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Tsunami Seismic Generation and Propagation: Validity of the Shallow Water Equations

Author(s): M. Le Gal; D. Violeau

Linked Author(s): Marine Le Gal, Damien Violeau

Keywords: No keywords

Abstract: Most of tsunamis are generated by earthquakes, i.e. kinematic seafloor deformations. Usually the kinematic aspect of the deformation is not taken into account supposed to be instantaneous. However, some events, called “Tsunami earthquakes” as proposed by Kanamori (1972), involve slow dynamics that can impact the form and properties of the generated wave. In this article, this impact is studied. Two temporal parameters are introduced: the rise time t r as define by Hammack (1973) that corresponds to the time for the vertical deformation, and the rupture propagation velocity v p, studied by Todorovska&Trifunac (2001). For a simplified deformation of the sea ground, including these two temporal parameters, a linear solution of the free surface is built. A potential energy ratio is defined, estimating the quantity of potential energy that is lost if the shallow water equations are used for modeling the tsunami propagation. For a large range of values for t r and v p, this ratio is figured out and it follows that a resonance appears when v p is close to the celerity of long waves and t r is null. For these particular values, the energy lost by the shallow water approximations is larger than half of the total potential energy generated.


Year: 2016

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