Did the 2004 Sumatra–Andaman Earthquake Involve a Component

Bulletin of the Seismological Society of America, Vol. 97, No. 1A, pp. S296–S306, January 2007, doi: 10.1785/0120050615
Did the 2004 Sumatra–Andaman Earthquake Involve a Component
of Tsunami Earthquakes?
by Tetsuzo Seno and Kenji Hirata
Abstract Tsunami earthquakes are characterized by (1) slow slip and (2) tsunamis
larger than expected from seismic slip. We examine whether the 2004 Sumatra–
Andaman earthquake had these features and thus involved a component of tsunami
earthquakes. Fitting the effective moment versus frequency curve, we obtain characteristic times s (Kanamori, 1972) of 70 and 290 sec. The former is on the scaling
for normal earthquakes; the latter is longer. In the area off northern Sumatra, by backprojecting the wavefront recorded on the sea surface height (SSH) by the satellite
altimetry, we estimate the seaward edge of the fault plane to be located at the deformation front. We then invert the SSH, assuming that the seaward edge of the fault is
at this location, and obtain a maximum slip of 40 m, which was estimated to be 15 m
previously. This amount of slip, approximately twice the slip estimated seismologically
and geodetically, suggests that additional crustal deformation, such as inelastic uplift
of the trench sediments, might have occurred near the deformation front. We propose
that a similar, possibly slow, slip occurred in the shallow subduction boundary, extending from all over the rupture zone derived by the body-surface waves, with a
smaller northward propagation velocity, corresponding to the longer s. This rupture
mode would solve the enigmatic features of this event seen in the seismological and
tsunami data. The 2004 Sumatra–Andaman earthquake, having both features (1) and
(2) that characterize tsunami eathquakes, likely had a component of tsunami earthquakes.
Introduction
The 2004 Sumatra–Andaman earthquake caused huge
damage amounting to more than 250,000 casualties due to
its disastrous tsunamis around the Bay of Bengal. Although
its magnitude (Mw 9.1–9.3, Lay et al., 2005) is smaller than
that of the great 1960 Chilean earthquake (Mw 9.5), the damage caused by the tsunamis is much greater. The rupture of
this event does not seen simple. Although the studies of
short-period seismic waves and the ocean-bottom T-phase
data indicate that the rupture propagated with a velocity of
2.5–2.8 km/sec over the entire length of the aftershock zone
(⬃1200 km) (Ammon et al., 2005; Ishii et al., 2005; Ni et
al., 2005; Kruger and Ohrnberger, 2005; Tolstoy and Bohnenstiehl, 2005), many pieces of evidence, from the tsunamis, crustal deformation, and long-period seismic records,
show that the event might have involved a slow slip–long
rupture duration component with a time constant more than
1000 sec (Banerjee et al., 2005; Bilham et al., 2005; Lay et
al., 2005; Park et al., 2005; Stein and Okal, 2005; Hirata et
al., 2006; Singh et al., 2006).
There is a class of earthquakes called tsunami earthquakes that cause tsunamis larger than expected from their
seismic waves. The slow slip is one of the known characteristics of tsunami earthquakes (Kanamori, 1972; and many
others). Therefore, it is important to examine whether the
Sumatra–Andaman earthquake belongs to this genre of
earthquakes or not, or if it involved a component of tsunami
earthquakes. In this article, we examine available data on the
rupture and tsunamis of this earthquake to see whether it
involved a component of tsunami earthquakes, and we discuss its rupture mode.
Definition and Characteristics of Tsunami
Earthquakes
Although it is almost evident from previous studies that
the 2004 Sumatra–Andaman earthquake had a long time
constant in its rupture process, it is important to compare it
with those of tsunami or nontsunami normal earthquakes.
Also, it is important to examine whether the event possessed
other characteristics of tsunami earthquakes. Generally, a
tsunami earthquake is characterized by the relation
Mt ⬎ Ms
(1)
(Abe, 1989), where Mt is the tsunami magnitude (Abe, 1979)
and Ms is the surface-wave magnitude measured at a period
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Did the 2004 Sumatra–Andaman Earthquake Involve a Component of Tsunami Earthquakes?
of 20 sec. However, this definition fails for earthquakes with
Mw (the moment magnitude measured at a period of ⬃100–
300 sec) larger than ⬃8 because of the saturation of Ms at
these long periods (Geller, 1976; Kanamori, 1977). Obviously, the 2004 Sumatra–Andaman earthquake is such a big
event. Then replacing Ms in equation (1) by Mw seems to be
one way to avoid this saturation. In fact, there is some literature that defines tsunami earthquakes by this way. However, it omits the important character of tsunami earthquakes: seismic-wave radiation at shorter periods is deficient
compared with at longer periods.
In order to make the definition of tsunami earthquakes
more suitable for great earthquakes, we decompose equation
(1) into two relations
Mw ⬎ Ms
(2)
Mt ⬎ Mw .
(3)
and
Inequality (2), in the case of tsunami earthquakes, means
that Ms is unusually small compared with Mw predicted from
a scaling relation for normal (nontsunami) earthquakes. Kanamori (1972) first pointed out this deviation. Letting the moment time function be represented by
M0 (t) ⳱ M0 (1 ⳮ exp (ⳮt/s)) ,
(4)
where s is a time constant during which the moment rapidly
increases. The shape of this function indicates that the total
source duration is a few to several times larger than s. Kanamori (1972) showed that the 1896 Sanriku and 1946 Aleutian tsunami earthquakes had s values approximately 10
times larger than that of the 1933 outerrise earthquake with
a similar fault area, resulting in the anomalous reduction of
Ms compared to Mw. Then relation (2) can be modified into
a better formula:
s(A) ⬎ s0 (A) ,
(5)
where s0(A) is the scaling relation of s for normal earthquakes against fault area A. We call earthquakes having inequality (5) K-type tsunami earthquakes, after the work by
Kanamori (1972).
On the other hand, inequality (3) implies that tsunamis
are larger than expected from the seafloor deformation
caused by the seismic slip on the fault. This feature of tsunami earthquakes was first noted by Fukao (1979) for the
1969 and 1975 S. Kuril earthquakes near the trench axis. He
states: “The results show that the time constants involved in
the tsunami earthquakes are relatively long but not long
enough to explain the observed disproportionality between
the tsunamis and the seismic waves” (p. 2303). Fukao (1979)
attributed the unexpected amplitude of tsunamis to the spray
fault through the accretionary wedge branched from the
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main thrust; the high angle of the spray fault and the low
rigidity of the prism both may have enhanced the amplitude
of tsunamis.
However, recent studies of tsunami earthquakes, including these two Kuril earthquakes, showed that their fault
planes had very shallow dip angles and that the faulting approached near the trench axis (Satake and Tanioka, 1999;
Pelayo and Wiens, 1992) (see references cited in Lay and
Bilek [2006]). Seno (2000) proposed that the slip of this
shallow decollement causes a push-up of the sediments
trapped in the trench, resulting in the inelastic deformation
and abnormal uplift, based on the observation of the anomalous uplift of the river bed at the time of the 1999 ChiChi
earthquake. Tanioka and Seno (2001a, b) demonstrated that
this sediment deformation could contribute anomalous amplitudes of tsunamis for the 1896 and 1946 tsunami earthquakes, satisfying inequality (3). We call earthquakes that
satisfy inequality(3) F-type tsunami earthquakes after the
work by Fukao (1979). If any anomalous frictional sliding
property in the shallow portion of the subduction boundary
produces a slow slip, the K- and F-type features of tsunami
earthquakes are mutually related to each other through the
faulting in this portion.
Landslides may be one possible factor that causes
anomalous tsunamis (Tappin et al., 1999). In this study,
however, we do not include landslides into the genre of tsunami earthquakes because they are not a common character
associated with tsunami earthquakes; landslides are often local phenomena.
As stated previously, tsunami earthquakes rupture the
unusually shallow thrust zone close to the trench axis, which
is generally aseismic. Therefore examining the updip end of
the rupture zone is important to test whether the event is a
tsunami earthquake. However, it should be noted that although they are very rare, nontsunami earthquakes may rupture a shallow thrust zone; the 1965 Rat Island earthquake
and the 1995 Colima–Jalisco earthquake might be such examples (see references in Lay and Bilek [2006] and Hyndman [2006]). It is thus necessary to examine whether the
event actually produced larger tsunamis than expected from
the slip in the shallow portion.
We will examine the 2004 earthquake in terms of the
aforementioned features of tsunami earthquakes to see
whether it possesses some of them.
Examination of the Characteristics of Tsunami
Earthquakes for the 2004 Sumatra–Andaman
Earthquake
Slow Slip Character. To compare directly with the results
of the analysis of s by Kanamori (1972), we conduct fitting
of the theoretical effective moment versus frequency curve
to the data of the 2004 Sumatra–Andaman earthquake
(Fig. 1). This curve is the Fourier spectrum of equation (4),
normalized by the response of the step function. The seismic
moments derived from the free oscillations (Stein and Okal,
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T. Seno and K. Hirata
Figure 1.
Fitting of the effective moment versus
frequency curve to the seismic moment data of the
2004 Sumatra–Andaman earthquake. The seismic
moments are indicated by the larger solid circles for
those derived from free oscillations (Stein and Okal,
2007), the star from Mw of Harvard Centroid moment
tensor solution (Harvard Seismology, 2006), and the
solid triangle for that converted from Ms of the USGS.
The broken curve best fits the data by a single moment
functon with s ⳱ 110 sec and M0 ⳱ 9.55 ⳯ 1022 N
m. The solid curve best fits the data by two functions
with s ⳱ 70 sec, M0 ⳱ 4.96 ⳯ 1022 N m, and s ⳱
290 sec, M0 ⳱ 5.86 ⳯ 1022 N m. The dotted curve
shows the predicted one from our preferred model
having two functions with s ⳱ 90 sec, M0 ⳱ 6.5 ⳯
1022 N m, and s ⳱ 290 sec, M0 ⳱ 3.5 ⳯ 1022 N m.
2007), from Mw 9.01 of the Harvard Centroid Moment Tensor solution and from Ms 8.6 determined by the U.S. Geological Survey (USGS), are plotted in this figure; the conversion of Ms to the effective moment follows Kanamori
(1972). The scismic moments of the 2004 event are firstly
fitted by a single function, producing s ⳱ 110 sec and M0
⳱ 9.55 ⳯ 1022 N m as a best fit in the least-squares sense;
the theoretical curve is shown by the broken line in Figure
1. The fitting by a single function does not seem satisfactory
to explain the amplitude of the longest-period free oscillation. As Park et al. (2005) made a fitting to the moment
versus frequency plot by two boxcar functions, we fit the
data by combination of two functions and obtain s ⳱ 70 sec,
M0 ⳱ 4.96 ⳯ 1022 N m, and s ⳱ 290 sec, M0 ⳱ 5.86 ⳯
1022 N m as a best fit; the theoretical curve is shown by the
solid line in Figure 1. This results in 59% variance reduction
compared to the fitting by a single function. The ambiguity
in estimation of the moments may result from the assumed
dip angle of the fault (e.g., Banerjee et al., 2005; Park et al.,
2005) but does not affect the estimation of s seriously be-
cause the location of the curve to the abscissa is not dependent on the moment level. The two characteristic times of
320 sec and 800 sec obtained by Park et al. (2005) may
represent rather a whole duration. To be consistent, their
values are 3–4 times larger than obtained in this study.
The s of the normal 1933 Sanriku earthquake is
⬃10 sec, and those of the 1896 and 1946 tsunami events are
⬃100 sec. Because s includes both the effect of the slip
growth at a particular point on the fault and that of the rupture propagation, it is natural to consider that s is proportional to the linear dimension of the fault area for normal
earthquakes. The source dimension of the 1933 event is
100 km ⳯ 180 km (width ⳯ length) (Kanamori, 1971) and
that of the 2004 event is ⬃200 km ⳯ 1300 km (e.g., Lay et
al., 2005; Stein and Okal, 2005). These give 冪A and L
(length) of the 2004 event 3.8 and 7.2 times larger, respectively, than those of the 1933 event. The s0 of the 2004 event
expected from the above scaling of normal earthquakes is
then 38–72 sec. The s of 70 sec is within this range and
290 sec is beyond it. The s of 110 sec by a single function
fitting is marginally beyond this range.
The seismic moment derived from a single function fitting is much larger than the seismic moment derived from
body and long-period surface waves (6.5 ⳯ 1022 N m) (Ammon et al., 2005). This indicates that the rupture is more
complex than represented by a single function such as equation (4), and might have contained a slow slip feature characterized by inequality (5), overlapping a normal earthquake. This is also noted by Stein and Okal (2007), who
failed to fit the moment versus frequency plot by a single
boxcar function. This is also consistent with the indications
from the tsunamis, crustal deformation, and long-period
seismic records, showing that the event likely involved a
slow slip–long rupture duration component with a time constant more than 1000 sec (Banerjee et al., 2005; Bilham et
al., 2005; Lay et al., 2005; Park et al., 2005; Stein and Okal,
2005; Hirata et al., 2006; Singh et al., 2006). We will discuss
the amount of this longer period component in relation to
the rupture mode later.
The characteristic time of 70 sec does not conflict with
the moment rate function obtained by Ammon et al. (2005),
which shows that the moment release rate grows rapidly during the first 100 sec and gradually decreases in the following
few 100 sec. Therefore, we regard s of 70 sec as a value
corresponding to the source duration of ⬃500 sec derived
from the seismic waves (Ammon et al., 2005; Ishii et al.,
2005; Kruger and Ohrnberger, 2005; Ni et al., 2005). We
assume that the same proportionality of s to the source duration holds also for the longer s, which is expected from
the shape of equation (4), and estimate the corresponding
source duration of ⬃2000 sec. The source durations obtained
by Park et al. (2005), 320 sec and 800 sec, are shorter than
⬃500 sec and ⬃2000 sec, respectively. This may be due to
the simple shape of the boxcar function they used.
To supplement the previous results, we examine the
scaling of the source duration to the moment (Bilek and Lay,
Did the 2004 Sumatra–Andaman Earthquake Involve a Component of Tsunami Earthquakes?
2002), showing that the source duration of 500 sec is within
that of normal earthquakes. In their scaling, the source duration proportional to L gives the source duration propor3
tional to M1/3
0 , with M0 proportional to L . Using Mw 9.15–
9.3 (Lay et al., 2005; Park et al., 2005; Stein and Okal, 2005)
and the total source duration of 500 sec (Ishii et al., 2005;
Ni et al., 2005), we obtain a source duration of 13.0–11.3 sec
if it is normalized to an Mw 6.0 event. This source duration
apparently falls into the category of the long duration events
near the trench axis (Bilek and Lay, 2002). However, a question arises whether the previous scaling is applicable to such
a huge event as the 2004 event. For a very large event, fault
width W might be limited by the width of the seismogenic
zone, while L may become large. Such a deviation from the
scaling for smaller events occurs around W ⳱ L ⳱ 150 km,
beyond which M0 should be proportional to L.
Taking this into account, we reexamine whether the
source duration is anomalously long or not. The source duration for a normal Mw 6.0 event at a seismogenic depth is at
most ⬃5 sec (Bilek and Lay, 2002). We first extrapolate this
to that of a normal event with W ⳱ L ⳱ 150 km and the
stress drop of 2 MPa using the scaling of Bilek and Lay
(2002) and obtain a source duration of 50 sec. We then estimate the duration of a normal event with L ⳱ 1300 km
using the scaling with M0 proportional to L and obtain a
duration of 425 sec. This source duration is comparable to
the source duration of ⬃500 sec, but ⬃2000 sec is much
longer.
Summarizing, a s value of 70 sec, probably corresponding to the short source duration (⬃500 sec), is on the scaling
of normal (nontsunami) earthquakes, but a s value of 290 sec
probably corresponding to the long source duration (⬃2000
sec), is beyond the scaling of normal earthquakes and is
close to that seen for tsunami earthquakes.
Mt ⬎ Mw and the Updip Edge of the Fault Zone. Mw of
the Sumatra–Andaman earthquake measured in the very
long-period seismological band is 9.1–9.3 (Lay et al., 2005;
Park et al., 2005; Stein and Okal, 2005), and Mt is 9.1 (Abe,
2005). Then Mt does not exceed Mw and inequality (3) does
not hold for this earthquake. However, a closer examination
of the relation between the tsunamis and the seismic slip is
necessary for this event whose rupture zone is elongated
over more than 1000 km. This is because Mt is defined assuming a point source (Abe, 1979). In the case of a huge
event as the 2004 Sumatra–Andaman earthquake, successive
wave trains may emerge from different part of the fault as
rupture propagates. In this case, defining Mt by the maximum
amplitude on tide gauge records may be misleading. We
should rather compare the tsunamis and the seismic waves
generated in a particular fault segment. This can be done by
comparing the slip of the fault model inverted from the tsunami data with that of the fault model inverted from the
seismological data.
Because the tsunami inundation and runup heights are
particularly large in the northwestern coast of Sumatra, we
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examine the slip in both types of models off northwestern
Sumatra. In Table 1, we list the maximum slip in this region
obtained from seismological or tsunami data. We exclude
models that incorporate geodetic or geomorphologic data because they may contain postseismic slip with a time constant
more than one day. We also list the depth range and the
location from the trench where the maximum slip was obtained. The dip angles of the faults assumed in the tsunami
models are all 10⬚, except for Piatanesi and Lorito’s (2007),
which has a dip of 11⬚. Those of the seismological models
might be similar; however, we do not list them because we
could not obtain them from the original literature. The
amount of slip in the tsunami models is generally more than
20 m, and, in contrast, that retrieved seismologically tends
to be smaller than those estimated from the tsunami models.
If this is taken at face value, there were more tsunamis than
can be explained by seismic slip in this region.
However, amount of the slip in both types of models is
affected by the fault geometry (e.g., Banerjee et al., 2005).
It is also noted that there does not seem to be a consensus
among researchers whether the slip to explain tsunamis is
larger than the seismic slip (e.g., Song et al., 2005; Geist et
al., 2007). Therefore, a more detailed examination is necessary.
For this purpose, we first estimate the updip edge of the
fault plane on which the slip is assumed to have caused the
tsunamis. The southwestward migrating wavefront recorded
on the sea surface height (SSH) by the satellite altimetry
(Jason-1 and TOPEX/Poseidon) is back-projected using the
tsunami travel time to the source; the travel time is corrected
for the delay by the rupture propagation of 300 km from the
epicenter with a velocity of 3 km/sec. We identify the location of the wavefront as indicated by the arrow directing
upward in Figure 2a and assign the possible behind limit of
the wavefront as indicated by the arrow directing downward,
considering the signal-to-noise ratio of the observed SSH
south of 5⬚ S. We use the bathymetric data by Smith and
Sandwell (1997) to calculate the velocity of the tsunami
waves by a long-wave approximation. The estimated seaward edge of the tsunami source off northern Sumatra
(Fig. 2b) is located close to the deformation front, which is
the intersection of the flat trench-wedge sediments with the
lower trench slope (Moore et al., 1980). This location is
⬃30 km landward from the trench axis (the deepest point).
If the rupture velocity of 2.8 km/sec. (Ishii et al., 2005; Tolstoy and Bohnenstiehl, 2005) is used, the source location
will be shifted by 1.5 km seaward, which is even closer to
the deformation front.
From the results shown in Figure 2b, we judge that the
rupture of the 2004 event reached the deformation front. The
following additional pieces of evidence seem to support this.
Based on the remotely operated vehicle (ROV) survey conducted after the earthquake, Moran and Austin (2005) stated
that seafloor disturbance occurred at and near the deformation front and, in contrast, the stable seafloor conditions were
observed in the vicinity of the epicenter (see also Mosher et
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T. Seno and K. Hirata
Table 1
Maximum Slip off Northwest Sumatra Estimated by Various Models
Authors
Type*
Data
Location†
Depth (km)‡
Maximum Slip
Ammon et al. (2005) Model B
Ammon et al. (2005) Model C
Ji (2005)
Yamanaka, Y. (personal comm.,
January 2006)
Fujii and Satake (2007)
Hirata et al. (2006))
Tanioka et al. (2006)
Piatanesi and Lorito (2007)
S
S
S
S
Body and surface waves
Body and surface waves
Body waves
Body waves
N-F
F
N
N
⬃10–50 km
30–50 km
14–26 km
—
7.5 m
15 m
20 m
14 m
T
T
T
T
Tide gauges and SSH
SSH
Tide gauges
Tide gauges
3–20 km
10–36 km
10–26 km
0–10 km
25 m
29 m
24 m
18 m
N
N
M
N
*S and T denote seismic and tsunami source models, respectively.
†
Indicates how far the upper edge of the fault from the deformation front: N (near) ⬍50 km; M (middle)
50–100 km; F (far) ⬎ 100 km.
‡
Depth indicates the depth range of the maximum slip is derived.
al., 2005). Soh et al. (2005) showed that the seafloor on the
outer-arc ridge near the trench slope break was severely disturbed by a strong ground motion. McNeill et al. (2005)
noted numerous morphotectonic compressional features at
the toe of the lower trench slope and inferred that ruptures
of great earthquakes in this region would have propagated
to the seafloor close to the deformation front. The aftershocks of the 2004 event detected by the ocean-bottom seismograph (OBS) or global network are distributed up to the
deformation front (Fig. 3a,b) (Araki et al., 2006; Dewey et
al., 2006; Engdahl et al., 2007), which suggests that the
rupture propagated to this place.
In the tsunami model of Hirata et al. (2006), the seaward
edge of the fault was placed 15 km seaward of the deformation front at a depth of 10 km (Fig. 3b). Because the
location of the seaward edge seriously affects the inversion
of the tsunami data, we conduct the inversion shifting the
location of the edge of subfaults E3 and E4 (Fig. 4a) at a
depth of 1 km beneath the deformation front (Fig. 3b). The
1-km depth is to avoid the numerical instability in the calculation of the surface deformation using Okada’s (1985)
expression. The part of the thrust shallower than 10 km
newly implanted in the model has been regarded as generally
aseismic (Byrne et al., 1988; Scholz, 1998). The newly obtained amounts of slip in segments E4 and E3 are 28
(Ⳳ2.3) m and 40 (Ⳳ2.8) m (Fig. 4b), while the previous
ones were 29 (Ⳳ2.1) m and 15 (Ⳳ2.6) m, respectively. This
enlargement of the slip in segment E3 is probably caused by
the change in pattern of the vertical displacement; the shallower edge produces a narrower, larger peak above the edge
with relatively smaller displacements over a broader region
behind.
The derived slip of 40 m to explain the tsunamis is
larger than that of the seismic slip at least by a factor of 2
(see Table 1). We should not imagine that this amount of
slip actually occurred but instead regard it as an effective
slip to explain the tsunamis. The slip estimated from the GPS
horizontal displacements observed in northern Sumatra has
a maximum value of 25 m off the coast at a seismogenic
depth (Irwan et al., 2005), which is slightly larger than
amounts of the seismic slip (Table 1). The other studies (Banerjee et al., 2005; Vigny et al., 2005; Hashimoto et al.,
2006; Kreemer et al., 2006) using GPS outside the Sumatra
Island give the values similar to the seismic slip. These indicate that, off northern Sumatra, the slip on the thrust zone
at a seismogenic depth might have reached an order of 20 m
but did not exceed it. Because the strength of the shallow
thrust zone seems to be lower than at the deeper zone, there
is no physical reason for the slip larger than at depth to have
been accumulated at this shallow portion before the 2004
event. We can, therefore, infer that the slip on this portion
was also on the order of ⬃20 m at most. The fact that the
slip to explain the tsunamis exceeded this amount by more
than by a factor of 2 implies that additional deformation,
such as inelastic uplift at the sedimentary wedge, occurred
near the toe of the lower trench slope, having enhanced the
tsunamis. Our inversion results thus indicate that the 2004
Sumatra–Andaman earthquake had also a feature of an Ftype tsunami earthquake, at least in the region off northern
Sumatra.
Discussion
We have shown that, as far as can be seen from the
seismic and tsunami data, the 2004 Sumatra event seems to
possess a component of tsunami earthquakes. Many studies
already suggested it possibly involved a longer-period
source than expected from the body- and surface-wave data
and that a delayed slow slip might have occurred near the
northern terminus of the rupture zone (Bilham et al., 2005;
Lay et al., 2005; Stein and Okal, 2005). It is interesting to
discuss how the longer s and the amount of slip in the shallow subduction boundary off northern Sumatra obtained in
this study are related to these.
Bilham et al. (2005) noted that the subsidence at Port
Blair on the tide gauge record occurred about 36 min later
than the origin time of the mainshock. Later it was found
that the clock of the tide gauge was out of order (Neetu et
Did the 2004 Sumatra–Andaman Earthquake Involve a Component of Tsunami Earthquakes?
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Figure 3.
Figure 2. (a) Observed sea surface height (SSH)
by the satellite altimetry from Jason-1 and TOPEX/
Poseidon measurements. Triangle and solid circles indicate observed data in cycles 108 and 109, respectively, for Jason-1 (upper panel), and cycles 451 and
452, respectively, for TOPEX/Poseidon (lower panel).
The estimated location of the wavefront is indicated
by the arrow directing upward in each panel. The possible behind limit of the wavefront, which is estimated
by taking into account the signal-to-noise ratio of the
observed SSH south of 5⬚ S, is indicated by the arrow
directing downward. (b) The backprojected location
of the wavefront using the travel time, which is corrected for the effect of a 300-km rupture propagation
from the epicenter with a velocity of 3 km/sec. The
solid and dotted lines are the locations from the upward and downward arrows in (a), respectively. The
location is near the deformation front where the lower
trench slope meets the trench sediments at the 4000-m
isobath around 4⬚ N.
(a) Map view and (b) Cross section of
the aftershock activity detected by a temporal OBS
network after the 2004 earthquake (Araki et al.,
2006). The cross section displays only aftershocks occurring within the dotted rectangle in the map view.
Those detected during 7 days from 20 February are
indicated by the blue circles, and those listed in the
Preliminary Determination of Epicenter (PDE) catalog
and relocated by the OBS are indicated by the red
circles. The original PDE locations are indicated by
the red stars. The OBSs are shown by the triangles.
The aftershock activity seems to extend continuously
to the location of the deformation front, along the surface of the subducting plate. The fault planes (subfaults E3 and E4, see Fig. 4) assumed for the tsunami
inversion in this study and Hirata et al. (2006) are
indicated by the red double lines in the cross section.
The seaward edge of the fault in Hirata et al. (2006)
is placed about 15 km oceanward from the deformation front at a depth of 10 km, and that in this study
is placed at a depth of 1 km beneath the deformation
front. The dip angle is 10⬚ in both of the models.
al., 2005). However, Bilham et al. (2005) argued that the
slip during a rapid northward rupture is not enough to explain a few meters uplift of the west coasts of the Andaman
Islands and a meter subsidence at Port Blair, and a delayed
slow slip might be necessary. Singh et al. (2006), using the
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T. Seno and K. Hirata
Figure 4.
(a) Horizontal projection of the subfaults used in the inversion of the SSH
data. The entire length of 1400 km from northern Sumatra to the Andaman Islands are
covered by subfaults E1 through E14 parallel to the trench. Aftershocks within 1 day
after the mainshock, including the mainshock, are also shown. (b) Vertical displacements at the ocean bottom calculated from the best-fit model in this study. Only the
fault geometries of subfaults E3 and E4 are modified from those in Hirata et al. (2006),
as indicated by Figure 3b.
corrected tide gauge data at Port Blair, suggested that delayed slow slip occurred during the 35 min after the rupture
arrival. Stein and Okal (2005) argued that the seismic moment at the longest periods is 2.8 times larger than the moment of the Harvard CMT solution (Harvard Seismology,
2006) and thus the additional slow slip is necessary in the
northern segment. Lay et al. (2005) inferred that one third
of the total seismic moment was released in the Andaman–
Nicobar segments in association with a slow slip.
Tsunami excitation becomes small beyond the characteristic time t ⳱ L/冪gH , where H is the water depth, L is
the source dimension, and g is the acceleration of gravity; t
is ⬃1000 sec for L ⳱ 100 km and a water depth of 1 km.
Although geodetic methods might have captured the slip of
a period longer than this, it does not contribute much to
tsunamis or seismic waves. We thus restrict the discussion
of the delayed slip with a period shorter than ⬃1 hr.
One possible rupture mode of the 2004 event, simplified
from Lay et al. (2005), is shown in Figure 5a. In this model,
the slow slip is more or less isolated in the spatial and temporal domain from the rapid rupture derived from body and
surface waves (e.g., Ammon et al., 2005; Ishii et al., 2005).
The difficulty of this model is that if the faulting is a composite of two large fault segments with different geometries,
onset times, and durations, it would cause spectral interference in the free oscillations at long periods, as pointed out
by Park et al. (2005). The fact is that there is no such interference in the spectrum, and Park et al. (2005) successfully
explained the observed spectrum by the rupture models based
on the body and surface waves (Ammon et al., 2005). This
indicates that the rupture mode shown in Figure 5a is unlikely.
On the other hand, the delayed slip nature has been most
evidently emergent in the tsunami data. Lay et al. (2005),
Hirata et al. (2006), and Song et al. (2005) discussed that a
tsunami source in the northernmost segment more than
1000 sec later than the mainshock is needed to explain the
Did the 2004 Sumatra–Andaman Earthquake Involve a Component of Tsunami Earthquakes?
Figure 5.
Schematic illustration representing two
possible modes of the delayed rupture of the 2004
event. (a) The rupture zone derived from the body and
surface waves, and the delayed slow slip in the northernmost segment (modified from Lay et al. [2005]);
(b) continuous delayed rupture with a slow slip extending seaward from the rapid rupture at depth (this
study). The thin arrows indicate the extension directions of the rupture. The delayed slow part is a possible tsunami source, as discussed in the text.
waveform in the SSH data. Hirata et al. (2006) also showed
that such a delayed rupture is consistent with the tsunami
travel times of the two northernmost tide gauge stations (Paradip and Vishakhapatnam). Taking into account that the slip
in the shallowest portion of the boundary does not generate
seismic waves efficiently, but does generate tsunamis, as has
been shown by tsunami earthquakes, we propose an alternative model (Fig. 5b); the slip gradually developed seaward
around the periphery of the rupture zone that was derived
from the body-surface waves. This extended portion had a
seismic moment smaller than ⬃3 ⳯ 1022 N m, not much
isolated from the rapid rupture spatially or temporally, and
thus did not contribute to the centroid or interfere the free
oscillations. Referring to the values of s and M0 obtained by
fitting two moment functions, we propose a model having
s ⳱ 90 sec, M0 ⳱ 6.5 ⳯ 1022 N m for the rapid slip, and
s ⳱ 290 sec, M0 ⳱ 3.5 ⳯ 1022 N m for the delayed extended
slip. This is obtained by adjusting the value of the shorter s,
fixing the moment for the rapid slip in Ammons et al. (2005),
and the longer s, such that the total moment is 1023 N m.
The fitting to the effective moment versus frequency plot is
shown by the dotted line in Figure 1, which has a 29% variance reduction compared to the single-function fitting. Although this model has the shorter s of 90 sec, which is longer
than the 70 sec previously obtained, the arguments for a
long-duration component conducted so far do not depend on
this small change of the shorter s. The proposed model is
consistent with the centroid location, only ⬃4⬚ north from
the epicenter and the Harvard centroid, derived from the free
oscillations (Park et al., 2005; Stein and Okal, 2005). Because the extended slip occurred in the shallow portion of
S303
the subduction boundary, it would have caused tsunamis efficiently with a source moving more slowly to the north than
the rupture at a seismogenic depth.
If we accept this, we can estimate the source duration
of the delayed slip independently from the tsunami data.
Hirata et al. (2006) obtained the best-fit rupture velocity of
0.7 km/sec in the tsunami source modeling using the SSH
data. This gives ⬃1860 sec (⬃30 min) for the tsunami
source to travel a distance of 1300 km to the northernmost
segment. Tanioka et al. (2006) inverted the tide gauge data
around the Bay of Bengal and obtained 1.7 km/sec as the
best-fit rupture velocity. This gives the travel time of
765 sec. Fujii and Satake (2006) inverted the SSH and tide
gauge data simultaneously and obtained the best-fit rupture
velocity of 1 km/sec. This gives the travel time of ⬃1300
sec. These values are far beyond ⬃500 sec of the source
duration derived from seismic waves but similar to or on the
same order of ⬃2000 sec corresponding to the longer s. We
suggest that the slow seaward extension from the rupture at
a seismogenic depth had a source duration of ⬃2000 sec.
Tsunamis like the 2004 Sumatra–Andaman event have
not been known in the region around the Bay of Bengal.
Historically, part of the rupture zone of the 2004 event was
ruptured by smaller events in 1841, 1881, and 1945 near the
Nicobar and South Andaman Islands (Ortiz and Bilham,
2003; Bilham et al., 2005). The occurrence of the 2004 event
in this arc does not seem to be explained by the simple asperity model (Lay and Kanamori, 1981), in which an asperity has to break when the shear stress reaches its critical
level, or by recurrence of events due to accumulation of the
slip deficit by the relative plate motion (Stein and Okal,
2007). It is interesting to note that tsunami earthquakes
scarcely have their historical precedence. To explain this,
Seno (2002) proposed that the frictional property in the shallower decollement might change temporarily, from stable
sliding to unstable one, due to the elevation of the pore fluid
pressure. A similar transition might have happened in the
northern Sumatra–Andaman segment of the plate boundary,
but as for the cause of such long recurrence intervals, we
must await future elaborate studies.
From a viewpoint of constructing a warning system of
tsunamis, it has been pointed out that the magnitude of the
2004 event was not adequately determined (Kerr, 2005), and
improvement of the procedure of the determination has been
proposed (e.g., Menke and Levin, 2005). However, if an
earthquake contains a component of tsunami earthquakes,
the magnitude determination may not get to the core of the
matter, because anomalous tsunamis might have arisen from
the small moment release portion of the rupture zone. It
should be noted that the 1896 Sanriku tsunami earthquake
caused 22,000 casualties with a magnitude of only ⬃7.
For detecting such tsunami earthquakes, rapid analyses
of short-period seismic-wave radiations compared with
long-period ones have been proposed (Kanamori and Kikuchi, 1993; Newman and Okal, 1998). However, in the case
of a hybrid earthquake such as the 2004 event, this method
S304
T. Seno and K. Hirata
might not work well. For the 2004 Sumatra event, the logarithm of the ratio of the seismic-wave energy (Lay et al.,
2005) to the moment gives ⳮ4.77–ⳮ4.96 if Mw 9.15–9.3
is used. This is close to the average value of ⳮ4.7 for subduction zone earthquakes and far above the threshold of
ⳮ5.7 typifying tsunami earthquakes (Newman and Okal,
1998). We note that if the seismic moment associated with
the short duration (⬃500 sec) is large enough, the deficiency
of the energy release with the longer duration would be
masked by the larger short-period one. In such a hybrid case,
rapid detection of the updip end of the rupture is more effective for predicting anomalously large tsunamis. Deploying the ocean-bottom crustal deformation monitoring system
(e.g., Ando et al., 2005), incorporating offshore tsunami observation and real-time data assimilation (Titov et al., 2005),
would be one way to realize this.
The use of deficiency of short-period seismic-wave radiation with respect to that of long-period seismic waves for
predicting anomalous tsunamis would not be effective in a
hybrid case of normal and tsunami earthquakes, as the 2004
event may be. Detecting rapidly the upper edge of the rupture to see whether it reaches the trench is more effective in
such a case. Deploying the ocean-bottom crustal deformation monitoring system would be one way to realize this, but
is expensive. Rapid adequate determination of the magnitude
should not be considered definitive, and offshore direct tsunami observation systems may be more useful.
We propose that the 2004 Sumatra–Andaman earthquake is a hybrid of normal and tsunami earthquakes, which
is key to understanding the various enigmatic features of this
earthquake.
Acknowledgments
Conclusions
We examine whether the 2004 Sumatra–Andaman
earthquake had features of a tsunami earthquake. We infer
that the rupture of the event likely involved a component of
a source duration as long as ⬃2000 sec from fitting the effective moment versus frequency curve to the data of the
free oscillations (Stein and Okal, 2007), the Harvard CMT
(Harvard Seismology, 2006), and the surface-wave magnitude. This is longer than expected from the scaling of source
duration versus size for normal nontsunami earthquakes. We
conduct a back-projection of the tsunamis recorded on the
SSH by the satellite altimetry and show that the seaward edge
of the subfault off northern Sumatra reached the deformation
front near the trench axis. The inversion of the SSH data,
assuming the seaward edge at a depth of 1 km beneath
the deformation front, gives the maximum slip of 40 m on
the subfault. This is larger at least by a factor of 2 than the
seismic slip at a deeper seismogenic depth, although we do
not think that this amount of slip actually occurred but instead regard it as an effective slip to explain the tsunamis.
These indicate that the 2004 event involved a component of
tsunami earthquakes in the sense that it contained a long
duration and yielded larger tsunamis than expected from the
seismic slip.
The enigmatic aspect of the 2004 event is that the rupture in the seismological band is explained by the rupture
models with a source duration of ⬃500 sec (Park et al.,
2005), and, on the contrary, the tsunami data indicate a
longer source duration of ⬃2000 sec. This could be reconciled if we assume a slip occurred at the shallow portion of
the subduction boundary, expanding slowly from the deeper
source that generates body and surface waves. This slow
expansion of the source, probably corresponding to the long
duration of ⬃2000 sec and having ⬃35% of the total seismic
moment, is not effective to radiate the short-period seismicwave energy, but it is effective to cause large tsunamis by
the inelastic deformation near the deformation front and to
the longest-period free oscillations.
We thank two anonymous reviewers and Kenji Satake for their critical
comments. We also thank Yoshiko Yamanaka, Yuji Yagi, Yuichiro Tanioka, Eiichiro Araki, Yushiro Fujii, and Meilano Irwan for providing us
their unpublished material, and Hiroo Kanamori for helpful comments. This
work was partially supported by Ministry of Education, Culture, Sports,
Science and Technology, Japan.
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Earthquake Research Institute
University of Tokyo
Tokyo 113, Japan
[email protected]
(T.S.)
Institute for Research on Earth Evolution
Japan Agency for Marine-Earth Science and Technology
Yokosuka 237, Japan
(K.H.)
Manuscript received 13 January 2006.