HR: 1340h
AN: S53A-1036    [Abstracts]
TI: New Theory for Tsunami Propagation and Estimation of Tsunami Source Parameters
AU: * Mindlin, I M
EM: ilia.mindlin@gmail.com
AF: Nizhny Novgorod State Technical University, Minina St., 24, Nizhny Novgorod, 603155, Russian Federation
AB: In numerical studies based on the shallow water equations for tsunami propagation, vertical accelerations and velocities within the sea water are neglected, so a tsunami is usually supposed to be produced by an initial free surface displacement in the initially still sea. In the present work, new theory for tsunami propagation across the deep sea is discussed, that accounts for the vertical accelerations and velocities. The theory is based on the solutions for the water surface displacement obtained in [Mindlin I.M. Integrodifferential equations in dynamics of a heavy layered liquid. Moscow: Nauka*Fizmatlit, 1996 (Russian)]. The solutions are valid when horizontal dimensions of the initially disturbed area in the sea surface are much larger than the vertical displacement of the surface, which applies to the earthquake tsunamis. It is shown that any tsunami is a combination of specific basic waves found analytically (not superposition: the waves are nonlinear), and consequently, the tsunami source (i.e., the initially disturbed body of water) can be described by the numerable set of the parameters involved in the combination. Thus the problem of theoretical reconstruction of a tsunami source is reduced to the problem of estimation of the parameters. The tsunami source can be modelled approximately with the use of a finite number of the parameters. Two-parametric model is discussed thoroughly. A method is developed for estimation of the model's parameters using the arrival times of the tsunami at certain locations, the maximum wave-heights obtained from tide gauge records at the locations, and the distances between the earthquake's epicentre and each of the locations. In order to evaluate the practical use of the theory, four tsunamis of different magnitude occurred in Japan are considered. For each of the tsunamis, the tsunami energy (E below), the duration of the tsunami source formation T, the maximum water elevation in the wave originating area H, mean radius of the area R, and the average magnitude of the sea surface displacement at the margin of the wave originating area h are estimated using tide gauges records. The results are compared (and, in the author's opinion, are in line) with the estimates known in the literature. Compared to the methods employed in the literature, there is no need to use bathymetry (and, consequently, refraction diagrams) for the estimations. The present paper follows closely earlier works [Mindlin I.M., 1996; Mindlin I.M. J. Appl. Math. Phys. (ZAMP), 2004, vol.55, pp. 781-799] and adds to their theoretical results. Example. The Hiuganada earthquake of 1968, April, 1, 9h 42m JST. A tsunami of moderate size arrived at the coast of the south-western part of Shikoku and the eastern part of Kyushu, Japan. Tsunami parameters listed above are estimated with the theory being discussed for two models of tsunami generation: (a) by initial free surface displacement (the case for numerical studies): E=1.91· 10¹²J, R=22km, h=17.2cm; and (b) by a sudden change in the velocity field of initially still water: E=8.78· 10¹²J, R=20.4km, h=9.2cm. These values are in line with known estimates [Soloviev S.L., Go Ch.N. Catalogue of tsunami in the West of Pacific Ocean. Moscow, 1974]: E=1.3· 10¹³J (attributed to Hatori), E=(1.4 - 2.2)· 10¹²J (attributed to Aida), R=21.2km, h=20cm [Hatory T., Bull. Earthq. Res. Inst., Tokyo Univ., 1969, vol. 47, pp. 55-63]. Also, estimates are obtained for the values that could not be found based on shallow water wave theory: (a) H=3.43m and (b) H=1.38m, T=16.4sec.
DE: 3285 Wave propagation (0689, 2487, 4275, 4455, 6934)
DE: 4564 Tsunamis and storm surges
SC: Seismology [S]
MN: 2007 Fall Meeting