Proceedings of OMAE 2009 28th International Conference on Ocean, Offshore and Arctic Engineering May 31-June 5, 2009, Honolulu, USA OMAE2009-79767 DRAFT: HOW DOES SEDIMENTARY LAYERING AFFECT THE GENERATION OF TSUNAMIS? Denys Dutykh Universit ´ e de Savoie, CNRS Laboratoire de Math´ ematiques LAMA - UMR 5127 Campus Scientifique 73376 Le Bourget-du-Lac Cedex Email: Denys.Dutykh@univ-savoie.fr Fr´ ed´ eric Dias ∗ ENS Cachan, CNRS CMLA PRES UniverSud 61 Av. President Wilson 94230 Cachan Frederic.Dias@cmla.ens-cachan.fr ABSTRACT This article presents preliminary results on the influence of sediment layers on the process of tsunami generation. The main scope here is to demonstrate and especially quantify the effect of sedimentation on vertical displacements of the seabed due to an underwater earthquake. The effects in the far field are left for future work. The elastodynamics equations are integrated with a finite element method and the fault is modelled as a disloca- tion in a half-space. A comparison between two cases is per- formed. The first one corresponds to the classical situation of an elastic homogeneous and isotropic half-space, which is tra- ditionally used for the generation of tsunamis. The second test case takes into account the presence of a sediment layer sepa- rating the oceanic column from the hard rock. Some important differences are revealed. We conjecture that deformations in the generation region may be amplified by sedimentary deposits, at least for some parameter values. The mechanism of amplifica- tion is studied through careful numerical simulations. INTRODUCTION The primary application of this study is that of tsunami gen- eration by the deformation of the sea bottom following an under- water earthquake [1]. We do not explicitly compute the tsunami waves. The coupling between solid and water motions was al- ready performed in our previous work [2] and can be done again ∗ Address all correspondence to this author. if necessary. Here we are mainly interested in the extreme am- plitudes of the seabed displacements during the first minutes of a tsunamigenic earthquake. Recall that the free surface motion roughly follows these displacements. There are two fundamental reasons for this. The first one is that the rupture velocity of the seismic source, V , is much larger than the phase velocity of the tsunami, c. In practice, for seismic sources, V is on the order of 3 km/s, whereas c is typically less than 250 m/s, even for the deep- est ocean basins [3]. It means that the gravitational forces do not have enough time to change the shape of the free surface during the characteristic time of the seabed motion [4]. If the rupture velocity is smaller (for example V = 900 m/s), the free surface motion can be slightly different from the bottom displacement. The second reason is that water is assumed to be incompressible and shallow. Altogether it means that for our purpose we can re- strict our attention to the motion of the ocean bottom. Profiles of the ocean free surface are not computed in this paper. The two fundamental reasons mentioned above are often used to justify the passive approach for tsunami generation where the static sea-bed displacement is simply translated to the free surface to generate the initial condition. Our previous investi- gations [2, 5, 6] showed important differences between passive and active generations when the resulting wave is generated by a moving bottom. The present study is rather theoretical at this stage and must be followed by a thorough study of the influence of the various parameters such as rupture velocity, focal depth, dip angle, slip 1 Copyright c  2009 by ASME