RUSSIAN JOURNAL OF EARTH SCIENCES VOL. 8, ES5001, doi:10.2205/2006ES000208, 2006
To analysis of source mechanism of the 26 December 2004 Indian Ocean tsunamiL. I. Lobkovsky1, R. Kh. Mazova2, I. A. Garagash3, L. Yu. Kataeva2, and I. Nardin2 1P. P. Shirshov Institute of Oceanology, Russian Academy of Sciences, Moscow, Russia2Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia 3Institute of Physics of the Earth, Russian Academy of Sciences, Moscow, Russia Contents
Abstract[1] Tsunami in the Indian Ocean generated by a strong earthquake in Sumatra-Andaman region on 26 December 2004 led as known to catastrophic results at the coast of many countries of this region. In spite of intensive study of this event by a number of groups, the character of seafloor displacements in the source during this earthquake remains to be controversial. In this work, it is performed an analysis of physical aspects of similar earthquakes on the basis of keyboard model of tsunamigenic earthquakes. The numerical simulation of generation, propagation and run-up of surface water waves on the basis of simplified keyboard model of tsunamigenic earthquakes with vertical displacements of keyboard blocks in approximative geometry (without taking into account the real bathymetry) is also performed. It is obtained that tsunami waves generated by various combinations of keyboard block displacements are essentially different in character which fact leads to quite different picture of maximum run-up distribution along the near-field coast. It is performed the estimative computation for 26 December 2004 Sumatra-Andaman earthquake with taking into account of oblique character of the subduction zone characteristic for this earthquake. The computations performed explain the complex character of run-up distribution at nearest to the source coasts and are in a good agreement with run-up values at the Thailand coast. It is noted that such a model can account for more adequately the tsunami wavefield character in another regions of the Indian and the Pacific Ocean basins as well. 1. Introduction[2] It is well known that 26 December 2004 and 28 March 2005 in the Indian Ocean there occurred two earthquakes: the first one, with magnitude 9.2, produced a largest tsunami which caused almost 300.000 deaths; and the second one, with magnitude 8.8, led to significant damages due to ground shaking but not produced a noticeable tsunami [for review, see, e.g., Lay et al., 2005]. Both earthquakes occurred in the Indian Ocean west of the Sumatra Island and Thailand and they are related to the same part of Philippine and Sunda island arcs. Which cause is for so different results of earthquakes at so close earthquake magnitude? And though the cause of absence of strong tsunami due to 28 March, 2005 earthquake is not clear up to now, then it can be supposed that the difference is connected with features of seafloor displacements in the earthquake source. [3] As known, the formation of tsunami depends on character and dynamics of displacements in earthquake source zone, i.e. on the initial seafloor displacements. As a rule, under computations of tsunami wave generation there are used the seismic data which indicate the rupture orientation in the source and the energy of tsunami. Then, the static hydrodynamical problem on the recount of seafloor displacement distribution to the ocean surface shape is considered. Further, the obtained displacements of the water surface with fixed length and height of the wave are taken as initial conditions and then it is performed the numerical simulation of wave propagation in given basin with taking into account the real bathymetry. In present time, there are a number of numerical models and program complexes [see, e.g., Goto et al., 1997; Titov et al., 2005; etc.], which permits to perform accurately enough computations of tsunami wave propagation up to the coast. After the Indian Ocean tsunami the accuracy of such computations can be estimated by comparison of 3D-section in the Indian Ocean with satellite data on the water surface displacement at tsunami propagation [see, e.g., Kulikov et al., 2005]. However, the question on the adequateness of the source model used at such simulations remains to be open. The features of tsunami generation, its parameters, initial velocity, characteristics of the coast (especially in the near-field zone) directly depend on the numerical model used to determine the initial movements of the seafloor in the earthquake source. Large uncertainty in these calculations stems from often poorly-defined seafloor displacements. Typically for the modeling purposes, the rupture orientation and associated displacement discontinuity is presupposed. Then, the distribution of the sea-bottom displacements is inferred from the static solution for a dislocation in the elastic half-space [Okada, 1992]. Such approach does not take into account the real structure of the Earth crust and lithosphere, and the initial stress-strain distribution in the zone of earthquake preparation [Garagash and Ermakov, 2001; Garagash and Lobkovsky, 2006]. In addition, the static solution does not allow to study the dynamic process of formation of sea-bottom displacements. The length of tsunami wave and its amplitude depend on all of the factors listed above. Development of an adequate numerical model to predict the sea-bottom movements at the moment of the earthquake will raise the accuracy of the situational modelling of a tsunami and its influence on the shore.
[6] In this work, the simplified keyboard model with vertical displacements of blocks is analyzed. The long-term factors which determine the tectonic stress distribution in the Earth's core are the inhomogeneity of Earth's core mechanical properties and its density variations [Lobkovsky et al., 2004]. At earthquake, initial stress distribution determines essentially the character of motion in the vicinity of the earthquake source. The earthquake occurs when stress at any region of contact surface overcomes the breaking point and the motion on it is accelerated. This process depending on earthquake preparation process and the initial stress level will proceed quite differently. And at the same vertical displacements the tsunami waves generated by them will be essentially different in character [Lobkovsky et al., 2005a, 2005a]. In first part of this work (Sections 2-4) it is considered a formation of tsunami source without taking into account the initial tectonic stresses in the earthquake source. In second part of the work (Section 5) there is performed evaluation of affect of initial stress in zone of earthquake preparation. 2. Numerical Scheme to Model the Tsunami2.1. Statement of the Problem
2.2. Governing Equations[8] To describe the process of wave generation and propagation in correspondence with above assumptions it was used the nonlinear system of shallow water equations (1),
![]() 3. Numerical Simulation of Tsunami Generation, Propagation and Run-up: Keyboard Model of Source (Direct Subduction Zone)
![]() [10] The following scenarios were considered:
[11] Variations of these five scenarios are presented in Table 1.
[12] From Table 1 it is seen that value of run-up on a beach depends on the
distance between the source and the coast (lines 2.2; 2.4; 2.5 in Table 1),
on the velocity of block vertical motion in the source: slower motion, smaller
run-up (lines 1.1; 1.2 in Table 1), and on the block size: at the same source
(500 km long), its cutting to 5 blocks with lengths of 50, 100, 150, 50, and 150 km
(with maximum size 150 km
3.1. Vertical Displacements of Keyboard Blocks in the Source Only Upwards
3.2. Vertical Displacements of Keyboard Blocks in the Source Upwards and Downwards
[17] The analysis performed demonstrates that at motion of keyboard blocks in the earthquake source the sequence of their displacements, the change of the keyboard block size in 1.5-2 times, and the change of rise velocity in two times provides only insignificant change of the run-up value. However, the distribution of maximum run-ups and maximum run-downs along the coast is essentially different, this difference can be of up to 8-10 times. 4. Numerical Simulation of Tsunami Generation, Propagation and Run-up: Keyboard Model of the Source (Oblique, Sumatra-Andaman-Like, Subduction Zone)[18] The above performed study was then applied under analysis of tsunami wave generation due to the 26 December 2004 Indian Ocean earthquake. The earthquake source was located west of Sumatra Island northward along the oceanic subduction zone. The extent of the source was estimated near 1000 km [see, e.g. Lay et al., 2005]. [19] In this work, there are considered two possible scenarios of seafloor motions in the earthquake source (subduction zone) for geometry close to that of oblique subduction zone (Figure 3) in the source of Sumatra-Andaman earthquake [cf. with Lobkovsky et al., 1991]. These motions were approximated by motion of several keyboard blocks with different size. The location of the source relative to the Sumatra Island and Thailand beaches, the ocean depth in the source zone, extent of the near-coast zone (slope length and shelf slope angle), as well as possible parameters of the earthquake process were taken into account at given simulation. It was considered a run-up on a plane slope. However, modelness of the problem is that it was not taken into account the real bathymetry of the ocean and estimations were made for wave propagation on the even bottom. Such approach corresponds to small-scale tsunamizonation when ocean bottom relief can be considered as smoothed one [Soloviev et al., 1977]. It was mainly considered run-up at the nearest to the earthquake source beach corresponding to the Thailand coast. 4.1. Source Consisting of Three Keyboard Blocks
![]() 4.2. Source Consisting of Eight Keyboard Blocks[21] The location of the first keyboard block also corresponds to northwest Sumatra Island and is 300 km long while all another blocks are 100 km long and 150 km wide. The keyboard blocks moves successively in the following order:
[22] The further performed numerical simulation of the surface water wave generation by motions of keyboard blocks in the source of given earthquake demonstrates that under keyboard block motion in the source from south to north, along the subduction zone, the keyboard block sizes and velocity with which they move upward (downward), as well as velocity with which this motion comes along the subduction zone are the essential factors. 5. Influence of Initial Stress Distribution in Zone of Earthquake Preparation to Tsunami Formation5.1. Analysis of Initial Stress Distribution in Seismic Source
5.2. Numerical Simulation of Tsunami Wave Generation, Propagation and Run-up with Taking into Account the Dynamics in the Earthquake Source
![]() [25] Since it is considered local problem then temporal picture of wave coming to shoreline will reflect the process of surface water wave formation in seismic source. It is well seen that if period of bottom oscillations is of the order of 30-40 s (i.e. time of uplift and subsidence of keyboard block is of the order of 20 s) then such movements can be considered as instant bottom displacements. Then, because of incompressibility of liquid and hydrostatic pressure the tsunami source is formed as in the piston model, and the wave height above seismic source will be that as value of displacement in the source. Second uplift of bottom after 35-40 s gives no possibility for the first front to be formed clearly. As result, there occurs superposition of two fronts and depending on the source the wave height will be between 1 m and 2.5 m. Mostly it is a first wave.
[27] The Figure 19a corresponds to process of instant release of elastic stress at the rupture surface. It occurs as result of sharp decrease of the friction angle (from 20o to 8.2o for given case). If it takes place a transient process and friction angle is a function of time f(t) then the effect of this to character of surface displacements will be changed. The jump is a "rigid reaction", in prolongated f(t) process the period of sea bottom oscillations will be larger. The increase of oscillation period in three to five times essentially changes the character of formation of surface water wave by seismic source.
[29] Thus, analysis of the scenarios of generation of tsunami wave with using of elastoplastic model of subduction zone permits to explain unexpected nonuniform distribution of tsunami waves for both near-field and far-field coasts. 6. Conclusion[30] The numerical simulation of dynamical process in the earthquake source performed in this work on the basis of keyboard model demonstrates that tsunami waves generated by different combination of keyboard block motions have an essentially different character what leads to different picture of distribution of maximum run-ups along the coast. Taking into account of oblique character of the subduction zone characteristic for 26 December 2004 Sumatra-Andaman earthquake gives a good agreement with run-up values observed at the Thailand coast. It is noted that such a model can more adequately account for the character of the wavefield in other regions of the Indian and the Pacific oceans also. Electronic Supplement[31] The online version of this paper includes four animations showing processes of generation, propagation and run-up of tsunami waves on the beach. Animations 1 and 2 show tsunami waves generation for the simplified model of seismic source, which consists of three and eight blocks correspondingly, propagation of tsunami waves and running-up them on the beach. Sizes and locations of blocks correspond to the seismic source, caused the catastrophic tsunami of 26 December 2004 in the Indian Ocean. Successive motion of blocks with different velocities was set (see text for more detail). [32] Animation 3 shows movements of blocks in the seismic source during the earthquakes. Calculations were made for the stressed state of blocks at the earthquakes preparatory stage. (see text for more detail). [33] Animation 4 for the tsunami in the Indian Ocean of 26 December 2004 is based on the results of numerical simulation of surface waves generation for the seismic source consisting of 14 blocks (see [Hirata et al., 2006]). Movements of blocks in the seismic source were calculated for the stressed state of blocks, the propagation tsunami waves from seismic source was calculated up to 10-m isobath. ReferencesGaragash, I. A., and V. A. Ermakov (2001), Use of geological and geophysical models for simulating of crust stress state on the example of Sakhalin and Tien-Shan, in: Problems of Seismicity of the Far East, p. 33, Nauka, Khabarovsk. Garagash, I. A., L. I. Lobkovsky, O. R. Kozyrev, and R. Kh. Mazova (2003), Generation and run-up of tsunami waves due to submarine landslide, Oceanology, 43, (2), 185. Garagash, I. A., and L. I. 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Pyaskovsky (1977), Preliminary tsunamizonation of Kurile-Kamchatka coast on the basis of hydrodynamical computations, in: Theoretical and Experimental Research on the Tsunami Problem, p. 131, Nauka, Moscow. Titov, V., A. Rabinovich, H. Mofjeld, R. E. Tomson, and F. I. Gonzalez (2005), The global reach of the 26 December Sumatra tsunami, Science, 309, 2045, doi:10.1126/science.1114576. [CrossRef] Received 5 September 2006; revised 18 September 2006; accepted 5 October 2006; published 29 October 2006. Keywords: tsunami generation, seismic source, wave propagation, subduction zones, keyboard-blocks. Index Terms: 3060 Marine Geology and Geophysics: Subduction zone processes; 3285 Mathematical Geophysics: Wave propagation; 4255 Oceanography: General: Numerical modeling; 7209 Seismology: Earthquake dynamics. ![]() Citation: 2006), To analysis of source mechanism of the 26 December 2004 Indian Ocean tsunami, Russ. J. Earth Sci., 8, ES5001, doi:10.2205/2006ES000208. 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