaluated may not be perfectly reliable. Even so, the temporal change in probability may provide some clues for the actual publication of earthquake prediction.
1. Introduction A large number of earthquake precursor data have been accumulated in Japan in recent years, mostly under the nationwide programme on earthquake prediction launched in 1965. Although not conclusive, much of the empirical law that seems to govern the nature of precursors of various 0040-1951/88/$03.50
0 1988 Else&r Science Publishers B.V.
disciplines has now been brought to light, as summarized by R&take (1987). It is intended in this paper to present a practical way of predicting an earthquake, based only on the empirical nature of precursors thus disclosed, although debate about the physical mechanism that gives rise to a precursor will be put aside.
196
In Section detectable function
2 will be shown
distance, of main
approximately
O,,,,, shock
of a precursor magnitude,
determined
from
the
obtained
precursor-like
is observed
servation
point,
the epicenter located
by drawing
with a radius cursor
of a future
discipline,
a circle centered provided
assigned to M. On the condition precursors observed points, we are able
The
When
peculiar
be
at that point to that prevalue is
The disciplines
we have a number
of
at different observation to find an area which is
and numbers
for which the distance observation For
of main
activity
epicenter.
data,
epicenter
and
are shown in Table
it is meaningless
of the definition
the seismic
of precursor
D between
point is known,
foreshocks,
because shock
that
detectable distance as a function
a
at an ob-
that a certain
Maximum
shock magnitude
is different
should
magnitude
be
an area in which
earthquake
equal to D,,
data.
of precursor.
we can define
as a
M, can
relationship thus M-D,, from discipline to discipline phenomenon
2. Prediction of epicenter location and main shock
that the maximum
to define
of foreshock,
1. D
which
is
in an area close to the main Discipline
m,
or
microearth-
quake, in Table 1 denotes the foreshock activity of microearthquakes that occur in an area significantly distant from the main shock epicenter. Figures 1A and B are the M-log D plots for the precursors given in Table 1. D is measured in
common to all the circles. When the assumed magnitude is too small, some of the circles do not overlap. In this way, it is possible to say some-
kilometers.
thing about the epicenter magnitude in favourable
location and main shock cases. The method will
plines are indicated with the abbreviations given in Table 1. A straight line, which approximately
be applied to the precursors of the Izu-Oshima Kinkai (M = 7.0, 1978) and the Niigata (it4 = 7.5, 1964), Japan, earthquakes, with remarkable success. Temporal change in earthquake occurrence
detectable disrepresents D,,,,, , the maximum tance, is drawn in each plot. When the number of data is small, the straight lines are not quite
probability in association with the appearance of a precursor can be estimated by analyzing the precursor time vs. main shock magnitude relationship, or the frequency distribution of precursor time, depending on disciplines of precursor.
TABLE
Evaluation of such changes in probability will be made for a number of precursor disciplines in Section 3. When a series of precursors are observed one by one, temporal change in synthetic probability of earthquake occurrence fluctuates, reflecting the characteristics of each precursor. Taking the series of precursors preceding the Izu-Oshima Kinkai earthquake as an example, temporal changes in the probability of the main shock occurring in a specified time interval will be estimated in Section 4. Such probability clues for forecasting main shock.
changes may provide some the occurrence time of the
In these
figures
the precursor
1
Precursor
data
between
epicenter
of various
disciplines
and observation
Discipline
Geodetic
for which
the distance
point is known Abbre-
Number
viation
of data
1,k
21
survey and tide-gauge
observation I Microearthquake
m
10
Tilt (~ndulum)
t
46
Tilt (water-tube)
T
11
Strain (extensometer)
h
17
Strain (borehole
H
25
Geomagnetic
strainmeter)
field
g
5
Earth currents
e
70
Resistivity
(variometer)
r
30
Resistivity
(long-distance R
9
w
7
electrodes) Electromagnetic Radon
disci-
radiation
and other geochemical
elements Underground springs There are a number for different
i
15
U
10
water/hot
of data that give the same distance
observations.
value
197
accurate. However, the integrated M-log D plot for all precursors becomes as shown in Fig. 2, in which we clearly see that the overall detectability limit is confirmed fairly definitely as a function of
As a matter of fact, an attempt is made to draw the lines for each discipline with an inclination which is as close as possible to that of the line shown in Fig. 2. M.
M 80 0
6
v 0
5 I
?-
I
/
00
6-
0
50
0””
4-
/ /
/
3O
0
1
2
3
log
3’
D
2
I
0
(I)+(k)
3
log
D
CT)
M
I M
a-
8
?-
I-
5-
3
1
3O
ICY
D
(HI
M 8
(h)
(t) Fig. 1. A. M-log observation
D relationships
(k); microearthquake
(H); and strain by extensometer resistivity geochemical
by variometer elements
(r);
for the following
disciplines:
(m); tilt by pendulum (h). B. M-log resistivity
(i); and underground
D relationships
by long-distance
land deformation
tiltmeter
for the following electrodes
water and hot springs
as revealed
(t), tilt by water-tube
(u).
(R);
by geodetic
tiltmeter
disciplines:
electromagnetic
survey (1) and tide-gauge
(T); strain
geomagnetic radiation
by volume
strainmeter
field (g); earth currents (w) and
radon
and
(e); other
198
I
3.
1
3
log
0
3
log
D
M 8-
8’ 0 5.
3.
1
3
log
D
M
8
50
0
4-
,,/..li
3.
1
,2
I
3O
2
1
(u)
Fig. 1 (continued).
/O
3
log
D
199 TOTAL
0
-0.87t2.61os
I
36
/
1
Fig. 2. M-log
I
I
2
3
D
log
D
D plots for all the available precursor data.
The maximum detectable distance for each precursor discipline can be read off from the lines shown in Figs. 1A and B, as given in Table 2 for various M’s. The reason why the M-log D relationship is different from discipline to discipline is not fully understood. It is known, however, that these precursors seem to be characterized by a sensitivity for detection peculiar to each discipline (Rikitake, 1987). TABLE
DATA
Epicentral area and magnitude of main shock
When a precursor of a particular discipline is observed at an observation point, we can draw a circle centered at that point with a radius equal to D -9 which is given in Table 2, on the condition that M takes on a certain value. In that case the epicenter of a future earthquake should be located within the circular area. On the assumption that
2
Maximum distance of precursor detection for various disciplines (D,,,,) Discipline
%,
(W
M= 5.0
M = 5.5
M = 6.0
M = 6.5
M = 7.0
M= 7.5
M = 8.0
Geodetic survey and 10
17
27
46
69
117
190
69
81
93
112
138
166
204
Tilt (pendulum)
37
60
93
144
234
363
501
Tilt (water-tube)
43
60
85
131
182
257
363
102
138
190
282
398
589
813
89
126
174
257
398
589
813
tide-gauge observation Microearthquake
Strain (extensometer) Strain (borehole strainmeter) Geomagnetic field Earth currents Resistivity (variometer) Resistivity (long-distance electrodes) Electromagnetic
radiation
Radon and other geochemical elements Underground water/hot springs
25
30
55
100
182
25
4.6
39
60
98
144
234
346
158
245
380
562
912
1380
2040
13
22
37
63
107
182
269
398
616
4.4
8.7
7.6
60
85
132
117
174
257
380
562
812
1150
21
39
72
151
282
589
1050
200
there are a number
of observation
observe
of various
precursors
have a number epicenter
of circles with different
should
common
points where we
disciplines,
be located
tion at N, and N, and volume
we may
are so large that
radii. The
in an area which
is
of the circles thus drawn
to all the circles. Kinkai earthquake
A considerable
number
of precursors
istered prior to the 1978 Izu-Oshima southwest
that
of Tokyo,
observation
points
occurred as shown
were reg-
Kinkai
150 km
in Table
3. The
The cross and the rectangle
the epicentral
N,, N,, N,, O,, O,, S and T are the observation precursory I-earth at Oz.
signals currents
at the respective at N,; S-anomalous
points.
points
and
small.
cerned.
given in Table
land uplift centered
0,
do not that
the circles
overlap
with
the prescribed
On the other
hand,
1979)
centered one
at
another,
magnitude
the assumption
is too that
M = 7.5 leads to an epicentral area that seems too extensive for an earthquake of that magnitude. It is also hard to think of an earthquake of such a large magnitude occurring in the Izu area con-
water at N,;
These
Kinkai
the actual epicenter
I-underground
of
area thus determined.
area of the Izu-Oshima represent
projection
are located in the epicentral
suggesting
curred in the Tokyo Bay area. Assuming M = 7.0, D,, circles are drawn as shown in Fig. 3. The Dmax’s for radon concentra-
area represents
to note that the
and the horizontal
If M = 6.5 is assumed,
A, I, N,, N,, N,, Or, O,, S and
Fig. 3. The shaded
epicenter
and Somerville,
N,
T are shown in Fig. 3. T is the mean location of a number of microearthquake epicenters that oc-
M = 7.0 is assumed.
be
the source model (Shimazaki earth-
about
at A and I
is shown by the shaded
one in the figure. It is interesting
(I) Izu-Oshima
(M = 7.0)
strain
for them cannot
shown in the figure. An area that is covered by all
actual
quake
the circles
considerations
earthquake
and the horizontal
3. Circles
&-geomagnetic
as determined projection
1 to 8 are drawn
level at S; 2-the
same
lead to the conclu-
by the D_
with D,,,,‘s
at 0,;
for the following
3-microearthquake
field at N,; 7-resistivity
method.
of the source fault. A, I, at T;
at N,; B-resistivity
201
sion that the magnitude should be close to 7.0. In this way the D_ method leads to remarkable success in assessing the epicenter and magnitude of the Izu-Oshima Kinkai earthquake, although the precursor data were compiled well after the earthquake.
(2) Niigata earthquake Prior to the 1964 Niigata earthquake (M = 7.5), anomalous uplift at a number of benchmarks on a national highway running along the Japan Sea coast was observed, as shown in Fig. 4 (Dambara, 1973). Kasahara (1973) reported on a precursor-
NI IGATA EARTHocw(E ,(M=7.5)
Fig. 4. Anomalous
land uplift precursory
to the 1964 Niigata earthquake.
202
like ground tilt observed at a crustal movement observatory near Niigata City. Fujita (1965) also reported on geomagnetic precursors at a number of magnetic stations in the earthquake area. Assuming M = 7.5, the Dmaxmethod applied to the seven benchmarks leads to an epicentral area shown in Fig. 5 with thin shading. The circle for
the tilt precursor at the observatory denoted by M is too large to be shown in the figure. If we further take the geoma~etic precursors at nine magnetic stations into account, the epicentrai area becomes narrower, as also shown in the figure with hatching. Meanwhile, the actual epicenter and the horizontal projection of the source model are ob-
Fig. 5. The outer shaded area is the epicentraf area of the Niigata earthquake as obtained by the D,,,_ method centered at the seven Ievefhng benchmarks (solid circles) on the assumption that M= 7.5. If the anomaly in the geomagnetic
field at the nine magnetic
stations (open circles) is taken into account, the epicentral area becomes the one which is shown with the inner hatched area. The rectangle and cross show the projection of source model and epicenter, respectively. where a water-tube tiltmeter has been in operation.
M-the
Maza crustal movement observatory,
203
TABLE
3
Geoscientific No.
precursors
to the Izu-Oshima
Discipline
Kinkai
earthquake Precursor
Abbreviation
time
Epicentral distance
(day)
Observation
1
Land upheaval
1
ca. 1100
30
Nakaizu
2
Resistivity
R
300
15
Izu Oshima
distance
(long-
point
(km) (Nr) Is. (0,)
electrodes)
3
Underground
4
Radon
5
Resistivity -period
water (short-
U
285
35
Shuzenji (S)
i
195
29
Nakaizu
(Na)
90
30
Nakaizu
(N,)
Nakaizu (N3)
R
geomagnetic
variation) 6
Radon
i
82
25
7
Earth currents
e
65
30
Nakaizu (N,)
8
Geomagnetic
60
30
Nakaizu (Nl)
9
Volume strain
g H
42
41
Irozaki (I)
10
Volume strain
H
26
34
Ajiro (A)
m
38
100
U
18
90
Gmaezaki Nakaizu
field
10a
Microearthquake
11
Underground
12
Radon
i
5
25
13
Volume strain
H
4
41
14
Foreshock
f
0.65
Near the epicenter
15
Foreshock
f
0.17
Near the epicenter
water
Tokyo Bay (T)
Iro&i
(0,) (Ns)
(I)
of main shock of main shock
tained by Abe (1975), as shown in the figure. Although the accuracy of the magnetic survey at that time is not as high as it is today, it is interesting to see that the epicentral area as deduced from the precursor analysis roughly agrees with the real one. If we assume that M = 7.0, some of the D,, circles tend not to overlap. On the other hand, the epicentral area due to the present method seems TABLE
3. Prediction of occurrence time Probabiliry of earthquake occurrence cursors of the 1st and quasi-1st kin&
due to pre-
4
Parameters, cursors
too wide if M = 8.0 is assumed. It also seems unlikely that an earthquake with a magnitude as large as 8.0 will occur in the area in question. It is therefore concluded that the main shock magnitude takes on a value around 7.5.
data
numbers
and
standard
deviations
for pre-
of the 1st kind
logT=a+bM n
b
11
-0.260
0.475 0.367
7
-0.460
0.484 0.352
T
5
-1.23
0.567 0.378
Strain (extensometer)
h
17
-1.28
0.491 0.412
b-value
b
14
-0.524
0.446 0.724
Seismic wave velocity
v
17
-1.78
0.727 0.411
Anomalous
a
12
-1.60
0.754 0.142
Seismic quiescence
q
10
Geomagnetic
g
4
Discipline
Abbre-
Dam
viation
number
1 k
Tilt (water-tube)
Geodetic
survey
Tide-gauge
observation
seismicity field
Rikitake (1975, 1979) showed that a relation:
%
0.936 0.269 0.784 -2.08
0.781 0.585
(1)
approximately holds good between precursor time T and main shock magnitude M for precursors of some kinds, where a and b are parameters peculiar to a precursor discipline. When T is measured in days, he obtained a = - 1.01 and b = 0.60 for a then-available data set of precursors. It is also demonstrated by Rikitake (1987) that a relation such as eqn. (1) holds for each individual discipline of precursors of some sort: those disciplines are land deformation by geodetic survey
204
(I), land deformation by tide-gauge observation (k), ground tilt by a water-tube tiltmeter (T), strain by an extensometer (h), b-value of seismic activity (b), change in seismic wave velocity (v), anomalous seismic activity (a), seismic gap/quiescence (q) and change in geomagnetic field (g). These precursors are called precursors of the 1st kind. In Table 4 are shown the parameters determined for these precursors. Putting
while [i and t2 correspond to t, and f,, respectively. Making use of error function G(x), defined by:
E = log T
Q(X) = $iX
for the ith precursor, is given by: P,(ti,
t2) = $iC2
e-h:(c-to)2 d.$
(3)
1
as discussed by Rikitake (1969) where: h, = l/fi,
(2)
the standard deviation Us of E - &,, where co is the mean value of log T as determined by eqn (l), for each discipline is also included in the table. As can be seen in the table, the available data are scarce for some of the disciplines, probably resulting in an inaccurate estimate of a, b and Us. Such a defect certainly influences the probability evaluation in the later part of this section. This point could be improved in the future when a larger data set is compiled. For precursor disciplines such as earth currents (e), resistivity with long-distance electrodes (R), radon and other geochemical elements (i) and underground water/hot springs (u), it has been shown by Rikitake (1987) that the log T-M relationship leads to a value of T which is significantly smaller than those for precursors of the 1st kind, although a relationship similar to eqn. (1) holds. Precursors belonging to these disciplines are called precursors of the quasi-1st kind, and the parameters and their standard deviations are given in Table 5. Assuming that 6 - &, is governed by a Gaussian distribution, the probab~ity of an earthquake occurring between t, and t, (ti < tz), as evaluated
(4)
e-“‘du
(5)
eqn. (3) can be rewritten as:
(6) Subscript i to be attached to some of the quantities in eqns. (3), (4) and (6) is ignored for the sake of simplicity. On the condition that no earthquake occurs during a period between t = 0 and t = t,, the probability of an earthquake occurring between t, and f2 becomes: Pi(&, t2) = Pitt,? t,)/[l
- Pz(O, &>I
(7)
Using u(‘s given in Tables 4 and 5, temporal changes in the probability of an earthquake occurring within a prescribed period, 1 day say, from a specified date when a precursor of the 1st or quasi-1st kind is observed are estimated as shown in Figs. 6, 7 and 8. M = 7 is assumed in the estimate. No probability curve for discipline a (anomalous seismicity) is presented here because the probability for the time-span covered by these figures is extremely low. It is apparent from the probability curves thus
TABLE 5 Parameters, data numbers and standard deviations for precursors of the quasi-1st kind Discipline
Abbreviation
Data number
LI
h
mt
Earth currents Resistivity (long-distance electrodes) Radon and other geochemical elements Underground water/hot springs
e R i ”
3 9 14 9
.- 0.542 -2.00 - 0.468 -- 4.10
0.348 0.627 0.278 0.794
0.306 0.579 0.656 0.577
205
2.5
TIME
Fig. 6. Probabilities when
precursors
(days)
of an earthquake of disciplines
occurring
g, k,
within
1 day
I and v are observed.
M = 7 is assumed.
Fig. 8. Probabilities when
precursors
Probability of earthquake occurrence
due to pre-
cursors of the 2nd and 3rd kinds
Rikitake (1979) named the precursor of discipline r (resist&y observed using a variometer) as
in0
200
300 T
Fig. 7. Probabilities when
precursors
M = 7 is assumed.
within
1 day
u are observed.
a precursor of the 2nd kind. The precursor time for this kind of shock takes a value which ranges from 2 to 3 hours, regardless of the main shock magnitude. The precursor time for foreshocks (f) ranges from a few minutes to thousands of days, no indication of magnitude dependence being known. Such a precursor is called a precursor of the 3rd kind. Disciplines such as microearthquake (m), change in seismicity pattern (p), tilt by a pendulum tilt meter (t), volume strain (H) and the like seem to belong to this kind of precursor. The frequency distributions of logarithmic precursor time, log T, in units of days for the foreshock (f) and the volume strain (H), are shown in Figs. 9 and 10. Let us assume that logarithmic precursor time is governed by a Weibull distribution such as: A(s) =Ks”
log
VA<
occurring
e, i, R and
M = 7 is assumed.
obtained that the probability value and its temporal change are different from discipline to discipline of precursor. For disciplines i and u, the peak probability takes place within several days after the precursor appearance, with a peak value around 0.03. Precursors of these disciplines may be useful for short-term prediction. In contrast, for disciplines 1. v, g and the like, it takes several hundred days until the probability reaches its maximum, which is of the order of 10p4. These are regarded as long-term precursors. The differences in temporal change between precursor disciplines seriously affect the synthetic probability to be evaluated in the following section.
OO
of an earthquake of disciplines
400
500
600
700
800
I ME (days)
of an earthquake of disciplines
occurring
within
1 day
b, h, q and T are observed.
T+c)
(s=log
(8)
FREQUENCY ____*_---*----*--__*____*____*_--
1
-3.0
-
-2.6
-2.5
-
-2.1
n
-2.0
-
-1.6
W
-1.5
-
-1.1
m
-1.0
-
-0.6
-
-0.5
-
-0.1
-
14
0.0
-
0.4
0.5
-
0.9
-
14
1.0
-
1.4
1.5
-
1.9
2.0
-
2.4
-
2.5
-
2.9
I
3.0
-
3.4
3.5
-
3.9
Fig.
9. Histogram
measured
in days.
0 1 3 5 10 28 25 -
10 10 2 0 0
of log T for discipline
f (foreshock).
T is
206
log -3.@
-
-2.6
-2.5
-
-2.1
-2.0
-
-1.6
I
1
-1.5
-
-1.1
n
1
0 0
-1.0
-
-0.6
m
-0.5
-
-0.1
I
0.0
-
0.4
-
0.5
-
0.9
m
4 2 11 3
1.4
l
1.5
-
1.9
I
2.0
-
2.4
0
2.5
-
2.9
0
3.0
-
3.4
u
3.5
-
3.9
0
1.0
Fig. 10. Histogram is measured
FREQUENCY _---*----*----*--
T
1 2
of log T for discipline
H (volume strain).
T
in days.
Fig. 11. Plots of In In (l/R) fitting
for discipline
straight where X is the probability for log T to fall in an interval between s and s + As, where As is much smaller than s. c is a constant which may be chosen in such a way as to make actual calculation easy: ‘a value of c = 3 is assumed here. Denoting a cumulative probability for s to take on a value between 0 and s by P(s), we define a function: R(s)
= 1 -P(s)
As R(s) R(s)
(9)
is given by:
= exp[ -KY+r/(m
+ l)]
eqn. (11) can be drawn
respectively. Making use of the parameters
%I
=
[PA%)
It is also possible
+ l)] + (m + 1) In s
thus determined,
the cumulative probability P,(s) of an earthquake occurring in a period between 0 and s for the i th precursor can readily be calculated. On the condition that no earthquake occurs for a period between 0 and sr, the probability of an earthquake occurring between sr and s2 is obtained as: P;(S,,
= ln[ K/(m
line representing
by means of the least-squares method. In this way parameters K/(m + 1) and m + 1 are obtained from actual data. The parameters thus determined are given in Table 6 for disciplines f, t, r and H,
(IO)
we obtain: In ln(l/R)
vs. In s and a Weibull distribution
f (foreshock).
-P,h)l/[l-
to estimate
phdl (12) the mean value of
(IO). Since P can be calculated from the frequency distribution such as shown in Figs. 9 and 10 for an
s and consequently that of T as denoted by To using the parameters, although no formula for estimation is shown here. To’s are also given in Table 6. Judging from the mean precursor time thus obtained, it is clear that the precursor disciplines in Table 6 provide extremely short-term
appropriate As, we can have In ln(l/R) vs. In s plots for actual data as shown in Figs. 11 and 12, respectively, for disciplines f and H. In that case, a
ones. With the parameters given in Table 6, temporal changes in the probability p, of an earthquake
(11) by taking
TABLE
double
logarithms
of both sides of eqn.
6
Parameters,
data numbers
and mean precursor
times for precursors
of the 2nd and 3rd kinds
Discipline
Abbreviation
Data number
V(m+f)
l?t+1
Foreshock
f
122
0.0159
3.17
Tilt (pendulum)
t
46
0.00000359
8.30
Resistivity
(variometer)
Strain (volume)
G (day) 2.00 18.6
r
30
0.0254
5.24
0.0708
H
25
0.0142
3.65
0.776
207
p is given by: p=l/
[
1+
i
~~~(l/Pi-l))/(l/P~-l).-l
1
03)
Fig. 12. Plots of In In (l/R) fitting
for discipline
vs. In s and a Weibull distribution
H (volume
strain).
occurring within a prescribed period, 1 day say, are calculated as shown in Fig. 13 for disciplines r, H, f and t, respectively. 4. Temporal change in synthetic probability of
earthquake occurrence in association successive appearances of precursors
with
Utsu (1977, 1979, 1982, 1983), Aki (1981), Hamada (1983) and others have developed theories for evaluating the synthetic probability of earthquake occurrence when multiple precursors are observed. Following Utsu (1977), a formula for the probability of success of an earthquake prediction is used in the following to evaluate the synthetic probability of earthquake occurrence when a number of precursors of various disciplines are observed one by one. According to Utsu (1977), synthetic probability
I\f‘.. t“i Ii
---__
u
-
10
Fig. 13. Probabilities when precursors
20
TIME
30
of an earthquake
of disciplines
40
50
(days) occurring
within
r, H, f and t are observed.
1 day
on the condition that n independent precursors are observed and that the probabilities of respective precursors are given by pl, p2, . . . , p,,. p. is the probability of success when a prediction is made at random. The evaluation of p. is a matter of dispute, although it is customary to estimate p. from the seisrnicity in the area to be treated. As for pl, p2, . . . . p,, which are functions of time, we may rely on the probabilities for various disciplines evaluated in the last section. An example of estimating the synthetic probability will be given in the following, based on the reported precursors prior to the Izu-Oshima Kinkai earthquake (M = 7.0, 1978). The precursors are already given in Table 3. As assumed by Utsu (1979) we presume that the preliminary probability p. is given by: p. = T/( 100 x 365.25)
04)
on the assumption that an A4 > 6.5 earthquake occurs once in a lOO-yr period in the Izu Peninsula area concerned, where 7 denotes the time interval during which an earthquake is expected to occur. pi can be obtained using eqns. (7) and (12) and 7 is equal to t, - t,. When 7 is assumed as 3 h, 1, 3, 10 and 100 days, we have p. = 0.00000342, 0.0000274, 0.0000822, O.ooO274 and 0.00274, respectively. It is highly likely that precursor signals contain much noise. In other words, the probability that a precursor-like signal is false is very high. Sato and Inouchi (1977) pointed out that only 9 instances out of 56 anomalous land uplifts in Japan culminated in the occurrence of an earthquake. Therefore, the true probability of earthquake occurrence should be equal to aipi instead of pi, where pi’s are the probabilities for various precursor disciplines which can be calculated using the parameters given in Tables 4, 5 and 6, and (Y~‘S are the factors indicating the rate of appearance of the true precursor. In the case of land uplift revealed by geodetic surveys, the above data leads to (pi = 0.16, the subscript being written as 1 with
reference to the precursor numbers in Table 3, Mogi (1963), who examined about 1500 earthquakes of magnitude equal to or greater than 4 in Japan, concluded that only 4% of the earthquakes are accompanied by foreshocks. He also showed, however, that the rate of earthquakes with foreshocks amounts to 20% in the vicinity of the Izu Peninsula. We therefore assume that cy14and ty,, are equal to 0.2 for discipline f (foreshock-precursors 14 and 15) in the following probability evaluation. At the present stage of investigation, however, no exact value of LY;is available for other disciplines because of scarcity of data. In the circumstances, it can be assumed rather arbitrarily that (Y,= l/20 (i = 2, 3, . . . , 13) for precursor disciplines in Table 3 except 1 and f. Such a procedure is certainly unsatisfactory for the act& evaluation of probabihty~ but no other means that leads to a better result can be found at the moment. It is hoped that the accurate evaluation of (Y~will, in future, be achieved as more and more precursor data are accumulated. Replacing pi in eqn. (13) by arpi and using appropriate values of pay temporal changes in synthetic probability are calculated as shown in Figs. 14-18 respectively for r = 3 h, 1, 3, 10 and 100 days. It is assumed that precursor 1 (the land upfift at Nakaizu) was observed at d = 0. In Figs.
z
3
5678
9-m
III/
IllHI M.
$
s.
Ii ii
2
3
I I
1-P
I
.8
il 800
850
900 TIME
1100 (days)
Fig. IS. Changes in synthetic probability for 1‘= 1 day.
14-18, only the changes in probability after t = 800 days are shown. Up to that point, the probability is so small that it is virtually coincident with the zero line. The precursor appearances are indicated by the bars at the top of each figure; it can be seen that discontinuous increases in probability curves take place when short-term precursors such as numbers 3 (underground water, u), 4 (radon, i), 6 (radon, i} and so on are observed. On the other hand, whenever we have long-term precursors such as numbers 7 (earth currents, e) and 8 (geomagnetic field, g), the probability tends to drop to some extent. Such a tendency is observed more markedly for probability curves for a smaller value of 7. It is observed, however, that when a large value is assigned to T the probability increases successively with no marked fluctuations as precursors appear one by one. Assuming 7 = 100 days, for instance, the probability reaches 0.95 at around
I I
I
~
0 800
i’ 1 IA,, ti
l-
850
900 TIME
950
1000
1050
1100
(days)
Fig. 14. Changes in synthetic probability of earthquake occurrence for ‘I = 3 h. The occurrence times of respective precmsors are shown by vertical bars at the top, while the occurrence time of the main shock of the fzu-Oshima Kin&i earthquake is indicated by an arrow. The abscissa denotes the time (in days) after the appearance of precursor 1.
Fig. 16. Changes in synthetic probability for T = 3 days.
209
a
I
II
I I
II
III II NJ%
1-P .a .6 .4
0
800
850
900 950 T 1ME (days)
1000
1050
1100
Fig. 17. Changes in synthetic probability for 7 = 10 days. t = 1020
days. If one were to issue a prediction at about that date that an earthquake would occur within a period of 100 days, the prediction would be successful because the main shock occurred about 80 days later. For an extremely short-term or imminent prediction, the actual publication of the prediction seems to be no easy matter because of the fluctuations of synthetic probability as shown in Figs. 14-17. It might be better for such a prediction to rely only on short-term signals such as volume strain (H), underground water (u), radon (i), foreshock (f) and the like, assuming that signals belonging to long-term precursors observed at that stage are all false. 5. Conclusions Analyzing the data set of earthquake precursors so far collected in Japan, it is shown that we can define D,_ , the maximum detectable distance of 4
ii
1000
T I ME (days)
1050
1100
Fig. 18. Changes in synthetic probability for 7 = 100 days.
a precursor, as a function of main shock magnitude M. D,,,, is different from discipline to discipline of precursor. When a number of precursors are observed, we may draw circles with a radius peculiar to the precursor discipline, centered at respective observation points. In the procedure we assume a suitable value of M. In that case the epicenter of a future earthquake should be located in the area which is common to all the circles. If the assumed magnitude is too small, some of the circles do not overlap with one another. If it is too large, the area becomes too wide to be regarded as an actual epicentral area. In such a way we may infer the approximate location of the epicenter and the rough value of the earthquake magnitude at the same time. Applying the above-mentioned procedure to the reported precursors of the 1978 Izu-Oshima Kinkai (M = 7.0) and the 1964 Niigata (M = 7.5) earthquakes, remarkable success is achieved in assessing the main shock epicenter and magnitude. When a number of precursor-like signals are observed in series, it is also possible to evaluate changes in the synthetic probability of earthquake occurrence within a specified time interval 7, based on the empirically obtained probability of earthquake occurrence for precursors of various disciplines. The main shock magnitude involved in the evaluation has to be assessed in some way. An approach as discussed in the earlier half of this paper may be useful for that purpose. As an example, temporal changes in synthetic probability are estimated on the basis of the data taken before the Izu-Oshima Kinkai earthquake, for which a considerable number of precursor-like signals have been observed, as shown in Table 3. It turns out that the probability of earthquake occurrence in a time interval 7 generally increases as precursors are observed one by one. Such an increase is considerable for a short-term precursor. When a long-term precursor happens to appear, however, the probability drops discontinuously, although it tends to increase again as time goes on. Such a fluctuation is more considerable for smaller values of 7, so that a short-term earthquake prediction is more difficult than a long-term one.
210
The difficulties involved in the above evaluation of probability are twofold: the first is that the preliminary probabi~ty involved is not known very well, and the second is that the accurate probability of a signal representing a true precursor is hard to evaluate for most precursor disciplines. In the circumstances, it appears that no accurate estimate of the absolute value of probabi~ty is possible at the present stage of investigation. Even so, temporal changes in probability as presented in this paper may provide some clues for issuing earthquake predictions, which are strongly demanded by the public at large. The precursor-like phenomena analyzed here are identified as precursors after occurrence of the earthquake. In order to prove the validity of the approach proposed here, it is necessary to apply the method to actual precursors observed before an earthquake. It is hopefully expected that we will be able to monitor precursors for the Tokai earthquake which, it is feared, will occur in Central Japan in the near future, using a well equipped observation network. In that eventuality, the present approach could be tested. Judging from the speed of accumulation of precursor data under the nationwide programme of earthquake prediction in Japan, the empirical nature of precursors of various disciplines will be brought to light more clearly in the foreseeable future. In that case a more accurate evaluation of the synthetic probability of earthquake occurrence will certainly be accomplished.
Aki, K., 1981. A probabilistic mena.
In:
D.W.
Earthquake
synthesis
Simpson
Prediction,
and
of precursory
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The author is grateful to Professor M. Bath who reviewed the manuscript and suggested a number of improvements.
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Acknowledgment
pheno(Editors),
associated
their relationships.
with earthquake
Earthquake
Predict.
predicRes., 2: