Numerical Simulation of the December 26,2004: Indian Ocean Tsunami

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1 Numerical Simulation of the December 26,2004: Indian Ocean Tsunami J. Asavanant, 1 M. Ioualalen, 2 N. Kaewbanjak, 1 S.T. Grilli, 3 P. Watts, 4 J.T. Kirby, 5 and F. Shi 5 1 Advanced Virtual and Intelligent Computing (AVIC) Center, Department of Mathematics, Faculty of Science, Chulalongkorn University, Bangkok, 10330, Thailand Jack.A@chula.ac.th, narongrit.k@gmail.com 2 Geosciences Azur (IRD, CNRS, UPMC, UNSA), Villefranche-sur-Mer, France Mansour.Ioualalen@geoazur.obs-vlfr.fr 3 Department of Ocean Engineering, University of Rhode Island, Narragansett, RI grilli@oce.uri.edu 4 Applied Fluids Engineering, Inc., 5710 E. 7th Street, Long Beach, CA 90803, USA phil.watts@appliedfluids.com 5 Center for Applied Coastal Research, University of Delaware, Newark, DE 19761, USA kirby@udel.edu The December 26, 2004 tsunami is one of the most devastating tsunami in recorded history. It was generated in the Indian Ocean off the western coast of northern Sumatra, Indonesia at 0:58:53 (GMT) by one of the largest earthquake of the century with a moment magnitude of M w = 9.3. In the study, we focus on best fitted tsunami source for tsunami modeling based on geophysical and seismological data, and the use of accurate bathymetry and topography data. Then, we simulate the large scale features of the tsunami propagation, runup and inundation. The numerical simulation is performed using the GEOWAVE model. GEOWAVE consists of two components: the modeling of the tusnami source (Okada, 1985) and the initial tsunami surface elevation, and the computation of the wave propagation and inundation based on fully nonlinear Boussinesq scheme. The tsunami source is used as initial condition in the tsunami propagation and inundation model. The tsunami source model is calibrated by using available tide gage data and anomalous water elevations in the Indian Ocean during the tsunami event, recorded by JASON s altimeter (pass 129, cycle 109). The simulated maximum wave heights for the Indian Ocean are displayed and compared with observations with a special focus on the Thailand coastline.

2 2 J. Asavanant, M. Ioualalen, N. Kaewbanjak, et al 1 INTRODUCTION On December 26,2004 at 0:58:53 GMT a 9.3 Magnitude earthquake occurred along 1300 km of the Sundra and Andaman trenches in the eastern Indian Ocean, approximately 100 km off the west coast of northern Sumatra. The main shock epicenter was located at 3.32 N and E, km deep. Over 200,000 people across the entire Indian Ocean basin were killed with tens of thousands reported missing as a result of this disastrous event. In accordance with modern practice, several international scientific team were organized to conduct quantitative survey of the tsunami characteristics and hazard analysis in the impacted coastal regions. Numerous detailed eyewitness observations were also reported in the form of video digital recordings. Information concerning the survey and some ship-based expeditions on tsunami source characteristics can be found in Grilli et al (2006), Moran et al (2005), and McNeill (2005), Kawata et al (2005), Satake et al (2005), Fritz and Synolakis (2005). In this paper a resonable tsunami source based on available geological, seismological and tsunami elevation and timing data is constructed using the standard half-plane solution for an elastic dislocation formula(okada, 1985). Inputs to these formula are fault plane location, depth, strike, dip, slip, length, and width as well as seismic moment and rigidity. Okada s solution is implemented in TOPICS (Tsunami Open and Progressive Initial Conditions System) which is a software tool that provides the vertical co-seismic displacements as output. Tsunami propagation and inundation are simulated with FUNWAVE (Fully nonlinear Wave Model) based on the dispersive Boussinesq system. Comparisons of simulated surface elevations with tide gage data, satellite transect and runup observations show good agreement both in amplitudes and wave periods. This validates our tsunami source and propagation models of the December 25,2004 event. Dispersive effects in the simulations are briefly discussed. 2 SOURCE AND PROPAGATION MODELS The generation mechanism for the Indian Ocean tsunami is mainly due to the static sea floor uplift caused by abrupt slip at the India/Burma plate interface. Seismic inversion models (Ammon, 2005) indicate that the main shock propagated northward from the epicenter parallel to the Sumatra trenches for approximately 1,200 km of the fault length. In this study, the ruptured subduction zone is identified by five segments of tsunami source based on different morphologies (Fig.1). 2.1 Source Model The main generating force of a tsunami triggered by an earthquake is the uplift or subsidence of the sea-floor. Determining the actual extent of sea-floor

3 Numerical Simulation of the December 26,2004: Indian Ocean Tsunami 3 change in a sub-sea earthquake is very difficult. In general, the displacement can be computed from the formulae which output surface deformation as a function of fault strike, dip, slip, length, width, depth, moment magnitude, and Lame s constants for the surrounding rock (Okada, 1985). The underlying assumptions are based on the isotropic property and half-plane homogeneity of a simple source configuration. Okada s formulae are used in this study to compute ground displacement from fault parameters of each segment shown in Table 1. The total seismic moment release is M o = J, equivalent to M w = 9.3. Okada s solution is implemented in TOPICS (Tsunami Open and Progressive Initial Conditions System) which are then tranferred and linearly superimposed into the wave propagation model (FUNWAVE) as an initial free surface condition. The five segments are distinguished by their unique shape and orientation. Segment 1 covers the Southern arc of the ruptured subduction zone with length L = 220 km. Segments 2 and 3 are relatively straight sections of the subduction zone in a NNW direction along the trench with the lengths of 150 and 390 kms respectively. The last two segments (4 and 5) have a marked change in orientation and shape. Segment 4 (L = 150 km) is facing southern Thailand whereas a significant number of larger islands are located on the overriding plate of segment 5 (L = 350 km). 2.2 Wave Propagation Model Usually tsunamis are long waves (as compared with the ocean depth). Therefore, it is natural first to consider the long-wave (or shallow-water) approximation for the tsunami generation model. However, the shallow water equations ignore the frequency dispersion which can be important for the case of higher frequency wave propagation in relatively deep water. In this paper, a fully nonlinear and dispersive Boussinesq model (FUNWAVE) is used to simulate the tsunami propagation from deep water to the coast. FUNWAVE also includes physical parameterization of dissipation processes as well as an accurate moving inundation boundary algorithm. A review of the theory behind FUNWAVE are given by Kirby (2003). 3 TSUNAMI SIMULATIONS Simulations of the December 26, 2004 tsunami propagation in the Bay of Bengal (72 to 102 E in longitude and 13 S to 23.5 N in latitude) are performed by using GEOWAVE, which is a single integrated model combining TOPICS and FUNWAVE. The application of GEOWAVE on landslide tsunami is discussed in Watts et al (2003). We construct the numerical simulation grid by using ETOPO2 bathymetry and topography data together with denser and more accurate digitized bathymetry and topography data provided by Chulalongkorn University Tsunami Rehabilitation Research Center. These data

4 4 J. Asavanant, M. Ioualalen, N. Kaewbanjak, et al were derived by a composite approach using 30 m NASA s Space Shuttle Radar Topography Mission (SRTM) data for the land area with digitized navigational chart (Hydrographic Department of the Royal Thai Navy) and overlaid onto the 1:20,000 scale administrative boundary GIS (ESRI Thailand, Co Ltd). The projection s rectification was verified and adjusted, whenever needed, using up to two ground control points per square kilometer. We regridded the data using linear interpolation to produce the uniform grid with km, which approximately corresponds to a 1 minute grid spacing, yielding 1,793 by 2,191 points. The time step for each simulation is set at 1.2 sec. Two kinds of boundary conditions are used in FUNWAVE, i.e. total reflected wall and sponge layer on all ocean boundaries. In the simulations, the five segments of tsunami sources are triggered at appropriate times t o according to the reduced speed of propagation of the rupture. Based on the shear wave speed prediced by seismic inversion models, the delay between each segments can be estimated and the values t o are provided in Table 1. 4 DISCUSSION OF RESULTS The maximum elevations above the sea level are plotted in Fig. 2 showing the tsunami s radiation patterns. Details of regional areas of Banda Aceh and Thailand s westcoast are shown in Figs. 3a,b. The estimate of sea surface elevation about two hours after the start of tsunami event is obtained along the satellite track No. 129 (Jason 1). The comparison between the model results with the satellite altimetry illustrated in Fig. 4 shows satisfactory agreement, except for a small spatial shift at some locations. This may be due to the noise in satellite data. During the event, sea surface elevations were measured at several tide gage stations and also recorded with a depth echo-sounder by the Belgian yacht Mercator. Table 2 lists the the tide gage and the Belgian yacht with their locations. Fig. 5 shows both measured and simulated time series in the Maldives (Hannimaadhoo, Male), Sri Lanka (Columbo), Taphao Noi (east coast of Thailand) and the yacht. Simulated elevation and arrival times at these locations agree well as compared to those of observations. As expected from seismological aspects, all of the tide gage data (both observed and modeled) show leading elevation wave on the western side (uplift) of the sources and depression waves on the eastern side (subsidence) of the source area. As shown in Fig. 3b, the largest runups are predicted near Banda Aceh (northern Sumatra) and in western coast of Thailand (Khao Lak area). The largest runup measured on the west coast of Banda Aceh are underpredicted by 50% likely due to the lack of detailed coastal bathymetry and topography. However, better agreement on the extreme runup values can be found in the Khao Lak area, Thailand where more accurate coastal topography was specified in the model grid.

5 Numerical Simulation of the December 26,2004: Indian Ocean Tsunami 5 5 FINAL REMARKS For several decades, models based on either linear or nonlinear versions of the shallow water theory are most generally used within the tsunami problem. This shallow water model basically neglects the effects of dispersion. Here we propose the use of dispersive (yet fully nonlinear) Boussinesq equations which is also another long wave propagation model. The earthquake tsunami sources consisting of five segments for vertical coseismic displacement are simulated in TOPICS based on parameters provided in Table 1. We simulate tsunami propagation and inundation with FUNWAVE which is a public domain higher order Boussinesq model developed over the last ten years at the University of Delaware (Wei and Kirby, 1995). To estimate dispersive effects, FUNWAVE can also be set to perform the simulations under the Nonlinear Shallow Water Equations (NSWE) for the same set of parameters. Grilli, et al (2006) reported, in the regions of deeper water in WSW direction of main tsunami propagation west of the source, that dispersion can reduce the wave amplitude by up to 25% compared to the nondispersive shallow water equation model. These differences occur very locally which may be associated with local topographic features and decrease significantly after the tsunami has reached the shallower continental shelf. Furthermore the eastward propagation towards Thailand exhibits a very weak dependence on frequency dispersion. A more detailed discussion on these dispersive effects can be found in Ioualalen, et al (2006). 6 ACKNOWLEDGEMENTS The authors would like to gratefully acknowledge the National Electronics and Computer Technology Center (NECTEC) under the Ministry of Science and Technology, Thailand for the use of their ITANIUM computer cluster and Dr. A. Snidvongs, Head of Chulalongkorn University Tsunami Rehabilitation Research Center, for providing the digitized inland topography and sea bottom bathymetry along the westcoast of Thailand. M. Merrifield from UHSLC for kindly providing us with the tide gage records. S. Grilli, J. Kirby, and F. Shi acknowledge continuing support from the Office of Naval Research, Coastal Geosciences Program. 7 REFERENCES Ammon, C.J. et XII alia (2005). Rupture process of the 2004 Sumatra- Andaman earthquake. Science, 308, Fritz, H.M. and C.E. Synolakis (2005). Field survey of the Indian Ocean tsunami in the Maldives. Proc 5th Intl on Ocean Wave Meas and Analysis

6 6 J. Asavanant, M. Ioualalen, N. Kaewbanjak, et al Table 1. Tsunami source parameters Parameters Segment 1 Segment 2 Segment 3 Segment 4 Segment 5 x o (longitude) y o (latitude) d (km) ϕ (degrees) λ (degrees) δ (degrees) (m) L (km) W (km) t o (s) µ (Pa) M o (J) λ o (km) T o (min) η o (m) -3.27; ; ; ; ;+4.6 Locations Table 2. Tide gage locations Coordinates Hannimaadhoo, Maldives (6.767, ) Male, Maldives (4.233, ) Columbo, Sri Lanka (7.000, ) Taphao Noi, Thailand (7.833, ) Mercator (Phuket), Thailand (7.733, ) (WAVES 2005, Madrid, Spain, July 2005), ASCE Publ, paper 219. Grilli, S.T., Ioualalen, M., Asavanant, J., Shi, F., Kirby, J., and Watts, P. (2006). Source constraints and model simulation of the December 26, 2004 Indian Ocean Tsunami., J Waterway Port Coast and Ocean Engng (in press). Ioualalen, M., Asavanant, J., Kaewbanjak, N., Grilli, S.T., Kirby, J.T., and Watts, P. (2006) Modeling the 26th December 2004 Indian Ocean tsunami: Case study of impact in Thailand., J Geophys Res (in revision). Kawata, T. et XIV alia (2005). Comprehensive analysis of the damage and its impact on coastal zones by the 2004 Indian Ocean tsunami disaster. Disaster Prevention Research Institute, sumatra2004/report.html. Kirby, J.T. (2003). Boussinesq models and applications to nearshore wave propagation, surf zone processes and wave-induced currents., Advances in

7 Numerical Simulation of the December 26,2004: Indian Ocean Tsunami 7 Fig. 1. Earthquake tsunami source Coastal Modeling, V.C. Lakhan (ed), Elsevier Oceanography Series 67, McNeill, L., Henstock, T. and D. Tappin (2005). Evidence for seafloor deformation during great subduction zone earthquakes of the Sumatran subduction zone: Results from the first seafloor survey onboard the HMS Scott, 2005., EOS Trans. AGU, 86(52), Fall Meet. Suppl., Abstract U14A-02. Moran, K., Grilli, S.T. and D. Tappin (2005). An overview of SEATOS: Sumatra earthquake and tsunami offshore survey., EOS Trans. AGU, 86(52), Fall Meet. Suppl., Abstract U14A-05. Okada, Y. (1985). Surface deformation due to shear and tensile faults in a half-space. Bull. Seis. Soc. Am., 75(4), Satake, K. et XI alia (2005). Report on post tsunami survey along the Myanmar coast for the December 2004 Sumatra-Andaman earthquake. unit.aist.go.jp/actfault/english /topics/myanmar/index.html.

8 8 J. Asavanant, M. Ioualalen, N. Kaewbanjak, et al Fig. 2. Maximum elevations in Bay of Bengal (a) (b) Fig. 3. (a)maximum elevations along Banda Aceh and (b)maximum elevations along the westcoast of Thailand

9 Numerical Simulation of the December 26,2004: Indian Ocean Tsunami 9 Fig. 4. Comparison of tsunami measured with satellite altimetry by Jason1 and results of tsunami simulation (a) (b)

10 10 J. Asavanant, M. Ioualalen, N. Kaewbanjak, et al (c) (d) (e) Fig. 5. Comparison of numerical tide gage data for (a) Hanimaadhoo, (b) Male, (c) Colombo, (d) Taphao Noi, and (e) mercator yatch

11 Numerical Simulation of the December 26,2004: Indian Ocean Tsunami 11 Watts, P., Grilli, S.T., Kirby, J.T., Fryer, G.J., and Tappin, D. (2003). Landslide tsunami case studies using a Boussinesq model and a fully nonlinear tsunami generation model. Nat. Hazards and Earth Sci. Systems, 3 (5), Wei, G. and Kirby, J.T. (1995). Time-dependent numerical code for extended Boussinesq equations. J. Waterway Port Coast and Ocean Engng., 121 (5),