Co-seismic fault geometry and slip distribution of the 26 December 2004, giant Sumatra–Andaman earthquake constrained by GPS, coral reef, and remote sensing data
We analyze co-seismic displacement field of the 26 December 2004, giant Sumatra–Andaman earthquake derived from Global Position System observations, geological vertical measurement of coral head, and pivot line observed through remote sensing. Using the co-seismic displacement field and AK135 spherical layered Earth model, we invert co-seismic slip distribution along the seismic fault. We also search the best fault geometry model to fit the observed data. Assuming that the dip angle linearly increases in downward direction, the postfit residual variation of the inversed geometry model with dip angles linearly changing along fault strike are plotted. The geometry model with local minimum misfits is the one with dip angle linearly increasing along strike from 4.3o in top southernmost patch to 4.5o in top northernmost path and dip angle linearly increased. By using the fault shape and geodetic co-seismic data, we estimate the slip distribution on the curved fault. Our result shows that the earthquake ruptured ~200-km width down to a depth of about 60 km. 0.5–12.5 m of thrust slip is resolved with the largest slip centered around the central section of the rupture zone 7ºN–10ºN in latitude. The estimated seismic moment is 8.2 × 1022 N m, which is larger than estimation from the centroid moment magnitude (4.0 × 1022 N m), and smaller than estimation from normal-mode oscillation data modeling (1.0 × 1023 N m).
KeywordsSumatra–Andaman earthquake Fault geometry Co-seismic slip distribution Geodetic data
The 26 December 2004 Sumatra–Andaman megathrust earthquake was one of the largest earthquakes of the past century (Sieh 2005; Lay et al. 2005). This event ruptured a section of the Sumatra–Andaman subduction zone, separating the Australia and Sundaland plate in the south, and the India and Burma plate in the north (Simoes et al. 2004; Prawirodirdjo et al. 1997; Shearer and Bürgmann 2010). Approximately 300,000 human lives were lost as the result of this devastating earthquake and the tsunami it generated. Despite of its great size and catastrophic consequences, however, the magnitude and rupture distribution of the earthquake are still being debated. Early Harvard centroid moment solution using the first 500 s of seismic data suggested a seismic moment release of M = 4.0 × 1022 N m, equivalent to MW 9.0 (http://www.globalCMT.org). A subsequent study of normal-mode free oscillation data derived a seismic moment release of 1.0 × 1023 N m, equivalent to MW 9.3 (Stein and Okal 2005). The spatial distribution of aftershocks suggested that the earthquake ruptured a portion of the subduction zone of about 1400 km long, spanning ~2ºN–14ºN in latitude. More detailed seismic waveform studies, using surface wave data, revealed that the slip was extended to the Andaman islands region, and the maximum slip appeared to have occurred south of 9.5ºN, along a segment of the plate interface offshore of the northwestern Sumatra and the southern Nicobar Islands (Ammon et al. 2005). The moment release was estimated 6.5 × 1022 N m, equivalent to an MW 9.15 earthquake (Ammon et al. 2005). The same estimate was yielded also by Park et al. (2005) from free oscillation data modeling. Multiple source analysis by Tsai et al. (2005) specified 5 sources, 3 larger ones along the southern (<9ºN) segments, and 2 smaller ones along the northern (>9ºN) segments of the subduction zone, respectively. The total seismic moment was 1.17 × 1023 N m, equivalent to MW 9.3 (Tsai et al. 2005).
Although a lot have been learnt from the seismic studies mentioned above, determination of displacements along the northern segment of the fault was difficult because the seismic studies are less sensitive to slow slip, which, as evidence showed, was likely happened there (Ni et al. 2004; Bilham 2005). Such a deficiency can be addressed by geodetic studies, as geodetic data usually measure displacements resulted from overall slip along a fault. Analyzing a GPS data set from continuous GPS tracking stations in the region of east Asia and around India Ocean, Banerjee et al. (2005, 2007) derived station co-seismic displacements induced by the earthquake, and used the data set to invert for fault slip. Their result suggested that although maximum slip was probably at the southern segment, significant slip took place along the northern part of the rupture zone, contributing to a total seismic moment release of ~6 × 1022 N m, equivalent to MW 9.2. Their study, however, was done using mainly far-field data and could not provide detailed solution for slip distribution. Another geodetic study by Vigny et al. (2005) incorporated continuous GPS data from a network located in the Malai Peninsular, which strengthened observations in the intermediate field and enabled them to improve the spatial resolution of rupture distribution. Their result showed two peaks of slip along fault, spanning regions 4ºN–7ºN and 8ºN–12ºN, respectively. The total moment release estimate was also equivalent to an MW 9.2 earthquake. By using campaign mode GPS measurements of co-seismic displacements at 13 sites in the Andaman–Nicobar Islands before and after the 2004 Sumatra–Andaman earthquake, Gahalaut et al. (2006) estimated co-seismic slip under the Andaman and Nicobar Islands as 3.8–7.9 m and 11–15 m, respectively. More co-seismic deformation data were obtained by Subarya et al. (2006), including GPS data acquired from the northern Sumatra island, sea floor vertical uplift/subsidence from coral reef measurements, and positions of pivot line from satellite image data around the Simeulue, Nicobar, and Andaman islands. Combined with GPS data of Vigny et al. (2005), they attempted two models: one after Ammon et al’s (2005) fault geometry and the other approximating a curved fault plane. Both of the models deduced seismic moment of 8.8 × 1022 N m, corresponding to MW 9.22. If using Vigny’s data only, their result is almost identical to that of Vigny’s. They also show three distinct patches of high slip from 4°N to 6°N, 8°N to 10°N, and 12°N to 13.75°N.
These co-seismic studies described above differ in many ways, not only in data type and quantity but also in model parameterization. Among all the studies, Subarya et al. (2006) have ensembled the most complete geodetic dataset. Nevertheless, a more accurate slip model could be obtained if the following ingredients are incorporated in one model: (a) more data, from near to far field, (b) a layered spherical instead of flat half space Earth model for deformation modeling, and (c) more exploration of the parameter space in fault geometry. The last two items are especially important because precise flat Earth assumption can produce significant bias in modeling intermediate-far-field deformation and the slab geometry in the region is yet to be determined (Shearer and Bürgmann 2010).
In the intermediate-far field, our result shows that station SAMP located on the northwest of the Sumatra island moved 135 mm west-southwesterly, and station NTUS located at Singapore moved 14 mm west-northwesterly (Fig. 1). Centimeter level displacements are also observed in southern India and South China Sea, with the Indian sites moved eastward and the South China Sea sites west-southwestward, respectively. East-northeastward motion of around a centimeter is also observed at stations located in northern Indian Ocean. Millimeter level displacements are detected throughout south and east China, with the furthest observable sites at the level of a couple of millimeters located in North China which is almost 4000 km north of the earthquake epicenter. Co-seismic displacements are small in Australia, probably no more than a couple of millimeters at most, despite of its closer distance to the earthquake than south China. This is probably because these stations are located near the nodal plane of the rupture. Displacements at the 5 SuGAR sites were also small in view of their locations with respect to the earthquake rupture plane, which, again, is probably due to their proximity to the nodal plane of the rupture.
In addition to the data set mentioned above, we have included five other co-seismic data sets in this study. The first one is derived from GPS observations from a group of survey mode stations located in southeast Asia area, particularly in the Malaysian Peninsula (Vigny et al. 2005). This data set provides crucial constraints to the intermediate field of co-seismic deformation for this earthquake. Another data set is from Banerjee et al. (2005), who, like us, estimated co-seismic offsets of the IGS stations in the region, plus nine continuous stations in India. We do not use their results of the regional IGS sites since they are pretty much the same as ours, but incorporate the results from the nine India stations which are useful to constrain the northwest section of the co-seismic deformation of the quake. The third data set we incorporated in the study is from three survey mode stations located at the Andaman and Nicobar Islands, on the hanging wall of the Sumatra–Andaman subduction zone. The data were collected several years in a row before, and once after the megathrust event, by survey teams organized from the Center for Earth Science Studies (CESS), India. Their co-seismic offsets are provided in the CESS website (http://www.seires.net/content/view/122/52/), and show 2–6 m west-southwestward motions, respectively. The fourth data set is the 13 GPS campaign measurements on the Andaman and Nicobar Islands carried out by survey of India, which is used by Gahalaut et al. (2006); Banerjee et al. (2007) and Chlieh et al. (2007). The fifth data set is the 3-D co-seismic displacements derived from survey mode GPS data in Sumatra by Subarya et al. (2006). The last data set is vertical displacements obtained from coral reef measurements and pivot lines of satellite images reported also by Subarya et al. (2006) and Meltzner et al. (2006). Although this sort of data have large uncertainty (tens of centimeter), it can constrain the fault model for its near distance. All of the co-seismic offset results are showed in Figs. 1 and 2, and used for the inversion of co-seismic rupture distribution and fault geometry.
3 Earthquake rupture geometry
We use the co-seismic displacement data set derived above to invert for fault rupture which is devised as dislocation in a layered elastic media. A dislocation code modified from the one used in Zeng (2001) is employed to compute the Green’s functions linking fault rupture to surface displacements. We also adopt the “Earth flattening” method (Biswas and Knopoff 1970) to accommodate the curvature effect of the Earth’s surface, which is significant at the far field and should not be neglected (Banerjee et al. 2005). The fault model is composed of multiple tiles, 13 by 6 along strike and dip, respectively. Each tile spans ~1º latitude at trench and extends ~40-km down dip, with the dipping directions change gradually from NW in the south to ESE in the north. These tiles mesh the subduction slab interface in the aftershock zone ~2ºN–15ºN latitude.
Although the horizontal scale of the rupture can be approximately constrained by aftershock distribution, the fault dipping profile is not well constrained for this part of the plate boundary. In our model, we start with fault geometry close to that of Model B of Subarya et al. (2006). The dip angle increase linearly from south to north, from ~24º at the southernmost bottom patch to ~38º at the northernmost bottom patch (star in Fig. 4). The upper boundary of the top layer patches at trench is assumed at 4-km depth, taking into account the initial bending effect there. We then allow the dip angle to vary linearly both along strike and downward, and search for the optimal fault model through an iterative procedure. The best model corresponds to the one with the least data postfit residual χ2.
In Fig. 3, the line AC is the asymptote extrapolated from three of the largest postfit residual χ2 points, and the line AD is the asymptote extrapolated from three of the least postfit residual χ2 points. The point near to the cross point of the two asymptote lines is the best first order smoothing constraint (Wan et al. 2008). In this case we determine that the optimal model constraint corresponds to the uncertainty of the a priori smoothing constraint as 3.0 m.
4 Slip distribution
Many slip distribution models have been published for the 2004 Sumatra earthquake constrained using seismic and/or geodetic data. Here we compare our model and results with that of the previous studies. We start our geometry model search with the model of Subarya et al. (2006). To our surprise, we found that their model is not the one with minimum postfit residual. Although the models of Ammon et al. (2005); Tsai et al. (2005); Subarya et al. (2006) and Rhie et al. (2007) place the largest peak rupture at the southmost of the aftershock zone, which is different from our slip model, Pietrzak et al. (2007) argued that the tsunami data favor models with slip maxima that are as high (~20 m) in the northern portion (near 8ºN–10ºN) of the rupture as in the south (3ºN–5ºN), which is supported by the studies of Gahalaut et al. (2006); Chlieh et al. (2007) and Banerjee et al. (2007). The largest peak rupture in our model placed at the latitude of 8ºN–10ºN. This may be resulted from slow slip occurred at the largest peak zone in our model, which cannot be seismically resolved in the models of Ammon et al. (2005); Tsai et al. (2005) and Rhie et al. (2007). Although the geodetic determined models of Gahalaut et al. (2006); Chlieh et al. (2007) and Banerjee et al. (2007) can resolved the slow slip at the largest peak rupture in our model, lack of far-field data and densely distributed geodetic measurements in Aech and nearby will underestimate the slip value at this region. Constrained by near, intermediate, and far-field geodetic data, our model will reflect “reality” of the rupture. Six or more peak ruptures are resolved in the slip models of Chlieh et al. (2007) and Pietrzak et al. (2007) for their loosely smoothing constraints between adjacent subfaults added and near field data adopted. But such detailed rupture cannot be resolved in our model for tightly smoothing constraints and near, intermediate, and far-field densely geodetic data used. We pay more emphasis on large scale feature of the rupture.
Our estimate of the total seismic moment accumulated over the entire rupture plane is ~8.2 ± 0.05 × 1022 N m, equivalent to the energy release of a MW 9.2 earthquake. This result should be robust because of good station coverage in the near, intermediate, and far fields of co-seismic deformation and the sensitivity of geodetic data to the geometry of the seismic rupture. Our estimated moment release is consistent with Vigny et al. (2005, 7.0 × 1022 N m), Chlieh et al. (2007, 6.7–7.0 × 1022) N m, Banerjee et al. (2007, 7.62 × 1022 N m), larger than that from the centroid moment magnitude (4.0 × 1022 N m) and from Rayleigh waves analysis (Vallee 2007, 5.6 × 1022 N m), smaller than that from normal-mode oscillation data modeling Stein and Okal (2005, 1.0 × 1023 N m).
By using GPS, coral reef and remote sensing data, and a layered spherical instead of flat half space Earth model for deformation modeling, we firstly searched the co-seismic slip geometry model. Although large undulation of the postfit residual with different fault shape, one model is globally founded with the minimum postfit residuals, which shows possibility to estimate fault geometry from densely distributed geodetic data in near, intermediate, and far field. The geometry model with dip angle linearly increases along strike from 4.3o in top southernmost patch to 4.5o in top northernmost patch and dip angle linearly increased to 27º in bottom southernmost patch and 26º in bottom northernmost patch may reflect the reality of the rupture geometry (slab geometry). Then, by using the rupture geometry, the slip distribution is obtained, which shows that dominant thrust slip accompanied with meter level right-lateral slip occurred on the searched geometry model. The moment release is 8.2 ± 0.05 × 1022 N m, corresponding to a MW 9.2 earthquake. The new established rupture model from good converge of geodetic data and more realistic spherical layered earth model may be help in post-seismic relaxation study (e.g., Pollitz et al. 2008), seismic hazard analysis in the future (e.g., Nalbant et al. 2005; Pollitz et al. 2006) and volcano eruption analysis (e.g., Walter and Amelung 2007).
We thank Prof. Yun-tai Chen for his encouragement on seismic slip distribution inversion from geodetic data. Figures 1, 2 and 5c are plotted by using GMT software (Wessel and Smith 1998). This work was supported by the Special Fund of Fundamental Scientific Research Business Expense for Higher School of Central Government (Projects for creation teams ZY20110101), NSFC 41090294 and talent selection and training plan project of Hebei university.
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