Source Constraints and Model Simulation of the December 26, 2004, Indian Ocean Tsunami

Transcription

1 Source Constraints and Model Simulation of the December 26, 2004, Indian Ocean Tsunami Stéphan T. Grilli, M.ASCE 1 ; Mansour Ioualalen 2 ; Jack Asavanant 3 ; Fengyan Shi 4 ; James T. Kirby, M.ASCE 4 ; and Philip Watts 5 Abstract: The December 26, 2004 tsunami was perhaps the most devastating tsunami in recorded history, causing over 200,000 fatalities and widespread destruction in countries bordering the Indian Ocean. It was generated by the third largest earthquake on record M w = and was a truly global event, with significant wave action felt around the world. Many measurements of this event were made with seismometers, tide gauges, global positioning system stations, and a few satellite overpasses. There were numerous eyewitness observations and video digital recordings of coastal tsunami impact, as well as subsequent coastal field surveys of runup and flooding. A few ship-based expeditions also took place in the months following the event, to measure and map seafloor disturbances in the epicenter area. Based on these various data sets, recent seismic analysis estimates of rupture propagation speed, and other seismological and geological constraints, we develop a calibrated tsunami source, in terms of coseismic seafloor displacement and rupture timing along 1,200 km of the Andaman Sunda trench. This source is used to build a numerical model of tsunami generation, propagation, and coastal flooding for the December 26, 2004 event. Frequency dispersion effects having been identified in the deep water tsunami wavetrain, we simulate tsunami propagation and coastal impact with a fully nonlinear and dispersive Boussinesq model FUNWAVE. The tsunami source is specified in this model as a series of discrete, properly parameterized, dislocation source segments Okada, 1985, Bull. Seismol. Soc. Am., 75 4, , triggered in a time sequence spanning about 1,200 s. ETOPO2 s bottom bathymetry and land topography are specified in the modeled ocean basin, supplemented by more accurate and denser data in selected coastal areas e.g., Thailand. A 1 min grid is used for tsunami simulations over the Indian Ocean basin, which is fine enough to model tsunami generation and propagation to nearshore areas. Surface elevations simulated in the model agree well, in both amplitude and timing, with measurements at tide gauges, one satellite transect, and ranges of runup values. These results validate our tsunami source and simulations of the December 26, 2004 event and indicate these can be used to conduct more detailed case studies, for specific coastal areas. In fact, part of the development of our proposed source already benefitted from such regional simulations performed on a finer grid 15 s, as part of a Thailand case study, in which higher frequency waves could be modeled Ioualalen et al. 2007, J. Geophys. Res., 122, C Finally, by running a non-dispersive version of FUNWAVE, we estimate dispersive effects on maximum deep water elevations to be more than 20% in some areas. We believe that work such as this, in which we achieve a better understanding through modeling of the catastrophic December 26, 2004 event, will help the scientific community better predict and mitigate any such future disaster. This will be achieved through a combination of forecasting models with adequate warning systems, and proper education of the local populations. Such work must be urgently done in light of the certitude that large, potentially tsunamogenic, earthquakes occur along all similar megathrust faults, with a periodicity of a few centuries. DOI: / ASCE X :6 414 CE Database subject headings: Tsunamis; Surface waters; Earthquakes; Hydrodynamics; Wave propagation; Wave runup; Numerical models; Geophysical surveys; Simulation models. Introduction The December 26, 2004 Indian Ocean tsunami was likely the most devastating tsunami in recorded history, causing over 200,000 fatalities in more than ten countries across the entire Indian Ocean basin, with tens of thousands reported missing and over 1 million left homeless Kawata et al. 2005; Yalciner et al. 2005a. The tsunami was a truly global event, with significant wave activity recorded around the world, for which the Indian Ocean in fact only represented near-field tsunami wave propaga- 1 Professor, Dept. of Ocean Engineering, Univ. of Rhode Island, Narragansett, RI grilli@oce.uri.edu 2 Institute de Recherche pour le Développement, IRD, Géosciences Azur, CNRS-IRD-UNSA-UPMC, 2 Quai de la darse, 06235, Villefranche-sur-mer, France. mansour.ioualalen@geoazur. obs-vlfr.fr 3 Dept. of Mathematics, Chulalongkorn Univ., Bangkok 10330, Thailand. 4 Center for Applied Coastal Research, Univ. of Delaware, Newark, DE Applied Fluids Engineering, Inc., 5710 E. 7th St., Long Beach, CA Note. Discussion open until April 1, Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and possible publication on February 3, 2006; approved on July 17, This paper is part of the Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 133, No. 6, November 1, ASCE, ISSN X/ 2007/ /$ / JOURNAL OF WATERWAY, PORT, COASTAL, AND OCEAN ENGINEERING ASCE / NOVEMBER/DECEMBER 2007

2 Fig. 1. Tsunami simulation grid designed for Bay of Bengal using ETOPO2 bathymetry and topography contours every 500 m, with location of five independent rupture segments, S1-S5 Table 1 : * location of December 26, 2004 earthquake epicenter; locations of tide gauges; and location of yacht Mercator. JASON 1 s satellite transect. tion Titov et al The tsunami was generated in the Bay of Bengal by the third largest earthquakes ever recorded, with a moment magnitude M w = Ammon et al. 2005; Lay et al. 2005; Park et al. 2005; Stein and Okal The tsunami source was located along the Sunda and Andaman trenches Fig. 1, which mark the approximate boundary between the Indian Australian and Eurasian/Andaman plates, the former plate subducting under the latter at m/year with a largely East West direction of convergence. The Bay of Bengal consists mostly of the Indian Australian plate, with a sequence of islands running north-south along the eastern edge of the bay, denoting the plate boundaries and the edge of the subduction zone. In the Bay of Bengal, sediments from rivers contribute to a massive sediment fan that covers the entire downgoing plate from north to south, whose motion creates a large accretionary wedge east of the subduction zone Davis et al Characteristics of Rupture and Seabed Deformation The December 26, 2004 event started with a main shock at 0 h 58 min 53 s Greenwich meridian time GMT, when the locked fault between the plates ruptured at the megathrust earthquake s hypocenter, located 3.32 N and E, i.e., 160 km west of Sumatra, at a depth of km, liberating strain accumulated from subduction since the last large earthquakes occurred in the area, in 1861 and The main shock epicenter is marked on Fig. 1. Seismic inversion models e.g., Ammon et al indicate that the main shock, or rupture, propagated northward from the epicenter, parallel to the trenches, at a shear wave speed of 2 3 km/s, thus covering the 1,200 km of the ruptured fault length in about 500 s. This value was confirmed by hydroacoustic measurements de Groot-Hedlin The same models predict that the elastic rebound associated with the earthquake caused JOURNAL OF WATERWAY, PORT, COASTAL, AND OCEAN ENGINEERING ASCE / NOVEMBER/DECEMBER 2007 / 415

3 the seabed to uplift by as much as 6 m or subside by up to the same amount, slightly more in some areas, over a region km wide around the subduction zone Ammon et al. 2005; Lay et al Maximum uplift O 10 m; Bilham 2005 and subsidence a so-called asperity occurred west of Banda Aceh at the northern tip of Sumatra, around 5 N. Sea level changes in Andaman and Nicobar Islands, in the North, indicate that the coseismic crustal deformation extended that far north Kayanne et al. 2005; Satake 2005b, further confirming the source length. The seafloor motion displaced an estimated 30 km 3 of water on the ocean surface, causing the killer tsunami in the process Kawata et al Seismic inversion models also predict that fault slip was significantly nonuniform along the rupture length: up to m slip in the bottom two-thirds of the rupture zone and much less in the north. Global positioning system GPS measurements confirm these interpretations of rupture and deformation processes and also show that fault slip was deep and nonhomogeneous, very small in the south, very large off of Sumatra s Northern tip and Phuket about 200 km north of the epicenter, and decreasing to smaller values beyond 7 N Chlieh et al. 2005; Vigny et al Distributions of aftershocks and seafloor deformations show an arched rupture zone, with a minimum of 3 4 separate subzones or segments, which also correspond to the time progression of the rupture along the fault Ammon et al. 2005; Lay et al. 2005; de Groot-Hedlin 2005; Tanioka et al We point out here that, in such a large event, there can be many faults that experience rupture along the subduction zone, and especially along secondary structures running from the subduction zone up to the seabed, within the accretionary wedge. These secondary structures are evident, for instance, in the 3 km high face of stepped or echelon thrust faults rising above the Sunda subduction trench in the southern part, and in the rough tapestry or fabric of the seafloor on the overriding plate over the whole rupture zone McNeill et al. 2005; Henstock et al Seismic profiles using twin air guns and direct video recording using a remotely operated vehicle ROV were made across some of these structures during the Sumatra Earthquake and Tsunami Offshore Survey cruise in May 2005 SEATOS Moran et al. 2005; Mosher et al. 2005; Moran and Tappin 2006, and confirmed the existence of complex systems of faults. It is along these secondary faults that co-seismic displacement from the main shock is expressed, with many local variations about uplift/ subsidence values calculated in seismic inversion models, in which simplifying assumptions are made regarding seabed and subduction zone geology. We will also see later that constraints on the tsunami source from surface elevation measurements will lead us to reduce the speed of co-seismic seabed deformation to much less than the deep shear wave speed predicted by these models. Characteristics of Tsunami and Its Coastal Effects Many direct measurements of the generated tsunami and its coastal effects were made during the December 26, 2004 event, including a few satellite overpasses e.g., JASON 1; Gower 2005; Kulikov 2005 and tide gauge records see for instance Rabinovitch and Thomson The latter provided approximate tsunami arrival times for many locations in the Indian Ocean, of which we selected seven, for which accurate digital records were readily available. Such tide gauge records were used in the first few days following the event, when little detailed seismic information was available, to quickly estimate the tsunami source area through inverse propagation of the tsunami leading wave, at the long wave speed. Thus, Satake personal communication, 2005, for instance, found using only tsunami arrival times at Vishakapatnam, India 156 min and Cocos Islands 140 min, that the main area for tsunami generation was the bottom 500 km of the rupture zone outlined in Fig. 1. Similar analyses that further constrained the tsunami source area were performed later using arrival times at more gauges. Perhaps for the first time in the history of tsunami science, there were numerous detailed eyewitness observations of coastal tsunami impact in the form of video digital recordings. These provided visual estimates of wave height and, in some cases, rough arrival times of successive tsunami waves e.g., After completing field surveys, such video recordings were further processed by some of the international scientific teams to estimate tsunami flow velocity over land e.g., Vatvani et al. 2005, in Banda Aceh. In the weeks and months following the event, multiple international scientific teams surveyed coastal areas impacted by the tsunami, documenting damage, measuring runup and inundation, and assembling careful reconstructions of wave activity. Given the length of damaged coastline and number of countries involved, each team restricted their survey to a limited geographical area Fritz and Synolakis 2005; Gusiakov 2005; Kawata et al. 2005; Liu et al. 2005; Satake et al. 2005, 2006; Sannasiraj and Sundar, 2005; Synolakis et al. 2005; Yalciner et al. 2005a,b; Yamada et al A few ship-based expeditions took place, in the months following the event, to measure seafloor disturbances in the epicenter area, notably the HMS Scott s, a British Navy ship that conducted a high resolution multibeam survey in January February 2005 of 40,000 km 2 of the seafloor in the main tsunami generation area, north of the epicenter McNeill et al. 2005, and SEATOS Moran et al. 2005; Moran and Tappin 2006 already mentioned. It appears from the various data sets available that, upon generation and following the distribution of seafloor uplift and subsidence caused by the earthquake, the westward propagating tsunami had a leading elevation wave, subsequently hitting Sri Lanka, India, the Maldives and Somalia, whereas the eastward propagating tsunami had a leading depression wave, eventually impacting Indonesia, Thailand, Malaysia, and Myanmar. Performing global analyses of tide gauge data as well as numerical modeling albeit linearized and on a coarse grid, Titov et al showed that the December 26, 2004 tsunami was very directional in the cross-source east-west direction, due to a combination of source focusing because of the long and narrow earthquake source region and bathymetric waveguides. This explains why the tsunami caused serious damage and deaths as far as the east coast of Africa and why substantial wave energy propagated to distant coasts, including different oceans. In some cases, wave heights measured at far distant tide gauges were larger than those at some near-field gauges located in the long-source south-north direction. Bangladesh, for instance, which lies at the northern end of the Bay of Bengal, did not experience much tsunami effect and had very few fatalities, despite being a low-lying country relatively near the epicenter. A few, usually three, large tsunami waves were reported to arrive in most impacted coastal areas in the Indian Ocean, with one of the latter waves usually being the largest. Tsunami coastal effects were the most severe in Banda Aceh, which is nearest the area of maximum fault slip and seafloor uplift, causing the majority of fatalities. The tsunami arrived in Banda Aceh within 34 min of the start of the event, and runup and inundation reached a 5 30 m height in most locations, advancing up to 4 km inland 416 / JOURNAL OF WATERWAY, PORT, COASTAL, AND OCEAN ENGINEERING ASCE / NOVEMBER/DECEMBER 2007

4 with current velocities up to 8 m/s Kawata et al. 2005; Vatvani et al. 2005; Yalciner et al. 2005a. One of team even reported measuring a 49 m inundation height in Rhiting, 5 25 N about 15 km southwest of Banda Aceh Shibayama et al Most impacted next was Thailand, where the tsunami arrived at the southern tip of Phuket Island within 1 h 40 min of the start of the event. Runup reached a 3 11 m height in most places, with the largest runup measured on the west coast in Khao Lak about 8 40 N, m depending on the source, with 6 8 m/s current Kawata et al. 2005; Satake et al. 2005, 2006; Yalciner et al. 2005a. By contrast, in Myanmar, just north of Thailand, runup only reached 1 3 m, with the tsunami first arriving within 2 h 30 min of the start of the event. These smaller values are likely due to the smaller fault slip in the northern part of the rupture area and to the protection offered the coast of Taninthayi Division by offshore islands Satake et al. 2005, In Malaysia, Yalciner et al. 2005b also report similar m runup at most places, with one extreme 3.7 m value. On the western side of the Indian Ocean, tsunami waves arrived in Sri Lanka and southeast India, 2 h 2 h 30 min after the start of the event, causing m runup for the most part with a few extreme values reaching 8 12 m in southern Sri Lanka Liu et al. 2005; Synolakis et al. 2005; Yalciner et al. 2005a. In the Maldives, which are made of a series of atolls, runup varied greatly depending on exposition, but is generally reported to have reached m with the tsunami first arriving within 3 h 25 min of the start of the event Fritz and Synolakis 2005; Kawata et al Finally, in Somalia, where the tsunami arrived about 7 8 h after the start of the event, unexpectedly large runup values of m were measured, which can in part be explained by the high tsunami directionality briefly discussed above Frtiz and Borrero Purpose of This Work In this work, in light of the characteristics of the December 26, 2004 event briefly summarized above, we focus on constructing and constraining a reasonable tsunami source based on available geological, seismological, and tsunami elevation and timing data. We use this source to perform tsunami simulations with a numerical model of long wave propagation, coastal inundation, and runup. Here, however, we only aim at explaining the large scale tsunami propagation features measured during the event, as well as overall coastal tsunami impact runup surveyed following the event. In other work, reported elsewhere, we use our present analyses to conduct more detailed case studies of coastal tsunami impact on finer regional model grids, for selected areas such as Thailand Ioualalen et al Results obtained in the latter case not shown, particularly for higher frequency waves, were already used to constrain the present source, in order to ensure full consistency of the various simulations. Since our goal is to later perform regional case studies for western and southern Thailand, and northern Sumatra, where maximum runup was observed, it should be pointed out that, in our iterative development of tsunami sources, we gave priority to data reflecting east-west tsunami propagation rather than northsouth propagation. Numerical Model One specificity of our modeling approach is the use, perhaps for the first time for such a large scale event, of a fully nonlinear and dispersive Boussinesq long wave propagation model FUNWAVE, which was initially developed for modeling ocean wave transformation from deep water to the coast, including breaking and runup Wei and Kirby 1995; Wei et al FUNWAVE retains information to O kh 2 in frequency dispersion and to all orders in nonlinearity a/h where k denotes a wave number, a denotes a wave amplitude, and h denotes a water depth scale. FUNWAVE also has a physical parametrization of dissipation processes including breaking, as well as an accurate moving inundation boundary algorithm, both of which are necessary to correctly estimate coastal tsunami effects and runup over land Chen et al. 2000; Kennedy et al Wei et al showed that the retention in FUNWAVE of nonlinear effects beyond the usual order in standard weakly nonlinear Boussinesq models is crucial to the correct modeling of shoaling solitary waves or undular bores on slopes, up to near breaking, and thus in the present case is important for modeling shoreline inundation. The presence of frequency dispersion in the model is important for the case of short or higher frequency wave propagation into relatively deeper water such as directly west of the December 26, 2004 event ruptured area, and allows for the mechanism of wave crest splitting during wave propagation over shallow bathymetry. FUNWAVE has been thoroughly validated and used to study small scale motions such as the propagation of waves in the nearshore Chen et al. 2000; Kennedy et al and the generation of wave-induced currents Chen et al. 2003, as well as regional scale tsunami propagation Day et al. 2005; Ioualalen et al. 2006; Watts et al. 2003; Waythomas and Watts Preliminary results for the modeling of the December 26, 2004 tsunami using the model have been reported by Watts et al A review of the theory behind FUNWAVE and other examples of its application are given by Kirby The Appendix gives a brief summary of equations implemented in the version of FUNWAVE used in this work. Considering the fairly small longitudinal and latitudinal extensions of the Bay of Bengal, which is our main area of interest, the present simulations were performed with a version of FUNWAVE implemented on a Cartesian grid. A spherical version of FUNWAVE, also including Coriolis corrections, has recently been derived and could be used in future work Kirby et al Sphericity corrections might play a role in simulating tsunami signals at far distant tide gauges i.e., the simulated tsunami would arrive too early in the Cartesian grid, while deviations due to Coriolis force might affect the tsunami propagation. As discussed above, FUNWAVE features more complete physics than standard models used for tsunami modeling, which are typically based on nondispersive linear or nonlinear shallow water wave equations NSWE. Specifically, for the December 26, 2004 tsunami, Kulikov 2005 performed a wavelet frequency analysis based on satellite altimetry data recorded in the Bay of Bengal in deep water, and showed the importance of dispersive effects on wave evolution. His results indicate that the leading edge of the wave components with order 10 km wavelength were significantly delayed in comparison with the much longer waves in the main wave front. He concluded that a long wave model including dispersion such as FUNWAVE should be used for this event. This result is not surprising in light of Ward s 1980 simple scaling analyses, which showed, in a constant 4,000 m deep ocean, that any wave of length less than a couple of hundred km should be dispersive. Okal 1982 had also similarly stressed the importance of modeling dispersion. Hence, in the present case, FUNWAVE can potentially yield more accurate results, JOURNAL OF WATERWAY, PORT, COASTAL, AND OCEAN ENGINEERING ASCE / NOVEMBER/DECEMBER 2007 / 417

5 given the same data and tsunami source parameters, than more standard models, which typically neglect dispersion. Tsunami Source Based on rupture parameters estimated by seismic inversion models i.e., slip and speed of rupture, and other seismological and geological constraints, some of these discussed above, we estimate a reasonable earthquake tsunami source for the December 26, 2004 event, in terms of magnitude and timing of the coseismic seafloor displacement along 1,200 km of the Andaman- Sunda trench. We then iteratively refine this estimate by further constraining the source and simulated tsunami to match salient features of tide gauge and satellite track records. Our earthquake tsunami source is based on the standard halfplane solution for an elastic dislocation with maximum slip Okada Thus, we define an oblique planar fault of horizontal length L and width W, with centroid located at latitudelongitude x 0,y 0, and depth d of the earthquake at the centroid, and discretize it into many small trapezoids. The vertical coseismic displacement on the ocean floor surrounding the fault is calculated by summing up contributions of point source elastic solutions, based on the actual depth of each trapezoid. The shear modulus can be specified as a function of depth and other seismic and geological descriptors, although it will be assumed to be constant in this work. Okada s solution is implemented in Tsunami open and progressive initial conditions system TOPICS, a software tool that provides the vertical co-seismic displacements as outputs, as well as a characteristic tsunami wavelength 0 smaller of the fault dimensions L or W and a characteristic tsunami period T 0. A characteristic initial tsunami amplitude 0 is defined as the minimum or maximum elevation found from the bottom coseismic displacement. The seismic moment M 0 is proportional to, but slightly less than, LW, because a Gaussian slip distribution is assumed about the centroid. TOPICS allows for the superposition of multiple fault planes, which can be assembled into complex fault structures or slip distributions. To perform tsunami simulations with the propagation model FUNWAVE, we first define a model grid and specify the bottom bathymetry in the modeled ocean basin. We then trigger a series of discrete, properly parameterized, Okada s sources, in a time sequence spanning the selected rupture duration. In doing so, following the standard procedure, we assume that each source, which represents the final co-seismic bottom deformation induced by the earthquake over a given area, or fault segment, is instantaneously reproduced as an ocean surface elevation, with the water having no initial velocity. To facilitate such simulations, we combine TOPICS and FUNWAVE into a single integrated model, referred to as GEOWAVE, in which the tsunami sources calculated by TOPICS for a tsunami event are transferred and linearly superimposed into FUNWAVE, as an initial free surface condition. The application of this methodology to landslide tsunami sources is detailed in Watts et al Geological and Seismological Constraints The geologic structures responsible for the December 26, 2004 event are approximately identified in the offshore bathymetry by the Andaman-Sunda trench, unless they are buried under loose sediment. As mentioned in the Introduction, these structures are generally described as the Indian-Australian or downgoing plate subducting beneath the Eurasian/Andaman or overriding plate, with a largely east-west direction of convergence. In the Bay of Bengal the morphology of the seafloor is thus an expression of the three-dimensional tectonic structures that exist, as well as the tectonic processes that are taking place at depth. In our initial modeling of the December 26, 2004 event Watts et al. 2005, given the bathymetry of the Bay of Bengal, the geometry of the subduction zone, and distributions of rupture and aftershocks provided by initial seismic inversion models Tanioka Personal communication 2005, we first identified four fault segments with different morphologies and earthquake parameters. These four segments were L=220, 410, 300, and 350 km long, making up the 1,200 km of ruptured subduction zone, and were identified by their unique shape and orientation. Four Okada sources, corresponding to each of these segments, were specified in FUNWAVE to simulate the event. These were triggered at time t 0 =0, 105, 223, and 331 s, corresponding to a rupture speed initially estimated at 3 km/ s. The simulated tsunami agreed reasonably well with arrival times at seven tide gauges, reproduced salient features of JASON 1 s satellite transect, and predicted general ranges of variations of measured coastal runups Watts et al Details, however, were not well simulated, such as amplitudes and periods of successive tsunami waves arriving at tide gauges and the front and back of the satellite transect elevations. In this work, we gradually refined our initial tsunami sources by integrating further constraints from seismic inversion models Ammon et al. 2005; Lay et al ; GPS data Chlieh et al. 2005; Vigny et al. 2005, and other detailed seismological and geological analyses performed for the event. As discussed in the Introduction, we then iteratively adjusted the source parameters for the generated tsunami to better match observations. In doing so, however, we tried to have as small a number of sources/ segments as possible, in order to both reduce the number of free parameters to adjust and limit the generation of spurious tsunami waves at discrete segment junctions. This led us to replace our middle two segments by three segments and thus use a total of five segments that both better match the shape of the ruptured area and known rupture parameters. Let us consider each segment in turn Table 1; Fig. 1 : 1. Segment 1 L=220 km covers the southern arc of the ruptured subduction zone, facing in a general SW direction of tsunami propagation, perpendicular to rupture, and roughly extends NW of the epicenter. The faulting trends north along two relatively sharp bends, one to the north and one to the south of the segment. Here, the overriding plate is at its steepest, and the water depth is largest along the ruptured subduction zone, at around h=5, 100 m in the deepest part of the Java trench. 2. Segments 2 and 3 cover a long L=150 and 390 km and relatively straight section of the subduction zone in a NNW direction along the trench. The most notable feature is the nearly uniform profile of the overriding plate in the northern Segment 3, with a steep rise from the subduction trench to a shallow ridge, followed by a descent into a deeper basin farther east. The southern, shorter and wider Segment 2, covers the slip asperity, predicted off Banda Aceh in seismic inversion models, corresponding to a larger maximum slip likely responsible for the largest coastal runups measured in and around Banda Aceh. Direct effects of this large slip in the form of seafloor uplift may have been observed during the SEATOS cruise in the so-called ditch feature Moran et al. 2005; Moran and Tappin / JOURNAL OF WATERWAY, PORT, COASTAL, AND OCEAN ENGINEERING ASCE / NOVEMBER/DECEMBER 2007

6 Table 1. Tsunami Source Parameters Used in TOPICS for Okada s 1985 Source Segments S1 S5 Shown in Fig. 1. Total Surface Elevation Computed Using These Sources is Shown in Fig. 2. Parameters Segment 1 Segment 2 Segment 3 Segment 4 Segment 5 x 0 longitude y 0 latitude d km degs degs degs m L km W km t 0 s Pa M 0 J km T 0 min m 3.27; ; ; ; ; Note: A 60 s rising time is included in time delay of segment rupture from earthquake time in t 0 and maximum slip is Gaussian distributed and drops by 50% from each segment s centroid to L km from it. Initial time t=0 corresponds to 0 h 58 min 53 s GMT. The total seismic moment of all five segments is M = or M = Segments 4 and 5 L=150 and 350 km feature a marked change in orientation and shape, notably a widening of the distance between the subduction zone and the basin to the east. The basin is narrower here, more in the form of a trench. The ridge is shallow enough to form a number of small islands. Segment 4 is facing Northern Thailand, where very large runup was measured, e.g., in Khao Lak. In Segment 5, a significant number of larger islands the Andaman Islands are formed on the overriding plate these are better visible in Fig. 2. Finally, and this is one of our important findings, in order to match the arrival times of successive tsunami waves measured at far distant tide gauges, and at the same time reproduce the tail of JASON 1 s satellite transect in the simulation, the tsunami sources corresponding to the five selected segments must be triggered over about 1,200 s. This is a much longer time than used earlier, corresponding to a speed of co-seismic bottom deformation only averaging 0.8 km/ s, i.e., much smaller than rupture speed. Some of this reduction in speed can be explained by socalled rising time effects Heaton 1990 : the combination of rupture i.e., slip propagation along the fault plane at 1 km/s and of lateral rupture propagation in the segment width direction, at 2 3 km/s, yields in our case an average rising time of 60 s. However much of this reduction in speed remains unexplained. The ocean bottom in the subduction zone and accretionary prism is made of a number of layers of different materials, with quite different geological properties and shear moduli. In the softer sediment of the accretionary prism, the shear wave speed is typically smaller, km/s e.g., Kramer Hence, while it is well established that the earthquake recorded at seismographs did proceed at a deep shear wave speed of 2 3 km/s, one might conjecture that, because of the significant accretionary prism in front of the subducting plate, it would appear that the surface rupture, responsible for the co-seismic bottom deformation that generated the tsunami, occurred solely in softer sediment and hence at a much lower speed of propagation. Finally, it is important to point out that two other modeling groups independently reached a similar conclusion that the apparent rupture speed must be reduced in the tsunami propagation simulations, as compared to predictions of seismic inversion models or hydroacoustic measurements. Satake et al. 2005, 2006 and Fujii and Satake 2007, using over 20 independent Okada tsunami sources with parameters optimized using a linear inversion algorithm, found that it was necessary to reduce the rupture speed to about 1 km/s for the generated tsunami to match JASON 1 s and two other satellite transects and the many tide gauge data. Tanioka et al similarly significantly reduced the rupture speed. Tsunami Source Parameters We define five separate Okada tsunami sources for the five segments S1 S5 shown in Fig. 1 and detailed above. We trigger each source at increasing time t 0 in FUNWAVE, according to the reduced speed of propagation of co-seismic bottom deformation found necessary to match observations, i.e., over about 1,200 s from south to north. The earthquake parameters for each tsunami source are listed in Table 1. The total seismic moment released is M 0 = J, equivalent to M w = log M 0 9 /log 32=9.22, with = Pa. To reduce the number of free parameters in Okada s dislocation sources, in the absence of accurate geological information, we initially assumed all segments to have a rake angle =90 and a dip angle =12, such as to reproduce the correct distances between seafloor features. We adjusted the strike angle to closely follow the bottom bathymetry Fig. 1. The width W of each segment, which also represents the characteristic tsunami wavelength 0 and hence is proportional to the characteristic tsunami period T 0 0 / gh where h local depth and g is gravity, was initially selected based on the distribution of seafloor deformation obtained in seismic inversion models discussed above. The width was then iteratively adjusted for the simulations to better reproduce the main tsunami periods measured at tide gauges; thus W generally reduced from 130 km in the south to 95 km in the north. Based on slip distributions predicted in seismic inversion models and GPS data Ammon et al. 2005; Vigny et al. 2005, the earthquake depth d was fixed at 25 km, JOURNAL OF WATERWAY, PORT, COASTAL, AND OCEAN ENGINEERING ASCE / NOVEMBER/DECEMBER 2007 / 419

7 shape of co-seismic displacement. These differences arise largely out of the variations in width and slip between each segment, and are intended to mimic seafloor bathymetry and the known features of the rupture. Although the source in Fig. 2 does not perfectly match all seafloor features, it captures all major characteristics of the seafloor morphology and, as we will see, the generated tsunami agrees well with observed data. The first tsunami source, for Segment 1, is triggered at the start of the numerical simulation, t 0 =60 s, the chosen rising time. We then calculate the delay between the triggering of subsequent tsunami sources from the distance between epicentral locations along the rupture path to the segment center. In doing so, as discussed before, we assume a velocity of bottom deformation caused by the rupture down to about a third of what was predicted by seismic inversion models for the shear wave speed, i.e., 0.87 km/s in the south and 0.70 km/s in the north, with an average shear wave speed of 0.8 km/ s. This yields the triggering times listed in Table 1. Tsunami Simulations We simulate the December 26, 2004 tsunami propagation in the Bay of Bengal using FUNWAVE, with the main purpose of both constraining and validating our tsunami source. In the simulations, we specify the five earthquake tsunami sources in a time sequence, with parameters such as listed in Table 1, corresponding to the five rupture segments S1 S5 shown in Fig. 1. Performing more than 15 such simulations, we compared simulated tsunami elevations with data measured at tide gauges, one satellite transect, and coastal runup. Source parameters were iteratively adjusted in light of these comparisons, which eventually yielded parameters listed in Table 1. Fig. 2. Total tsunami source elevation computed for combination of five Okada sources, with parameters listed in Table 1. Thick lines indicate uplift and subsidence, contoured every 1 m; thin - lines show bathymetric contours every 500 m. and maximum slip was set to m, except in Segment 2 where it was increased to 23 m to model the asperity off Banda Aceh. The maximum vertical seafloor uplift or subsidence predicted by TOPICS for each source is listed in Table 1 and varies in the range 0 = 3.8 to 8.6 m, which is consistent with the range of values estimated by the seismic inversion models. The total coseismic seafloor vertical displacement obtained for the five combined tsunami sources is depicted in Fig. 2, with uplift and subsidence contours plotted at a ±1 m spacing. We note right away the similarity of our source with the uplift-subsidence contours inferred from seismic inversion models e.g., Ammon et al The maximum uplift 9 m is predicted west of the northern tip of Sumatra, in Segment 2. In the northern Andaman Islands the uplift is about 1 2 m, and slightly more for the middle and southern islands. Such uplifts of the Andaman Island were confirmed by field surveys Kayanne et al The five tsunami sources do not merge perfectly at all locations with one another, as a result of the division of the source in discrete segments, although this fact disappears from the wave front in model simulations, within a few minutes of tsunami propagation. We also note that the source for each segment has a slightly different Construction of Model Grids In order to include all relevant tide gauges in the Bay of Bengal, but minimize grid size while achieving maximum resolution, the model grid used for the ocean scale basin covers the area depicted in Fig. 1, from 72 to 102 E in longitude and from 13.0 S to 23.5 N in latitude. Simulations are performed on a 1 min by 1 min grid, or about km, which yields a grid with 1,793 by 2,191 points. At this resolution, the time step was selected at 1.2 s. Open boundary conditions were specified in FUNWAVE on all ocean boundaries. We constructed the numerical grid in the Bay of Bengal by interpolating the ETOPO2 bathymetry and topography data at grid points. Additionally, because of work performed for our case studies, we digitized and merged with this data set, denser and more accurate bathymetry and topography data provided by the Royal Thai Navy for coastal Thailand Fig. 3 shows where such points were used. In Fig 1, the resulting bathymetric contours are plotted every 1,000 m. Note that the mean water level specified in the model did not include effects of tides. Tides would slightly affect tsunami propagation, mostly in very shallow water, through small changes in depth and, hence, propagation speed. Most of the tide gauge records used in the following those from the University of Hawaii Sea Level Center UHSLC were already provided with a net tsunami signal, obtained after tide removal, and we similarly processed the Royal Thai Navy RTN tide gauge at Taphao Noi. Runup observations used in the following were tide corrected as 420 / JOURNAL OF WATERWAY, PORT, COASTAL, AND OCEAN ENGINEERING ASCE / NOVEMBER/DECEMBER 2007

8 Fig. 4. Maximum tsunami elevations in Bay of Bengal simulated with FUNWAVE, using source of Fig. 1 and Table 1 scale is in meters Fig. 3. Locations of bathymetric data adapted from Royal Thai Navy map data and depth contours every 50 m used for coastal Thailand to construct numerical grid well by the various post-tsunami survey teams. Consequently the comparison between observations and the simulation results is consistent. transect from 12 S and 20 N, between 2 h 51 min and 3 h 02 min UTC, or about 2 h after the start of the event. Each dot in Fig. 1 represents a numerical gauge whose time series was calculated in FUNWAVE during tsunami simulations. The actual motion of the satellite over time, given in Gower 2005 it tookabout 8 min for the satellite to travel from 5 S to 20 N, during tsunami propagation is then used to select the relevant numerical data for each gauge along the transect. Measured satellite eleva- Tsunami Simulation Results The maximum simulated tsunami elevations above sea level are depicted in Fig. 4 with details given in Fig. 5. As expected from other work e.g., Titov et al. 2005; Watts et al. 2005, the tsunami radiation patterns in Fig. 4 show high directionality, both because of the source length and in relation with various features of the seafloor. To the west, tsunami propagation depends on the sediment fan that covers most of the Bay of Bengal. To the east, a much more complex pattern emerges due to interference and interactions of multiple wave fronts propagating to and among various shorelines. Shallower water near the Andaman and Nicobar Islands also strongly affects east-west tsunami propagation. Satellite Transect In Fig. 6, we compare model results with estimates of surface elevation measured along JASON 1 s satellite transect, shown in Fig. 1. This estimate was obtained along satellite track No. 129, by calculating the difference between the anomaly of the sea surface elevation for transect 109, measured during the tsunami event, and the one of transect 108 measured about 10 days before Gower 2005; Kulikov The satellite traveled on this Fig. 5. Details of Fig. 4, maximum tsunami elevations simulated with FUNWAVE in Northern Sumatra, the Andaman Islands, and Thailand scale is in meters JOURNAL OF WATERWAY, PORT, COASTAL, AND OCEAN ENGINEERING ASCE / NOVEMBER/DECEMBER 2007 / 421

9 Fig. 6. Comparison of tsunami elevation measured with satellite altimetry by JASON and results of model simulation with: FUNWAVE ; and NSWE - tions appear quite noisy between 0 and 8 N, which suggests a high variability intraseasonal of the geostrophic current field structure in the area. Except for a small spatial shift at some locations, the overall agreement between measurements and simulations is quite good in Fig. 6, which is encouraging considering the uncertainties in the location of the mean water level and the noise in the satellite data. The two leading tsunami crests are well resolved in the model 3 5 S, although they are slightly smaller than measured. The overall crest to trough difference i.e., wave height of the leading waves is well predicted, at about 1.1 m as compared to 1.2 m in the data. The next main trough to crest height is also well predicted, to about 1 m, in between 2 S and 2 N, and some of the smaller oscillations are well resolved as well. Finally, the agreement with the tail of the satellite data, north of 5 N is quite remarkable, particularly north of 10 N, where the tsunami is due to generation in the northernmost Segments 4 and 5 and is somewhat affected by the Andaman Islands. This in itself justifies the slower timing we adopted for the triggering of our sources, than predicted by seismic inversion models alone. The main discrepancies between simulations and observations are observed in between 2 and 5 N, an area for which, due to its directionality Fig. 4, the tsunami is generated by Segment 3 in the model. This segment is the longest in our tsunami source, and the time lag between actual start of uplift at its southern end and the modeled start at t 0, considering each segment is treated as a single source, may explain some of the spatial lag seen in the simulated satellite track. This could be improved by using a larger number of segments in the source. Also, in this region, simulations are more strongly affected by propagation through the Nicobar Islands, where errors in the ETOPO2 shallow water bathymetry near the islands may affect the accuracy of the simulated tsunami. Finally, the use of discrete sources, whose edges tend to produce spurious secondary waves bouncing off the islands and disturbing the main lower frequency wavetrain, can also be responsible in part for these discrepancies. Tide Gauges Tsunami elevations were measured at various coastal tide gauges in the Indian Ocean Merrifield et al. 2005, Rabinovitch and Thomson 2007, of which we use seven locations marked in Fig. 1, for which accurate digital data were available. Data shown in Fig. 7 are for three tide gauges in the Maldives Hannimaadhoo, Male, Gan; the northern two being in direct line of sight along the main direction of tsunami propagation from the source ; Diego Garcia, south of the Maldives; Columbo, on the sheltered west side of Sri Lanka; Cocos Island, directly south of the tsunami source; and Taphao-Noi on the east coast of Thailand but on the sheltered east side of Phuket. In addition, the tsunami was recorded with a depth echo sounder by the Belgian yacht Mercator which was anchored 1.6 km off Nai Harn Bay SW of Phuket, in approximately 12 m of water at the time of the event. Table 2 lists the tide gauge and yacht names and their approximate locations. Fig. 7 shows both measured and simulated time series at the tide gauges and the yacht. The actual data points are marked by circles and we see that the time resolution varies between tide gauges, from 1 to 6 min, Taphao Noi being manually digitized. In the latter case, this introduces a significant filtering of the tsunami signal. Note in Fig. 7 e that the tide gauge failed in Columbo right after the arrival of the first tsunami crest. Also note, for the first six tide gauges, measured elevations were filtered by applying a moving average over a 120, 240, 240, 360, 120, and 60 s time window. For sake of comparison, a similar filter was applied to the simulated tsunami elevations shown in Fig. 7. Table 2 lists computed and observed arrival times of the tsunami at the gauges, which we define as the time of the extremum of the first depression or elevation wave, whichever comes first. Estimated depth h 1 at the gauges is also given. Simulated and measured arrival times agree well in most cases. The simulated tsunami usually arrives slightly too early, by up to 3 min, except as expected from the above discussions on sphericity and Coriolis effects, at the two southernmost locations, Diego Garcia and Cocos, where the simulated tsunami arrives 16 and 11 min too early, respectively. In addition, due to the coarse 1.85 km grid size used in the model, with respect to coastal waters, the depth h 0 of the boundary grid cell where the tide gauge is located does not typically match the actual tide gauge or yacht depth h 1 but is usually larger. This means that part of the slowing down of the tsunami, roughly proportional to gh in shallow water, is not correctly modeled and having this present would produce a slight tsunami delay in the simulations. More specifically, in Figs. 7 a and b, we see that, except for a gauge resolution effect, the agreement is good between simulations and observations at the two northern tide gauges in the Maldives, Hannimaadhoo and Male, for the elevation and period of the first three waves. A good match is expected at these gauges, as they lie on a fairly direct path of tsunami propagation, orthogonal to the source axis Figs. 1 and 4. At Gan, farther south, Fig. 7 c shows that the agreement is reasonable for the first crest but not so good for later waves. However, this gauge is located within a somewhat protected area, which yields a weaker signal quite affected by local coastal topography not resolved in the model. Except for a time shift, the agreement is reasonable at Diego Garcia, for the first two waves in Fig. 7 d. In Columbo, in 422 / JOURNAL OF WATERWAY, PORT, COASTAL, AND OCEAN ENGINEERING ASCE / NOVEMBER/DECEMBER 2007

10 Fig. 7. Comparison of tsunami elevation measured and simulated with: FUNWAVE - ; NSWE -, at tide gauges and yacht, marked in Fig. 1: a Hannimaadhoo; b Male; c Gan; d Diego Garcia; e Columbo; f Cocos Island; g Taphao-Noi; and h Mercator yacht Fig. 7 e, the agreement for the first crest before the tide gauge failed is quite good, particularly considering the tsunami had to propagate around the southern tip of Sri Lanka to reach the tide gauge, very much like an edge wave e.g., Liu et al In Cocos, in Fig. 7 f, despite the southern location off the main direction of tsunami propagation, the agreement is quite good in amplitude and period for the first three waves, except for a time shift. The tide gauge in Cocos is located inside a lagoon in shallow water, and part of the time shift can be explained by the poor representation of slowing down effects of waves in very shallow water in the model. In Taphao Noi, east of Phuket in southern Thailand, a depression wave first arrives, as expected, and the Table 2. Comparison of Observed Tsunami Arrival Times and Simulated with FUNWAVE, at Tide Gauges and Yacht Fig. 1. Tide Gauge Depth Is Assumed 5 m When Unknown. Data for First Five Gauges Are from University of Hawaii Sea Level Center; Cocos Data Are from National Tidal Center, Australia; and Taphao-Noi s Data Are from Hydrographic Department, Royal Thai Navy. Locations Coordinates Lat., Long. Model arrival time Data arrival time Hannimaadhoo, Maldives 6.767, h 39 min 3 h 40 min 5 Male, Maldives 4.233, h 26 min 3 h 25 min 4 Gan, Maldives 0.667, h 25 min 3 h 28 min 5 Diego Garcia 7.233, h 39 min 3 h 54 min 5 Columbo, Sri Lanka 7.000, h 56 min 2 h 59 min 5 Cocos Island , h 16 min 2 h 27 min 5 Taphao-Noi, Thailand 7.833, h 15 min 2 h 18 min 5 Mercator, Phuket 7.733, h 49 min 1 h 48 min 12 Depth h 1 m JOURNAL OF WATERWAY, PORT, COASTAL, AND OCEAN ENGINEERING ASCE / NOVEMBER/DECEMBER 2007 / 423