STEIN-OKAL: STUDY OF THE DEC. 26, 2004 IO EARTHQUAKE...

Prof. Seth Stein

Prof. Emile A. Okal

Long period seismic moment of the 2004 Sumatra earthquake and implications for the slip process and tsunami generation

Research of Stein and Okal appearing in the journal Nature and elsewhere says the Indian Ocean earthquake that caused the devastating December tsunami was more intense than first thought, making it the second-largest quake in recorded history.

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Analysis of seismograms from the December 26, 2004 Sumatra earthquake that generated the devastating tsunami shows that it was much bigger than previously thought and explains in part why the tsunami was so destructive. Measurements of seismic energy at vibration periods much longer than previously studied show that the earthquake was approximately three times larger than previously reported. Its revised moment magnitude, Mw= 9.3 instead of the previously reported 9.0, makes it the second largest ever recorded since the invention of the seismometer about 100 years ago. The rupture occurred by slip along the 1200-km long fault delineated by aftershocks, making the rupture zone much larger than previously thought from analysis of shorter period waves. The amplitudes of the earth's split normal modes show the larger fault area, because they are better fit by a source at 7N, in the center of the rupture zone, than by one at the epicenter at 3N. 
 
This long rupture played a key role in generating the devastating tsunami. In particular, the large tsunami amplitudes in Sri Lanka and India result from rupture on the northern, north-trending, segment because tsunami amplitudes are largest perpendicular to the fault. This effect is shown by comparison of snapshots from two tsunami animations. 

 
Because the entire rupture zone slipped, strain accumulated from subduction of the Indian plate beneath the Burma microplate has been released, leaving no immediate danger of a comparable tsunami being generated by water moved by an earthquake on this segment of the plate boundary. However, the danger of a local tsunami generated by a large aftershock or a comparable ocean-wide tsunami resulting from a great earthquake on segments to the south remains. 
 These results come from analyzing the earth's normal modes - ultra long vibrations by which the earth rings like a bell (or more precisely rattles like a garbage can) for days and even weeks after such a gigantic earthquake. Analysis of long seismograms shows distinct energy peaks whose height reflects the earthquake's seismic moment, which gives its magnitude. Because the magnitude scale is logarithmic, the threefold increase in seismic moment raises the magnitude by 0.3 units, making it second only to the 1960 Chile earthquake. 
Curiously, the analysis technique relied on results we developed with Robert Geller (now at the University of Tokyo) as graduate students almost 30 years ago. However, because such gigantic earthquakes are rare, these methods had been essentially unused until records of the Sumatra earthquake on modern seismometers became available. These data were provided by the Global Seismographic Network of the Incorporated Research Institutions for Seismology .

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Examples of seismic data from around the world that we analyzed.  
The size of the earthquake is given by its moment magnitude Mw, defined as Mw = (log Mo / 1.5) - 10.73 from the seismic moment Mo in dyn-cm. Thus the Harvard CMT solution at periiods 300s and below measured a moment of 4e29 dyn-cm giving Mw 9.0, and the longest period normal mode 0S2 gives Mo 1.0e30 dyne-cm or Mw 9.3. The moment and magnitude rise smoothly with period, as shown in the technical report linked below. This makes the earthquake gigantic, as illustrated by comparison with some other earthquakes below. 

 
The relative plate motions between the Indian, Sumatra, and Burma plates give insight into the tectonic setting of the earthquake, how often it may recur, and the extent of the rupture. GPS studies show that both India and Sunda move northeastward relative to Eurasia, and the rate of spreading between the Burma sliver and Sunda (green arrow) has been measured using marine magnetic data. Combining these results yields an Euler vector whose rotation pole (dot) shows that the net convergence between India and Burma is oriented NW-SE (red arrows). The component perpendicular to the trench (blue arrows) presumably is released in great earthquakes like this. Because this component is about 15-25 mm/yr, depending on the pole position, rate, and location along the trench, we would expect earthquakes like this to occur at least 400 years apart on average. 

 

As an outgrowth of these studies, we have been working with Geoffrey Blewitt, Corne Kreemer, Bill Hammond, and Hans-Peter Plug of of the University of Nevada, Reno, geodetic laboratory  to improve tsunami warning systems. Although seismological systems can detect large earthquakes, assessing the earthquake's true size and tsunami potential is challenging. The challenge is illustrated by the fact that seismic magnitude estimates for the first hour after the Sumatra earthquake were far too low incorrectly indicating no danger of a major oceanwide tsunami. However, using the positions of ground sites derived from the GPS satellites, we have shown that the earthquake's true size and tsunami potential could be accurately determined using only GPS data recorded up to 15 minutes after the earthquake origin time. 

 

GPS detection of ground deformation associated with great thrust fault earthquakes at a subduction zone. Between earthquakes, strain associated with the subduction accumulates of the locked plate interface. The earthquake releases this strain, causing ground motion that generates the seismic waves in the earth and the tsunami in the ocean. The resulting motion of GPS sites(click here) can be combined with results from seismic waves to determine the size of the earthquake and the geometry of faulting. 
Seth Stein and Emile A. Okal 
Department of Geological Sciences 
1850 Campus Drive 
Northwestern University, Evanston Illinois 60208 USA 
seth@earth.northwestern.edu 
emile@earth.northwestern.edu 
(847) 491-5265 FAX: (847) 491-8060
http://www.earth.northwestern.edu/people/seth 

For a primer on earthquake magnitudes (pdf) click here .

For an initial paper reporting these results (pdf, Nature, 31 March 2005, vol 434 pp 581-2) click here .

For a more detailed subsequent paper (pdf, BSSA, January 2007, vol 97 pp S279-S295) click here .

For a general audience article explaining these results (pdf) click here .

For this article in spanish (pdf) click here .

For an article from New Scientist about these results click here .

For a department presentation discussing these results (power point) click here 
(Download the tsunami animations at the URLs given and insert) 
For media articles (pdf) about these results click here .

To listen to an NPR interview about these results click here .

For the article about using GPS for tsunami warning click here 
For the press release about using GPS for tsunami warning click here 
For a Geotimes article about using GPS for tsunami warning click here

 http://www.earth.northwestern.edu/people/seth/research/sumatra2.html

Ultralong Period Seismic Study of the December 2004 Indian Ocean Earthquake and Implications for Regional Tectonics and the Subduction Process (Text)

by Seth Stein and Emile A. Okal 

Abstract

Analysis of the earth’s longest period normal modes shows that the December 2004 Sumatra–Andaman earthquake was much larger (Mw 9.3) than initially inferred from surface-wave data and involved slip on a much longer fault than initially inferred from body-wave data. The seismic moment and relative excitation of the normal modes indicate that the entire aftershock zone ruptured, consistent with the large tsunami amplitudes in Thailand, Sri Lanka, and India. An apparent increase in seismic moment with period results from interference between parts of the fault. The earthquake resulted from subduction of the Indian plate beneath the Burma microplate, a sliver plate between the Indian and Sunda plates. Hence, the rate and direction of convergence depends on the motion of the Burma plate, which is not well known. Convergence would be highly oblique if the rate of motion between Burma and Sunda is that inferred from spreading in the Andaman Sea, and less if a slower rate is inferred from the Sagaing fault. The December earthquake was much larger than expected from a previously proposed relation, based on the idea of seismic coupling, in which such earthquakes occur only when young lithosphere subducts rapidly. Moreover, a global reanalysis finds little support for this correlation. Hence, we suspect that much of the apparent differences between subduction zones, such as some trench segments but not others being prone to Mw  8.5 events and hence oceanwide tsunamis, may reflect the short earthquake history sampled. This possibility is supported by the variability in rupture mode at individual trench segments.

Introduction

The 26 December 2004 Sumatra–Andaman (or “Sumatra”) earthquake was the first “giant” or “extreme” (moment magnitude Mw  9) earthquake since the 1964 Alaskan event. Its enormous size and the devastating tsunami that resulted prompted a wide range of studies by earth scientists world wide. These studies were greatly facilitated by the availability in near-real time of high-quality seismological, geodetic, and other geophysical data. Information became rapidly available, making this the best-studied earthquake of its size and providing a basis for studies that will likely continue for many years. Our purpose here is to extend our initial study of the earthquake by using the earth’s longest-period normal modes. This study (Stein and Okal, 2005), published three months after the event, showed that the earthquake was much larger and involved slip on a much longer fault than at first thought. This analysis provided insight into the generation of the tsunami, the recurrence time of similar earthquakes, and the regional tectonics. Our subsequent studies and those of many other investigators (e.g., Banerjee et al., 2005; Ni et al., 2005; Park et al., 2005; Tsai et al., 2005; Vigny et al., 2005) in general support these initial findings and provide considerably more information. Hence, we extend our initial results in the light of subsequent studies both of the December earthquake and the Mw 8.7 Simeulue–Nias earthquake that occurred on 28 March 2005 on a segment of the trench immediately to the south. The Sumatra earthquake also provides an impetus to reexamine ideas about the conditions required for such giant events. It has long been recognized that subduction zones differ in many ways, including the fact that (at least on the short timescales over which we have observations), some have much larger and more common earthquakes at the thrust fault interface between the overriding and subducting plates. As a result, considerable effort has gone into trying to characterize this variation and interpret it in terms of the physical properties and stress state of the interface. A particularly important question is whether such earthquakes can occur at any subduction zone, or whether certain combinations of convergence rate, age of the subducting plate, or trench sediment thickness (Ruff and Kanamori, 1980; Ruff, 1989) are required. This issue is important for assessing tsunami hazards and improving tsunami-warning systems. As summarized in Figure 1, the danger of an oceanwide or far-field (as opposed to local) tsunami is low for earthquakes with Mw 8.5, significant for earthquakes with larger moment magnitude, and becomes extreme for Mw  9. Hence neither body-wave magnitude mb nor surface-wave magnitude Ms, the most traditional measures of earthquake size easily determined in the first few minutes after a major earthquake, are suitable for tsunami warning. This limitation arises from the spectra of earthquake sources. In theory, a plot of the logarithm of amplitude of the radiated waves versus the logarithm of the frequency is flat at low frequency (long period) with amplitude proportional to the static moment M0, and then decays for periods shorter than the rupture time TR needed for the rupture to propagate along the length of the fault and the rise time TD needed for slip to be completed at a point on the rupture. Thus, once earthquakes reach a certain size, both mb, measured around a period of 1 sec, and Ms, measured at 20 sec, saturate and do not exceed about 6.3 and 8.2, respectively (Geller, 1976). This effect prompted development of the moment magnitude which is calculated from the seismic moment (in dyne cm) using Mw   (log M0/1.5) 10.73 (Hanks and Kanamori, 1979), and defined so that the moment magnitude correlates with the other magnitudes when they have not fully saturated. Magnitude saturation is a serious problem for tsunami warning because “great” earthquakes, traditionally defined as ones with Ms  8, can be either too small to generate an ocean wide tsunami, or large enough that the risk is great. As a result, algorithms have been developed to more rapidly assess the seismic moment (Okal and Talandier, 1989; Tsuboi et al., 1995; Weinstein and Okal, 2005) and decide if a warning should be issued. The first crucial hours after the Sumatra earthquake illustrate the challenge (Kerr, 2005a). The Pacific Tsunami Warning Center’s first bulletin, 15 min after the earthquake, estimated its magnitude using longperiod body waves (not mb) at Mwp 8.0, with little risk of an oceanwide tsunami. Forty-five minutes later, using mantlewave data, the estimate was raised to 8.5, for which an oceanwide tsunami was likely. Four hours after the event, the Harvard Centroid Moment Tensor (CMT) project used longer-period surface waves to infer a moment magnitude of 9.0, for which the tsunami risk would have been recognized to be very high. By then, the coasts of Thailand and Sri Lanka lay devastated. Figure 2 summarizes the information about the earthquake source available within a few days after the earthquake. The first day’s aftershock zone extended 1200 km northward along the Sumatra trench from the epicenter off Sumatra (3.3 N, 95.8 E) to the Andaman Islands. The Harvard CMT solution showed a nearly pure thrust mechanism, and using surface waves with period up to 300 sec found M0 4 1029 dyne cm, corresponding to Mw 9.0. Initial body wave inversions (e.g., Ji, 2005) found that rupture started at the epicenter at the south end of this zone and propagated northward, but was limited to the southern third of the aftershock zone. The result that most slip occurred on the southern portion of the aftershock zone was surprising for two reasons. First, aftershocks occurring within the first day after great subduction-zone earthquakes in general are assumed to delineate the rupture area (Kanamori, 1977a). Second, because tsunami amplitudes are largest perpendicular to the fault, slip limited to the southern northwest-trending portion of the af- tershock zone would not have been expected to produce the large tsunami amplitudes in Thailand, Sri Lanka, and India.

Initial Results

Our analysis took an alternative approach by using the earth’s longest-period normal modes. Fourier analysis of long seismic records showed split modes, illustrated in Figure 3 for the five singlets making up the 0S2 multiplet, the earth’s fundamental mode with period 3232 sec. The records also showed beautifully split 0S3 and 0S4 multiplets. We modeled these multiplets, using Stein and Geller’s (1977) approach, which includes the effects of rotation and ellipticity, but not lateral heterogeneity. We also modeled radial modes 0S0 and 1S0 which contain only one singlet and thus are not split. We used the focal mechanism and depth reported by the Harvard CMT project and singlet eigenfrequencies including the effects of rotation and ellipticity. We obtained consistent estimates of seismic moment and Q for 0S2, 0S3, and 0S4 in both the time and frequency domains. The moment measured for 0S2, 1 1030 dyne cm, is approximately three times larger than measured from 300-sec surface waves, giving a magnitude Mw of 9.3, significantly larger than the previously reported Mw 9.0. Our interpretation of these results was that faulting had occurred along the entire aftershock zone, rather than only its southern third (Stein and Okal, 2005). This larger moment was consistent with 11 m of slip on a fault 1200 km long and 200 km wide (down-dip dimension). A longer rupture is also consistent with the fact that split modes are better fit by a source with centroid at 7 N than by one at the epicenter at 3 N, where rupture started and propagated northward (Fig. 4). This interpretation was also consistent with several key tsunami observations. The large tsunami amplitudes in Sri Lanka and India also favor rupture on the northern, northtrending, segment because tsunami amplitudes are largest perpendicular to the fault. This effect is due to directivity, the amplitude variation with azimuth due to radiation from a moving source. The amplitude varies with azimuth from the fault strike as sin X xL sinc(X)   where X   (c/VR cos ) X 2c where L is fault length, c is the radiated phase velocity, and VR is the velocity of rupture (Aki and Richards, 1980). For seismic waves, c/VR is about 1, so the maximum amplitude is along the direction of rupture propagation. In contrast, the tsunami speed under the shallow-water approximation, (gh) 1/2 is about 200 m/sec for a depth h   4 km, much slower than the rupture velocity of about 2.8 km/sec. As a result, c/VR K 1, and the amplitude is largest at right angles to the fault (Ben-Menahem and Rosenman, 1972). Hence modeling the tsunami assuming that slip occurred along the entire fault predicts larger amplitudes in Sri Lanka and India than assuming only slip on its southern part (Fig. 5).

Subsequent Results

We and a subsequent analysis by Park et al. (2005) were left with a puzzling initial result, a systematic increase of moment with increasing period (Fig. 6). We interpreted this as a consequence of the fact that the normal-mode solution found a larger moment and longer fault than the initial bodyand surface-wave studies, implying that slow rupture had taken place on the northern two-thirds of the aftershock zone. Hence, we began this study by attempting to model this effect as a direct consequence of the fault size. As shown in Figure 6 (top), the moment increased with period approximately as T0.4, or decayed with frequency as x0.4. However, source theory predicts x1 decay from the static moment (Fig. 1) for frequencies above the first corner frequency. Although simple models assuming various source durations predict a general increase in moment with period, they do not fit the moment values well, as illustrated in Figure 7 using simple “boxcar” models of constant moment rate release regularly spread over a duration D: M0 M˙ ˙ (t)   (0 t D); M (t)   0 otherwise. 0 0 D This model makes no direct assumption of any rupture slowness. The amplitude of its Fourier transform at angular frequency x is sinc(x D/2). which is plotted in logarithmic coordinates for source durations ranging from 200 to 800 sec. None of these models explains the full set of bestfitting moments. A short duration of 200 sec would reconcile the 300-sec CMT solution with the gravest modes, but would misfit 0S0 and especially 1S0, whereas longer durations would misfit the CMT solution. A satisfactory model must therefore involve a more complex behavior of the source, in which the moment rate release varies more irregularly with time. The increase in moment with increasing period also did not appear to be a result of the fault dip assumed. Although the absolute moment inferred trades off with dip (Fig. 8), both for the normal-mode and CMT solutions, the relative moments between the different modes would be unaffected. These issues have become clearer due to many results reported simultaneously with, and subsequent to, our first article’s publication (31 March 2005). Analyses using body waves (Ammon et al., 2005; Ishii et al., 2005; Ni et al., 2005), surface waves (Lay et al., 2005; Tsai et al., 2005), normal modes (Park et al., 2005), GPS (Banerjee et al., 2005; Vigny et al., 2005), and hydrophones (deGroot-Hedlin, 2005; Guilbert et al., 2005; Tolstoy and Bohnenstiehl, 2005) all found that rupture extended along the entire aftershock zone. We thus modeled the data by generating synthetic normal mode seismograms for a set of point sources using Tsai et al.’s (2005) composite CMT source model of five sources offset in time along the rupture with varying amplitudes and focal mechanisms. This solution gives an excellent fit to the normal mode data (Fig. 9) with a total moment of 1.2 1030 dyne cm, corresponding to Mw 9.3 and consistent with Tsai et al.’s (2005) surface-wave value. Hence the total moment remains approximately three times that inferred from the initial CMT solution. However, the increase in moment with period we had inferred using a single point source model is no longer required, because it results from interference between energy radiated from parts of the fault, rather than purely from the fault size. Tsai et al.’s (2005) model implies an irregular rupture velocity, varying from 4 km/sec to less than 2 km/sec. The average velocity, 2.8 km/ sec, is somewhat slower than typical values (about 2.5– 3.5 km/sec) without, however, reaching the very low values (1 km/sec) observed for so-called tsunami earthquakes (Polet and Kanamori, 2000; Lo´pez and Okal, 2006). This irregularity in rupture velocity and in geographic distribution of moment release is why simple duration models fail to account for the apparent increase of moment with period. It also explains why a similar increase did not occur for the 28 March earthquake, which was smaller but in a similar location and with a similar fault geometry (Fig. 6, bottom). In our view, the crucial result is not the precise value of the moment or moment magnitude. The Sumatra earthquake, which is the most studied large earthquake to date with the best and most diverse data, demonstrates again that these quantities have uncertainties (typically 0.1–0.2 units in moment magnitude) owing to the data type, specific data used, and assumptions required in the analysis. As in most such situations, the true uncertainty will reflect the systematic errors that exceed the formal uncertainty associated with measurements from a specific set of data with a specific technique. Hence whether the earthquake’s “real” magnitude is 9.2 or 9.3 is not the issue. The important point, as discussed next, is that the entire aftershock zone ruptured.

Plate Motions and Earthquake Recurrence

The view emerging from the normal modes and other seismological studies gives interesting insight into the regional tectonics and the recurrence interval of such giant earthquakes. Unlike its 1960 Chile and 1964 Alaska cousins, the Sumatra earthquake occurred in a complex and poorly understood tectonic setting (Fig. 10). In a mega-sense, the earthquake is related to the collision between the Indian and Eurasian plates. As a result, it is natural to think of the earthquake as releasing strain accumulated at the Sumatra trench by the  40 mm/yr of northeastward motion of India with respect to Eurasia. However, the actual plate geometry and motions are complex and not well known. One complication is that much of southeast Asia, including Thailand, the Malay Peninsula, and the South China Sea is presently viewed as forming the Sunda plate. Global Positioning System (GPS) data show that Sunda moves relative to Eurasia and is thus a distinct plate (Chamot-Rooke and Le Pichon, 1999; Michel et al., 2001). A second complication is that the oceanic lithosphere subducting at the trench consists of the Indian plate to the north, the Australian plate to the south, and possibly a diffuse boundary between them extending as far north as about 10 N (Royer and Gordon, 1997). Hence, some of the subducting plate involved in the December 2004 event might be regarded as part of Australia, but for simplicity we do not do so. The most crucial complication is that between the subducting Indian plate and the Sunda plate is the Burma microplate, a sliver plate. The presence of a distinct Burma microplate is shown by magnetic anomalies at the Andaman spreading center recording active seafloor spreading at 37 mm/yr between the Burma and Sunda plates (Curray et al., 1979; Raju et al., 2004). This relative motion is also shown by normal-faulting earthquakes on the Andaman spreading center (Guzman-Speziale and Ni, 1993) and strike-slip events on the major transform zone to the south that connects the Andaman spreading center to the Sumatra fault. It is intriguing that after the December earthquake both strike-slip and normal-fault earthquakes occurred on this feature (M. Nettles, personal comm.) A component of extension across it, or short spreading segments within it (Curray et al., 1979), would be consistent with the mechanisms and its trend’s deviation from the assumed spreading direction orthogonal to the spreading axis and parallel to the short transforms bounding the axis. However, the extent of the Burma plate is unclear. Curray et al. (1979) include both the oceanic region between the Andaman spreading center and the Sumatra trench, and the region on land between the Burma arc and Sagaing fault. In this geometry, the Burma arc is an India–Burma subduction zone (Ni et al., 1989; Holt et al., 1991; Satyabala, 2003) and the Sagaing fault is a Burma–Sunda transform (Nielson et al., 2004). Bird (2003), however, considers the land area north of about 15 N on both sides of the Sagaing fault to be a broad deforming region, not part of either the Burma or Sunda plates. Bird’s (2003) geometry is easier to visualize because the 18 mm/yr of strike-slip motion on the Sagaing fault measured using GPS (Vigny et al., 2003) and its trend are not compatible with the rate and direction of Burma– Sunda motion inferred from the magnetic data and transform trends. Because in this geometry the “Burma” plate does not include Burma, it might better be called the “Andaman” plate except for the risk of creating even more confusion. There is also discussion about where (presumably on Sumatra) the south end of the Burma plate is. Even with these complexities, it seems that most or all of the convergence at the portion of the Sumatra trench that broke in the December 2004 earthquake is between the subducting Indian and overriding Burma plates. To estimate the motion between the Indian and Burma plates, we use a procedure similar to that in our initial study (Stein and Okal, 2005). We first find the motions of the major plates from the differences between Euler vectors determined from GPS data in the International Terrestrial Reference Frame (ITRF) for the motions of Sunda (Vigny et al., 2003), India, Australia, and Eurasia (Sella et al., 2002). In doing so, we neglect small differences resulting from the former being in ITRF-2000 and the latter in ITRF-97. Although all of these Euler vectors have uncertainties, the biggest challenge is constraining Burma’s motion with respect to Sunda. The rate of back-arc spreading is known only across one ridge segment. The only directional data are transform segments, which do not give consistent trends. The short transforms bounding the spreading segment imply relative motion oriented about 153, as would assuming motion in the direction orthogonal to the ridge. Because this azimuth is insufficient to constrain the location of the Euler pole, Curray et al. (1979) and Bird (2003) used additional directional assumptions based on the regional plate geometry to estimate Euler vectors. Although these Euler vectors differ, both are constrained by the spreading rate and transform azimuth and so make similar predictions along the nearby trench. We used Euler vectors of both Curray et al. (1979) and Bird (2003) to infer India’s motion with respect to Burma (Table 1). The pole derived from Bird’s Burma–Sunda motion is somewhat north of both our earlier estimate, which averaged the Bird and Curray et al. Euler vectors, and Bird’s (2003), which connected his Euler vector to the other plates using the NUVEL-1a geologic plate motion model (DeMets et al., 1994). We illustrate the geometry by considering linear velocities (Fig. 11) at 7 N, 92 E, a point on the trench near the center of the rupture. Although only two of the plates are physically present at this point, this construction shows the relationships involved. Relative to Sunda, India moves northeastward at 36 mm/yr. However, Burma moves northwestward relative to Sunda much faster, and thus northwest relative to India. Hence at this point on the trench, India subducts beneath Burma at about 44 mm/yr in a southeast (106) direction for the Bird Euler vector, or about 35 mm/ yr in the 93 direction for the Curray et al. one. Although this result is not intuitive, it emerges from the relative plate motions unless one or more of them differs significantly from that assumed. This is certainly possible. Our inferred motion of Sunda relative to Eurasia and India differs slightly from that inferred by Chamot-Rooke and Le Pichon (1999) and Michel et al. (2001) because for consistency we use the other plates’ motion from GPS data, whereas they combine Sunda motion from GPS with the NUVEL-1a geologic plate-motion model (DeMets et al., 1994). The major uncertainty is the Burma–Sunda plate motion, which the Bird and Curray models infer from the rate and direction on the Andaman spreading center. In contrast, Nielson et al. (2004) use the 18 mm/yr rate and 355 direction from the Sagaing fault to infer linear velocities further north, at about 16 N. The slower Burma–Sunda motion predicts India moving northeast relative to Burma. Although this would be easier to reconcile with the earthquake mechanism, it implies that either the magnetic data have been misinterpreted or spreading on the Andaman spreading center has slowed and changed direction from that inferred by Curray et al. (1979). As shown in Figure 11 (top and center), the predicted convergence increases southward from 21 mm/yr at 13 N to 55 mm/yr at 4 N for the Bird Euler vector or 28 mm/yr to 39 mm/yr for the Curray vector. The nearly pure thrust fault mechanism (or mechanisms, if the subevents are considered) indicates that the 2004 earthquake reflects primarily the corresponding arc-normal components of convergence, 19–48 or 28–36 mm/yr. Because the poles are nearby, the predicted convergence direction varies along the rupture zone. However, because these poles are not close to the north end of the rupture, we no longer suggest that motion became strike-slip there, explaining why rupture ceased. The area shows a form of slip partitioning, in which the oblique convergence between India and Sunda gives rise to motion of the Burma microplate. This effect is seen at many trenches where convergence is oblique to the trench and a forearc sliver moves separately from the overriding plate. As a result, earthquake slip vectors at the trench trend between the trench-normal direction and the predicted convergence direction (Jarrard, 1986; Ekstro¨m and Engdahl, 1989; DeMets et al., 1990; DeMets and Stein, 1990; McCaffrey, 1991, 1992, 2002) and strike-slip motion occurs between the forearc and the stable interior of the overriding plate. In the limiting case of pure slip partitioning, pure thrust faulting would occur at the trench, and all the oblique motion would be accommodated by trench-parallel strike-slip. The situation here appears more complicated than typical slip partitioning, however. The slip vector is rotated toward the trench normal (Fig. 11), consistent with partial slip partitioning. Yet, Burma moves northwest faster than expected even for pure slip partitioning (Fig. 12). This peculiarity would favor Nielson et al.’s (2004) argument for Burma–Sunda motion slower than inferred from the magnetic anomalies. This possibility is illustrated in Figure 11 (bottom), drawn assuming Burma–Sunda motion is given by the Sagaing fault motion. A key result of our earlier analysis was that, because the entire aftershock zone slipped, strain accumulated from subduction of India beneath Burma on the northern part of the rupture had also been released. This leaves no immediate danger of a similar oceanwide tsunami being generated by slip on this segment of the plate boundary. If such earthquakes involve at least 10 m of slip, the plate motions predict they should be 200–1000 years apart, with the longer intervals corresponding to failure of the northern portions. Long recurrence times would be consistent with the lack of cultural memory of such events, and initial paleoseismic results from India suggesting a major tsunami about 1000 years ago (Rajendran et al., unpublished manuscript, 2006). However, we noted the danger of a large tsunami resulting from a great earthquake on segments of the Sumatra trench to the south. McCloskey et al. (2005) showed that stress transfer from the December earthquake increased stress on the segment immediately to the south and increased the likelihood of a large earthquake. In fact, an Mw 8.7 earthquake occurred on 28 March 2005, shortly after their article appeared on 17 March. However, it did not generate an oceanwide tsunami because its rupture did not extend to the seafloor and because of the presence of islands whose uplift does not excite a tsunami (Kerr, 2005b). However, the March event bears out the risk of both local and oceanwide tsunamis generated by the rupture of segments further south (Nalbant et al., 2005), as implied by paleoseismic data (Zachariasen et al., 1999; Natawidjaja et al., 2004).

Implications for Giant Earthquake Occurrence and Tsunami Generation

The December earthquake revived interest in the longstanding question of what are the conditions required for such giant earthquakes and hence oceanwide tsunamis. An important question is whether such earthquakes can occur at any subduction zone, or whether certain combinations of convergence rate, age of the subducting plate, or trench sediment thickness (Ruff and Kanamori, 1980; Ruff, 1989) are required. We thus re-examined Ruff and Kanamori’s (1980) proposal that the largest (Mw  8.5) earthquakes occur only when young lithosphere subducts rapidly. Although this correlation appeared plausible with the data then available (r   0.8), much of the correlation vanishes (r   0.4) (Fig. 13) using new data (Table 2). The largest earthquakes are still on the left (younger) side of the plot, but there is no clear effect of age. The new data contain most of the same earthquakes, but a few are added or updated. For example, the Mw 9.3 of the December 2004 earthquake would not have been predicted. Points for the Chile and Peru trenches shift “downward” because recent plate-motion models derived using either magnetic anomalies (DeMets et al., 1990, 1994) or space geodesy (Norabuena et al., 1998, 1999; Sella et al., 2002) find that Nazca-South America convergence is significantly slower than previously thought. Conversely, GPS rates (Bevis et al., 1995; Calmant et al., 2003) shift the Tonga and Vanuatu points “upward.” A further difficulty is that, because large trench events can be normal faults (Kanamori, 1971a), the largest known earthquakes at a trench need not be interplate thrusts. For example, the 1974 Ms 7.5 Lesser Antilles earthquake used in the earlier dataset was a normal fault (Stein et al., 1982). Thus for older events, we face the challenge that not only are their magnitudes poorly known, but they may not have been thrust events. Although paleoseismic evidence can sometimes resolve this issue, many events remain suspect, especially in areas where modern catalogs such as the Harvard CMT dataset contain only very small interplate thrust solutions (e.g., Marianas, Lesser Antilles). Accordingly we use open symbols in Figure 13 for those regions where the largest event is either confirmed or likely to be nonthrust, and reserve solid symbols for those featuring interplate thrust, either documented from a modern seismic solution or strongly suggested by geological evidence, for example, in the 1700 Cascadia earthquake (Satake et al., 2003). The lack of strong correlation between the maximum size of trench earthquakes and convergence rate and age is consistent with other results. Ruff and Kanamori’s (1980) proposal was based on the hypothesis of seismic coupling, in which large earthquakes reflect the mechanical properties of subduction zones. Although the term “seismic coupling” is widely used, a variety of definitions have been offered and its relation (if any) to the mechanics of plate coupling is still unclear (Wang and Dixon, 2004). This hypothesis was originally posed in terms of two end members: coupled Chileantype zones with large earthquakes and uncoupled Marianastyle zones with largely aseismic subduction (Uyeda and Kanamori, 1979). Hence zones with young, rapidly subducting, and thus warm buoyant lithosphere were expected to be the most strongly coupled in terms of either the largest earthquakes or the highest fraction of the plate motion re- leased as earthquakes. However, although most subduction zones appear to show significant components of aseismic slip, no obvious correlation of the seismic-slip fraction with convergence rate and plate age has been found (Peterson and Seno, 1984; Pacheco et al., 1993). Although the initially proposed correlations do not seem strong, others remain under investigation. Several studies find a relation between seismic coupling, defined by the seismic-slip fraction, and absolute plate motions, which may affect the mechanics of the interface (Peterson and Seno, 1984; Scholz and Campos, 1995). Another possibility is that thick trench sediments lubricate the interface and allow rupture to propagate long distances, allowing events with Mw  8.5 (Ruff, 1989). Although the initial correlation seems reasonable, there are counterexamples. For example, the Makran zone has 6000 m of sediment, but the maximum observed Mw is 8, so thick sediment may be a necessary but not sufficient condition. A further complication is that sediment thickness varies along the long rupture zones of such earthquakes. It is also not clear how sediment affects the trench mechanics. Although strong “seismic coupling,” in general, is assumed to be related to strong mechanical coupling, the converse has also been proposed. Lamb and Davis (2003) argue that such sediment-rich trenches have low stresses on the interface, so these trenches have strong seismic coupling but weak mechanical coupling. They propose that the south Peru and north Chile trench segments, seaward of the high Andes, do not have large trench earthquakes, and so are more strongly coupled mechanically (or less coupled seismically) than segments to the south, such as the south Chile segment  where the 1960 Mw 9.6 earthquake occurred. In their model, Cenozoic climate change deprived the Peru trench of sediment and thus strengthened mechanical coupling there, causing uplift of the high Andes. However, it is not clear that the south Peru and north Chile trench segments differ in seismic coupling from segments to the south. In particular, numerical tsunami modeling shows that the 1868 Peru earthquake ruptured farther to the north than traditionally assumed, implying Mw  9.2 (Okal et al., 2006). This observation argues against the location of the high Andes being controlled by unusually strong mechanical coupling. A significant problem with these arguments is that large trench earthquakes are infrequent, and both the instrumental and historic seismic records are short. As a result, inferring “seismic coupling” from either the size of the largest earthquakes or the seismic-slip fraction is challenging. First, the uncertainties in estimating source parameters of earthquakes from historical data are considerable. Fault areas and amounts of slip must be estimated, and moments and thus magnitudes depend on both these and the rigidity assumed. Second, the seismic cycle is typically much longer than the instrumental record (McCaffrey, 1997), and the size and recurrence interval of earthquakes on a given trench segment can be quite variable (Thatcher, 1990). Third, some large earthquakes have significant slow slip associated with the main event, on timescales of days to years (Kanamori and Cipar, 1974; Cifuentes and Silver, 1989; Barrientos, 1995; Heki et al., 1997). The seismic moment released by these processes, termed slow or silent earthquakes or afterslip, is associated with earthquakes but is not included in conventional seismic-moment calculations, and hence produces a spurious seismic-slip deficit at the plate boundary. Hence, it is difficult to assess whether an apparent seismic-slip deficit indicates a seismic gap where large earthquakes are overdue, or that much of the interplate motion occurs aseismically (Stein, 1992). Fourth, the seismic slip is a fraction of an assumed plate convergence rate, so different plate-motion models give different results (Stein et al., 1986). We suspect, therefore, that much of the apparent differences between subduction zones, such as some trench segments but not others being prone to Mw  8.5 events, may reflect the short earthquake history sampled. This possibility is supported by the variability in rupture mode at individual trench segments. For example, the Nankai trough history shows that sometimes the entire region slipped in large earthquakes, whereas in other intervals slip divided into smaller events. Although the specific segment sizes that broke are under discussion, various authors agree on the general pattern. Figure 14 shows possible magnitudes for these earthquakes, inferred from a variety of sources (Kanamori, 1972; Ando, 1975; Ishibashi, 1981; Rikitake, 1999). Although none can be assigned with confidence, the relative magnitudes illustrate how the sequence could give rise to earthquakes of quite different magnitudes during different periods. Another example is the trench segment that produced the Mw  9.6 1960 Chilean earthquake. It appears that its rupture mode must be variable because the seismicslip rate inferred assuming that the 1960 earthquake is this segment’s characteristic earthquake exceeds the convergence rate (Fig. 15). Hence Stein et al. (1986) proposed that either the characteristic earthquake is smaller than the 1960 event, the average recurrence interval is greater than observed in the past 400 years, or both. Recent paleoseismic studies support this analysis, showing that events in 1737 and 1837 were smaller than the 1960 one, whereas one in 1575 was comparable (Cisternas et al., 2005). Paleoseismic studies also find evidence for variable size of thrust events, presumably due to the differences between multisegment and single-segment rupture, for Cascadia (Kelsey et al., 2005) and the Kuril trench (Nanayama et al., 2003). Viewed this way, problems resulting from the short earthquake history would not be surprising. If Mw 8 events are three times more common than Mw 8.5, following a Gutenberg–Richter prediction, then Mw  8.5 will be rarer and thus absent from the short record for some trenches. This effect will be enhanced if the larger earthquakes are rarer than this prediction, which is the case globally. As a result, distinguishing real differences among trenches from apparent differences due to the short earthquake history will remain a major challenge. Each new Sumatra-sized earthquake will provide important new data.

Acknowledgments

This research was supported in part by National Science Foundation Grant CMS-03-01054. Several figures were drafted using the GMT package (Wessel and Smith, 1991). We thank Meredith Nettles for access to the Composite Harvard CMT solution before publication.

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Manuscript received 16 January 2006.

https://cpb-us-e1.wpmucdn.com/sites.northwestern.edu/dist/8/1676/files/2017/05/sumatrabssa-1l49ryh.pdf

Ultralong Period Seismic Study of the December 2004 Indian Ocean Earthquake and Implications for Regional Tectonics and the Subduction Process

Stein,S. et al.

Bulletin of the Seismological Society of America(2007),97(1A):S279

http://dx.doi.org/10.1785/0120050617