A TSUNAMI GENERATION TOOL FOR DYNAMIC SEA BOTTOM DEFORMATION AND ITS APPLICATION TO THE 17 JULY 2006 JAVA EARTHQUAKE TSUNAMI

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1 A TSUNAMI GENERATION TOOL FOR DYNAMIC SEA BOTTOM DEFORMATION AND ITS APPLICATION TO THE 17 JULY 2006 JAVA EARTHQUAKE TSUNAMI STEFAN LESCHKA 1, STEFFEN HESSELINK 2,WIDJO KONGKO 3 and OLE LARSEN 4 1 Hydrodynamics and Coastal Engineering, DHI-WASY, Syke, Germany, sle@dhigroup.com 2 Hydrodynamics and Coastal Engineering, DHI-WASY, Syke, Germany 3 UNU-EHS / DHI-WASY, Syke, Germany 4 DHI-NTU Water & Environment Research Centre and Education Hub, Singapore ABSTRACT: In tsunami runup modelling there are still many open questions. Beside bathymetry the influence of the tsunami source description is an important issue. Widely used in tsunami modelling is Okada s (1985) double-couple model. Usually, it is applied to the sea surface assuming that the sea bottom movement results in an abrupt deformation of the water surface, which is used as an initial condition for tsunami modelling. There may be more exact geophysical models, but as a first guess Okada s method is advantageous because it is fast and has easy access to input parameters. That s why it has been chosen to be first implemented in the tool, called QuakeGen. It calculates variable bathymetry with control of the temporary development of the earthquake. The time variable bathymetry was used to create a tsunami with the landslide module in MIKE 21. The results have been compared to the observed runup heights and arrival times from the 17 July 2006 Java Earthquake tsunami, chosen as a reference case. The generated waves are used as a boundary condition on one bathymetry just beside the generation zone. The runup heights are compared with field survey data reported in Fritz et al. (2007) and Lavigne et al. (2007). Furthermore, the influences of time step length during the simulation is investigated. Additionally to the M W = 7.7 earthquake, the first M W = 7.2 earthquake is included into the hydrodynamic simulation. A comparison of the results shows that the tsunami generated using QuakeGen and calculated with MIKE 21 gives the modeller the advantage of further adjustments by controlling the time in source modelling. The combination of QuakeGen and the MIKE 21 landslide module has been proven to yield more reliable results in simulation regarding runup and arrival time due to the possibility of considering all earthquakes which occured within the simulation period. 1. INTRODUCTION In tsunami modelling one has to account for three phases: (a) wave generation, (b) wave propagation and transformation and with (c) wave runup at the shore and inundation. While wave propagation and transformation can be modelled quite satisfying, the processes of wave generation and runup and inundation are very complicated and still suffer from leaks in physical understanding. There are numerous works which deal with source modelling so far. Within them, Okada s (1985) double-couple method plays an important role, because it has been the first easy to use sequence of closed equations. It accounts for deformations, strain and inclination in a half-space for point sources and bounded rectangular sources. It does not account for earth bending, layers, gravity, temperature, magnetism and heterogeinity of the surface. Instead of that, a half-infinite medium is considered, which is homogeneous and isotropic. It has heen included already in various hydrodynamic simulation tools. Usually, it is applied to the water surface as an initial condition. Beside the already mentioned simplification, this neglects horizontal displacements also. However, after an earthquake, guessed seismic parameters can be used which are available from Internet within short time. Thats why the double-couple method has been chosen to be used as a first method in a tool named QuakeGen, to generate time variable bathymetries for hydrodynamic simulations with MIKE 21. MIKE 21 is a general numerical modelling system for the simulation of water levels and flows in estuaries, bays and coastal areas. It simulates unsteady 2D flows in one layer (vertically homogeneous) fluids when presented with the bathymetry and the relevant conditions (e.g. resistance coefficients, wind fields, hydrographic boundary conditions. MIKE 21 contains a landslide module, 1

2 which can use time varying bathymetries. It has already been applied to numerous studies and has been validated on a landslide at the reservoir Embalse de Arenós, Spain (Kofoed-Hansen et al., 2001). The conservation equations of mass and momentum account for a varying bathymetry using the equations of Slingerland and Voight (1979). Combining Okada s double-couple method with the landslide module comprises the possibility to account for horizontal displacements, to control the period of an earthquake itself and to include Subfaults. On the 17 July 2006 several earthquakes occured in the Java Trench. The mayor earthquakes took place at 15:19:26 (local time) at South, East with a moment magnitude of M W = 7.2 and at 15:20:38 at South, 107,78 East with a moment magnitude of M W = 7.7 (USGS). Kongko et al. (2006) and Tsuji et al. (2006) reported from a post-tsunami field survey, that the earthquake has not been or only slightly felt by the residents at the Southern coastline of Java. The long duration, slow rupture velocity and slight ground shaking would indicate that this earthquake generated abnormally large tsunamis than expected from seismic waves (Fujii and Satake, 2006). In order to get good agreement when comparing calculated tsunami runup heights and arrival times with post-tsunami field survey data for the validation of the process of tsunami generation, potential errors within wave propagation, runup and inundation have to be as small as possible. This might only be possible when satisfying bathymetrical data is used. Since the above mentioned tsunami hit the coastline of Cilacap and since there very good bathymetrical data is available, the 2006 West Java Earthquake tsunami has been chosen to test QuakeGen with the help of post tsunami field survey data. 2. NUMERICAL MODEL MIKE 21 Flow Model The hydrodynamic model in the MIKE 21 Flow Model (Mike 21 HD) is a general numerical modeling system for the simulation of water levels and flows in estuaries, bays and coastal areas. It simulates unsteady two-dimensional flows in one layer (vertically homogeneous) fluids and has been applied in a large number of studies. For the conservation of mass and momentum the non-linear shallow water equations (the depth-integrated incompressible Reynolds-averaged Navier-Stokes equations) describe the flow and water level variations. The momentum equation includes wind friction, bed resistance, Coriolis terms and lateral stresses due to viscous friction, turbulent friction and differential advection (DHI Software 2008). A method for landslide generated waves has been implemented into the model where the landslide is represented by the dynamic vertical deformation of the bathymetry plus additional terms representing the effect of the landslide due to viscous and inertia forces. Thus, the model describes the interaction between the landslide and water directly in the hydrodynamic model using forcing terms by a time varying bathymetry (Kofoed-Hansen et al., 2001). Source generation using QuakeGen The source generation tool for MIKE 21 comprises the functionality of adding time controlled vertical and horizontal displacements to a bathymetry. Several theories are available to account for earthquakes (e.g. Mansinha and Smylie, 1971; Wang et al., 2003) and landslides (e.g. Slingerland and Voight, 1979). As a fist method, Okada s double-couple method has been chosen to be implemented in the QuakeGen. Okada (1985) reviewed available methods for the source generation and gave a complete sequence of closed analytical expressions for the surface displacements, strains and tilts due to inclined shear and tensile faults in a halfspace for point and rectangular sources. In the so-called double-couple method the elementary dislocations are expressed using strike slip, dip slip and tensile strength. They are calculated using the parameters dip angle, slip angle, strike angle, length of the slip vector, depth, 2

3 width, length of the finite fault, Young s modulus and the Poisson ratio. Information on width and length of the finite fault is usually not available immediatelly after the earthquake while estimations of other parameters are published already a few minutes after an event. Also the moment magnitude M W of the earthquake can be received from Internet. It can be used to calculate the seismic moment, length of the slip vector and width and length of the finite fault, using equations derived by Okal (reported in Hesselink, 2008). The set of equations in QuakeGen follows straight forward the work of Okada (1985) and Okal and will therefore not be described in detail here. The method has been used first to calculate the displacements of the landslide module in MIKE 21 HD. Its application to a time varying bathymetry gives the opportunity to include earthquake time as an additional parameter for the earthquake description. 3. MODEL APPLICATION TO THE 2006 WEST JAVA EARTHQUAKE TSUNAMI Various test cases have been carried out in order to investigate the influences of parameters which can be manipulated within hydrodynamic simulations. The difference between the dislocations applied to the initial water surface and to the bathymetry over different time periods is shown. Then, the influence of horizontal displacements calculated with the equations given by Okada (1985) is investigated. Furthermore, the influence of different faults within the simulation period in the domain is shown on the example of the 2006 West Java Earthquake tsunami. Table 1 gives the applied parameters for the earthquakes considered here. Table 1. Parameters from 17 July 2006 West Java Earthquake (USGS). Earthquakes UTC Lat Long Depth [km] M W [-] Strike Dip Slip 1 08:19: :20: This is followed by a test, where the influence of uncertainties of earthquake parameters provided within minutes after an earthquake is investigated. For that earthquake parameters derived from tide gauges, given by Fujii and Satake (2006), have been applied. The results have been compared with data obtained on surveyed locations by Fritz et al. (2007) and Lavigne et al. (2007) after the tsunami, presented in figure 1.b). From the data, points have been selected which lie near the coastline in order to reduce the influences of energy losses due to buildings and vegetation. 3.1 Model setup Two independent simulations have been done for each test case. One on a rectangular grid using MIKE 21 HD, where the moving bottom generates the tsunami. The simulation period has been two hours. The surface elevation on a line between 108 and East at 8.5 South has been recorded which serves as boundary condition for the second simulation of the Cilacap area on the Southern coast of Java. For this simulation, MIKE 21 Flexible Mesh Module (MIKE 21 FM) has been used. It uses also the non-linear shallow water equations but the equations calculate on triangular and quadrangular finite volumes, which conserve mass and momentum for each element. Furthermore, the element size can be adjusted to bathymetry data density and water depth MIKE 21 HD Setup The bathymetry, made from GEBCO data, represents the Indian Ocean and parts of Java between 105 and East and and 12 South with a grid spacing of 1620 m (400x310 cells). The bathymetry and earthquake locations are shown in figure 1.a). 3

4 A constant roughness of the Manning value n = 32 m 1/3 /s has been applied in the whole domain, but at the open boundaries it is reduced to n = 0.01 m 1/3 /s in order to make shure, that reflections will not influence the model results in the area of interest. Furthermore, in all simulations a flux based eddy viscosity with a Smagorinsky constant of 0.5 has been used. The simulation period has been two hours with a step of two seconds leading to a Courant number of Figure 1. a) Bathymetry for moving bottom with earthquake locations, b) Nearshore bathymetry with post-tsunami field data points MIKE 21 FM Setup On land, the bathymetry consits of a digital terrain model provided by DLR. In the nearshore region in front of Cilacap multibeam echosounder data obtained during a survey of BPPT Jakarta with DHI- WASY for IFM-Geomar has been used. Offshore, the data is completed by navigation charts from C- Map. Outside of the areas of interest, the bathymetry is filled with GEBCO data. It is shown in figure 1.b). In order to account for the influence of the tide on the runup, the predicted tide gauge for Cilacap for the time of the arrival of the first wave has been used to adjust the bathymetry data. The nearshore bathymetry has been reduced with this value. For a comparison with surveyed runup heights this value has been added to the maximum water surface elevations in all test cases. This is in accordance to the measurement corrections done by the survey teams as reported in Fritz at al. (2007). The element lengths vary from 1500 m in the deep ocean to 20 m near the shoreline. The time steps have been automatically adjusted between 0.01 and 1 s not exceeding a CFL number of 0.8. Flooding, wetting and drying depths have been set to 0.05, 0.1 and m. The eddy viscosity has been 6 calculated with a Smagorinsky constant of 0.28, allowing eddy viscosities between and m 2 /s. The value has been selected to account for lateral stresses due to viscous friction, turbulent friction and differential advection. 3.2 Results The surface elevations have been recorded from each simulation at four lines perpendicular to the coast from the first dry point to the coordinates of surveyed locations by a) Fritz et al. (2007) and b) Lavigne et al. (2007). This has been done, because in some test cases the runup did not reach the surveyed point. The details are shown in table 2. 4

5 Location x Table 2. Positions of result comparisons (UTM 49S). y Source Runup Details on Max. distance between field survey and simualtion [m] [m] [m] [-] [m] a) 2.26 eyewitness, debris line a) 2.57 debris line b) 2.2 house 144 4a b) 1.9 riverbank 142 4b a) 3.26 mud in rise field Runup for the M W = 7.7 earthquake simulations varying earthquake period length 10 The Okada computations have been done using a Young s Modulus of E =1 10 N/m 2. The time in which the bottom is moved during the hydrodynamic calculation has been varied in order to see its influence on the runup. The underlying M W = 7. 7 earthquake parameters have been selected from table 1. As reference case, the displacement has been applied to the initial surface elevation. For the test cases, the full displacement has been represented by the bathymetry motion within one time step of the calculation (two seconds), linearly over 10 seconds and over 190 s, which is approximatelly the time for the whole earthquake. Figure 2.a) shows the maximum runups for these cases. In general, the calculated runups are half as big as reported from field surveyers. The difference between the cases where initial surface elevation, a bottom displacement within one calculation timestep of two secondes and over 10 seconds is less than 1 cm. Applying the bottom displacement over 190 seconds leads to a smaller runup at the locations 1 and 3. The differences to the initial surface elevation case are 16 and 17 cm, for location 2 only 2 cm. This indicates that the shorter the period is, in which the displacement is applied, the higher the runup. The larger differences between the runups at location 1 and 3 might be due to bathymetrical features near these locations, e.g. the representation of the nearshore area and distance of the shoreline and the highest runup. To clear that, the surface elevations for the four cases have been recorded at one position between the earthquake and the coast of Cilacap, where the water is still very deep ( , -8,5, m) (Leschka et al., 2007). The result is shown in figure 2.b). Figure 2. a) Maximum runups for displacement time variations, b) Sea surface elevations at East, 8.5 South on the 17 July 2006 between 15:27:00 and 15:41:00 (Local Time) 5

6 The water level in the case, where the displacement application has been applied within the first calculation timestep matches the initial surface elevation test case. Since the hydrodynamic module works with a depth-integrated equation, it does not play a role if the displacement is applied to the surface or to the bottom. For the wave generated by the earthquake covering 190 seconds, figure 3.b) shows that the wave is considerably slower and has a smaller amplitude also, causing a smaller runup. It can further be assumed, that time for a bottom motion within an initial application and a 10 second range does not influence the runup remarkably. Thats why for further test cases a 10 seconds time step has been chosen for the moving bathymetry. The difference in runup measurements between locations 4a and 4b give rise to the question of the importance of very good bathymetrical data and its representation in the bathymetry Runup and arrival times for horizontal variations The horizontal displacement of the M W = 7.7 has been included in a test case. Then, the M W = 7.2 earthquake has been applied (see table 1). Finally, the inverse solution derived from tide gauges by Fujii and Satake (2006) is tested. This method has been chosen because it prevents the hydrodynamic modeler from changing seismic parameters. The horizontal displacement has been applied also. Staying with the total duration of the earthquake of 185 seconds, a rupture velocity of 1 km/s has been chosen for the test case. The subfault configurations for this case are shown in figure 3.a). Figures 3.b) to e) present the result of QuakeGen at four different time steps during the earthquake. Following 10 Fujii and Satake (2006), a Young s modulus of E = N/m 2 has been chosen for the calculation of the subfaults. Figure 3. a) subfaults from inversion method (Fujii and Satake, 2006), b) QuakeGen result for the subfaults 1 to 4 at 08:20:06, c) for the subfaults 1 to 6 at 08:20:46, d) for the subfaults 1 to 8 at 08:21:16, e) for the subfaults 1 to 10 at 08:21:46 (UTC) These cases are compared with an initial surface elevation test case and the M W = 7.7 earthquake case, where only the vertical displacement is considered. In figure 4, these examples are set into relation with observations from Fritz et al. (2007) and Lavigne et al. (2007). 6

7 Figure 4. a) Runup heights for horizontal variations, b) tsunami arrival times at the shore near location 3 In general, at locations 1 and 2 the runups are smaller than reported by Fritz et al. (2007) and Lavigne et al. (2007). This accords to results of various researchers before which investigated the runups and adjusted earthquake parameters, e.g. Imamura and Shuto (1993). On the other hand, bathymetrical features may be responsible for that. Even if in the front multibeam measurement data is available in front of the city of Cilacap, the bathymetry near the island Nusa Kambangan in front of Cilacap is not available. Futhermore, it has to be considered, that locations 1 and 2 lie behind that island and that the non-linear shallow water equations do not account for frequency dispersion. In the cases where earthquake sources have not been modified, only at 4a the calculated values meet the observations reported by Lavigne et al. (2007) very good. With the inversive modifications from tide gauges done by Fujii and Satake (2006), the runups have been reproduced at the locations 3 and 4b. Figure 4.b) shows the arrival times, which is here defined as the time in which the water surface at the coastline exceeds the still water level for the first time. From Lavigne et al. (2007) the arrival time of the tsunami at the power plant has been reported to be 09:19:02. Location 3 lies within one kilometer distance. In all cases, the modelled wave has been arrived almost in time. 4. CONCLUSION A tool for modifying the bathymetry has been combined with the landslide module in MIKE 21 HD as a fast possibility use tsunami sources data for tsunami modelling by including it directly into a hydrodynamic simulation. First, the double-couple method of Okada (1985) has been implemented. It has been shown, that it can be used for vertical and horizontal displacements as well as for subfault approaches. On the example of the 2006 West Java Earthquake tsunami it could be resumed, that batymetry time steps of up to 10 seconds can reproduce runups as big as initial surface applications. Furthermore, the tsunami arrival time could be reproduced very well. Using the inverse solution of Fujii and Satake (2006) for this earthquake, the runup heights have been reproduced also in zones, where the coastline lies directly in front of the approaching tsunami. Further calculations with past tsunami events should be done. In order to avoid bathymetrical influences on the result, it should be tried to reproduce boi measurements. Further on, more advanced methods for the estimation of tsunami sources should be applied in the tool which make use of the advantage that temporal resolution of an earthquake can be adjusted and manipulated. 5. ACKNOWLEDGMENTS The authors wish to thank Andreas Höchner from the GeoForschungszentrum Potsdam for his very friendly and valuable help and recommendations during this work. 7

8 6. REFERENCES Fritz, H.M., Kongko, W., Moore, A., McAdoo, B., Goff, J., Harbitz, C., Uslu, B., Kalligeris, N., Suteja, D., Kalsum, K., Titov, V., Gusman, A., Latief, H., Santoso, E., Sujoko, S., Djulkarnaen, D., Sunendar, H. and Synolakis, C. (2007) Extreme runup from the 17 July 2006 Java tsunami Geophys. Res. Let., Vol. 34, L FujiiY. And Satake, K. (2006) Source of the July 2006 West Java tsunami estimated from tide gauge records Geophys. Res. Let., Vol. 33, L Hesselink, S. (2008) Applikationsgestützte Erstellung zeitabhängiger Bathymetrien für die Echtzeit- Simulation von Tsunamis aus Erdbeben MSc. Thesis, Fachbereich Bauwesen und Geoinformation, University of Applied Sciences Oldenburg, Germany. Imamura, F. and Shuto, N. (1993) Estimate of the tsunami source of the 1992 Nicaraguan earthquake from tsunami data Geophys. Res. Let., Vol. 20 (14), Kofoed-Hansen, H., Cifres Giménez, E. and Kronborg, P. (2001) Modelling of landslide-generated waves in MIKE 21, 4th DHI Software Conference, Elsinore, Denmark, 6-8 June Lavigne, F., Gomez, C., Giffo, M., Wassmer, P., Hoebreck, C., Mardiatno, D., Prioyono, J. and Paris, R. (2007) Field observations of the 17 July 2006 tsunami in Java Nat. Hazads Earth Syst. Sci., Vol. 7, Leschka, S., Gaslikova, L., Larsen, O., Gayer, G., Günther, H. (2007) German Indonesian Tsunami Early Warning System: küstennaher Bereich und Run-up Report No. WP Okada, Y. (1985). Surface deformation due to shear and tensile faults in a half-space Bull. Seis. Soc. Am., Vol. 75, No. 4, Slingerland, R.L. and Voight, B. (1979) Evaluating hazard of landslide-induced water waves In Developments in Geotechnical Engineering 2 nd edition, Ed. B. Voight, Elsevier. Smylie, D.E. and Mansinha, L. (1971) The elasticity theory of dislocation in real earth models and changes in the rotation of the earth Geophys. J. R. Astr. Soc., Vol. 23, Tsuji, Y. et al. (1995) Field survey of the east Java earthquake and tsunami of June 3, 1994, Pure Appl. Geophys., Vol. 144, Wang, R., Martin, F.L. and Roth, F. (2003) Computation of deformation induced earthquakes in a multi-layered elastic crust-fortran programs EDGRN/EDCMP, Comput. Geosci., Vol. 29, DHI Software (2008) MIKE 21 Flow Model Short Description, Download/DocumentsAndTools/ShortDescriptions/~/media/Publications/Software/Download/DocumentsA ndtools/marine/mike213_fm_short_description_hd.ashx, 10 October Kongko, W., Suranto, Chaeroni, Aprijanto, Zikra and Sujantoko (2006) Rapid survey on tsunami Java 17 July 2006 ( 10 October USGS (2008) October