Numerical Study of Tsunami Propagation in Mentawai Islands West Sumatra

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1 Universal Journal of Geoscience 5(4): , 201 DOI: /ujg Nuerical Study of Tsunai Propagation in Mentawai Islands West Suatra Noverina Alfiany *, Kazuhiro Yaaoto, Masaji Watanabe Graduate School of Environental and Life Science, Okayaa University, Japan Copyright 201 by authors, all rights reserved. Authors agree that this article reains peranently open access under the ters of the Creative Coons Attribution License 4.0 International License Abstract Shallow water equations were analyzed nuerically for siulation of tsunai propagation fro the source area to coastal zone of Mentawai Islands along West Suatra Island. A triangular esh was set for spatial discretization and a syste of partial differential equation is reduced to a syste of ordinary differential equations. Initial displaceent based on Okada odel was applied. Our nuerical techniques were deonstrated with a siulation of tsunai generated fro an earthquake with epicenter near South Pagai Island, Mentawai Islands, Indonesia. Keywords Tsunai Siulation, Okada Model, Finite Eleent Method, ODE Solver, Mentawai Islands 1. Introduction On the West Suatra off coast, there are Mentawai Islands segent, which is a part of the Suatra subduction zone, which results fro the under-thrusting of the Indo-Australian plate beneath the overriding Eurasian plate, stretches over 5600 k [1]. In the last decade, these Mentawai Islands segent produced any great earthquake with potential tsunai events, including the October 25 th, 2010 Mentawai Islands tsunai earthquake. The earthquake occurred at 21:42:22.0 with the epicenter 3.48ºS, ºE and 20 k depth (NOAA Significant Earthquake Data), and generated a tsunai within estiated 8 inutes off the earthquake. Seisological analyses indicate that the Mentawai earthquake was a tsunai earthquake, which produced a uch larger tsunai than expected fro the seisic agnitude [2]. Ulutaş [3] applied two kinds of tsunai nuerical odels based on the shallow water equations to siulate the South Pagai Island, Suatra earthquake tsunai which occurred on 25 th, October The nuerical odels were analyzed by using nonlinear and dispersive long wave tsunai odels, and earthquake paraeters which are available fro U.S Geological website. Satake, et. al [2] coputed 25 th, October 2010, Mentawai Islands coastal tsunai heights fro the tsunai source odel which was proposed fro a field survey and wavefor recording with linear equations. The slip distributions on the fault planes were estiated through the inversion of tsunai wavefor, whereas the strikes and rakes were estiated fro USGS W phase solution. In this study the propagation of tsunai waves generated in Mentawai Islands segent were studied nuerically. A triangular esh was eployed for discretization of the governing equations, a syste of partial differential equations, to a syste of ordinary differential equations. The earthquake fault plane paraeters based on Satake, et. al [2] were used for coputation with Okada theory [4,5]. Nuerical results illustrate the tsunai waves propagation generated by the 2010 Mentawai Islands earthquake. 2. Materials and Methods A syste of partial differential equations consisting of oentu equations and a continuity equation were used, and reduced by using discretization based on a triangular esh to a syste of ordinary differential equations Governing Equations In the theory of long waves, the vertical acceleration of water particles are negligible copared to the gravitational acceleration except for an oceanic propagation of tsunai. Consequently, the vertical otion of water particles has no effect on the pressure distribution [6] which leads to two diensional equations with dynaic and kinetic conditions, this is called the shallow water theory, can be obtained. The nuerical odel is based on the nonlinear shallow water equations []. The following syste of partial differential equations (1)-(3) were solve nuerically for siulation of the tsunai propagation

2 Universal Journal of Geoscience 5(4): , M t M2 H N t MN H y MN H η t M N y y N2 H gh η gh η gn2 H3 gn2 y H3 = 0, (1) M 2 N 2 = 0, M 2 N 2 = 0. Variables M and N are the flux of x - and y-coponents, respectively which are defined by η η M = u dz, N = v dz (4) h h where u and v represent the x -coponent and y-coponent of velocity respectively, and H = η h is the total depth with sea depth h and the water surface elevation fro the ean sea level η. The constant g is the gravitational acceleration and n is the Manning roughness coefficient Finite Eleent Analysis Let x j, y j (j = 1, 2,, ) be nodal points of a triangular esh in xy -plane. A basis function ϕ i (i = 1, 2,, ) is a piecewise linear function that satisfies 1 if i = j, ϕ i x j, y j = (5) 0 otherwise, for i, j = 1, 2,,. For the analysis, functions are approxiated by linear cobinations of the basis functions M(x, y, t) j=1 M j (t)ϕ j (x, y), (6) (2) (3) N(x, y, t) j=1 N j (t)ϕ j (x, y), () η(x, y, t) j=1 η j (t)ϕ j (x, y), (8) h(x, y) j=1 h j ϕ j (x, y). (9) Then the governing equations (1)-(3) becoe syste of equations (10)-(12). M j j=1 t j=1 η j t ϕ j M N y = 0, (10) ϕ j M2 MN η g η (ηh) y (ηh ) j=1 j h j ϕ j F x = 0, (11) N j t ϕ j j=1 MN N2 η g η (ηh ) y (ηh ) y j=1 j h j ϕ j F y = 0, (12) where F x = F y = n 3 j=1η j h j Φj n 3 j=1η j h j Φj j=1 M 2 j N 2 j Φ j, (13) j=1 M 2 j N 2 j Φ j. (14) Syste of equations (10)-(12) becoe the syste equation (15)-(1) dm i dt dn i dt where dη i dt = M N y, (15) = M2 MN η g (η (ηh) y (ηh ) i h i ) F x, (16) = MN N2 η g (η (ηh ) y (ηh) y i h i ) F y, (1) F x = F y = (η i h i ) 3 (η i h i ) 3 M i M i 2 N i 2, (18) N i M i 2 N i 2. (19) The partial derivatives on the right-hand sides of the syste equation (16)-(1) becoe y y MN (ηh ) = MN (ηh ) = M2 (ηh) = 2 N2 (ηh ) = 2 N i M (η i h i ) The partial derivatives approxiated by η M i M (η i h i ) M 2 i (ηh) (η i h i ) 2 N i N N 2 i (ηh) (η i h i ) y (η i h i ) 2 M i N M in i (ηh) (η i h i ) (η i h i ) 2 N i M M i N M in i (ηh) (η i h i ) y (η i h i ) y (η i h i ) 2 (ηh) and η and respectively. y, (20) y, (21), (22) y. (23) (ηh) y Values of partial derivatives at a nodal point are approxiated by weighted averages of partial derivatives over eleents that have the nodal point as vertices. For exaple, η = 1 i l η = y i k=1 A k 1 l k=1 A k l k=1 A k η l k=1 A k η are (k), (24) y (k), (25) where A 1, A 2,, A l are the areas of the eleents which have the i-th node as a coon vertex, and η (k) is an approxiate value of the partial derivative η in the k-th eleents []. The collocation ethod was ipleented in analysis of the syste of equations above for discretization on a triangular esh, and the syste of partial differential equations was transfored to a syste of ordinary differential equations. The syste of those ordinary differential equations were solved nuerically using a standard ODE solver i.e the fourth order Ada-Bashforth-Moulton predictor-corrector in conjunction with the fourth order Runge-Kutta ethod to generate values of approxiate solutions at the first three steps Okada Model [4, 5] Nuerous theoretical forulations describing the

3 114 Nuerical Study of Tsunai Propagation in Mentawai Islands West Suatra deforation of an isotropic hoogeneous sei-infinite ediu have been developed with increasing copleteness and generality of source type and geoetry, and range fro the derivation of the surface displaceent due to a point source to the strain fields at depth [4]. The closed analytical expressions was checked and reviewed by Okada [4], which are already published to describe the surface deforation due to shear fault in a half-space. Furtherore, an unknown solution for the displaceents strains and tilts arising fro opening-ode dislocations. Okada [5] established a odel for calculation of internal deforation fields due to ultiple sources that can be arbitrarily coposed of shear and tensile faults of both point and rectangular types, where the surface deforation was forulated. This work is the extension of the previous work [4] to the internal deforation fields due to shear and tensile faults. The Okada odel was developed under the assuption that a rectangular fault plane is buried in a elastic sei-infinite half-space. On the case of sea surface deforation, the sea surface iics the deforation of seafloor, since an earthquake usually occurs in seconds and the water colun over the seafloor cannot escape within the short duration. The data of fault paraeters which are required to copute the surface deforation include longitude and latitude, focal depth, length and width of fault planes, dislocation, strike angle, slip angle and dip angle. Satake, et.al [2] divided the tsunai source area into 28 subfaults. The faults plane paraeters [2] were used to coputed the seafloor vertical deforation for a unit slip on each subfault. 101º respectively, were estiated fro USGS W phase solution. The dip angles were assued to be.5º for k depths subfaults and 12º for k depths subfaults [2]. All those paraeter values were eployed in the Okada forula. The vertical seafloor deforation for each subfaults which were coputed using Okada odel, was set as an initial condition to generate the initial tsunai wave. Figure 1 shows the initial surface deforation for the 28 subfaults in the fault plane source area. The results shown are the coputational outcoes obtained by using Okada odel. It shows the significant vertical surface displaceent at several subfaults area, where the highest vertical deforation is approxiately Discussion The syste of partial differential equations (1)-(3) was analyzed for siulation of the tsunai propagation for Mentawai Islands case on October 25 th, Finite eleent analysis was applied to solve the syste equations (1)-(3) nuerically Bathyetry Data and Tsunai Source The bathyetry data including latitude, longitude and depth fro BDOC, National Oceanographic Database, GEBCO one inute grid [8] were used. Those data ranges fro 85.0ºE to 106.0ºE and 15.0ºS to 6.0ºN. The data which originally given in for of latitude and longitude are transfored into projected coordinates by the Gauss-Krüger projection. The fault plane is stretched fro ºE to ºE and ºS to ºS which divided into 28 subfaults. Every subfaults have 30 k in length and 30 k in width. The strike and rake angle were 326º and Figure 1. The initial surface deforation for 28 subfaults 3.2. Siulation of the Tsunai Waves Propagation The tsunai wave propagation is siulated for 1800 seconds siulation, which is equal to 1 hour tsunais propagation. The initial tsunai wave for at 0 second, in the siulation area, is shown in Figure 2. Nuerical results for tsunai wave propagation after 300 seconds and 600 seconds are shown in Fig. 3A (left) and Fig. 3B (right). Nuerical results for the tsunai propagation after 900 seconds and 1200 seconds, 1500 seconds and 1800 seconds are shown in Fig. 4A (left) and Fig. 4B (right), Fig. 5A (left) and Fig. 5B (right), respectively. In siulation initial tsunai wave for was ruptured before the 300 seconds, which is equal to 10 inutes after initial tsunai wave for generated. Satake, et. al [2] assued that the tsunai arrival tie was at 21:50 WIB on 25 th, October It is approxiately 8 inutes after the earthquake which occurred at 21:42:22.0 WIB.

4 Universal Journal of Geoscience 5(4): , Figure 2. The initial tsunai wave at 0 second The highest initial wave was approxiately 3, and in siulation the highest wave of approxiated 4 was observed at several points in Mentawai Islands area, whereas the other wave heights are ranged fro 1 to 4. The results of this study showed the saller wave heights copared with those reported on the field survey. Field survey results of tsunai affected areas in the Mentawai Islands by Koresawa [9] reported that the highest and the lowest tsunai wave height at South Pagai Island was 9.3 and 2.5, respectively. North Pagai Island was affected by tsunai wave height 8.8 and 2.9 as the highest and the lowest. Satake, et. al [2] indicated that the easured tsunai heights were ostly between 4 and, where the largest tsunai heights were easured on the central and southern South Pagai Island and south-western North Pagai Island. Figure 3. Tsunai waves after 300 seconds (left) and 600 seconds (right). Figure 4. Tsunai waves after 900 seconds (left) and 1200 seconds (right)

5 116 Nuerical Study of Tsunai Propagation in Mentawai Islands West Suatra Figure 5. Tsunai waves after 1500 seconds (left) and 1800 seconds (right) 4. Conclusions Results fro nuerical study of tsunai event at Mentawai Islands, October 25 th, 2010, was presented. The Okada odel was used to calculate the initial surface displaceent, and the fault plane source paraeters of the earthquake were utilized. A triangular eleent esh was eployed to discretize the governing equation. The coputational results of the initial surface deforation by Okada odel shows that the highest initial wave height was 3. In siulation, tsunai wave reached the coastal areas of Pagai Islands in less than 300 seconds, at South Pagai Island and North Pagai Island, after the initial tsunai waves generated. In siulation the highest waves of approxiately 4 appear at several points around South Pagai Island and North Pagai Island. The siulation of this study showed the wave heights were saller than those reported on the field survey. The tsunai waves were distributed along South Pagai Island, North Pagai Island, Sipura Island, edge of Siberut Island and reached in part of the coastal area of Suatra Island at the province of Bengkulu. REFERENCES [1] R. Moereans, S. C. Singh, M. Mukti, J. McArdle, K. Johansen. Seisic iages of structural variations along the deforation front of the Andaan-Suatra subduction zone: Iplications for rupture propagation and tsunai genesis, Earth and Planetary Science Letters, Vol. 386, 5-85, [2] K. Satake, Y. Nishiura, P. S. Putra, A. R. Gusan, H. Sunendar, Y. Fujii, Y. Tanioka, H. Latief, E. Yulianto. Tsunai Source of the 2010 Mentawai, Indonesia Earthquake Inferred fro Tsunai Field Survey and Wavefor Modeling, Pure Appl. Geophys, Vol. 10, , [3] E. Ulutaş. Tsunai siulation of the October 25, 2010, South Pagai Island, Suatra earthquake, International Journal of the Physical Sciences, Vol. 6, No. 3, , [4] Y. Okada. Surface Deforation Due to Shear and Tensile Faults in A Half-Space, Bulletin of the Seisological Society of Aerica, Vol. 5, No. 4, , [5] Y. Okada. Internal Deforation Due to Shear and Tensile Faults in A Half-Space, Bulletin of the Seisological Society of Aerica, Vol. 82, No. 2, , [6] F. Iaura, A. C. Yalciner, G. Ozyurt. Tsunai Modelling Manual (TUNAMI Model). April [] Y. Otani, K. Yaaoto, Hashentuya, M. Watanabe. Nuerical Study of the Effects of Tsunais Using a Finite Eleent Method, ANZIAM J. 52, C1031-C1048, [8] British Oceanographic Data Centre (BODC): [9] A. Koresawa. Field Survey of Tsunai Stricken Areas in the Mentawai Islands: focusing on policy aspects, ICA-JST Indonesia Multi-disciplinary Hazard Reduction fro Earthquakes and Volcanoes in Indonesia, 5 th -10 th Noveber, Indonesia. ( 19.htl)