Geophys. J. Int. (2001) 147, 272–293
Aftershock zones of large shallow earthquakes: fault dimensions,
aftershock area expansion and scaling relations
C. Henry and S. Das
Department of Earth Sciences, University of Oxford, Parks Road, Oxford, OX1 3PR, UK. E-mail: [email protected]
Accepted 2001 May 22. Received 2001 May 5; in original form 2000 August 23
SUMMARY
We determine the aftershock areas from relocated hypocentres for 64 dip-slip and eight
strike-slip earthquakes in the period 1977–1996 together with those for three recent
earthquakes, the 1998 Antarctic plate earthquake, the 1999 Izmit, Turkey earthquake
and the 2000 Wharton Basin earthquake. We also include the data for 27 strike-slip
earthquakes from Pegler & Das (1996). We find that the location of the hypocentre is
essentially random along strike for both strike-slip and dip-slip earthquakes. Subduction
zone earthquakes appear to initiate more frequently towards the down-dip edge of the
fault, whereas the non-subduction zone dip-slip earthquakes do not have any preferred
depth of initiation. The aftershock zones of subduction zone earthquakes often expand
substantially along strike and up dip but far less in the down-dip direction, whereas
those for non-subduction zone earthquakes do not expand significantly in either the
up- or the down-dip direction. Subduction zone thrust earthquakes have larger and
more numerous aftershocks than earthquakes in all other tectonic settings. For strikeslip earthquakes, we find that slip increases at least linearly with length. For dip-slip
earthquakes, we find that the ratio of length to width increases systematically with length
for lengths >40 km, indicating that there is some restriction on fault width; slip is found
to be proportional to length over the moment range 1017 N m <M0<3r1021 N m,
taking our data in conjunction with the data of Wells & Coppersmith (1994).
Key words: aftershocks, earthquakes, fault dimensions, scaling relations.
1
INTRODUCTION
The 1952 Kern County, California earthquake was the first one
for which portable seismometers were set up in the field within
hours of the main shock in order to record the aftershocks, with
Gutenberg, Richter and Benioff all being involved in this project.
Richter (1955) was the first to associate clearly the location of
the aftershocks with the fault rupture area. Richter (1995) demonstrated the spatial complexity of the aftershock distribution and
noted a slight expansion of the rupture area with time. Since
then, one of the most widely used methods of obtaining the
rupture dimensions is by using aftershocks. The expansion of the
rupture area with time has been noted for many earthquakes,
and it is considered that if a short time period after the main
shock is selected, the aftershock area gives a good estimate of
the rupture area of the main earthquake. Although the total
moment of the aftershocks is usually only a few per cent of the
main shock moment, aftershocks have been disproportionately
well studied due to the possibility of deployment of arrays after
the main earthquake. In fact, for several reasons, this method
may be more reliable than trying to find the fault dimensions by
272
the fitting of seismograms. Locating aftershocks is relatively
reliable and the methods to do this have been well established
for several decades. On the other hand, the inverse problem for
the earthquake source is intrinsically very unstable (Kostrov
& Das 1988), and until very recently, sufficiently high-quality
seismograms and with sufficiently good spatial coverage were
not available for a reliable estimate of the fault dimensions of
the main shock. Even for an Mw=8.0 earthquake as recently as
1989 (the Macquarie Ridge earthquake), Das (1993) showed
that the teleseismic seismograms were unable to constrain the
fault area, and aftershocks had to be used to constrain it
a priori. The 1998 Antarctic earthquake is the first one for
which the seismograms did constrain the fault rupture area
(Henry et al. 2000), and hence this is a very promising tool for
future global studies. Previously, only in land areas with a very
dense local network had it been possible to constrain rupture
areas by inverting seismograms. A recent study by Mai & Beroza
(2000) using this latter method included mainly Californian
earthquakes.
The main purpose of this paper is to obtain the aftershock
areas of many earthquakes worldwide using teleseismic data,
# 2001
RAS
Aftershock zones of large shallow earthquakes
and to discuss the properties of the aftershock areas and the
implications of the aftershock dimensions for the problem of
earthquake scaling.
2
EARTHQUAKE SCALING
How earthquakes scale with size is a problem of great
importance. Without knowing the relationship between fault
size and other source parameters, it would be impossible to
make ground motion predictions, essential for the construction
of earthquake-resistant structures, for large, infrequent earthquakes based on the recordings from smaller, more frequent
ones in the same region. Scaling relations are also often used to
estimate seismic moment from length or vice versa, a very recent
example being Parsons et al. (2000). Finally, scaling relations
provide insight into the mechanics of earthquake rupture. The
problem was first considered by Aki (1967), and has been a
subject of vigorous research since. The seismic moment M0 is
mūA, where m is the rigidity, ū is the mean slip and A is the fault
area. The rupture area on any planar fault can be approximated either by a rectangle or by an ellipse (a circle being a
special case of this). For a rectangular fault of length L and
width W, M0=mūLW. For an elliptical fault, M0=(p/4)mūLW,
where L and W are now the lengths of the axes of the ellipse.
Thus, in general, M0=CmūLW, where C is a geometrical factor
lying between about 0.75 and 1. Empirical scaling relations
found between M0 and fault dimensions can be used to make
inferences regarding the factors that control mean slip. For
small earthquakes, which may be defined as those with rupture
dimensions smaller than the down-dip width of the seismogenic
layer, LyW. Hanks (1977) compiled seismic moments and fault
radii, r, for 390 earthquakes, mostly from southern California,
in the range 1011 N m<M0<1020 N m, and found that M0 3 r3,
indicating that ū 3 r. The scaling for large earthquakes is
expected to be different.
In a seminal paper, Scholz (1982) discussed scaling relationships for large earthquakes. If the base of the fault is clamped
during the rupture, then slip is limited by the rupture width.
Scholz (1982) called this the ‘W model’. It implies mean slip
is constant for large earthquakes as long as the stress drop is
constant, so that M0 3 L. In any such model, rupture takes the
form of a travelling pulse of slip (Archuleta & Day 1980; Das
1981; Day 1982). If the base of the fault is free, then rupture
width places no limit on fault slip. Scholz (1982) called such a
model the ‘L model’ because slip in this case is controlled by
fault length. Theoretical calculations (Das 1982) show that if
the base of the fault is free, slip continues in the interior of an
expanding rectangular earthquake fault until a healing phase
arrives from the longer ends of the fault. Models that lead
to narrow pulses propagating along the fault can also lead to
the slip increasing with fault length (Cochard & Madariaga
1996), with a limit on slip being reached at very great lengths
(L/W>10) in some models (Shaw & Scholz 2001). If slip 3
length, then M0 3 L2. Scholz (1982) showed that the parameters of large earthquakes, compiled by Sykes & Quittmeyer
(1981), indicate that M0 3 L2, both for strike-slip earthquakes
in the moment range 3r1018 N m<M0<7r1020 N m and for
thrust earthquakes in the moment range 3r1020 N m<M0<
2r1023 N m, and interpreted this as supporting an L model.
The empirical finding of Scholz (1982) for strike-slip earthquakes was challenged by Romanowicz (1992). She identified a
transition from M0 3 L3 to M0 3 L at M0y0.7r1020 N m
#
2001 RAS, GJI 147, 272–293
273
(Ly60), favouring a W model for large events. This was
disputed by Scholz (1994a) and further discussed by Romanowicz
(1994) and Scholz (1994b). There is more of a consensus, based
on the limited available data, that at least the very largest
strike-slip earthquakes (L>200 km) have some restriction on
slip and tend towards M0 3 L scaling (Scholz 1994b; Bodin &
Brune 1996; Fujii & Matsu’ura 2000). Most empirical studies of
earthquake scaling, including all of those cited above, have
been based on compilations of earthquake parameters from the
literature, in some cases using measurements made using very
different methodologies. Pegler & Das (1996) have argued that in
the observational study of scaling relationships it is important
to analyse all earthquakes in a uniform manner. They compared Harvard CMT (centroid moment tensor) moments to
fault lengths measured from relocated aftershock distributions
for large crustal strike-slip earthquakes from 1977–1992. They
found that M0 3 L2 over the moment range 5r1017 N m
to 1.4r1021 N m, with no indication of a break in slope
at y7r1019 N m as observed by Romanowicz (1992), and
thereby supporting the original finding of Scholz (1982).
No study comparable to Pegler & Das (1996) has been
carried out for dip-slip earthquakes. The recent compilation of
earthquake data by Wells & Coppersmith (1994) uses subsurface length (primarily determined from aftershocks occurring from a few hours to a few days after the main shock) and
the seismically determined scalar moment for 50 thrust and
24 normal earthquakes from 1952–1993 in the moment range
2r1016 N m<M0<3r1020N m. For this magnitude range they
found that M0 3 L2.2 for thrust earthquakes and M0 3 L2.3 for
normal earthquakes. The study by Wells & Coppersmith (1994)
includes both intraplate and interplate earthquakes, but of the
thrust earthquakes only two were clearly interplate subduction
zone earthquakes. Many large dip-slip earthquakes have occurred
since 1977, several of which have M0<1021 N m, and which
to our knowledge have not been included in any similar
compilation. The combination of the Harvard CMT catalogue
and International Seismological Centre (ISC) hypocentre and
phase data is a rich resource for studies of earthquake scaling
that has not yet been fully utilized.
3 DATA SELECTION AND
METHODOLOGY
We carry out an analysis similar to Pegler & Das (1996) to
study 64 shallow dip-slip earthquakes from 1977–1996. We
extend the data range for the dip-slip earthquakes covered by
the Wells & Coppersmith (1994) study to earthquakes an order
of magnitude greater in moment, using a uniform method
of estimating aftershock areas and seismic moment. We also
supplement the strike-slip data Pegler & Das (1996) with eight
earthquakes from 1993–1996, the 1998 Antarctic earthquake, the
largest strike-slip earthquake since 1977 (based on its Harvard
CMT moment), the 1999 Izmit, Turkey earthquake and the
2000 Wharton Basin earthquake.
Aftershocks are relocated using ISC phase arrival time data,
which were available up to mid-1997 at the time this work was
carried out. The seismic moments used in this study are taken
from the Harvard CMT catalogue (Dziewonski et al. 1983–1998),
which commences in 1977. Accordingly, we restrict our study
to earthquakes in the period 1977–1996. We study all earthquakes with M0<1020 N m, except for five subduction zone
earthquakes for which the close proximity in space and time of
274
C. Henry and S. Das
another earthquake of similar or greater moment prevents the
determination of the aftershock dimensions. For smaller earthquakes we include only those for which we have a sufficient
number of aftershocks to be truly representative of the fault
length, usually with a few mbj4.0 aftershocks reported by the
ISC, so as not to underestimate the lengths of small earthquakes. Throughout this study, we shall always call L the fault
dimension along the strike of the aftershock zone, even for
the small number of cases for which the other dimension, W, is
longer.
Following Pegler & Das (1996), we use relocated 1 day
aftershock lengths as our preferred measure of fault length.
For almost all the earthquakes studied here, high aftershock
activity continues for significantly longer than 1 day, and thus
our measurements represent an early phase of the evolution of
the aftershock distribution. Although for some earthquakes in
this study there are sufficient early aftershocks to permit the
determination of the length after a shorter time period, say a
few hours, this is not possible for all earthquakes and we prefer
to use a uniform time period of 1 day for all earthquakes. We
determine also 7 day and 30 day lengths in order to examine
the expansion of aftershock areas with time. We relocate
aftershock sequences using primarily P arrivals, with some S
arrivals, other reported phase types being too few to be useable.
In particular, for the shallow earthquakes under consideration
here, reliable depth phase arrival times are not available. For
most earthquakes, we perform relocations using the method of
joint hypocentre determination (JHD) (Douglas 1967; Dewey
1971, 1983), using the algorithm JHD89, with modifications
to improve stability (discussed in the Appendix). We use the
P-wave traveltime tables determined by Herrin (1968), and
the Jeffreys–Bullen S-wave tables; we note that since the JHD
method evaluates corrections to these tables, the exact choice
of traveltime tables has little impact on the solutions, as any
systematic errors within one traveltime table, or any inconsistencies between P and S tables are absorbed into the corrections
(Dewey 1971, 1983). First we relocate a subset of the bestrecorded aftershocks, preferably using only those recorded by
30 or more stations, and typically using 20 such earthquakes,
and then we use the station corrections determined for these
earthquakes to relocate the smaller aftershocks. When 10 or
fewer aftershocks are recorded by 20 or more stations each, the
master event relocation method (Evernden 1969; Dewey 1971,
1983) is used instead.
Fig. 1(a) shows a sample measurement of length. The strike
used for measurements of length is determined from comparison of the CMT strike, the orientation of the aftershock
distribution and the trend of features in the local marine gravity
field (Sandwell & Smith 1997) or land topography (Gesch
et al. 1999). The exact choice of strike does not significantly
affect determinations of fault length. We select aftershocks by
magnitude, using different selection criteria for the measurement of aftershock lengths of dip-slip and strike-slip earthquakes, as is explained below. For the determination of length,
we use only aftershocks located with epicentral location errors
of <25 km, and in addition exclude any single aftershock with
a relatively large error if the end of the fault is well defined by
better-located earthquakes. We determine errors in the 1 day
length by finding the range of lengths consistent with the 90 per
cent confidence ellipses of aftershocks near the edges of the faults.
This takes into account the uncertainties in our relocations,
but does not take into account the possibility of incomplete
sampling of the underlying rupture area by aftershocks, and
also assumes that we have correctly identified the aftershocks
that are directly associated with the main fault.
In the JHD relocations, the main shock is used as the
calibration event and although it is fixed during the calculation
of station corrections, it can later be relocated using the station
corrections evaluated during the relocation process. In most
cases the main shock hypocentre does not move significantly,
which is expected since the station corrections are evaluated
relative to the main shock hypocentre. This does not necessarily
indicate that the original location is correct, but that a set
of station corrections for the whole aftershock sequence was
found that is consistent with the original location. In a few
cases, the main shock location does change, indicating that no
consistent set of station corrections exists using the original
location, and we regard the relocated main shock hypocentre as
an improvement on the original location. In every such case in
this study, the relocated main shock hypocentre lies, within its
90 per cent confidence ellipsoid, on the plane of the relocated
aftershocks, although often the unrelocated position does not,
confirming that the relocated main shock hypocentre and the
relocated aftershocks are self-consistent. Note that we will not
use any absolute location information in this study, except in a
single case where we shall discuss the seismogenic depth.
We use seismic moments from the Harvard CMT catalogue.
The formal errors in the Harvard moment tensors are small
(typically 2 per cent error in the seismic moment), and systematic
errors are likely to be much greater than this. However, we
have no means of reliably estimating the magnitude of these
errors and do not attempt to do so.
3.1 Dip-slip earthquakes
Since a major goal of this study is to consider the scaling
relations for dip-slip earthquakes, and since we also wish to
consider differences in aftershock behaviour between dip-slip and
strike-slip earthquakes, we consider only pure dip-slip earthquakes. Whilst it is clear that earthquakes with large strike-slip
components should not be included as they are not directly
comparable to pure dip-slip earthquakes, the selection of a
criterion for inclusion is somewhat arbitrary. The large numbers
of earthquakes for which ISC and Harvard CMT data are
available allow us to adopt the fairly conservative criterion that
the rakes of both fault planes must be within 15u of pure
dip-slip. An increase in our tolerance to 20u would have
resulted in the inclusion of about 15 additional earthquakes. Of
the five shallow dip-slip earthquakes from 1997–1996 with
M0i1021 N m that do not meet this strict criterion, we include
four, for each of which the shallow-dipping nodal plane has an
oblique component. These are the 1977 Sumba normal earthquake, and the 1979 Colombia, 1985 Chile and 1996 Biak subduction zone thrust earthquakes. The fifth is the 1994 Kurile
Islands thrust earthquake, which has a large oblique component on both nodal planes. We consider only crustal and
shallow subduction zone earthquakes with centroid depths
from the Harvard CMT catalogue in the range 0–70 km. Many
of the thrust earthquakes in this study are located in subduction zones with high levels of background seismicity, in
some cases recorded by regional networks capable of detecting
earthquakes of mb<3. At this magnitude level, the aftershock
area is not clearly distinct from background seismicity for
some earthquakes, particularly at longer time periods. For this
#
2001 RAS, GJI 147, 272–293
Aftershock zones of large shallow earthquakes
275
Figure 1. Example of measurement of L and W for the 1995 December 3 Kurile Islands earthquake. (a) Map view. The epicentre is shown by an open
star, with the Harvard CMT mechanism also shown. Aftershocks occurring within 1 day of the main shock are shown by solid circles with error
ellipses, and aftershocks occurring between 1 and 30 days are shown by crosses without error ellipses. Only aftershocks with mb<4 and with 90 per
cent epicentral confidence ellipses <25 km are shown. The 1 day aftershock length of 185 km is measured along an azimuth of 45u, the strike of the
NW-dipping nodal plane of the Harvard CMT solution. This strike is confirmed by the good alignment of the aftershocks at the up-dip (SE) edge of
the aftershock distribution. (b) Cross-section looking from the direction of the open arrow in (a). Same symbols as (a), but now showing only
aftershocks with 90 per cent hypocentral confidence ellipsoid <20 km, with less well-located aftershocks being rejected for this earthquake, as they are
not reliably associated with the fault plane. The 1 day aftershock width of 80 km is measured along the dip (12u) of the Harvard CMT solution, which
is confirmed by the aftershocks.
reason only aftershocks with mbi4.0 are used in the determination of fault length for dip-slip earthquakes. In addition
we consider this common choice of cut-off magnitude to provide more consistent measurements of length between different
#
2001 RAS, GJI 147, 272–293
geographical regions and time periods. For 1 day lengths, the
aftershock region can usually be clearly distinguished from the
background seismicity, and the length is usually insensitive to
the precise choice of cut-off magnitude.
276
C. Henry and S. Das
For dip-slip earthquakes we also estimate the fault width, as
this allows the influences of length and width on mean slip to be
examined separately. A sample measurement of width is shown
in Fig. 1(b). To determine the down-dip width of the
aftershock zone, the fault plane of the earthquake must be
unambiguously identified. For many earthquakes, the bestlocated aftershocks are clearly aligned, when looked at in crosssection, with one of the nodal planes of the Harvard CMT
solution. For a few cases, all but one dating from 1982 or
earlier, the aftershocks are clearly aligned but differ by up to
20u in dip from the nearest CMT nodal plane; in these cases the
dip of the aftershock zone is adopted in preference to the CMT
nodal plane. For some other earthquakes, the aftershocks are
not sufficiently well located or are too few in number for the dip
to be accurately determined from the aftershocks alone, but are
compatible with only one of the nodal planes of the CMT; in
these cases the dip of that nodal plane is adopted. When the
aftershocks cannot be used to distinguish between the two nodal
planes no measurement of width is made. In some cases aftershocks occur on more than one plane; if one of these can be
identified as the main shock fault plane, by the location of the
hypocentre, by the extension of only one of the planes along
the whole length of the earthquake or by the occurrence of
early aftershocks, then the width of only this plane is measured.
If the identification is not clear, no measurement of width is
made. The different qualities of reliability are clearly indicated
for each dip-slip earthquake in this study. Overall, the fault
plane can be identified, and the width measured, for 48 of the
64 dip-slip earthquakes of this study. For the 16 earthquakes
for which it is not possible to determine the fault plane, there is
no ambiguity in the determination of the fault length.
Once the fault plane has been identified, aftershocks with
uncertainties in depth sufficiently great that it is not clear
whether or not they lie on the fault plane are excluded from the
measurement of fault width. We also use only earthquakes that
have an uncertainty of <25 km in their location along the
down-dip direction. We determine errors in the measured width
from the uncertainties in the aftershock locations in the same
way as for the aftershock lengths. The errors in aftershock
width are in general greater than those for the aftershock
length, because small subduction zone aftershocks are in
general located better along strike than down dip, due to poor
azimuthal distribution of stations. In addition, for earthquakes
with few aftershocks, the measurement of width is more
sensitive than the measurement of length to the selection of
fault strike.
The dip-slip earthquakes in this study are classified by ‘type’,
based upon the moment tensor, a consideration of the aftershock distribution in relation to the historic seismicity and
known tectonics of their location, and in some cases on studies
of individual earthquakes taken from the literature. For subduction zone thrust earthquakes, we distinguish between ‘simple’
subduction interface earthquakes and those earthquakes that
occur in regions of more complex tectonics or whose aftershock
patterns are not well described by a single fault plane. The
parameters of dip-slip earthquakes are listed in Table 1, with
details on earthquake ‘type’ and quality of measured fault
width.
The greatest thrust earthquakes of this century have moments
up to 2 orders of magnitude greater than those of the largest
earthquakes since 1977, and where reliable determinations
of their parameters are available, we compare them with the
earthquakes of Table 1. The parameters of three such earthquakes are listed in Table 2, with references. For the 1957
Aleutian Islands, Alaska earthquake and the 1960 Chile earthquake, modern redeterminations of the moments are available.
Dimensions of these two earthquakes are measured for this
study from published aftershock relocations. For the 1964
Prince William Sound, Alaska earthquake, no recent redetermination of the moment is available, but two independent
determinations from the early 1970s are in broad agreement,
and the dimensions are determined from ISC aftershocks.
Thus the parameters of these three earthquakes are obtained by
methods similar to those used for the post-1977 earthquakes of
this study.
3.2 Strike-slip earthquakes
For strike-slip earthquakes we do not attempt to obtain the
rupture areas, but only determine the lengths. This is because
we are unable to obtain the earthquake depths accurately
enough for the shallow earthquakes (with ISC main shock
depth between 3 and 40 km) in this study. We determine L
following the method of Pegler & Das (1996) to maintain
comparability with that study. However, we note that several
earthquakes were included that did not meet the mechanism
selection criterion stated in the text of Pegler & Das (1996), so
that this criterion had not been strictly adhered to. We use a
revised criterion that the dip of both nodal planes must be
greater than 60u, but only one nodal plane is required to have a
rake within 15u of x180u, 0u or 180u. This criterion is chosen to
include both earthquakes with strike-slip motion on steeply
dipping planes and also strike-slip earthquakes on near-vertical
fault planes with a small component of dip-slip motion, but
to exclude oblique thrust or normal earthquakes. We discard
earthquakes from Pegler & Das (1996) that do not meet this
revised criterion. These are earthquakes 3, 8, 9, 10, 18, 23 and
27 of that study. We restrict the study to crustal earthquakes,
mostly with depths reported by the ISC as less than 33 km.
For the three earthquakes from 1998–2000, we use aftershocks
reported by the National Earthquake Information Center
(NEIC) and relocated by us using their phase data. Following
Pegler & Das (1996), we use all well-located aftershocks reported
by the ISC in the determination of length. For the 11 new
strike-slip earthquakes studied here, the lengths obtained using
all the aftershocks were in most cases not significantly greater
than the lengths that would have been obtained using only
the aftershocks with mbi4.0, as was used for the dip-slip
earthquakes. The parameters of strike-slip earthquakes from
1993–2000 are tabulated in Table 3. We determine errors for
the 1 day length measurements of Pegler & Das (1996) using
the results of the original JHD relocations performed for that
study.
4 AFTERSHOCK DIMENSIONS FOR
DIP-SLIP EARTHQUAKES
The aftershock extents of the dip-slip earthquakes along strike,
dip and depth are shown in Fig. 2. The data summarized in
Fig. 2(a) shows that the hypocentres are located on average
26 per cent of the 1 day length along strike from the nearest end
of the 1 day aftershock zone; this number is 23 per cent for
‘simple’ subduction earthquakes and 22 per cent for ‘simple’
subduction earthquakes with L>W. If the hypocentre is equally
#
2001 RAS, GJI 147, 272–293
#
Date
(mm/dd/yyyy)
03/21/1977
06/22/1977
08/19/1977
11/23/1977
03/23/1978
02/28/1979
10/23/1979
12/12/1979
02/23/1980
07/08/1980
07/17/1980
10/10/1980
10/25/1980
11/23/1980
04/24/1981
07/15/1981
03/21/1982
07/23/1982
05/26/1983
03/19/1984
03/03/1985
09/19/1985
10/05/1985
12/21/1985
12/23/1985
05/07/1986
10/23/1986
11/14/1986
03/02/1987
04/22/1987
10/16/1987
01/10/1989
02/10/1989
03/25/1990
03/08/1991
06/20/1991
11/19/1991
05/15/1992
07/10/1992
09/02/1992
12/12/1992
06/08/1993
07/12/1993
09/03/1993
09/10/1993
06/02/1994
01/19/1995
02/05/1995
05/13/1995
No.
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
S. Iran
S. of Tonga Isl.
SW. of Sumba Is.
San Juan, Argentina
Kurile Isl.
SE. Alaska
Solomon Islands
Off Colombia
Kuril Isl.
Santa Cruz Isl.
Santa Cruz Isl.
Algeria
Loyalty Isl.
S. Italy
Vanuatu Isl.
Vanuatu Isl.
Hokkaido, Japan
Off Honshu, Japan
Off Honshu, Japan
Uzbekistan
Central Chile
Michoacan, Mexico
NW. Terr., Canada
Vanuatu Isl.
NW. Terr., Canada
Andreanof Isl.
Santa Cruz Isl.
Off Taiwan
N. Is. New Zealand
Off Honshu, Japan
Off New Britain
Ceram
Molucca Passage
Costa Rica
N. Kamchatka
Off Minahassa Pen.
Colombia
Papua New Guinea
Kuril Isl.
Off Nicaragua
Flores Is.
Off S. Kamchatka
Off Hokkaido, Japan
Off Chiapas, Mexico
Off Chiapas, Mexico
Off Java
Colombia
Off N. Is., New Z.
N. Greece
Location
T
NIa
NI*
SI
S
Tb
SIc
S*
Sxd
S
S
T
S
N
S
S
SI
S
SI
TI
S*
S
TI
S
TI
Sxe
Sxf
SI
NI
S
S
S
Sxg
S
TI
Sxg
S
S
S
S
SI
S
SI
S
S
S
T
NI
N
Type
Table 1. Parameters of dip-slip earthquakes 1977–1996.
27.59
x22.91
x11.16
x31.04
44.70
60.74
x10.68
1.62
43.47
x12.49
x12.48
36.16
x21.78
40.86
x13.40
x17.29
42.23
36.36
40.48
40.35
x33.08
18.54
62.22
x13.98
62.19
51.54
x11.04
23.95
x37.93
37.14
x6.21
x3.15
2.29
9.96
60.86
1.19
4.60
x6.09
44.62
11.75
x8.47
51.18
42.89
14.57
14.74
x10.41
5.09
x37.66
40.17
Lat.
56.38
x175.74
118.41
x67.76
148.17
x141.55
161.35
x79.34
146.59
166.37
166.06
1.40
169.60
15.33
166.44
167.59
142.46
141.63
139.09
63.36
x71.72
x102.32
x124.26
166.51
x124.27
x174.84
165.19
121.76
176.78
141.44
149.06
130.61
126.78
x84.78
167.02
122.82
x77.41
147.57
149.48
x87.37
121.90
157.82
139.23
x92.81
x92.69
112.93
x72.94
178.89
21.69
Long.
19
61
23
21
28
19
31
20
34
44
34
10
29
14
44
30
37
27
13
15
41
21
10
46
15
31
15
33
15
33
48
29
44
18
15
15
19
40
31
15
20
46
17
27
29
15
16
15
15
Depth
(km)
21
2
38
47
69
54
16
20
13
19
17
19
43
48
13
43
66
61
160
21
49
18
20
15
29
96
20
28
373
13
14
9
39
4
26
9
5
15
9
75
66
3
246
13
33
35
5
286
177
1
048
017
115
164
231
089
024
069
040
036
029
038
117
122
021
080
131
094
319
041
254
045
047
033
066
181
031
052
585
026
022
019
052
009
045
011
016
033
018
149
100
017
900
022
066
137
014
678
446
7
0070
0031
0197
0263
0208
0138
0032
0111
0053
.
0051
0052
0140
0163
0023
0107
0174
0124
0509
0057
0679
0084
0065
0055
0091
0267
0033
0074
0661
0060
0027
0027
0069
0013
0050
0013
0029
0056
0027
0231
0133
0023
1608
.
0112
0228
0015
0808
0735
30
No. Aftershocks
33+10x4
75+10x10
160+14x14
70+13x4
100+10x10
85+5x2
37+8x8
260+23x16
25+10x10
50+20x4
150+23x14
40+9x5
95+10x8
65+8x5
75+23x19
100+16x10
21+7x3
38+11x11
130+9x5
36+18x18
174+25x15
140+15x13
34+17x7
30+15x9
40+12x8
4210+7x4
60+19x15
65+9x9
45+26x13
20+4x4
37+13x13
45+28x28
45+20x9
26+9x6
29+8x8
40+22x16
25+9x5
50+28x23
12+12x4
250+27x27
150+22x16
55+3x3
165+14x8
30+13x13
55+10x10
80+17x7
20+9x9
55+24x11
45+5x4
1
040
100
200
080
145
085
065
260
100
115
150
045
185
075
105
115
024
050
145
036
195
145
034
070
040
245
060
080
045
027
037
045
060
036
045
050
025
070
012
280
170
095
180
050
060
125
021
100
045
7
Length (km)
050
115
240
090
145
085
065
265
100
.
205
060
185
075
105
150
031
050
160
045
200
225
039
075
050
245
060
080
055
027
037
050
060
055
050
050
025
080
013
280
170
095
180
.
155
145
021
100
045
30
037
070
025
036
075
090
090
017
085
026
070
033
065
050
055
035
050
036
039
023
014
035
030
014
030
032
045
080
110
045
055
040
070
012
023
021
45+9x7
25+15x6
36+15x7
55+15x13
65+8x8
80+28x28
17+15x10
60+19x6
21+6x3
40+17x8
21+9x6
50+7x5
50+17x12
34+15x11
35+27x10
50+18x15
36+8x8
39+14x11
23+32x15
14+13x10
29+12x10
30+14x2
14+5x5
26+18x18
27+23x9
15+20x9
70+12x9
27+14x12
40+13x5
37+17x3
40+24x11
50+21x13
9+19x8
15+9x4
17+8x4
7
37+19x9
1
Width (km)
2001 RAS, GJI 147, 272–293
120
045
.
065
070
027
023
022
030
050
045
085
034
019
036
039
023
055
035
050
060
045
070
033
065
050
100
.
120
017
085
026
070
025
036
037
30
c
c
b
c
a
b
b
c
a
a
a
b
a
b
c
a
a
a
a
cw
a
b
c
b
c
c
b
b
b
a
b
cw
a
a
c
c
a
b
a
a
c
a
b
a
a
a
b
b
b
Q
0.140
13.900
35.900
1.860
2.690
1.880
0.349
16.900
0.559
1.970
4.840
0.507
1.860
0.247
0.225
0.576
0.264
0.392
4.550
0.347
10.310
10.990
0.084
0.569
0.152
10.360
0.143
1.300
0.064
0.108
1.260
0.116
0.545
1.101
0.101
2.310
0.732
0.809
0.074
3.400
5.060
2.020
4.650
0.149
0.834
5.340
0.071
0.584
0.076
M0
(1020 N m)
6.7
8.0
8.3
7.4
7.6
7.5
7.0
8.1
7.1
7.5
7.7
7.1
7.4
6.9
6.8
7.1
6.9
7.0
7.7
7.0
7.9
8.0
6.6
7.1
6.7
7.9
6.7
7.3
6.5
6.6
7.3
6.6
7.1
7.3
6.6
7.5
7.2
7.2
6.5
7.6
7.7
7.5
7.7
6.7
7.2
7.8
6.5
7.1
6.5
Mw
Aftershock zones of large shallow earthquakes
277
05/16/1995
06/15/1995
07/30/1995
08/16/1995
09/14/1995
10/09/1995
11/24/1995
12/02/1995
12/03/1995
02/17/1996
02/21/1996
04/29/1996
06/10/1996
06/21/1996
07/15/1996
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
Loyalty Isl.
N. Greece
N. Chile
Solomon Isl.
Guerrero, Mexico
Jalisco, Mexico
Kurile Isl.
Kurile Isl.
Kurile Isl.
Biak Is.
Off Peru
Solomon Isl.
Andreanof Isl.
Off Kamchatka
Guerrero, Mexico
Location
N
N
S
Sxh
S
S
S
S
S
S*
Sxi
Sxj
S
S
S
Type
Long.
169.89
22.27
x70.21
154.17
x98.60
x104.20
149.11
149.21
149.31
136.95
x79.77
155.04
x177.61
159.08
x101.05
Lat.
x22.98
38.40
x23.30
x5.82
16.88
19.12
44.43
44.29
44.53
x0.94
x9.69
x6.54
51.55
51.55
17.57
25
15
29
46
22
15
34
16
26
15
15
54
29
24
22
Depth
(km)
142
244
107
72
11
19
3
67
219
301
11
22
157
27
6
1
204
271
177
199
021
034
020
.
330
570
025
087
255
146
008
7
0232
0468
0204
0281
0035
0045
.
.
0439
0682
0034
0129
0304
0200
0010
30
No. Aftershocks
135+32x13
9+4x4
205+23x23
135+22x12
32+16x10
140+12x5
18+5x5
31+14x5
185+15x8
290+20x20
125+20x20
39+20x13
150+12x8
30+7x5
13+5x5
1
160
012
240
135
032
145
030
.
185
315
125
095
160
060
013
7
Length (km)
185
020
240
135
040
160
.
.
195
315
125
095
160
075
013
30
075
013
085
040
040
033
.
085
050
065
040
031
37+24x15
39+20x17
55+12x8
80+12x7
50+14x13
65+9x7
24+10x6
27+12x9
7
75+12x7
13+8x5
85+21x10
1
Width (km)
070
052
031
050
040
.
.
085
050
075
013
085
30
a
b
b
c
a
a
a
a
a
a
c
cw
a
a
b
Q
3.900
0.060
12.150
4.620
1.310
11.470
0.081
0.088
8.240
24.100
2.230
0.755
8.050
0.146
0.099
M0
(1020 N m)
7.7
6.5
8.0
7.7
7.3
8.0
6.5
6.6
7.9
8.2
7.5
7.2
7.9
6.7
6.6
Mw
‘Off’ in place name means ‘Off the coast of’. Earthquake types: S=simple interplate subduction zone thrust earthquake, defined here to be an earthquake that, based on its focal mechanism and aftershocks, occurs on a
plane within, and parallel to, a Wadati–Benioff zone; Sx=complex interplate subduction earthquake, with the reason for its classification as complex given in a footnote; T=other interplate thrust earthquake;
SI=subduction-related intraplate thrust earthquake; TI=other thrust intraplate earthquake; N=normal interplate earthquake (including regions of continuous deformation); NI=normal intraplate earthquake.
Asterisks denote earthquakes that do not meet the strict rake criterion discussed in the text. Epicentral coordinates are from the ISC bulletin, centroid depths are from the Harvard CMT catalogue. Numbers of
aftershocks and aftershock area dimensions are given after time periods of 1, 7 and 30 days, as indicated. Uncertainties in the 1 day dimensions are given as the maximum increase(+) followed by the maximum
decrease(x) in the best value. Q is width quality: a=dipping zone clearly visible in aftershocks, b=correct nodal plane of CMT can be identified from aftershocks, c=fault plane could not be identified; cw indicates
that the width of the aftershock zone is greater than its length. ‘ . ’ indicates that a measurement could not be made, either because a subsequent event of similar size precludes measurements at later times or because
there are insufficient well-located early aftershocks.
a
Cuts across a subducting slab, with aftershocks mostly in the plane of the Wadati–Benioff zone.
b
Length is measured along the trend of the aftershocks, 40u from the CMT strike.
c
Cuts across a subducting slab.
d
Length is measured along the trend of the aftershocks, 30u from the CMT strike, which lie on a subducting feature of the ocean floor.
e
The hypocentre is at the upper limit of the Wadati–Benioff zone, and the aftershocks do not lie on a single plane.
f
At the junction of a subduction zone and a transform fault.
g
Both in complex regions with multiple subduction zones.
h
At the junction of two subduction zones.
i
1 day aftershocks cut across subducting slab, which conflicts with other studies of this earthquake; see text for details.
j
Aftershocks lie on two intersecting planes, one of which, containing the hypocentre, coincides with the Wadati–Benioff Zone.
Date
(mm/dd/yyyy)
No.
Table 1. (Continued.)
278
C. Henry and S. Das
#
2001 RAS, GJI 147, 272–293
Aftershock zones of large shallow earthquakes
279
Table 2. Parameters of great pre-1977 thrust earthquakes.
Date
(mm/dd/yyyy)
03/09/1957
05/22/1960
03/28/1964
Location
No. aftershocks
Aleutian Isl., Alaska
Chile
Prince Wm. Sound, Alaska
Length (km)
Width (km)
1
7
30
1
7
30
1
7
30
023a
011c
195e
083
019
489
127
028
775
790
700
845
1000
0930
0855
1000
0930
0855
090
240
190
145
240
190
145
240
200
M0
(1020 N m)
Mw
0088b
3200d
0750f
8.6
9.6
9.2
All aftershock lengths and widths were remeasured for this study, using the aftershock data from the sources indicated.
a
Aftershock data from Boyd et al. (1995). They estimate their magnitude of completeness as MS=5.5, although a small number of aftershocks have much lower
magnitudes. Note that the length of the aftershock zone until 22 hr after the main shock is 590 km.
b
Johnson et al. (1994), from inversion of tsunami data. A seismological determination using the only available non-nodal surface wave seismogram gives
50r1020 N m.
c
Aftershock data from Cifuentes (1989). The smallest aftershocks for which magnitudes are given have MS=5.8
d
Cifuentes & Silver (1989), from inversion of normal modes. This moment does not include the inferred slow precursor to this event.
e
Aftershock data from the ISC, with dimensions measured using only those aftershocks with mbi4. Aftershocks were not relocated, since the spatial extent of
the aftershock zone is large in comparison to typical distances to stations, and the assumptions underlying JHD are therefore not valid.
f
Kanamori (1970), from inversion of surface waves. Ben-Menahem et al. (1972) obtain 1000r1020 N m from analysis of normal modes; this result is
independent of their later choice of the vertical nodal plane as the rupture plane of the event. This difference in moment is not significant on the scale of
Fig. 7(b).
likely to occur at any position along strike, then the hypocentre
has uniform probability of occurring at any distance between 0
and 50 per cent from the closest end; thus the mean distance
from the closest end will be 25 per cent, very close to the values
we observe. For the six great subduction earthquakes, with
Mw<8.5, studied by Pérez & Scholz (1997), which include the
three great earthquakes of Table 2, the hypocentres occur on
average 20 per cent of the rupture length from the nearest end
of the rupture zone defined by aftershocks. Pérez & Scholz
(1997) comment that the hypocentres of these great earthquakes occur near the ends of the rupture. The data do support
this, but the difference between this and the mean location
predicted from an assumption of random hypocentre location
is small.
The patterns of aftershock area expansion of subduction and
non-subduction zone earthquakes are found to be different.
Since the numbers of earthquakes of each type of nonsubduction earthquake (SI, T, TI, N and NI) are too few to
draw firm conclusions about each individual type, we shall
discuss them collectively as non-subduction zone earthquakes.
Some of the earthquakes classified as ‘complex’ may not be
directly comparable to the ‘simple’ subduction zone earthquakes, but it is unclear whether they should be grouped with
the other dip-slip earthquakes. The 7 day length of ‘simple’ subduction zone earthquakes is on average 31 per cent greater
than the 1 day length, with the 30 day length being 43 per
cent greater. For non-subduction zone earthquakes the length
increases by an average of 20 and 37 per cent over the same
time periods, respectively. Earthquakes in Fig. 2(a) are oriented
so that the end of the 1 day aftershock zone that is furthest
from the hypocentre along strike lies in the positive direction
along the ordinate. This direction corresponds to the principal
horizontal direction of propagation of each earthquake. We
may consider earthquakes with L>W and with their hypocentres lying outside the central third of the 1 day aftershock
zone to be earthquakes unilaterally propagating in the horizontal direction. The expansion of aftershock zones is seen to
be strongly asymmetric for non-subduction zone unilateral
earthquakes. For these earthquakes, between 1 and 30 days,
the aftershock zone extends by an average 23 per cent of
the 1 day length in the direction opposite to the propagation
direction, but only 8 per cent in the propagation direction. This
Table 3. Parameters of strike-slip earthquakes 1993–1996
No.
65
66
67
68
69
70
71
72
*73
*74
*75
Date
(mm/dd/yyyy)
06/05/1994
12/15/1994
01/16/1995
03/19/1995
05/27/1995
10/23/1995
07/16/1996
07/23/1996
03/25/1998
08/17/1999
06/18/2000
Location
Off Taiwan
Off N. Is., New Z.
Honshu, Japan
W Irian
Sakhalin Is.
Szechwan, China
Off Kamchatcka
Off Kermadec Isl.
NW of Balleny Is.
Turkey
Wharton Basin
Lat.
24.46
x37.46
34.55
x4.16
52.60
25.99
56.05
x26.91
x62.88
40.75
13.80
Long.
121.86
177.59
135.04
135.09
142.85
102.24
165.00
x177.18
149.53
29.86
97.45
ISC Depth.
(km)
20
11
19
39
8
3
37
44
10
17
10
No. Aftershocks
Length (km)
1
7
30
1
7
30
21
104
394
34
20
16
12
8
25
59
11
41
190
596
49
40
33
13
11
43
84
19
60
239
721
55
48
42
15
15
54
122
20
17+12x8
34+14x7
55+6x3
80+11x11
65+12x10
28+11x8
40+18x6
30+25x18
315+5x5
90+9x3
100+25x25
17
34
55
80
65
28
40
30
315
105
105
20
34
60
80
70
29
40
30
325
105
105
M0
(1020 N m)
Mw
0.038
0.033
0.243
0.225
0.432
0.022
0.072
0.059
17.000
2.880
7.910
6.3
6.3
6.9
6.8
7.0
6.2
6.5
6.5
8.1
7.6
7.9
Aftershock numbers and fault lengths are given as for Table 1.
* For these earthquakes, no ISC data were available at the time the study was carried out. Hypocentre given is from NEIC, and lengths are measured from
aftershocks relocated using NEIC phase data.
#
2001 RAS, GJI 147, 272–293
280
C. Henry and S. Das
Figure 2. Aftershock extents of dip-slip earthquakes, labelled along the abscissa with their index number from Table 1. Earthquakes are grouped
according to the tectonic ‘types’ defined in Table 1, as indicated along the base of the figure. 1 day dimensions are shown by shaded bars and 30 day
dimensions are shown by open bars. Hypocentre locations are shown by open circles. The three pre-1977 earthquakes are labelled with their year of
occurrence, and the 22 hr aftershock dimensions of the 1957 earthquake are shown by a solid line. (a) Extent of aftershock zone along strike from
hypocentre, with each earthquake oriented so that the end of the 1 day aftershock zone that is furthest from the hypocentre is in the positive distance
direction. (b) Extent of aftershock zone up dip from hypocentre for those earthquakes for which width was determinable. (c) Absolute depth extent of
aftershock zones, determined from up-dip extent of aftershock zone and fault dip.
#
2001 RAS, GJI 147, 272–293
Aftershock zones of large shallow earthquakes
asymmetry could reflect either differences in the pattern of
stress change beyond the edges of the main shock rupture zone
due to differing slip distributions at the two ends of a unilateral
rupture, or different material properties, since the termination
of the rupture in the forward direction has presumably been
subjected to, and resisted, greater dynamic stresses than the
termination in the reverse direction. For unilateral ‘simple’
subduction zone earthquakes the asymmetry has the opposite
sense, but is very slight and may not be significant: between 1
and 30 days, aftershock zones expand by an average of 13 per
cent in the direction opposite to propagation and 18 per cent in
the direction of propagation. Fig. 2(b) shows that the ‘simple’
subduction earthquakes mostly initiate at or near the base
of the aftershock zone, with some initiating in the middle of
the depth range of the fault. No ‘simple’ subduction zone
earthquakes initiate at the top edge of the fault, although a few
initiate in the upper quarter of the depth range. This reconfirms
the observation of Kelleher et al. (1973) that subduction earthquakes usually initiate on the landward side of their aftershock
zones. Das & Scholz (1983) have explained this using the fact
that both stress drop and fault strength increase with depth
in the Earth. They showed, using numerical modelling, that
ruptures can propagate up dip easily due to the greater release
of strain energy at deeper regions but are inhibited from
propagating into higher stress drop regions down dip, and thus
small shallow earthquakes cannot generally develop into great
earthquakes. Our results show that most of the subduction zone
earthquakes do propagate upwards, but with some initiating at
mid-range and propagating both up and down dip. Many of
the largest subduction earthquakes fall in the latter category.
The aftershock width is seen in most cases to expand significantly only in the up-dip direction (Fig. 2b), with a notable
exception being earthquake 13. The aftershocks of several
earthquakes with very small 1 day depth extents later expand
significantly up dip. It is interesting to note that for the majority
of the subduction earthquakes with 1 day widths >60 km, the
width of the aftershock zone does not increase substantially
in the time period 1–30 days. For earthquakes with lower 1 day
widths, the width often increases substantially in this time period.
For most non-subduction earthquakes, the aftershock zone
does not expand in width between 1 and 30 days. This may
indicate that most of these earthquakes extend across the whole
of the local seismogenic zone. Other than type S, earthquakes
initiate at a range of depths, with a few initiating at the up-dip
edge of the aftershock zone. The latter include earthquake 27, a
‘complex’ subduction zone earthquake occurring in the ‘double
subduction zone’ of the Molucca passage, and earthquake 7,
the only thrust earthquake of this study identified as cutting
across a subducting slab.
In Fig. 2(c), depth extents are calculated from the down-dip
widths of the aftershock zones and plotted at their absolute
depths. These ranges represent the depth extent of the identified
fault plane for each earthquake. This is preferable to making a
direct measurement of the depth extent of the aftershock zone,
especially for shallow-dipping subduction zone earthquakes,
since vertical errors are large (on average t30 km at 90 per
cent confidence) in comparison to the depth extents of most
earthquakes. We plot the depth extents relative to the relocated
main shock hypocentral depths in Fig. 2(c); this is the only
use of absolute location information in this study, all other
measurements being relative to the location of the main shock
hypocentre.
#
2001 RAS, GJI 147, 272–293
281
Most ‘simple’ subduction earthquakes are seen to have their
lower edges at or above y50 km depth. Some exceptions are
discussed next. For earthquake 38 the CMT depth is 40 km,
it has a large depth extent, and two well-located aftershocks
occur 20 km above the upper termination of the fault plane, so
its lower edge must be at a depth of at least 50 km, and possibly
more. For earthquake 42, the CMT depth of this earthquake is
46 km, and it has a depth extent of 60 km, providing additional
evidence for a relatively deep initiation. For earthquake 5, the
CMT depth is 28 km, suggesting that the ISC depth of 56 km,
which was not significantly altered by relocation, is too large.
For the three pre-1977 great subduction earthquakes of Table 2,
neither the dip nor the depths of aftershocks are very well
known; the extents shown in Fig. 2(c) are based, for the 1957
and 1960 earthquakes, on dips taken from the references
to Table 2, which were assigned on the basis of the regional
seismicity, and for the 1964 earthquake on a dip consistent
with the ISC aftershocks. The absolute depths shown in
Fig. 2(c) for these three earthquakes are consistent with the
regional tectonics. The base of the rupture area for most nonsubduction earthquakes is significantly shallower than 50 km.
Of those approaching or exceeding 50 km, earthquake 7 cuts
across a subducting slab (as mentioned earlier), and initiates at
its upper edge. For the normal earthquake 50 occurring at the
junction between a subduction zone and a transform fault,
the depth extent is clear from its relocated aftershocks. For
earthquake 3, the 1977 Sumba earthquake, the ISC hypocentral
depth is 78 km. Lynnes & Lay (1988) give a hypocentral depth
of 25–30 km for this earthquake, and also presented evidence
from body wave modelling for a rupture extending from the
surface to a maximum depth of 30–50 km. The largest aftershocks have also been shown to have depths of less than 30 km
(Fitch et al. 1981; Spence 1986). The earthquake generated a
large tsunami and thus must have extended close to the surface.
On the basis of these studies we consider the ISC hypocentral
depth and our relocated hypocentral depth of 67 km to be too
large.
The observation in Fig. 2(c) that for most subduction earthquakes the maximum depth of rupture is at or shallower than
50 km may suggest that this limit is related to the subduction
interface seismogenic depth. It is interesting to note that had
we used a cut-off in centroid depth of 150 km rather than
70 km when choosing earthquakes for analysis, we would have
obtained only two more earthquakes satisfying our other
selection criteria (such as mechanism, number of aftershocks,
etc.) in the 20 yr time period covered by this study; thus this
depth limit is not an artefact of our event selection.
Earthquake 60 (Mw=7.5), which occurred in 1996 off the
coast of northern Peru, deserves special mention. Due to the
location of this earthquake, the station distribution used in
the relocations is much worse than most other earthquakes of
this study. By analysing broad-band body waves, Ihmlé et al.
(1998) obtained a centroid depth of 7t2 km for this earthquake. The earthquake generated a fairly large tsunami for its
moment (Ihmlé et al. 1998; Heinrich et al. 1998), indicating
significant slip at shallow depths. The ISC hypocentre is located
at 13 km but the poor azimuthal distribution does not allow
reliable relocation of it using the JHD method. Even though we
do not know the absolute depth of the hypocentre, we can still
consider its position relative to the aftershocks. The relocated
1 day aftershocks extend 70 km below the hypocentre, with
depth errors of t20 km for the best-located aftershocks. The
282
C. Henry and S. Das
30 day aftershocks form a diffuse cloud, with all well-located
aftershocks lying below the hypocentre. This strongly suggests
mainly downward rupture propagation. According to our
criterion of identifying the fault plane from the early aftershocks, we would select as the fault plane that nodal plane of
the CMT solution that dips 76uE. This is opposite to the dip of
the subduction zone. Ihmlé et al. (1998) used the nodal plane
consistent with the subduction zone dip as the fault plane in
their study. The surface wave fits to the data are not reported by
them and the P waves are poorly modelled. Most importantly,
no analysis attempting to use the vertically dipping nodal plane
as the plane of faulting is reported by them. Our experience
with the 1998 Antarctic earthquake (Henry et al. 2000) showed
that reasonably good fits can be obtained mistakenly using the
auxiliary plane as the fault plane. Moreover, Ihmlé et al. (1998)
find mainly up-dip propagation, which contradicts our earlier
suggestion based on the position of the hypocentre relative to
the aftershocks that the rupture propagated mainly downwards. Further work on this earthquake is clearly beyond
the scope of this study, and a more thorough analysis such as
that carried out by Henry et al. (2000) for the 1998 Antarctic
earthquake would be necessary to resolve this.
5 AFTERSHOCK LENGTHS FOR
SHALLOW STRIKE-SLIP
EARTHQUAKES
The extents along strike of the strike-slip earthquakes from this
(Table 3) and from Pegler & Das (1996) are shown in Fig. 3.
On average, the hypocentre is 26 per cent of the 1 day aftershock length from the nearest end of the fault, which is the
same result as that obtained above for dip-slip earthquakes.
The difference between the three lengths determined after 1, 7
and 30 days is insignificant for most of these earthquakes.
6 NUMBER AND MAGNITUDE OF
AFTERSHOCKS
It has been noted before that the number and magnitude of
aftershocks can be very variable for different earthquakes.
Here we carry out a comprehensive study of the aftershock
magnitude and number for the 102 post-1977 earthquakes in
this study in order to determine if such differences depend on
the tectonic regime in which the earthquake occurs. We only
consider aftershocks with Mwi5.0, with Mw taken from the
Harvard CMT catalogue. In particular, we do not use the body
wave magnitudes assigned to aftershocks by the ISC as they are
less reliable. Tables 4 and 5 give the number of aftershocks with
Mwi5.0 for the 1, 7 and 30 day periods, as well as the number
of aftershocks for the 30 day period in the magnitude ranges
5.0jMw<6.0, 6.0jMwj7.0 and Mwi7.0 for dip-slip and
strike-slip earthquakes, respectively. However, we note that
the annual number of shallow (<70 km) earthquakes in the
magnitude range 5.0jMw<6.0 for which a Harvard CMT
solution was obtainable has more than doubled between 1977
and 1999. For the other magnitude ranges the number has
remained steady with time, indicating that the CMT catalogue
is complete for Mwi6.0. The most rigorous comparison can
therefore only be made for aftershocks with Mwi6.0.
The number of aftershocks with Mwi6.0 for the 30 day
period following the main shock is plotted against M0 in Fig. 4.
We see that subduction zone earthquakes have larger and more
numerous aftershocks than all other types of earthquakes.
We see no distinction between non-subduction interplate and
intraplate earthquakes, nor between non-subduction oceanic or
continental earthquakes, nor between non-subduction dip-slip
and strike-slip earthquakes. The same pattern is also seen when
the aftershocks with 5.0jMw<6.0 are included (not shown).
The largest subduction zone earthquakes have a large variability
in numbers of Mwi6 aftershocks. A majority have one or
two such aftershocks, but several have more. The 1985 Chile
earthquake (earthquake 21 of Table 1) has seven Mwi6 aftershocks, the greatest number for any earthquake in this study,
its largest aftershock having Mw=7.4. The 1977 Sumba normal
intraplate earthquake (earthquake 3 of Table 1) has five aftershocks with Mw<6, all other non-subduction earthquakes
having two or fewer.
7 IMPLICATIONS FOR EARTHQUAKE
SCALING
7.1 Strike-slip earthquakes
Figure 3. Same as Fig. 2(a) but for strike-slip earthquakes, labelled
with their index number from Table 3. Selected data from Pegler & Das
(1996), using hypocentral locations from Pegler (1995), are also shown.
The 1 day length L is plotted against M0 for the strike-slip
earthquakes of this study in Fig. 5(a), together with the data
of Pegler & Das (1996). Since we have shown that aftershock
lengths of strike-slip earthquakes do not expand substantially
over time, the choice of time period has essentially no impact
on our results. Fig. 5(b) shows the uncertainties in the data,
together with the line of best fit, which has a slope of 0.37, close
to 1/3. Lines of slope 1, 1/2 and 1/3 are shown for reference.
Lines of slope 1 are clearly not consistent with the data, and
there is no sign of a change in slope within the range of the
data, ruling out the scaling M0 3 L, which has been proposed
by Romanowicz (1992) on the basis of non-uniform data sets
compiled from the literature. The data are probably not sufficient
to distinguish slopes in the range 1/2–1/3, allowing an exponent
#
2001 RAS, GJI 147, 272–293
Aftershock zones of large shallow earthquakes
Table 4. Numbers of aftershocks of dip-slip earthquakes.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
Table 5. Numbers of aftershocks of strike-slip earthquakes.
Date
(mm/dd/yyyy)
Mw
n1
n7
n30
5 6
n
6 7
n
7
03/21/1977
06/22/1977
08/19/1977
11/23/1977
03/23/1978
02/28/1979
10/23/1979
12/12/1979
02/23/1980
07/08/1980
07/17/1980
10/10/1980
10/25/1980
11/23/1980
04/24/1981
07/15/1981
03/21/1982
07/23/1982
05/26/1983
03/19/1984
03/03/1985
09/19/1985
10/05/1985
12/21/1985
12/23/1985
05/07/1986
10/23/1986
11/14/1986
04/22/1987
10/16/1987
01/10/1989
02/10/1989
03/25/1990
03/08/1991
06/20/1991
11/19/1991
05/15/1992
07/10/1992
09/02/1992
12/12/1992
06/08/1993
07/12/1993
09/03/1993
09/10/1993
06/02/1994
01/19/1995
02/05/1995
05/13/1995
05/16/1995
06/15/1995
07/30/1995
08/16/1995
09/14/1995
10/09/1995
11/24/1995
12/02/1995
12/03/1995
02/17/1996
02/21/1996
04/29/1996
06/10/1996
06/21/1996
07/15/1996
6.7
8.0
8.3
7.4
7.6
7.5
7.0
8.1
7.1
7.5
7.7
7.1
7.4
6.9
6.8
7.1
6.9
7.0
7.7
7.0
7.9
8.0
6.6
7.1
6.7
7.9
6.7
7.3
6.6
7.3
6.6
7.1
7.3
6.6
7.5
7.2
7.2
6.5
7.6
7.7
7.5
7.7
6.7
7.2
7.8
6.5
7.1
6.5
7.7
6.5
8.0
7.7
7.3
8.0
6.5
6.6
7.9
8.2
7.5
7.2
7.9
6.7
6.6
2
0
2
0
2
0
0
1
1
3
0
1
3
0
1
1
1
1
0
1
5
0
0
3
1
1
4
1
0
0
0
5
1
0
0
0
0
0
2
1
0
0
1
0
2
1
4
0
2
0
1
4
0
0
0
2
0
4
0
1
1
0
0
3
2
9
2
5
1
1
1
2
3
2
2
9
1
1
2
3
2
1
1
7
2
0
5
1
8
4
1
0
1
0
7
1
0
2
0
2
1
5
2
3
2
1
2
13
2
10
2
8
0
9
12
0
1
2
04
03
14
04
05
01
01
03
03
.
03
03
09
01
01
02
03
04
05
01
14
03
00
06
01
09
04
01
01
01
00
09
01
00
02
01
03
01
11
02
04
02
.
06
19
02
14
02
08
00
12
16
00
02
.
.
09
14
00
12
10
10
01
03
03
09
04
03
01
01
01
02
.
01
02
06
01
01
02
03
03
04
01
07
02
00
04
01
08
02
00
01
01
00
09
01
00
02
01
03
01
10
02
03
02
.
05
14
02
13
02
06
00
10
12
00
02
.
.
07
10
00
08
09
08
01
1
0
5
0
1
0
0
2
1
.
2
1
3
0
0
0
0
1
1
0
6
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
.
1
5
0
1
0
2
0
2
3
0
0
.
.
2
4
0
4
0
2
0
0
0
0
0
1
0
0
0
0
.
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.
0
0
0
0
0
0
0
0
1
0
0
.
.
0
0
0
0
1
0
0
.
6
9
0
10
9
8
1
n
Numbers in the first column refer to Table 1 of this study. Mw is listed for
the main shock. n1, n7 and n30 are the numbers of aftershocks with Mwi5
occurring in 1, 7 and 30 days, respectively. 5n6, 6n7 and 7n are the numbers of
aftershocks occurring in 30 days with 5jMw<6, 6jMw<7 and 7jMw,
respectively. ‘ . ’ indicates that a subsequent event of similar size precludes
counting the aftershocks at later times.
#
2001 RAS, GJI 147, 272–293
283
65
66
67
68
69
70
71
72
73
74
75
1
2
4
5
6
7
11
12
13
14
15
16
17
19
20
21
22
24
25
26
28
29
30
31
32
33
34
Date
(mm/dd/yyyy)
Mw
06/05/1994
12/15/1994
01/16/1995
03/19/1995
05/27/1995
10/23/1995
07/16/1996
07/23/1996
03/25/1998
M73
08/17/1999
06/18/2000
6.3
6.3
6.9
6.8
7.0
6.2
6.5
6.5
8.1
08/06/1979
09/12/1979
M2
06/09/1980
11/08/1980
05/25/1981
12/19/1981
08/06/1983
04/24/1984
09/10/1984
03/09/1985
05/10/1985
11/17/1985
02/08/1987
11/30/1987
03/06/1988
11/06/1988
05/23/1989
M22
03/03/1990
05/20/1990
06/14/1990
07/16/1990
08/17/1991
03/13/1992
04/06/1992
06/28/1992
M32
08/07/1992
11/06/1992
5.7
7.5
7.6
7.9
6.3
7.3
7.6
6.8
6.6
6.2
6.6
6.1
7.2
7.1
7.3
7.8
7.7
7.0
8.0
7.6
7.1
7.1
7.7
7.0
6.6
6.7
7.3
6.8
6.0
n7
n30
5 6
1993–2000
0
0
0
0
0
0
1
3
1
1
0
0
0
0
2
2
1
4
0
2
0
1
0
2
0
0
0
4
3
0
0
3
5
2
3
2
1977–1992
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
1
4
6
1
3
0
1
1
1
0
7
0
3
0
0
0
2
1
1
2
9
0
0
0
1
2
2
1
4
0
3
0
0
0
0
0
1
0
0
0
3
2
1
0
0
1
2
2
11
4
1
4
9
3
1
2
2
12
0
1
3
5
3
0
0
n1
n
7
0
0
0
4
3
0
0
2
4
2
3
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
1
2
1
10
4
1
3
9
3
1
0
2
10
0
1
3
4
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
n
6 7
n
Numbers in the first column refer to Table 3 of this study for the period
1993–1996 and to Table 1 of Pegler & Das (1996) for 1977–1992. Other
columns are the same as in Table 4. For earthquakes that have many
aftershocks on a feature that is clearly distinct from the main fault plane, the
aftershocks on the main plane only are also counted and listed separately
with an ‘M’ prefixed to the index number.
of 2–3 in the scaling relation of L to M0. For the large strikeslip earthquakes, the saturation of fault width at 10–15 km
allows inferences about slip to be made directly from the
observed scaling of length with moment. Then, our rejection
of M0 3 L implies a rejection of fault models where slip is
independent of length. If M0 3 L2, this would imply that slip
is proportional to length. If the exponent in the scaling relation is
in fact greater than 2, as indicated by the best fit to the data, then
this may indicate that the increase of slip with length is faster
than linear, or a slight increase in fault width for the largest
strike-slip earthquakes, beyond the 10–15 km widths observed
for smaller earthquakes (Scholz 1982; Wells & Coppersmith
1994). We do not favour the latter explanation due to the fact
284
C. Henry and S. Das
Figure 4. Plot of number of Mwi6 aftershocks occurring in a 30 day time period against main shock Mw for both strike-slip and dip-slip
earthquakes. Symbols refer to different types of earthquakes, as shown in the key. Earthquakes with one or more aftershocks of this magnitude are
numbered: for dip-slip earthquakes, bold numbers refer to Tables 1 and 4; for strike-slip earthquakes after 1993, bold numbers refer to Tables 3 and 5;
for strike-slip earthquakes before 1993, italic numbers refer to Table 5 and to Table 1 of Pegler & Das (1996).
that recent well-studied earthquakes do not appear to exceed
the normal seismogenic width. For the 1998 Antarctic intraplate earthquake (earthquake 73 of this study), no perceptible
slip occurred below 15 km (Henry et al. 2000). A width greater
than the depth of the Moho has been inferred for the 1989
Macquarie ridge earthquake (earthquake 22 of Pegler & Das
1996) by Anderson & Zhang (1991) from a centroid depth
of 15–28 km obtained from surface waves, but Das (1993) has
shown that the body waves of this earthquake could be explained
without the requirement of any moment release below the
Moho. Finally, the range of lengths of strike-slip earthquakes
since 1977 is not sufficient to address the possibility of saturation
of slip for L>200 km as proposed by Scholz (1994b).
We have identified in Fig. 5 intraplate earthquakes that
are not associated with regions of continuous deformation. It
can be seen that these generally have short lengths for their
seismic moments, corresponding to higher stress drops. The
one exception to this is the 1998 Antarctic earthquake, which
has a comparatively great length. However, Henry et al. (2000)
showed that this earthquake consisted of two high-stress-drop
subevents separated by a 70–100 km unbroken region, so that
its relatively greater length does not imply a lower stress drop.
We note also the very short length (and hence high stress drop)
of the 2000 Wharton Basin earthquake (earthquake 75 of this
study), occurring within the region of continuous deformation
separating the Indian and Australian plates (Robinson et al.
2001).
7.2 Dip-slip earthquakes
The 1 day width W is plotted against the 1 day length L for
the dip-slip earthquakes of this study in Fig. 6(a). Fig. 6(b)
shows the uncertainties in the data, with lines of constant L/W
superimposed; a systematic increase in L/W with L is seen.
Subduction earthquakes with L<50 km have L=2W, with some
having L<W (these being mostly subduction earthquakes that
occur at the ends of larger ones). Subduction earthquakes with
L>70 km have L>2W, and the three great earthquakes
with L>500 km all have large L/W. This last result agrees with
Purcaru & Berckhemer (1982), who find large L/W for the very
great subduction earthquakes, but our results contradict their
finding that L/W has a constant value of y2 up to fault lengths
of y250 km. We are also in disagreement with Geller (1976),
who found lower L/W for longer intraplate earthquakes than
for shorter ones.
The factors controlling the scaling of earthquakes with
LjW may be different from those with L>W, and these two
groups cannot be considered jointly. We shall consider the
scaling properties of L with M0 for the latter group only;
we have too few earthquakes with LjW to make a separate
study of these. For the 16 earthquakes for which we are unable
to determine the fault width reliably, we can still determine
whether L>W, and 13 of these are retained. Fig. 7(a) shows
the 1 day length L plotted against M0 for all earthquakes with
L>W, with Fig. 7(b) showing the uncertainties in the data.
There is more scatter than for strike-slip earthquakes, and a
general trend of increasing L with M0 is seen. The line of best
fit for the post-1977 thrust earthquakes of this study has a slope
of 0.46, close to 1/2. However, this line does not adequately
represent the complexity of the data. The data below
0.8r1020 N m mostly fall on or above this line, and there
is an apparent step change by a factor of 1.5–2 in the trend
at M0 of 0.8–1.0r 1020 N m, above which many, but not all,
earthquakes fall on the slope-1/2 line of best fit shown, with a
significant minority lying well below the line. This line describes
the larger earthquakes better than the smaller ones, because
larger earthquakes have smaller relative errors in their lengths.
A regression that does not take account of the uncertainties
produces a slightly lesser slope of 0.40, but this line also fails to
#
2001 RAS, GJI 147, 272–293
Aftershock zones of large shallow earthquakes
285
Figure 5. (a) Plot of 1 day aftershock length against moment for strike-slip earthquakes. Squares show data from this study, with bold numbers
referring to Table 3. Circles show selected data from Pegler & Das (1996), with numbers in italics referring to Table 1 of that study. Interplate
earthquakes, including earthquakes in regions of continuous deformation, are shown by solid symbols. Intraplate earthquakes are shown by open
symbols. (b) Same data, with uncertainties (discussed in the text) shown by solid lines. The line of best fit to all the data, determined using the
uncertainties in the lengths to weight the data (Press et al. 1992), is shown. Lines of slope 1, 1/2 and 1/3 are also shown separately for reference.
describe the data over the whole magnitude range, lying below
most of the earthquakes with M0i3r1020 N m. As discussed
above, dip-slip earthquakes often undergo substantial expansion of aftershock area with time. When the 7 and 30 day
lengths are plotted against M0 (not shown), they are found to
have greater scatter than the 1 day lengths, suggesting that they
are less closely related to the rupture length, and we regard the
1 day aftershock dimensions as the best estimate of the rupture
length. After 7 and 30 days, the step change in length at M0 of
0.8–1.0r 1020 N m is preserved, but lower-magnitude earthquakes expand on average by a greater fraction of their 1 day
lengths than larger earthquakes, leading to lesser slopes for the
lines of best fit.
Since we have shown that, for large dip-slip earthquakes, W
is neither constant nor proportional to L, and since W may be
#
2001 RAS, GJI 147, 272–293
different for different tectonic environments, it is not surprising
that the data are not described well by a single power law. We
argue that W must be taken into account in any discussion
of the scaling of L with M0. Examination of Table 1 shows
that earthquakes with M0<1020 N m, including most of the
subduction earthquakes of this study, have widths in the range
30–80 km, but that below this magnitude, widths are in the
range 10–40 km. Since L=M0/(CmūW), this can account for
the observed change in length.
Since, for reasons mentioned earlier, the errors in the
determination of fault width are greater than those for fault
length, we shall adopt two approaches for the consideration of
the effect of fault width. For subduction zone earthquakes, by
far the largest group of earthquakes of a single type in this
study, we shall first discuss the observed scaling of moment
286
C. Henry and S. Das
Figure 6. Plot of 1 day aftershock width W (km) against 1 day aftershock length for dip-slip earthquakes. Symbols refer to different types of
earthquake, as shown in key. (a) Numbers refer to Table 1, with asterisks indicating the earthquakes that do not meet the strict rake criterion discussed
in the text. The 22 hr dimensions of the 1957 Aleutian earthquake are indicated by an open square. (b) Same data, with uncertainties shown by lines.
The three large subduction earthquakes of Table 2 are also shown, labelled by their year of occurrence. Diagonal lines show L/W values of 1, 2, 4 and 8.
with length, interpreted using the estimated widths, but without
direct inclusion of these width values in the comparison. For
non-subduction earthquakes we have too few examples of each
type to draw individual conclusions. We shall then determine
Cmū for all earthquakes for which we have been able to obtain
the fault width, and examine its variation with width and
with length. The latter will allow comparison of earthquakes of
different types and over a wide range of length scales.
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Aftershock zones of large shallow earthquakes
287
Figure 7. Plot of 1 day aftershock length L (km) against moment M0 for dip-slip earthquakes. Only earthquakes with L>W are plotted. (a) Symbols
same as in Fig. 6(a). (b) Symbols same as Fig. 6(b). The line of best fit to the post-1977 thrust earthquake data, determined using the uncertainties in
the lengths to weight the data, is shown. Lines of slope 1, 1/2 and 1/3 are shown for reference.
7.3 Scaling relations for subduction earthquakes
without explicit consideration of W
For the subduction earthquakes with 70 km<L<300 km, W
is seen to be broadly independent of length (Fig. 6). Whether or
not this has a physical basis in the mechanics of subduction
zones, the empirical constancy of width means that for these
earthquakes the scaling of L with M0 provides direct information on fault slip, analogous to the case for strike-slip
earthquakes. In Fig. 8, length is plotted against moment for all
subduction earthquakes with M0<1020 N m. This includes all
‘simple’ subduction earthquakes with L>70 km except earthquakes 15 and 16, at the New Hebrides (Vanuatu) trench.
For both of these earthquakes the relocated aftershocks commence in a region much smaller than the 1 day area, and
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2001 RAS, GJI 147, 272–293
expand progressively over the first 24 hr, suggesting that
the 1 day aftershock lengths are significantly greater than the
true rupture lengths. This is confirmed for earthquake 16 by
Chatelain et al. (1983), who found the same expansion in
aftershock area using locally recorded aftershocks for earthquake 16, and that a smaller rupture area was supported by
local tiltmeter measurements.
A majority of the ‘simple’ subduction earthquakes with
L>70 km lie on a fairly narrow band, with a few earthquakes
lying far from the band, which will be discussed later. Linear
regressions of this small data set were found to be highly
sensitive to the exclusion or inclusion of data points far from
the band, and hence we do not report a preferred line of best fit.
Lines of slope 1, 1/2 and 1/3 are superimposed upon the data of
Fig. 8, and we discuss their compatibility with the data. The
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C. Henry and S. Das
during the rupture of shallow-dipping earthquakes which break
the Earth’s surface can lead to a breakdown of the relation
M0=mūA, and propose a corrected relationship M0=mūA/c,
where c>1.
The four earthquakes of Fig. 8 with L<70 km are worth
consideration here. Earthquake 31 and the ‘complex’ subduction earthquake 36 have sufficient aftershocks that the 1 day
lengths are likely to be a good estimate of the true rupture
length. It is interesting to note that earthquakes 22 and 31 have
the lowest measured widths of the earthquakes of Fig. 8. This
would lead us to expect them to have high lengths for their
moments, the opposite of the observed anomaly, indicating
that they have very high slips. Earthquakes 34 and 42 have very
few 1 day aftershocks, and the 1 day lengths are probably an
underestimate of their true rupture lengths.
7.4 Scaling relations taking W explicitly into account
Figure 8. Same as Fig. 7(b), showing only the post-1977 subduction
zone thrust earthquakes with M0<1020 N m of this study. The
earthquakes individually discussed in the text are numbered. Lines of
slope 1 (dotted), 1/2 (solid) and 1/3 (dashed) are superimposed.
main band of data is best described by lines with slope 1/2,
with lines of slope 1/3 describing the data across the full range
of moments slightly less well, although the difference rests on
relatively few earthquakes. The lines of slope 1 are clearly not
compatible with the earthquakes of L>70 km, with the lines of
slope 1/2 or 1/3 clearly providing a much better fit to the data.
Since the widths of these longest earthquakes are independent
of length, this indicates that for these earthquakes we can reject
categorically the possibility that ū is independent of length. The
good fit of the lines of slope 1/2 indicates that ū 3 L, with a
greater than linear increase also being consistent with the data.
Earthquakes 22 and 55, the 1985 and 1995 Mexican earthquakes, respectively, fall just below the main band of data, and
earthquake 46 falls substantially below the band. All three have
sufficient 1 day aftershocks that the 1 day aftershock lengths
may be considered reliable estimates of the true rupture length.
The only earthquake significantly above the general trend of
the data is earthquake 40, the 1992 Nicaragua earthquake, with
a length three times that of other earthquakes of its magnitude.
This was a slow earthquake with a source duration of y100 s
(Kanamori & Kikuchi 1993) associated with the subduction of
sediments, and a natural explanation for its position in Fig. 8
would be a low rigidity associated with these sediments. This is
supported by Satake (1994), who found that a low rigidity was
required to reconcile seismological models of this earthquake
with the large observed tsunami. An alternative explanation
for the anomalously low moments of tsunami earthquakes has
recently been advanced by Brune & Anooshehpoor (2000), who
suggest that dynamic separation of the two faces of the fault
We now consider the subduction earthquakes discussed above
together with the three great subduction earthquakes of Table 2,
and with earthquakes of other types. To extend the range of our
data to lower moments we combine our data with data for pure
dip-slip earthquakes given by Wells & Coppersmith (1994).
For the eight dip-slip earthquakes in common between the
two studies, we use the values of Table 1. Comparing the two
data sets, in general the moments are in very good agreement,
and the lengths agree within 25 per cent for six out of eight
earthquakes, with the worst disagreement being 50 per cent.
For the four of these eight for which we have been able to
measure widths, they agree within 50 per cent. Fig. 9 shows L
against M0 for the earthquakes of the combined data set with
L>W; the line of best fit for the thrust earthquakes of the
combined data set is shown, and has slope y1/3. The line of
best fit to only the thrust earthquakes with M0<1020 N m is
shown by a dashed line, and the step change in length at this
magnitude and the deviation of the largest post-1977 earthquakes from M0 3 L3 scaling are clearly seen. Fig. 10 shows
the relationship of L to W for the combined data set. For
L<40 km, L/W is fairly constant in the range 0.7–3. Above this
length, L/W is seen to increase systematically with length. This
reconfirms the necessity of taking fault width into account in
the analysis of these data.
Again selecting only those earthquakes with L>W, we
calculate M0/LW, here denoted Ū, for those earthquakes for
which width could be determined. Since M0/LW=Cmū, the
range of C is small, and rigidity is nearly constant across
the range of hypocentral depths of the earthquakes of this
study, Ū may be treated as a direct measure of fault slip. In
Fig. 11(a), Ū is plotted against length, with lines of slope 1
superimposed. We see that the majority of earthquakes of the
combined data set lie within a broad band of slope 1. The post1977 earthquakes with the greatest lengths are seen also to have
the greatest values of Ū. Thus we conclude that ū 3 L over the
range 1017 N m<M0<3r1022 N m. The slow earthquake 40
is seen to have an anomalously low value of Ū, reflecting the
previously discussed anomalously low rigidity. Of the other
post-1977 earthquakes of our study that fall outside the main
band, the ‘complex’ subduction zone earthquake 27, and the
intraplate normal earthquake 3, with the largest value of Ū
of any post-1977 earthquake, both have sufficient numbers of
well-recorded aftershocks that their fault dimensions can be
regarded as reliable. The uncertainties in the width of earthquake
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Aftershock zones of large shallow earthquakes
289
Figure 9. Plot of length against moment for the same earthquakes as Fig. 7. Symbols refer to different types of earthquakes and to data source, as
indicated in the key. Also shown are those dip-slip earthquakes of Wells & Coppersmith (1994) that have L>W, which have no strike-slip component
of slip, and for which there were no measurements in our data set (Table 1), marked by W&C. The line of best fit to the thrust earthquakes of the
combined data set with M0<5r1021 N m is shown by a solid line. The best fit to only the thrust earthquakes with 1020 N m<M0<5r1021 N m is
shown by a dashed line. Lines of slope 1, 1/2 and 1/3 are also shown separately for reference.
29 are large; aftershock locations using local data (Anderson
et al. 1990) give a width of 12 km, which should be regarded as
a more reliable value. We have previously discussed reasons for
considering the 1 day aftershock dimensions of earthquakes 16
and 34 unrepresentative of the corresponding ruptures.
The value of Ū for the 1957 Aleutian earthquake is seen to be
below the extrapolated bounds for smaller earthquakes, or just
within the bounds if its 22 hr length of 590 km is taken as more
representative of the true rupture length. The 1964 Alaskan
earthquake has Ū in the middle of the extrapolated bounds.
Ū for the 1960 Chile earthquake lies above the extrapolated
bounds. The low detection threshold of the time could have
caused the length to be underestimated, and if the 30 day
Figure 10. Plot of width against length for the same earthquakes as
Fig. 9 as well as those for which LjW. Solid lines show L/W values of
1, 2, 4 and 8.
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2001 RAS, GJI 147, 272–293
aftershock length were to be used instead the earthquake would
fall at the upper edge of the extrapolated band (not shown).
These three large earthquakes, with fairly similar lengths, have
values of Ū that span an order of magnitude and broadly agree
with the band extrapolated from smaller earthquakes.
Ū is plotted against aftershock width in Fig. 11(b) for the
same earthquakes. For widths up to y30 km, the data are seen
to be well described by a broad band with slope 1. This reflects
the well-known M0 3 L3 scaling of small earthquakes (Hanks
1977). Above this width, earthquakes still occur across the
whole of the marked band, but several subduction thrust
earthquakes occur at the very top of the band, or just above
it, with slip being independent of width for the subduction
earthquakes of this study. The earthquakes with greatest Ū are
not those with the greatest width, and there are a sufficient
number of earthquakes with high Ū to be confident that this is
not an artefact of the inverse relationship between errors in W
and errors in M0/LW. The 1957 Aleutian earthquake plots in
the centre of the marked band, and the 1964 Alaskan earthquake plots in the upper part. The 1960 Chile earthquake plots
clearly above the band, even if the 30 day length is used instead
(not shown), and if the width used is reliable, this implies that
the slip is not limited by its fault width.
Thus both our study of subduction zone earthquakes with
1020 N m<M0<25r1020 N m and L>70 km, for which aftershock width has been shown to be constant, and our analysis of
a combined data set covering four decades of seismic moment
(excluding the three great earthquakes of Table 2) and taking
into account variations in aftershock width have indicated that
fault slip is proportional to fault length for dip-slip earthquakes.
Romanowicz (1992) has stated that the broad pattern of L3
scaling for dip-slip earthquakes continues up to the magnitude
of the largest known events, with possibly some fine structure.
We have shown that there is indeed a definite structure to the
observed relationship, and that although L3 scaling operates
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Figure 11. Plot of Ū against (a) length and (b) width for the same earthquakes as Fig. 9. The 22 hr parameters of the 1957 Aleutian earthquake are
indicated by an open square. Solid lines of slope 1, chosen to delimit the majority of the data, are shown.
up to 1020 N m, above this magnitude there is a step change
in length (Fig. 9). This may be due to a change in the tectonic
environments represented in the available data. This step change
is followed by a change to slope 1/2 over the magnitude range
2r1020 N m<M0<25r1020 N m, caused by a limitation on
the widths of subduction zone earthquakes of this moment
range. These features can also be seen in Fig. 2 of Romanowicz
(1992) once it is realized that the data from Shimazaki (1986),
shown by diamonds in that figure, are strike-slip earthquakes
for moments below 1020 N m, and thrust-type above this
moment. Although the slope 1/2 trend definitely does not
continue up to the magnitude of the 1960 Chile earthquake, the
exact relationship above 40r1020 N m is unclear, as we hesitate
to make general inferences from only three earthquakes. It is
also possible that the scaling of island arc and continental arc
subduction zone earthquakes may differ above this moment
(Fujii & Matsu’ura 2000), although their finding is based on
data for a very limited number of earthquakes. Thus we advise
extreme caution in the use of scaling relationships for predictive
purposes above this magnitude. Romanowicz (1992) also infers
that there is no evidence for saturation of W. Fig. 10 clearly
shows a systematic increase in L/W with length, although no
absolute saturation of W is observed. If the largest subduction
zone earthquakes do fall systematically on the extrapolated
band with slope 1/3, then their slip must increase above the
amount predicted by an extrapolation of the proportionality of
slip to length.
8
CONCLUSIONS
We have estimated the rupture dimensions of 64 dip-slip earthquakes from 1977–1997 by relocating their aftershocks, and the
strike-slip earthquake data of Pegler & Das (1996) with 11
earthquakes from 1992–2000. We have used these dimensions
to investigate properties of aftershock zones and earthquake
scaling relations.
We find that the hypocentres for both dip-slip and strike-slip
earthquakes occur on average y25 per cent of the fault length
from the nearest end of the fault. This is consistent with the
hypocentre having a uniform probability of occurring anywhere along strike. Although it is generally believed that
earthquakes often nucleate at barriers, substantiating this from
aftershock areas requires the demonstration of a difference
from this null hypothesis (namely, that the hypocentre has
a uniform probability of occurring anywhere along strike).
Subduction zone earthquakes nucleate more frequently near
the base of the fault than near the top, with no ‘simple’ subduction earthquakes of this study nucleating at the top edge of
the fault. Only a small number of subduction zone earthquakes
propagate a significant distance down dip. This is in agreement
with the observation of Kelleher et al. (1973). Das & Scholz
(1983) suggested that it was more difficult for rupture to
propagate into stronger regions down dip. The aftershock zones
of large subduction zone earthquakes rarely exceed a depth
of 50 km, indicating that this is the maximum depth of the
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Aftershock zones of large shallow earthquakes
seismogenic part of the subduction zone plate interface. The
aftershock zones of subduction zone earthquakes often expand
substantially up dip, but not down dip, which again could be
explained in terms of increasing strength with depth. Subduction
zone earthquakes show no asymmetry in along-strike expansion.
Most non-subduction dip-slip earthquakes occur at depths
significantly less than 50 km, and show no preferred nucleation
position along the dip direction. The aftershock zones of these
earthquakes do not expand significantly up or down dip, which
may suggest that many of the earthquakes in this study have
ruptured the entire seismogenic thickness of the region in which
they occurred. For unilateral non-subduction dip-slip earthquakes, a strong preference is seen for expansion along strike in
the direction opposite to the direction of rupture propagation.
Subduction zone thrust earthquakes have larger and more
numerous aftershocks than earthquakes in all other tectonic
settings.
For dip-slip earthquakes, the M0–L relationship for
M0<1020 N m is not adequately described by a single power
law. We show that to explain the observed relationship, fault
width must be taken into account explicitly. By consideration
of only subduction zone earthquakes with 1020 N m<M0<
3r1021 N m, which are empirically shown to have broadly
constant width, we find that slip is proportional to length, or
possibly increases more than linearly with length, and so is
clearly not restricted by the limited fault width. By combining
dip-slip earthquakes of all types from our study with the data
of Wells & Coppersmith (1994), we have shown that L/W for
dip-slip earthquakes increases systematically with length above
a length of 40 km, and this trend persists up to the largest
subduction zone events. When the width of each earthquake is
explicitly taken into account, we find that slip is proportional to
length (M0 3 L2W) for dip-slip earthquakes for 1017 N m<
M0<3r1021 N m. The three great subduction zone earthquakes with M0<8r1021 N m span the range of slips that
would be predicted by an extrapolation of the scaling at lower
magnitudes, with the 1960 Chile earthquake having a slip at or
above the maximum slip predicted by this extrapolation. For
large (L&W) strike-slip earthquakes, M0 may scale as L2 or L3,
implying that slip increases at least linearly with length.
We find that neither the saturation of fault width for strikeslip earthquakes, nor the weak impediment on fault width for
dip-slip earthquakes, which is indicated by the increase in L/W
with length, appears to place any limit on fault slip, which
continues to increase with length up to the largest dip-slip and
strike-slip earthquakes of this study.
ACKNOWLEDGMENTS
CH was supported by a UK NERC studentship (GT04/97/
ES/217) and a Schlumberger CASE award. Some computations
were carried out on the Fujitsu VPP300 supercomputer at the
Manchester Computer Services for Academic Research under
grant GR9/03960. We thank Jim Dewey for use of his original
JHD programs.
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APPENDIX A: STABILITY OF JOINT
HYPOCENTRE DETERMINATION
ALGORITHMS
For several of the aftershock sequences relocated for this study,
the joint hypocentre determination algorithm JHD89 diverged.
This indicates that either the data could not adequately constrain the aftershock locations, or the starting locations were
insufficiently close to the solution, or that there were numerical
problems with the algorithm. In this appendix we investigate
the latter possibility.
Here we briefly describe the method of joint hypocentre
(JHD), following Douglas (1967). The equation of condition
for the location of a single earthquake is
LT
LT
LT
dtzdh
{dx cos aj
{dy sin aj
~dTj ,
Lh j
L* j
L* j
(A1)
where dt, dx, dy and dh are corrections to initial estimates of the
time, latitude, longitude and depth of the earthquake, Dj and
aj are the distance and azimuth of the jth station from the
epicentre, Tj is the traveltime to the jth station, and dTj is
the traveltime residual at the jth station.
In JHD, eq. (A1) is generalized to the case of multiple
earthquakes from a small physical region and includes, for each
station, a correction to the traveltime table used, which is
assumed to be the same for all earthquakes, and which is determined as part of the solution. This may be expressed as a
matrix equation:
Ax&b ,
(A2)
where x is the vector of changes to the hypocentres and station
corrections, b is the vector of traveltime residuals and A is the
matrix of traveltime derivatives.
This equation is solved for x in the least-squares sense,
and the new hypocentres are used to recalculate A and b for
the iteration. In the algorithm JHD89 (Dewey 1971, 1983) the
equation is first solved n1 times with depth constrained, to
obtain initial estimates of the epicentres and station corrections,
and then solved a further n2 times with depth free. In this study
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2001 RAS, GJI 147, 272–293
Aftershock zones of large shallow earthquakes
293
}
Figure A1. (a) Relocation of an aftershock (1996 February 22, 10:58:46) of earthquake 56 of Table 1. Cross shows ISC location of aftershock, used
as the initial location. The solid line shows the path taken by the aftershock during relocation using JHD89-SVD, the solid circle shows the relocated
position obtained, and the 90 per cent confidence ellipse is shown. Dashed line shows the path taken by the aftershock during unsuccessful relocation
using JHD89, for which division by zero occurred on the seventh iteration. The location of the aftershock after each iteration is indicated by a number
corresponding to the iteration. (b) Same as (a) for the aftershock (1995 February 15, 23:36:12) of earthquake 45 of Table 1. Symbols same as (a),
except that dashed line shows path taken by aftershock during successful relocation using JHD89, the open circle shows the relocated position
obtained, and the 90 per cent confidence ellipse obtained using JHD89 is shown dashed.
we use n1=4 and n2=6. In the algorithm JHD89, eq. (A2) is
solved by forming the matrix of normal equations (Press et al.
1992), and using Gaussian elimination for the first n1+n2x1
iterations. In the last iteration, Gauss–Jordan elimination is
used, which simultaneously determines both x and the inverse
of the matrix of normal equations, which is used in the
determination of error ellipses. In this study, the algorithm is
implemented at 32-bit precision.
To assess the stability of JHD89, a we used a modified
algorithm JHD89-SVD, which solved eq. (A2) directly using
the method of singular value decomposition (SVD) (Press et al.
1992), implemented at 64-bit precision. Direct solution of
eq. (A2) is intrinsically more stable than solution of the normal
equations, and SVD allows the identification of null and nearnull vectors in the solution space, which can then be excluded
from the solution if necessary. Its only drawback is that it is
significantly slower than Gaussian elimination or Gauss–Jordan
elimination.
It was found that all cases that had diverged when
solved using JHD89 converged when solved using JHD89SVD, without the need to exclude any near-null vectors from
the solution, indicating that the source of the divergence was a
numerical instability in JHD89. Fig. A1(a) shows an example
of the behaviour of one aftershock during the relocation of the
aftershock sequence of earthquake 56 of Table 1. JHD89 and
JHD89-SVD give identical results for the first four iterations.
However, when the depths are allowed to vary in the subsequent iterations, the solutions differ, and on the seventh
iteration, division by zero occurs in JHD89. Similar behaviour
was shown for all cases that diverged under JHD89. We also
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2001 RAS, GJI 147, 272–293
compared the results of JHD89 and JHD89-SVD for aftershock sequences that had not diverged under JHD89. In most
cases, the two solutions followed identical or near-identical paths.
However, for a few cases such as the aftershocks of earthquake 45 of Table 1, of which an example is shown in Fig. A1(b),
the two solutions do differ after the fourth iteration, but the
numerical error is sufficiently small that JHD89 remains convergent, and regains numerical stability as it approaches the
solution. The two algorithms JHD89 and JHD89-SVD arrive
at the same solution by two different paths, and the small
difference seen between the locations, representing incomplete
convergence, is insignificant in comparison to the formal location
errors.
The greater stability of Gauss–Jordan elimination in comparison to Gaussian elimination (e.g. Press et al. 1992) motivates
us to investigate a third algorithm, JHD89-M, which solved the
normal equations using Gaussian elimination for the first n1
inversions, with depth fixed, and Gauss–Jordan elimination for
all subsequent inversions, implemented at 32-bit precision. This
produces identical solutions to JHD89-SVD for all cases that
we tested, indicating that the greater precision and stability of
JHD89-SVD is not required by the present problem. We used
JHD89-M for all inversions in this study.
We recommend that authors using the method of joint
hypocentre determination should compare their algorithms
against a high-precision alternative, preferably based on direct
solution of eq. (A2) using SVD, for a few cases that have not
converged using their algorithms. It is possible that in such
cases the divergence may be due to numerical instabilities,
rather than being entirely due to poor data quality.