Teleseismic inversion of the 2004 Sumatra-Andaman earthquake rupture process using complete Green’s functions
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Spatial and temporal variations in coseismic slip distribution are often obtained by rupture process analyses using teleseismic body waves. Many analyses using teleseismic body waves were based on the ray theory because of the very efficiently computable direct P-, S-, and major reflected waves near the source. The 2004 Sumatra-Andaman earthquake was one of the largest earthquakes recorded in history, and the data that are required for the entire rupture process analysis include later phases such as PP waves and a very long period phase called a W phase. However, calculating these later phases using the conventional ray theoretical method is difficult. Here we investigate the rupture process of the 2004 Sumatra-Andaman earthquake using complete Green’s functions, including all later phases such as PP waves and W phase. We use the direct solution method, which computes complete synthetic seismograms up to 2 Hz for transversely isotropic spherically symmetric media, to calculate the Green’s functions. The obtained synthetic seismograms generated fit the observed seismograms quite well from a short period to a long period. The estimated slip distribution consists of four large slip areas: the largest slip occurred in the shallow part off the Sumatra west coast with a maximum slip of approximately 29 m, the second and third largest slips occurred in the shallow and deep parts of the Nicobar region with maximum slips of approximately 8 m and 7 m, respectively, and the fourth slip occurred in the middle Andaman region with a maximum slip of approximately 6 m. The estimated average rupture velocity is 2.8 km/s, but the rupture may have slowed between the Sumatra and the shallow Nicobar slip areas, and between the Nicobar and the middle Andaman slip areas. The delayed initiation of the shallow slips in the Nicobar region may possibly have been triggered by the deeper slip in the Nicobar region. There were no distinct depth-varying properties for the shallow and deep slips in the Nicobar region, as were reported for the 2011 Tohoku-Oki and 2010 Chile earthquake.
KeywordsFinite fault inversion Teleseismic body waves 2004 Sumatra-Andaman earthquake Direct solution method
The 26 December 2004 Sumatra-Andaman earthquake was one of the largest earthquakes ever to be instrumentally recorded; it caused the Indian Ocean tsunami, which killed over 250,000 people. Many high-quality geophysical data sets have led to a large number of proposed rupture models. This earthquake had a very long fault length of 1,200 to 1,300 km with a moment magnitude of 9.1 to 9.3 (Ammon et al. ; Stein and Okal ; Tsai et al. ). The source duration and rupture velocity were estimated to be approximately 500 s and 2 to 3 km/s, respectively, by high-frequency seismic and hydroacoustic data (Guilbert et al. ; Ishii et al. ; Ni et al. ; Tolstoy and Bohnenstiehl ).
Spatial and temporal variations in coseismic slip distribution are often obtained by rupture process analyses using teleseismic body waves. Many analyses of teleseismic body waves with short periods (in seconds) were based on the ray theory (e.g., Kikuchi and Kanamori ) because of very efficiently computable direct P, S, and major reflected waves near the source. Conventional teleseismic body wave inversion using the global broadband seismic network can be immediately analyzed after the occurrence of large earthquakes. However, some problems arise when these methods analyze that the total duration of a rupture process is longer than the time window between the later phase PP waves and the P waves, such as the 2004 Sumatra-Andaman earthquake (Ji ; Yagi ; Yamanaka ). These methods cannot accurately calculate later phases such as PP waves because such waves are complicated by the upper mantle structure. Furthermore, these conventional methods cannot explain the long-period (up to 1,000 s) W phase, which has been observed in the displacement records of huge earthquakes and can be explained as the superposition of the fundamental mode and several overtones of spheroidal modes or Rayleigh waves (Kanamori ; Kanamori and Rivera ).
The model III of Ammon et al. (), hereafter called Ammon-III, was employed to conduct finite fault inversion of the earthquake using long-period body waves and surface waves (20 to 2,000 s) with the spectral element method for a three-dimensional earth model. Such long-period waveforms constrain the general features of the rupture process. On the other hand, abrupt changes in the rupture velocity or slip magnitude radiate high-frequency seismic waveforms (Das and Aki ; Madariaga ). To obtain detailed characteristics, such as variations in the slip velocity or rupture velocity, it is important to use higher-frequency seismograms. The purpose of this study is to analyze the full duration rupture process of the 2004 Sumatra-Andaman earthquake using complete (including all later phases such as PP waves and W phase) Green’s functions including high frequency (i.e., seismic frequency bands that are the same as those for conventional teleseismic body wave inversion methods). The Green’s functions were calculated up to 1 Hz using the direct solution method (DSM; Geller and Ohminato ; Kawai et al. ), which computes complete synthetic seismograms for transversely isotropic, spherically symmetric media.
Data and methods
In this study, the Green’s functions were calculated by the DSM for transversely isotropic, spherically symmetric media (Kawai et al. ). We used the DSM software published on the Internet (Takeuchi ). The DSM computes synthetic seismograms by directly solving the Galerkin weak form of the equation of motion. Note that this program does not use geometrical optics or Earth-flattening approximations but efficiently computes highly accurate synthetic seismograms up to 2 Hz in a spherically symmetric, transversely isotropic Earth model. Detailed derivations of the DSM and extension to transversely isotropic spherically symmetric media up to 2 Hz were provided by Geller and Ohminato () and Kawai et al. (), respectively. In this study, we calculated the Green’s functions in the period range from 1/4,096 to 1 Hz using the IASP91 earth model (Kennett and Engdahl ) and applied the waveform inversion scheme of Kikuchi et al. (). We consider that the IASP91 earth model is appropriated for the Sumatra region (Additional file 1: Figure S1). We imposed two constraints: non-negative rake direction (Lawson and Hanson ) and spatial smoothness of the slip distributions. The smoothing constraint value is determined by inspecting whether the synthetic waveforms restore distinct phases of the observed waveforms and whether the slip distribution is not complex.
Teleseismic body wave inversion is a sensitive method for determining the depth of a slip area using the depth phases (i.e., the -pP and -sP phases). Ammon-III assumed three planar fault segments to express the very long and wide rupture area of the 2004 Sumatra earthquake; however, the subducting slab geometry obtained by seismicity is actually curved (Engdahl et al. ; Sibuet et al. ). The gap in depth between the assumed fault model and the true slab geometry causes a negative effect in the inversion results. It is important for teleseismic body wave inversion to use accurate fault geometry, particularly dip directions. Here we used the fault geometry model of Hoechner et al. (), which was constructed by an accurate discretization of subducting slab geometry. This fault geometry model consists of 12 × 36 = 432 subfaults with depths ranging from 5 to 53 km, based on regionalized upper mantle (RUM) slab geometry (Gudmundsson and Sambridge ). The average subfault length and width are 40 and 16 km, respectively. The detailed subfault parameters are cited in supplementary data set S3 of Hoechner et al. (). A single-point source is used as the subfault Green’s function (i.e., rupture propagation inside each subfault is not included). The slip rate function of each grid point was expanded into 20 triangle functions with duration of 6 s at an interval of 3 s. We assumed a maximum rupture front velocity of 3.0 km/s, which was selected by a grid search between 1.0 and 4.0 km/s.
The large slip segments are in located in four separate areas. The transitions of each segment along the strike direction are roughly consistent with the changes the physical properties of the subducted slab from seismic tomography (Kennett and Cummins ). Although the average rupture velocities in areas A and C have the same value as the maximum rupture front velocity of 3.0 km/s, the rupture in areas B and D started 30 to 40 s after arrival of the assumed maximum rupture front at a velocity of 3.0 km/s and propagated with average rupture velocities of 4.0 and 3.0 km/s, respectively. The southern sides of areas B and D are not ruptured. These areas may form a barrier region (velocity-strengthening behavior), and the barriers may cause the rupture velocities to be slow. The slow rupture initiation in the shallow Nicobar region was further supported by a recent joint inversion of tide gauge, satellite altimetry, and GPS data by Lorito et al. (). The slow rupture velocity of the Andaman region has been indicated in many studies (e.g., de Groot-Hedlin ; Guilbert et al. ; Tolstoy and Bohnenstiehl ; Tsai et al. ). Another interpretation of the delay onset of slip with respect to the maximum rupture front in area B is that the slip in area B may have been triggered by the slip in area C.
Ammon et al. () showed that three relatively energetic amplitude bursts (from 50 to 150, 280 to 340, and 450 to 500 s) can be identified in high-frequency seismograms. These energetic bursts correspond with the slip of our results in areas A, B and/or C, and D, respectively. Although the slip rate functions of areas A and D have large peak slip rate values and distinct peaks (the slip rate function of area A has two peaks), the variations of these functions for areas B and C are relatively moderate. Comparing the slip rate function in area B with that in area C, the slip rate in area B increases moderately and maintains the same value in the last time window, but the slip rate in area C rises rapidly and decreases with time. These features may represent depth-varying rupture properties of the subduction zone (e.g., Lay et al. ); however, there are no distinct variables in these functions, which is in contrast to distinguish the properties reported in the 2011 Tohoku-Oki and 2010 Chile earthquakes (e.g., Asano and Iwata ; Koper et al. , ; Wang and Mori ).
The obtained source time function is very similar to that of Ammon-III. A source time function is the most stable parameter despite some differences in fault parameters in finite fault inversion (e.g., Lay et al. ). The largest moment release occurred from 60 to 200 s in the Sumatra region (area A). This largest moment release in area A has been obtained in most rupture process analyses. The largest slip area of our study is located off the west coast of the Sumatra islands at a depth shallower than 30 km with a maximum slip of approximately 29 m. However, the largest slip area of Ammon-III is located in the deeper part of the Sumatra region with a maximum slip of approximately 12 m. Araki et al. () deployed the ocean bottom seismographic network around this region in February and March 2005. The aftershock distribution was mainly concentrated deeper than 25 km, and their focal mechanisms were dominantly the dip-slip type. These aftershocks are considered to have occurred at the plate interface. In contrast, aftershocks at depths shallower than 25 km were dominantly by a dip-extension type mechanism. The large reverse fault mechanism aftershocks greater than Mw7.0 occurred on the edge of the largest slip area of our study (Figure 2b). This relation between large slip areas and aftershocks has already been indicated in previous studies (e.g., Mendoza and Hartzell ; Houston and Engdahl ), and this comparison indicates the robustness of the rupture process analysis. These results support the shallow largest slip of our result.
A significant discrepancy is present in the amount of maximum slip between our study and Ammon-III. This discrepancy was caused by the different rigidities between our study (30 GPa) and Ammon-III (68 GPa), because the largest slip area of our study is located in the shallow region. Seno and Hirata () reported that the maximum slip of the tsunami models (approximately 30 m; e.g., Hirata et al. ; Tanioka et al. ; Fujii and Satake ) is generally larger than that of the seismological models (approximately 15 m; e.g., Ammon et al. ; Ji ; Yamanaka ). They suggested that additional crustal deformation, such as inelastic uplift of the trench sediments, might have occurred near the deformation front. However, the maximum slip value of our result is consistent with the tsunami models. This shows that no additional slip, such as inelastic deformation, is necessary.
Our results indicate that the rupture occurred in both shallow and deep parts of the Nicobar region (areas B and C); this result was further obtained by Lorito et al. (). Two large left lateral fault mechanism aftershocks (Mw7.2, Mw7.5) occurred in the Nicobar region. The depths of the aftershocks obtained by Global CMT were 12 and 33 km, respectively, and these aftershocks were considered to be a reactivation of the fracture zone of the subducted oceanic plate triggered by the main shock. Unless the rupture occurred in the shallow near-trench region, a positive Coulomb stress change for the two aftershocks was not produced (Delescluse et al.  On the other hand, the subsidences of approximately 3 m in the Nicobar Islands and Great Nicobar were not explained only by the shallow slip; to cause these subsidences, the deep part slip is necessary. These facts support both the shallow and deep part slips in the Nicobar region obtained by our result; however, these subsidences may be caused by not only coseismic slip but also postseismic slip in the deep part.
Next, the rupture propagated at 11° N near Little Andaman, and almost no slip occurred from 11° N to 13° N; however, a rupture occurred around 13° N to 14° N in the northern end (area D) 40 s after the arrival of the rupture front. The large normal fault mechanism aftershock (Mw7.5) in the Andaman region was considered to be an extension event caused by a slab pull force following the main shock (Andrade and Rajendran ).
We estimated the rupture process of the 2004 Sumatra-Andaman earthquake using teleseismic body waves. This was a giant earthquake with very long rupture duration of approximately 500 s; therefore, conventional teleseismic body wave analyses, which cannot calculate later phases such as PP waves and W phase, could not reveal the entire rupture process. Our source model satisfactorily reproduces the features of the observed waveforms, including later phases from short-period to long-period components. The largest slip area was determined to have been in the shallow Sumatra region with a maximum slip of approximately 29 m. The shallow largest slip is consistent with the large slip obtained by tsunami inversions and supported by the aftershock locations. Other slip areas were determined in the shallow and deep Nicobar region and Andaman region. Although the rupture started in the deep Nicobar region immediately after arrival of the assumed maximum rupture front velocity of 3.0 km/s, the beginning of rupturing in the shallow Nicobar region was delayed by 30 s and that in the Andaman regions was delayed by 40 s after this arrival. The southern areas of these delayed rupture initiations are not ruptured. These areas may a barrier region, and the rupture velocities are slow because of these barriers. Another interpretation of the delay onset of slip with respect to the maximum rupture front in the shallow Nicobar region is that the slip in shallow Nicobar region may have been triggered by the slip in the deeper Nicobar region. There were no distinct depth-varying properties of the shallow and deep slips in the Nicobar region.
For this study, we used the computer systems of the Earthquake Information Center of the Earthquake Research Institute, University of Tokyo. This study was supported by the Earthquake Research Institute cooperative research program. We thank Nozomu Takeuchi for helpful comments on using the DSM program. The authors would like to thank Enago (www.enago.jp) for the English language review. We appreciate Hiroshi Takenaka and two anonymous reviewers for their helpful comments and suggestions for improving this manuscript.
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