Did the 2004 Sumatra Andaman Earthquake Involve a Component of Tsunami Earthquakes?

Transcription

1 Bulletin of the Seismological Society of America, Vol. 97, No. 1A, pp. S296 S306, January 2007, doi: / 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 (M w , Lay et al., 2005) is smaller than that of the great 1960 Chilean earthquake (M w 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 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 M s (1) (Abe, 1989), where M t is the tsunami magnitude (Abe, 1979) and M s is the surface-wave magnitude measured at a period S296

2 Did the 2004 Sumatra Andaman Earthquake Involve a Component of Tsunami Earthquakes? S297 of 20 sec. However, this definition fails for earthquakes with M w (the moment magnitude measured at a period of sec) larger than 8 because of the saturation of M s at these long periods (Geller, 1976; Kanamori, 1977). Obviously, the 2004 Sumatra Andaman earthquake is such a big event. Then replacing M s in equation (1) by M w 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 and Mw M s (2) Mt M w. (3) Inequality (2), in the case of tsunami earthquakes, means that M s is unusually small compared with M w predicted from a scaling relation for normal (nontsunami) earthquakes. Kanamori (1972) first pointed out this deviation. Letting the moment time function be represented by M (t) M (1 exp( t/s)), (4) 0 0 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 M s compared to M w. Then relation (2) can be modified into a better formula: s(a) s (A), (5) 0 where s 0 (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 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,

3 S298 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 M w of Harvard Centroid moment tensor solution (Harvard Seismology, 2006), and the solid triangle for that converted from M s of the USGS. The broken curve best fits the data by a single moment functon with s 110 sec and M N m. The solid curve best fits the data by two functions with s 70 sec, M N m, and s 290 sec, M N m. The dotted curve shows the predicted one from our preferred model having two functions with s 90 sec, M Nm,ands 290 sec, M Nm. 2007), from M w 9.01 of the Harvard Centroid Moment Tensor solution and from M s 8.6 determined by the U.S. Geological Survey (USGS), are plotted in this figure; the conversion of M s 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 M 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, M N m, and s 290 sec, M 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 because 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 A and L (length) of the 2004 event 3.8 and 7.2 times larger, respectively, than those of the 1933 event. The s 0 of the 2004 event expected from the above scaling of normal earthquakes is then 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 ( 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,

4 Did the 2004 Sumatra Andaman Earthquake Involve a Component of Tsunami Earthquakes? S ), 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 proportional to M, with M 0 proportional to L 3 0. Using M w /3 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 sec if it is normalized to an M w 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 M 0 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 M w 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 M 0 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. M t M w and the Updip Edge of the Fault Zone. M w of the Sumatra Andaman earthquake measured in the very long-period seismological band is (Lay et al., 2005; Park et al., 2005; Stein and Okal, 2005), and M t is 9.1 (Abe, 2005). Then M t does not exceed M w 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 M t 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 M t 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 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

5 S300 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 S Body and surface waves N-F km 7.5 m Ammon et al. (2005) Model C S Body and surface waves F km 15 m Ji (2005) S Body waves N km 20 m Yamanaka, Y. (personal comm., S Body waves N 14 m January 2006) Fujii and Satake (2007) T Tide gauges and SSH N 3 20 km 25 m Hirata et al. (2006)) T SSH N km 29 m Tanioka et al. (2006) T Tide gauges M km 24 m Piatanesi and Lorito (2007) T Tide gauges N 0 10 km 18 m *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) 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 ( 2.3) m and 40 ( 2.8) m (Fig. 4b), while the previous ones were 29 ( 2.1) m and 15 ( 2.6) 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 F- type 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

6 Did the 2004 Sumatra Andaman Earthquake Involve a Component of Tsunami Earthquakes? S301 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. Figure 3. (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

7 S302 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/ 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

8 Did the 2004 Sumatra Andaman Earthquake Involve a Component of Tsunami Earthquakes? S303 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 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 M 0 obtained by fitting two moment functions, we propose a model having s 90 sec, M N m for the rapid slip, and s 290 sec, M 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 Nm. 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 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

9 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 if M w is used. This is close to the average value of 4.7 for subduction zone earthquakes and far above the threshold of 5.7 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. 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. 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. 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