Bulletin of the Seismological Society of America, 89, 5, pp. 1147-1155, October 1999
Worldwide Doublets of Large Shallow Earthquakes
b y Y. Y. K a g a n a n d D. D. J a c k s o n
Abstract
We investigated all the pairs of Mw >-- 7.5 shallow earthquakes in the
Harvard catalog that occurred at a centroid distance of less than 100 km. We showed
that most of these pairs have similar focal mechanisms. Because these earthquakes
generally should have focal regions in excess of 100 km diameter, their rupture zones
apparently intersect. For all these pairs, the time interval is significantly less than the
time span needed for plate motion to accumulate the strain released by the first event.
These observations conflict strongly with quasi-periodic recurrence models on which
the seismic gap hypothesis is based. Power-law recurrence fits these earthquake observations much better.
Introduction
Many models used to forecast long-term seismic hazard
are based on the quasi-periodic or seismic cycle hypothesis
of large earthquake occurrence. This hypothesis assumes
that the probability of a large earthquake is low after significant release of seismic energy and that danger increases only
when tectonic plate motion accumulates strain sufficient for
a new strong event. Several models have been formulated to
apply this idea to long-term earthquake prediction (McCann
et al., 1979; Shimazaki and Nakata, 1980; Nishenko 1991;
for more complete discussion, see Kagan and Jackson,
1995).
Kagan and Jackson (1995c, and references therein)
tested one of the seismic cycle models, the seismic gap
model, and showed that its forecasts were less accurate than
those of the Poisson model. Moreover, it can be shown that
shallow earthquakes are clustered in time and space (Kagan,
1991a, and references therein; Kagan and Jackson, 1991).
This clustering, which strongly manifests itself in aftershock
sequences, contradicts the basic assumption of the quasiperiodic recurrence model. Historic data (Mulargia and Gasperini, 1995; Goes, 1996; Marco et aL, 1996) also suggest
that large earthquakes are not quasi-periodic, as the seismic
cycle hypothesis would imply.
Lay and Kanamori (1980), Vidale and Kanamori
(1983), Astiz and Kanamori (1984), Wesnousky et al.
(1986), Xu and Schwartz (1993), Tanioka et al. (1996), Nomanbhoy and Ruff (1996), and Tanioka and Gonzalez
(1998) noticed that earthquake doublets and multiplets (large
earthquakes close in time and space) occur in various parts
of the Earth. In this article, we present a systematic study of
these clusters based on uniform criteria. We specify doublets
as pairs of large earthquakes whose centroids are closer than
their rupture size and whose interevent time is shorter than
the recurrence time inferred from the plate motion.
The seismic gap model in one form or another is still
used to calculate seismic hazard (e.g., Nishenko and Sykes,
1993; Roeloffs and Langbein, 1994). The advocates of the
quasi-periodic recurrence hypothesis propose that earthquake clustering is a property of small and intermediate
events. They posit that for very large earthquakes that rupture the whole brittle crust and are characterized by displacement in meters, the clustering should give way to a quasiperiodic, cyclic behavior. The obvious clustering of very
large earthquakes (M --> 8) compiled in instrumental catalogs
(Kagan, 1991a; Kagan and Jackson, 1991) is rationalized by
pointing out that although epicenters of such earthquakes
may be in close proximity, their ruptures may propagate in
opposite directions. Thus the rupture surfaces of such events
may not intersect. Moreover, in the absence of information
about the focal mechanisms, one can argue that close earthquakes may have different focal mechanisms, thus contradicting the conclusion that such events rupture a similar or
the same fault segment.
Accumulation of global high-quality centroid-moment
tensor data collected in the Harvard catalog (Dziewonski et
al., 1999) allows us to test the hypothesis that similar large
earthquakes rupture the same seismic zone segment in a time
interval too small for earthquake slip to be replenished by
plate motion. Because the solutions yield centroid (center of
the deformation release) coordinates, the centroid closeness
signifies that patterns of significant deformation in both
earthquakes should overlap. We can also use the seismic
moment tensor data to ensure the similarity of focal parameters for both earthquakes.
Although the earthquake pairs can be studied case by
case using additional data, such as local earthquake catalogs,
historic records, and so forth, the results of such investigations are not of uniform quality and lack the homogeneity
and stability necessary for statistical analysis. Moreover, the
variety of interpretative methods and the assumptions involved in data processing make comparing the results difficult. While statistical results can be used to forecast future
1147
1148
Y.Y. Kagan and D. D. Jackson
earthquake occurrences quantitatively, case studies cannot
usually be extrapolated into the future because they essentially analyze a unique seismic sequence.
In this article, we investigate all the pairs of M w --> 7.5
shallow (depth less than 70 km) earthquakes in the Harvard
catalog that occur at centroid distances of less than 100 km.
Focal zones of these earthquakes extend over 50 to 100 kin.
Thus, if the distance between their centroids is less than 100
km, their focal zones should intersect. Nishenko and Sykes
(1993, p. 9912) suggest that for subduction zones events
M w >-- 7.5 are "large earthquakes," that is, they rupture
through the whole width of the seismogenic crust.
The total number of earthquakes with the scalar seismic
moment Mo -> 10 20.25 N.m (Mw >- 7.5) in the Harvard catalog (1 January 1976 to 31 December 1998) is 70. There are
several slightly different formulas for calculating the moment magnitude. We use
Mw =
_2 ×
3
logl0Mo
-
6.0
(1)
in this work because it is simplest. The magnitude calculated
by (1) is used here only for illustration purposes; all pertinent
computations are carried out with the moment M o values. In
the following, where there is no possibility of confusion, we
use the notation M for the moment magnitude.
Earthquake Doublets
Nine pairs of earthquakes satisfy the foregoing conditions for the doublets. In Figure 1, we display focal mechanisms of earthquakes M w >-- 7.5 and mark all the pairs discussed in this article. In Tables 1 to 3, we display the most
important parameters of earthquakes as well as the distance,
magnitude, and time differences between the event pairs. As
Figure 1 and Tables 1 to 3 testify, all are subduction zone
earthquakes, but they are not concentrated in any particular
part of the world or particular geological province.
The three-dimensional angle of rotation (Kagan, 1991b)
between two solutions (~b) is also shown in Table 1; for six
pairs, it is less than 30 ° . Therefore, both earthquakes in these
pairs have similar mechanisms. We calculate the degree of
fault rupture overlap
r/-
L 1 + L2
2R
'
(2)
where L1 and L 2 a r e the respective rupture lengths for the
first and second earthquakes in the pair and R is the distance
between the centroids. The rupture length is estimated assuming that the coseismic slip is proportional to it and the
earthquake stress drop Act = 3 MPa (30 bars) (Scholz,
1990); the rupture width W is assumed to be 25 km.
/ Mo
L = ./
AaW
'
(3)
The values of ~/ in excess of 1.0 suggest that the rupture
zones of both earthquakes overlap. Six out of nine ~ values
are larger than 1.0. Even if we take W = 50 km, the ~/value
decreases by a factor of f2. Four q values exceed ]2.
Equation (3) yields a conservative estimate of the rupture length. If we use estimates of rupture length based on
aftershock patterns (Pegler and Das, 1996) or from a variety
of sources (Wells and Coppersmith, 1994), the t/ values
would be significantly higher. For example, according to (3),
L = 48.7 km for a magnitude 7.5 earthquake (M0 = 1020.25
N.m), and L = 115.5 km for magnitude 8.0 (Mo = 1021
N-m). Using expressions in Wells and Coppersmith (1994,
Table 2A), we obtain for the foregoing events the values of
L = 93 km and L = 183 kin, respectively. From Figure 1
in Pegler and Das (1996), we estimate the appropriate L
values as about 100 and 250 kin, respectively. Accepting
such estimates for rupture length would increase the q values
in Table 1 by a factor of about 2, implying greater overlap
of rupture zones.
All the pairs occur on plate boundaries (subduction
zones), identified, for example, by McCann e t al. (1979),
Nishenko (1991), and Jarrard (1986). The calculation of the
theoretical recurrence time shown in the last column of
Table 1 is based on plate tectonics (NUVEL-1A model
[DeMets et al., 1994]). For M w = 7.5, we take the average
slip of 2.50 m, the rupture length of 100 km, the width of
25 km, and elastic modulus/z equal to 30 GPa (Scholz, 1990,
p. 182). The computations indicate that the second earthquake in each pair occurred much sooner than would be
expected for the average slip to be recovered by tectonic
motion. Most earthquakes in the table are greater than magnitude 7.5. Thus, for them, the discrepancy would be higher.
In addition, if we assume Act = 3 MPa and L ~ 50 km (see
previous text), the slip would equal 5 m, and the theoretical
recurrence time would be two times longer.
In Table 3, we compare the Harvard solutions with those
in the USGS catalog (Sipkin and Zirbes, 1997) and the PDE
worldwide catalog of earthquakes (U.S. Geological Survey,
1997) for all the earthquakes shown in Table 1. Different
methods give quite different earthquake source estimates
(Frohlich and Davis, 1999). This points out why it is important to use a data set with consistent methodology, such
as the Harvard catalog in our case. The hypocenter is usually
located at some distance from the centroid, the difference
being due to location errors and rupture originating closer
to the edge of the focal area (Smith and Ekstr6m, 1997). As
can be expected, the distance increases on average with increasing magnitude, although the correlation coefficient is
small.
The number of pairs in Table 1 is too small for any
reliable conclusions about the statisticalinterearthquake time
distribution or dependence of the rotation angle dp and the
Worldwide Doublets of Large Shallow Earthquakes
1149
...........
a.=,
J
I
I
i
r"i
--.I ............
®
l ............
'r . . . . . . . . . . . .
~ .........
...',,~
7 8"'~
............
t ..........
2
--4
............
I ............
I, . . . . . . . . . . . .
'- . . . . . . . . . . . .
1. . . . . . . . . . . .
l .....
,
11:2
!9
............
t ............
~ ............
F ............
. . . . . "1. . . . . . . . . . . .
F--
t-.
®
Figure 1.
Map showing the locations of all 70 earthquakes with moment magnitude
7.5 and greater in the Harvard catalog, 1976 to 1998. Beach ball patterns show the
focal mechanisms. The paired events studied in this article are shown with their compressional quadrants fully darkened; unpaired events have compressional quadrants
shaded. Numbers near earthquake symbols identify sequence number of paired events
in Tables 2 and 3.
Table 1
Pairs of Shallow Earthquakes Mw ~ 7.5
First Event
No.
1
2
3
4
5
6
7
8
9
1
3
3
4
5
6
7
9
11
Date
1978/03/23
1980/07/08
1980/07/08
1980/07/17
1983/03/18
1984/02/07
1985/09/19
1987/03/05
1990/04/18
Second Event
M w
No.
7.6
7.5
7.5
7.8
7.8
7.6
8.0
7.6
7.7
2
4
15
15
14
10
8
13
12
Date
1978/03/24
1980/07/17
1997/04/21
1997/04/21
1995/08/16
1988/08/10
1985/09/21
1995/07/30
1991/06/20
Difference
Mw
7.6
7.8
7.8
7.8
7.8
7.6
7.6
8.1
7.6
R
(kin)
25
62
33
92
83
85
71
33
37
Tectonic Rate
r/
qb (deg)
At (day)
V (cm/yr)
A T (day)
2.31
1.06
1.94
0.86
0.95
0.68
1.26
2.81
1.62
7
18
43
35
26
50
14
7
29
2
9
6131
6122
4534
1645
2
3069
428
8.2
8.9
8.9
9.0
10.2
9.5
5.1
7.9
5.5
11,000
10,300
10,300
10,100
9,000
9,600
17,900
11,600
16,600
Earthquake numbers(No.) correspond to that of Tables 2 and 3, R, distance;t/, degree of zones overlap, ~, 3D rotationangle; AT, time intervalbetween
events; V, plate velocity; AT, calculatedinterearthquaketime.
distance between the centroids on the interearthquake time.
To investigate the time and rotation distribution, we repeated
our calculations for pairs of M --> 7.0 earthquakes separated
by 50 km and then by 100 km. The former distance may be
comparable to location errors, but that should not strongly
influence the time statistics. Smith and E k s t r t m (1997) suggest that the combined relative error in locations of centroids
and hypocenters is on the order of 25 kin. The total number
of M --> 7.0 events is 227, and there are 29 and 119 earthquake pairs satisfying the conditions R -----50 and --< 100 km,
respectively. For 15 doublets, the value of t/ exceeds ~ .
Thus, focal areas of these events exhibit a strong overlap.
The number of M ----- 7 pairs at the 100-kin distance
suggests that the stronger earthquakes (M --> 7.5) are distrib-
1150
Y . Y . Kagan and D. D. Jackson
Table 2
Earthquakes Mw -----7.5 in Pairs, Harvard Catalog
T axis
1
2
3
4
5
6
7
Date
Time
1978/03/23
1978/03/24
1980/07/08
1980/07/17
1983/03/18
1984/02/07
1985/09/19
3:15
19:47
23:19
19:42
9:05
21:33
13:17
1:37
9:17
4:38
13:39
5:18
5:11
10:27
12:02
8
1985/09/21
9
10
11
12
13
14
15
1987/03/05
1988/08/10
1990/04/18
1991/06/20
1995/07/30
1995/08/16
1997/04/21
Centroid Coordinates
44.12
44.20
- 12.92
- 12.44
-4.86
-9.81
17.91
17.57
- 24.38
- 10.49
1.31
1.04
- 24.17
-5.51
- 13.21
149.27
148.98
166.21
165.94
153.34
160.42
- 101.99
- 101.42
- 70.93
160.77
123.35
123.23
- 70.74
153.64
166.20
P axis
H (kin)
Mo
Mw
P1.
Str.
PI.
Str.
Geographic
Region
28.3
30.7
43.6
34.0
69.9
21.9
21.3
20.8
41.9
16.2
33.2
15.0
28.7
45.6
51.2
269
228
197
484
463
252
1099
249
248
254
331
231
1215
462
439
7.62
7.57
7.53
7.79
7.78
7.60
8.03
7.60
7.60
7.60
7.68
7.58
8.06
7.78
7.76
56
63
81
74
68
51
62
62
66
61
66
52
67
86
57
312
309
320
49
150
130
9
33
73
35
135
185
90
259
131
34
27
4
14
0
20
28
28
23
28
17
38
23
3
15
132
131
75
253
59
247
199
209
270
235
0
8
267
48
245
Kuriles
Kuriles
S. Cruz Is
S. Cruz Is
N. Ireland
Solomon Is
Mexico
Mexico
Chile
Solomon Is
Borneo
Borneo
Chile
N. Ireland
Vanuatu Is
Seismic moment M0 is measured in 10TM N-m; H, depth; PI., plunge of an axis; Str., its strike (azimuth).
Table 3
Earthquakes Mw-->7.5 in Pairs, P D E a n d U S G S C a t a l o g s
USGS
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Date
Time
1978/03/23
1978/03/24
1980/07/08
1980/07/17
1983/03/18
1984/02/07
1985/09/19
1985/09/21
1987/03/05
1988/08/10
1990/04/18
1991/06/20
1995/07/30
1995/08/16
1997/04/21
3:15
19:47
23:19
19:42
9:05
21:33
13:17
1:37
9:17
4:38
13:39
5:18
5:11
10:27
12:02
Hypocenter Coordinates
44.93
44.24
- 12.41
- 12.52
-4.88
- 10.01
18.19
17.80
-24.39
- 10.37
1.19
1.20
- 23.34
-5.80
- 12.58
148.44
148.86
166.38
165.92
153.58
160.47
- 102.53
- 101.65
-70.16
160.82
122.86
122.79
- 70.29
154.18
166.68
PDE
H (km)
M0
M~
mb
Ms
Geographic
Region
33
33
33
33
89
18
28
31
62
34
25
31
45
30
33
-----51
-240
240
64
140
160
1000
260
--
-----7.14
-7.59
7.59
7.20
7.43
7.47
8.00
7.61
--
6.4
6.5
5.9
5.8
6.5
6.6
6.8
6.3
6.5
6.1
6.2
6.2
6.6
6.5
6.4
7.5
7.6
7.5
7.9
7.6
7.5
8.1
7.6
7.3
7.4
7.4
7.0
7.3
7.8
7.9
Kuriles
Kuriles
S. Cruz Is
S. Cruz Is
N. Ireland
Solomon Is
Mexico
Mexico
Chile
Solomon Is
Borneo
Borneo
Chile
N. Ireland
Vanuatu Is
H, depth.
u t e d in s p a c e similarly: the e x p e c t e d n u m b e r o f pairs, 119/
10, is c l o s e to 9 as a c t u a l l y o b s e r v e d ( T a b l e 1) (cf. K a g a n ,
1991a). T h e n u m b e r in t h e d e n o m i n a t o r is t h e s q u a r e o f t h e
r a t i o o f the n u m b e r s M --> 7 v e r s u s M -> 7.5 e a r t h q u a k e s ;
a s s u m i n g t h a t t h e b - v a l u e in the G u t e n b e r g - R i c h t e r l a w
e q u a l s 1.0, w e o b t a i n t h e v a l u e o f 10. T h e r e are 9 5 0 pairs
o f e a r t h q u a k e s M --- 6.5 w i t h R -< 100 k m , c o n f i r m i n g the
p r e v i o u s c o n c l u s i o n . M a n y M --> 7.5 e v e n t s (15 o u t o f 70,
i.e., a b o u t 2 2 % ) o c c u r i n d o u b l e t s or m u l t i p l e t s , a n d b e c a u s e
all t h e s e p a i r s h a v e a s m a l l e r r e c u r r e n c e t i m e t h a n t h e l e n g t h
o f the c a t a l o g ( T a b l e 1), w e s h o u l d e x p e c t t h e r e l a t i v e n u m b e r o f d o u b l e t s to i n c r e a s e w i t h time. I n d e e d , t h e n u m b e r o f
e a r t h q u a k e s i n c r e a s e s l i n e a r l y w i t h time, w h e r e a s the n u m b e r o f pairs is p r o p o r t i o n a l to the s q u a r e o f the total n u m b e r
o f events.
F i g u r e 2 a d i s p l a y s t h e d e p e n d e n c e o f r o t a t i o n a n g l e (I)
o n t h e t i m e i n t e r v a l f o r M ~ 7 a n d R --< 5 0 kin. M o s t o f t h e
r o t a t i o n a n g l e s ((I)) are less t h a n 25 °, c o n f i r m i n g t h a t t h e
e a r t h q u a k e s in the pairs h a v e s i m i l a r f o c a l m e c h a n i s m s . T h e
r o t a t i o n a n g l e i n c r e a s e s w i t h t i m e ( K a g a n , 1992), a l t h o u g h
the c o r r e l a t i o n c o e f f i c i e n t is small. F o r t i m e i n t e r v a l s c l o s e
to zero, t h e a n g l e qb a p p r o a c h e s 10°; F r o h l i c h a n d D a v i s
( 1 9 9 9 ) s u g g e s t t h a t in the b e s t d e t e r m i n a t i o n s o f e a r t h q u a k e
f o c a l m e c h a n i s m s , the a n g u l a r u n c e r t a i n t y is o f s u c h m a g nitude.
It is o b v i o u s t h a t t h e M --> 7 d i s t r i b u t i o n is s t r o n g l y
c o n c e n t r a t e d t o w a r d s m a l l t i m e intervals, w h i c h is c o m p a t i b l e w i t h a p o w e r l a w ( K a g a n a n d J a c k s o n , 1991); t h e n u m b e r o f p a i r s is 3, 3, 4, 8, a n d 11 for the i n t e r v a l s less t h a n 1
day, 1 to 10, 10 to 100, 100 to 1000, a n d > 1 0 0 0 days,
Worldwide Doublets of Large Shallow Earthquakes
1151
(a)
(b)
50
301
,
,
i
i
45
'
40
35
201"
m
~J ,-'i///"
.~[_~.."
; ,, /
Cumulativedistribution
Power-law( t - ° ' 7 5 ) / "
O
/
O
F
0 25
//
"
o
20
o
15
10Fi. I!I,' ,, ~/
o
//'
10
o o
0
0
1000
5F
0
//
p=0.34
o
-10oo
0
2000
3000
5000
'
~' 00
. .
Time interval days
Poissonlaw
/
6000
.
.
7000
8000
9000
-1000
°'
0
1o'0o
2000
'
3000
'
~' 00
5000
'
6000
'
7000
'
8o'00
9000
Time interval days
Figure 2. Distribution of Mw -->_7 earthquake pairs. (a) Dependence of the 3D rotation angle between focal mechanisms on the time interval between events. Solid line
is the linear regression approximation. Correlation coefficient p is also shown. Pairs
with smaller time intervals generally have more similar focal mechanisms, indicating
that they are not fundamentally different from one another. (b) Cumulative number of
pairs versus time separation for magnitude 7.0 and larger events within 50 km of each
other. Poisson and power-law distributions are shown for comparison. The number of
pairs with short interval times clearly exceeds the number expected for Poisson recurrence. A similar conclusion holds for magnitude 7.5 and greater events within 100 km,
although the number of pairs is insufficient to draw statistical conclusions.
respectively. In Figure 2b, the cumulative distribution of pair
numbers (N) is shown. We approximate the distribution by
two theoretical curves, the Poisson distribution [equation (1)
in Kagan and Jackson, 1991] and a power-law density qb(dN)
t -0"75. It is obvious that the Poisson law predicts a much
smaller number of pairs for small time intervals than is observed. As we mentioned earlier, the quasi-periodic recurrence model in effect prohibits any subsequent earthquake
to occur in the rupture area of another large event before
sufficient strain accumulates through plate motion. The interval values (At) for M --> 7.5 earthquakes in Table 1 are
also compatible with the power-law dependence.
We investigate the spatial distribution of aftershocks for
each earthquake in Tables 1 to 3. We define as aftershocks
all the earthquakes mb >- 4.5 in the PDE catalog occurring
within one day and 200 km of the centroid location. The
number of aftershocks varies greatly from 67 for event 2 in
Tables 2 and 3 to none for event 10, the average number
being 23.9 _ 21.1. In Figure 3, we display aftershock patterns for one representative pair of earthquakes (pair 1 in
Table 1), demonstrating the overlapping of epicentral
regions. (The diagrams for other pairs are accessible in a
PostScript form through WEB electronic supplement: tip://
minotaur.ess.ucla.edu/pub/kagan/pair#.ps, where # corresponds to the pair number in Table 1). In general, the aftershock areas overlap, suggesting that the rupture zones of
both earthquakes in a doublet intersect significantly.
Several earthquake pairs listed in Tables 1 to 3 have
been studied by various researchers who displayed aftershock patterns and commented on possible overlap of focal
regions. Tajima and Kanamori (1985, Figure A.13 and Figure A.57) show that aftershock areas of the 1980 Santa Cruz
Islands doublet (pair 2 in Table 1) overlap: aftershocks of
the first event are surrounded to a large degree by the aftershocks of the second earthquake. Tajima et al. (1990, p.
283f) confirm these findings and suggest that "the major
energy of the 1980 main event was also released within the
aftershock area of the foreshock." The authors refer to our
event 4 in Tables 2 and 3 as the main event; their foreshock
corresponds to event 3 in Tables 2 and 3. UNAM (1986)
suggest that aflershock regions for the 1985 Mexico doublet
(pair 7 in Table 1) are different, while Mendoza (1993, p.
8206 and Fig. 10) obtained coseismic slip maps for both
events that partially overlap. There are also contradictory
conclusions for the Chilean doublet (pair 8 in Table 1): Delouis et aI. (1997, p. 430) suggest that the 1987 shock is
located in the SE part of the 1995 rupture region, whereas
Ihml6 and Ruegg (1997, p. 156f) see little overlap in both
focal regions. In contrast, Ihml6 and Ruegg (1997, Fig. 14)
display aftershock patterns for the doublet that imply a significant overlap.
Discussion
An important question in seismology is whether large
earthquakes differ fundamentally from small ones. With few
1152
Y.Y. Kagan and D. D. Jackson
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Figure 3. Focal mechanisms (from the Harvard catalog) and epicenters (from the PDE catalog) of mainshocks and one day aftershocks for two large 1978
Kurile Islands earthquakes (the first pair in Table 1).
Latitude limits are 43.0 to 45.0° N, longitude limits
148.0 to 150.0° E, and the magnitude thresholds are Mw
=> 5 and mb => 4.5. The beach balls for the first mainshock and its aftershocks have solid filling, for subsequent sequence, the filling is striped. Solid circles represent the first aftershock sequence, the open circles are
for the second sequence. Mainshock PDE epicenters are
shown by a circle with a cross (the first event) or a dot
(the second event) inside. The size of a symbol is approximately proportional to magnitude.
exceptions, small earthquakes appear to have fractal distributions in magnitude, time, and space. The implied clustering seems plausible because the events are not large enough
to reduce the ambient stress field very much. Large earthquakes, in contrast, are often presumed to release most of
the accumulated potential displacement, stress, and elastic
energy, thus preventing similar earthquakes until displacement, stress, and energy recover. The classical seismic gap
models (Fedotov, 1968; McCann et al., 1979; Nishenko,
1991) further assume that plate boundaries are divided into
segments and that for each segment there is a typical earthquake (now called a characteristic earthquake [Schwartz
and Coppersmith, 1984]) large enough to dominate the seismic moment release and so reduce the probability of large
earthquakes within the segment. These assumptions allow
the frequency of characteristic earthquakes to be deduced
from the rate of interplate motion. An important question for
seismic gap models is how to recognize large characteristic
earthquakes. The size of the characteristic earthquake is assumed to vary from one segment to another, but for most
segments, the characteristic magnitude is between 7 and 8.
Nishenko and Sykes (1993) argue that on average, earthquakes above magnitude 7.5 are large enough to rupture the
entire width of the plate boundary, so that they should generally have the properties of large characteristic earthquakes.
In our study of earthquake pairs, we focused on earthquakes
above this threshold. Our results show that since 1976, even
earthquakes above magnitude 7.5 can have intersecting focal
zones and appear to have fractal distributions in time and
space. The magnitude distribution has no sudden change in
slope near 7.5 (Kagan, 1997), and such earthquakes cluster
in space and time as smaller events do (Kagan and Jackson,
1991).
We found that 15 out of 70 very large events occurred
in clusters with overlapping focal zones. Do the 55 counterexamples show that earthquake clusters are relatively unimportant? The clusters are important for two reasons. First,
they should not occur at all under the seismic gap hypothesis,
at least as it is commonly used in hazard studies. Even under
the Poisson assumption, one would expect very few clusters
given the total number of events and size of the Earth. Second, the power-law distributions revealed by the clusters
have predictive power and important implications for earthquake physics.
Kagan and Jackson (1991) and Kagan (1991a) show that
both the time and space earthquake fractal dimensions are
independent of magnitude for events up to magnitude M -7.5. This finding implies no space-time repulsion effect even
for such large events; that is, all earthquakes are clustered.
Inspection of aftershock maps (see, for example, Mendoza,
1993; Tanioka et al., 1996; Delouis et al., 1997) and special
studies of aftershock distribution in comparison with coseismic displacement pattern (Mendoza and Hartzell, 1988;
Gross and Btirgmann, 1998, and references therein) show
that although the maxima of aftershock concentrations do
not coincide with the zones of maximum slip, the latter zones
are not immune to a large number of aftershocks occurring
in the zone or nearby. Some earthquakes listed in Tables 1
to 3 would clearly qualify as members of a foreshock-mainshock-aftershock sequence, which would suggest that strong
earthquakes could reoccur at a small time interval in essentially the same area.
It is still possible that earthquakes become large enough
to deter others at some greater threshold. Time will tell as
future data include more pairs of even larger earthquakes
and provide tighter bounds on the degree of rupture area
overlap for doublet earthquakes. Note that one of our paired
events had a magnitude of 8.0 and was followed within two
days by a magnitude 7.6 earthquake. Although the second
earthquake may be described as an aftershock, it shows that
plenty of elastic energy remained after the first event.
According to the classical gap models, characteristic
earthquakes on a given segment should overlap completely
(t/--> oo) with interval times (At) sufficient for recovery of
the slip; characteristic earthquakes on different segments
should have almost no overlap, and their interval times
should be much more diverse. Thus for pairs of large events,
Worldwide Doublets of Large Shallow Earthquakes
the time difference should be directly correlated with the
degree of overlap. But inspection of Table 1 indicates no
obvious interdependence of t/ versus z = At~AT. Large
earthquakes do not behave as assumed by the gap models.
According to the classical seismic gap model, each plate
boundary segment has a characteristic earthquake whose size
can be inferred from the historical record for many segments.
Several recent modifications of the seismic gap hypothesis
offer a more complex view of the characteristic earthquake
idea: large earthquakes may include combinations of characteristic events on multiple segments; plate boundaries may
have multiple fault systems, each with its own characteristic
earthquakes; or large events may leave some of the fault
plane unruptured, leaving fuel for future earthquakes. We
discuss each of these hypotheses in turn, showing that each
variant sacrifices the predictive capability promised by the
classical gap model.
Thatcher (1990), Nomanbhoy and Ruff (1996), and
Grant (1996) pointed out that in many historic and instrumental catalogs, rupture areas of large events on a given fault
segment may vary considerably. A modified recurrence hypothesis assumes that focal areas of subsequent earthquakes
may only partially overlap but would still require tectonic
motion to make up for moment release. There are two problems with this model, however. First, it conflicts with our
data, which show that sometimes virtually no tectonic motion occurs before a new rupture. For all pairs listed in Table
1, the z value is less than 1.0, and the distribution of interearthquake time is closer to a power law than to the quasiperiodic function that a cyclic model would imply. Second,
the number of characteristic earthquakes describing plate
boundary motion increases from that in the classical seismic
gap models, and precise slip patterns of past earthquakes
must be known to calculate their recurrence times. Presently
available data are insufficient for this purpose so the model
has little predictive power.
Some would argue that the occurrence of large doublet
earthquakes does not invalidate the seismic gap model if the
events occur on separate faults. In most cases, we cannot
determine whether paired earthquakes rupture the same fault
surface. However, the doublets still pose a major problem
for gap models even under the separate fault scenario. First,
from a physical point of view, an earthquake on one fault
should reduce the shear stress on a parallel fault, delaying
the next earthquake there. Because the later events can follow the earlier ones so quickly, it is hard to argue that the
stress would have recovered by normal tectonic processes.
Second, if the separate fault model holds, then characteristic
earthquakes would have to be defined for each fault segment
rather than for each plate boundary segment. Even seismic
data available now are inadequate to resolve these fault
planes adequately, and we have no basis on which to "set
the clock" for future earthquakes on most plate boundaries.
Finally, from a hazards perspective, the occurrence of a large
earthquake does not preclude nearly immediate recurrence
1153
of damage in the same area, regardless of how we try to
modify the seismic gap model.
Some have suggested (Mendoza, 1993; Tanioka et al.,
1996; Delouis et al., 1997; Ihml6 and Ruegg, 1997; Tanioka
and Gonzales, 1998; Schwartz, 1999) that displacement on
the fault plane may be quite inhomogeneous in large earthquakes, so that localized patches of large displacement may
intermingle with nearly unbroken patches. Later earthquakes
may then fill in some gaps in the rupture pattern left by their
predecessors. We refer to this idea as the checkerboard hypothesis. In this hypothesis, the earlier and later earthquakes
may have similar average displacements and stress increments when averaged over the common rupture surface, but
on a more local scale, they would differ from one another
strongly. It is difficult to test the checkerboard hypothesis
because the inversion of seismic data to determine the displacement patterns on a fault produces nonunique results.
One cause of the nonuniqueness is the limited frequency
content of seismic data. Another problem is that the inhomogeneity of the estimated displacement pattern depends arbitrarily on the trade-off between resolution and variance
(Menke, 1989, p. 76). For the latter reason, displacement
patterns determined by different investigators cannot be
safely compared because scientists may have chosen quite
different points on the trade-off curve. Even if many large
pairs can be explained by the checkerboard model, the observation of strong clustering requires complete revision of
the seismic gap model. First, in the checkerboard model,
there is no unique characteristic earthquake that ruptures an
entire segment and starts the clock. There would be many
modes of rupture, each with its own clock, for each segment.
The seismic gap model has been formulated and tested using
earthquakes that occurred before modern global networks
were in place (Fedotov, 1968; McCann et al., 1979; Nishenko, 1991). If the checkerboard model applies, then it is
impossible with available data to identify the mode of past
earthquakes. Second, the checkerboard model would make
the seismic gap model irrelevant for purposes of estimating
seismic hazard, since damage from large events depends
more on the rupture dimensions and average slip than on the
local displacement pattern.
Our estimate of the degree of overlap ~1 in earthquake
pairs is surely oversimplified. It is derived simply from a
point representation of the moment centroids and a simple
scalar estimate of the length of ruptures derived from empirical correlations. However, this simple measure has one
great advantage: it can be uniformly applied to all event pairs
without introducing biases inherent in case studies of selected earthquake pairs using different data types for different events. Moreover, our results are not strongly dependent
on our definition of t7. Maps of aftershock zones (e.g., Fig.
3) and independent studies of the rupture patterns of many
earthquakes in this study (Mendoza, 1993; Tanioka et al.,
1996; Delouis et al., 1997; Ihml6 and Ruegg, 1997; Tanioka
and Gonzalez, 1998; Schwartz, 1999) all indicate that for the
1154
Y . Y . Kagan and D. D. Jackson
paired events the focal volumes, and probably the rupture
surfaces, overlap significantly.
Conclusions
Large earthquakes, like small events, cluster in time and
space, implying that the probability of a new significant moment release in the same general area increases, not decreases, after a strong earthquake. Observed large earthquake pairs conflict with the basic tenets of the seismic gap
models of earthquake recurrence. Adapting the seismic gap
model to fit these observations would require a radical redefinition of characteristic earthquakes and would yield a
model with virtually no predictive power.
Acknowledgments
We appreciate partial support from the Southern California Earthquake Center (SCEC). SCEC is funded by NSF Cooperative Agreement EAR8920136 and USGS Cooperative Agreements 14-08-0001-A0899 and 1434HQ-97AG01718. We thank M. Wyss of University of Alaska, R. Madariaga
of Ecole Normale Suprrieure, W. Ellsworth of USGS (Menlo Park), H.
Houston of UCLA, and R. Geller of Tokyo University for their useful comments, and S. Schwartz of UC Santa Cruz for sending a preprint of her
article prior to publication. Reviews by S. Schwartz and R. Madariaga have
been very useful in revising the manuscript. Publication 476, SCEC.
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Department of Earth and Space Sciences
University of California
Los Angeles, California 90095-1567
E-mail: [email protected] and [email protected]
Manuscript received 14 January 1999.