Numerical simulation of Middle-America Trench generated tsunamis, their coastal arrival and inundation patterns in Mexico

Transcription

1 Numerical simulation of Middle-America Trench generated tsunamis, their coastal arrival and inundation patterns in Mexico S. Farreras,(l) M. Ortiz/*) O. Ramirez (2) (1) Oceanology Division, CICESE Research Center of Mexico, P.O. Box 434&K &z% Dz'ego, CaZf/brm'a 92743, [/.^.v4. (2) Instituto de Oceanologia de Cuba, Calle 27 #8208, Cojimar, Ciudad Habana, Cuba Abstract To assess the extent and consequences of Middle America Trench generated tsunami impact to Eastern Pacific coastal communities of Mexico, computer simulations are performed. The tsunami source is described as an ocean water disturbance generated by an earthquake sea-floor deformation, assumed as a mirror sea-surface motion image. Deep water linear wave theory for the generation and far ocean propagation, and shallow water non-linear wave theory close to the shore are considered. Nonlinear discharge-depth relationships conditioned to the state of the water level at the boundaries, are used to model the flooding and recession at the coast. The computations are carried out through an explicit finite-difference numerical integration algorithm for interconnected discrete grids of different sizes. One of the most recent and well documented tsunamis in Mexico, considered as representatives of highly probable average cases, is satisfactorily modeled. Source parameters from large tsunamigenic past-earthquakes at seismic gaps off the Middle America Trench are used to simulate extreme future tsunamis. Inundation maps showing water runup and extension of flooding for some densely populated coastal areas and major industrially developed ports of the Eastern Pacific coast of Mexico, are produced for civil protection purposes.

2 204 Coastal Engineering and Marina Developments 1 Introduction Computer models are an efficient tool to determine the extent and consequence of disasters and an aid in the optimum utilization of available resources to cope with them. Accurately modeling enables a better understanding of the response to extreme conditions in areas which are frequently densely populated or are the sites of major industrial or tourist developments, helping among others in the design of coastal protections, remediation works and the operation of local warning systems. Historic accounts from the last three centuries show that tsunamis that are locally generated in the Middle-America subduction zone constitute a serious threat to the southwestern coast of Mexico (Sanchez & Farreras[l]). 68 records from 21 events were registered during 37 years of operation of the tide gauge network since 1952 until Figure 1 summarizes date, gauge, location and source type of the records. The historic 16 November 1925 and 22 June 1932 tsunamis, with estimated 7 and 10 m maximum wave heights respectively, were the two largest and most destructive contemporary events in the zone. More recently, the 19 September 1985 and the 9 October 1995 events with maximum wave heights of 2.5 and 5 m respectively produced widespread damage in several communities along this coast (Farreras & Sanchez[2], Borrero et al[3]). To reduce the loss of life and property, and minimize the socioeconomic disruption caused by tsunamis, microzonation risk analysis and vulnerability assessment studies are performed. An important element for these analysis and studies is the determination of probable tsunami wave elevations and expected inundation limits at each location. Presently, the best alternative to determine these parameters is through numerical simulation of wave generation and propagation from the source to the shoreline and inland areas considering, among other factors, the beach slope, bottom friction, tectonic subsidence or uplifting, wave profile and directionality, and the presence of vegetation and man-made structures (Farreras & Sanchez[4]). 2 The Model Recognizing that the majority of the populations at risk from tsunamis reside in developing countries which lack the necessary knowledge and technology to reduce their impact, the International Coordination Group for the Tsunami Warning System in the Pacific (ICG/ITSU) of the Intergovernmental Oceanographic Commission (IOC) of UNESCO and the Tsunami Commission of the International Union of Geodesy and Geophysics (IUGG) launched the Tsunami Inundation Modeling Exchange (TIME) project, under the framework of the International Decade for Natural Disaster Reduction (IDNDR) of the United Nations. The objective of the TIME project is to transfer advanced tsunami computer inundation modeling technology to developing nations, with

3 Coastal Engineering and Marina Developments 205 RECORDED TSUNAMIS "** " ! # NOMRJLMYNOMfkrrOCMRFEOCMYJANOJANOMRDEOCSESE REC O O O O O ENSENA I O GUADALUPE} 3 O O O O GUAYMAS- LORETO- 4 O O O O TOPOLOBAMPO- 6QO QO O# LA PAZ- 2 O O SAN LUCAS" 6 O OOO O# MAZATLAN' 2 OO VALLARTA' 8 O OO O#OO # MANZANILLCT 19 O#OO##OOO O#OO## O### ACAPULCO' I I OO#O OOOO #OO SALINA CRUZ- QQ 15 RECORDS FROM 9 LOCAL EVENTS # _5^RECORDS FROM J2_ DISTANT EVENTSO 68RECORDS FROM 21 EVENTS TOTAL "5* "0* 105" 100* Figure 1: Date, gauge location, source type, and number of tsunami records of the western coast of Mexico from 1952 to the purpose of producing inundation maps for planning and prevention activities. After extensive discussions among tsunami modeling experts, it was agreed that the tsunami inundation models from the Tohoku University (Japan) were the most advanced and suitable for this project. Since the start of the project in 1991, the Disaster Control Research Center of the Tohoku University has already transferred the tsunami modeling technology to 11 countries: Australia, Canada, Colombia, Greece, Indonesia, Italy, Korea, Mexico, New Zealand, United States of America and Turkey (Shuto[5]). In addition, Chile and Mexico organized in 1996 a training and technology transfer course for Latin-American experts from Chile, Colombia, Costa Rica, Ecuador and Mexico, and more recently, from Peru (Intergovernmental Oceanographic Commission[6]). 2.1 Governing Equations, Initial and Boundary Conditions The Tohoku University tsunami numerical model code consists of the vertically integrated equations of motion and the equation of continuity, without the Coriolis effect, as given by Goto et al[7]: _+ + = 0 (1) a ax ay

4 206 Coastal Engineering and Marina Developments a /MS a /MN\ an gn^ (2) an a /MN - + ( gd + -NQ = 0 (3) a ax ^ D ^ ayd/ ay being: r = vertical displacement of the water surface above the still water level, D = total water depth, M & N = vertically integrated components of the horizontal and vertical transport per unit width (flow flux), g = acceleration of gravity, Q = (M^+N^)^ = transport magnitude, and n~ 10"^= Manning bottom friction coefficient. Sommerfeld[8] offshore boundary condition as free radiation of waves outward to infinity, is assumed. The land-water boundary condition considers a non-linear discharge q if the water level for two neighboring squares of the integration grid mesh shows a higher value A > 0 in the underwater one with respect to the dry exposed one, as in Iwasaki & Mano[9]: If A < 0, the discharge q is zero. (4) For the initial condition (tsunami generation by an undersea earthquake), a perturbation of the ocean surface as an image of the temporal displacement of the bottom ah/at, evaluated through integration over the fault plane of the source points contribution to the vertical motion, as given by Mansinha & Smylie[10], is considered: ah being: \i = Lame elastic constant «5x10^ dyne/cm^, U = down slip of the dip-slip fault, u^ = components of the dislocation magnitude, 2 & 3 ~ horizontal spatial coordinates at the fault plane, and 8 = dip angle of the fault plane (Figure 2). 2.2 Numerical Solution All the terms of the equation of continuity (eqn 1) and the equations of motion (eqns 2 & 3) are discretized in an explicit finite difference scheme, with the exception of the friction term of the last two equations where an implicit scheme is used to avoid instabilities. Numerical integration is performed by means of

5 Coastal Engineering and Marina Developments 207 Figure!: Parameter scheme for the evaluation of the tsunami initial perturbation the leap-frog central difference algorithm with second order truncation errors. An upwind scheme, where the differences are taken in the direction of the flow, is applied in order to ensure the stability of the computation (i.e. keep the virtual diffusion coefficient positive). Deep water linear wave approximation of the equations is used for the generation and far ocean propagation, while the shallow water non-linear wave equations are used close to the shore. Coarse grids in the deep sea and fine grids in the near shore zone are considered, with continuity of computation at the boundaries of the regions of these interconnected grids of different sizes. The temporal and spatial grid lengths were carefully selected to satisfy the CFL stability condition. Accordingly, grid sizes of 1350 m, 150 m and 50 m were sequentially used from the deep sea to the near shore zone. 3 Application in Mexico and Results On 19 September 1985 an 8.1 Ms earthquake, composed of two subevents with 80 km source separation and a 26 sec time lag, occurred in the subduction zone of the northwest portion of the Cocos Plate (Anderson et al [11]). The generated tsunami affected several coastal communities in the States of Michoacan and Guerrero. Waves of 2 to 2.5 m height arrived to the port of Zihuatanejo. Considerable flood damage was caused by the water that came to the first floor

6 208 Coastal Engineering and Marina Developments land contours above mean sea-level computed inundated area maximum computed water level , kilometers meters Figure 3: Maximum computed water level and inundation area for the 19 September 1985 tsunami at Zihuatanejo Bay. of the major beachside hotels, restaurants and residences and invaded a distance of about 200 m inland (Farreras and Sanchez [2]. This tsunami can be considered as representative of a highly probable average case of occurrence in the region. A numerical simulation of the tsunami was made using the model described above. Initial fault parameters were taken from the preliminary Harvard Centroid Moment Tensor solution and adjusted by a trial-and-error method constrained by the analytical relation defining the seismic moment. The bathymetry used was from the ETOPO-5 files. Integration time step was 1 sec and the simulation was carried on for two hours time. The best fit of the numerical simulation with recorded sea levels, wave forms and arrival times at the site was the one assuming a reverse fault of 50 km width and 175 km length along the strike and a constant slip of 90 cm. Figure 3 shows the maximum computed water level during the two hours of simulation and the extension of

7 Coastal Engineering and Marina Developments 209 the inundated area at the coast of Zihuatanejo Bay. Computed values agree reasonably with field survey measurements reported previously by Farreras and Sanchez [12]. The two most destructive contemporary tsunamis in the zone were the 16 November 1925 and the 22 June 1932 events, with estimated 7 to 10 m maximum wave heights respectively. A computer simulation using earthquake source fault parameters appropriate to these extreme events, with an initial vertical ground displacement of 250 cm, was performed. Results are shown in Figure 4. The numerical simulation underestimates in about one half the maximum wave heights observed, suggesting the presence of a secondary source mechanism (i.e. a submarine landslide) triggered by and in addition to the earthquake itself. From the results of the numerical simulations on maximum computed water levels and flooding areas, inundation maps including land use patterns, vulnerability assessment and recommendations to minimize the loss of life and land contours above mean sea-level J& computed inundated area maximum computed water level (meters) Figure 4: Maximum computed water level and inundation area for an eventual extreme tsunami at Zihuatanejo Bay. 8

8 210 Coastal Engineering and Marina Developments Figure 5: Land use pattern, vulnerability assessment and recommendations for an industrial port area under the eventual occurrence of an extreme tsunami. damage to property produced (Figure 5). in case of the occurrence of extreme tsunamis, can be 4 Conclusions The maximum water level height of 2.3 m simulated by the model in Zihuatanejo Bay for the 19 September 1985 tsunami is in the range of the observed values at the site: 2.0 to 2.5 m. The horizontal inundation extension and wave arrival time simulated are similar to the ones observed. Hence, the model can be considered adequately valid to simulate small to medium size tsunamis generated at the Middle-America Trench. The model simulation of an eventual extremely large and destructive tsunami underestimates the maximum wave heights in one half with respect to the observed ones in two historical cases, suggesting the presence of a secondary triggering source mechanism in addition to the earthquake itself. However, these numerical simulations are a useful tool as a first estimate to produce inundation maps that can be used for hazard planning purposes and prevention measures to minimize the loss of life and damage to property in coastal communities (industrial ports, tourist resorts and residential areas) exposed to the tsunami threat.

9 Coastal Engineering and Marina Developments 211 References 1. Sanchez, AJ. & Farreras S.F., Catalog of Tsunamis on the Western Coast ofmexico, World Data Center, NOAA, Boulder, pp. 1-27, Farreras, S.F. & Sanchez AJ. Generation, wave form and local impact of the September 19, 1985 Mexican tsunami, Science of Tsunami Hazards, 5, pp. 3-13, Borrero, J., Ortiz, M., Titov, V. & Synolakis, C. Field survey of Mexican tsunami produces new data, unusual photos, EOS, 78(8), pp , Farreras, S.F. & Sanchez A.J. The tsunami threat on the Mexican west coast: a historical analysis and recommendations for hazard mitigation, Natural Hazards, 4, pp , Shuto N., Progress Report of the TIME Project, Intergovernmental Oceanographic Commission of UNESCO, Paris, pp. 1-5, Intergovernmental Oceanographic Commission, COI-SHOA-CICESE Curso sobre Modelacion Numerica de Tsunamis, Proyecto TIME, Valparaiso, pp. 1-3, Goto, C., Ogawa, Y., Shuto,N. & Imamura F. IUGG/IOC TIME Project: Numerical Method of Tsunami Simulation with the Leap-Frog Scheme, Intergovernmental Oceanographic Commission, Paris, pp. 1-19, Sommerfeld, A. Partial Differential Equations, Academic Press, New York, Iwasaki, T. & Mano A., Two-dimensional numerical computation of tsunami run-ups in the Eulerian description, Proc. of the 26th Conf. on Coastal Engineering, Japan Soc. Civil Eng, Tokyo, pp , Mansinha, L. & Smylie D.E. The displacement field of inclined faults, Bulletin Seismological Society ofamerica, 61, pp , Anderson, J.G., Bodin, P., Brune, J.N., Prince, I, Singh, S.K., Quaas, R. & Onate, M. Strong ground motion from the Michoacan-Mexico earthquake, Science, 233(4768), pp , Farreras, S.F. & Sanchez A.J., Mexico 1985 retrospective assessment, Chapter 5, Planning for Risk: Comprehensive Planning for Tsunami Hazard Areas, ed. Urban Regional Research, Seattle, pp , 1988.