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IUGG XXIV General Assembly July 2-13, 2007 Perugia, Italy
(S) - IASPEI - International Association of Seismology and Physics of the Earth's
Interior
JSS002 Poster presentation 1792
New theoryfor tsunami propagation and estimation of tsunami parameters
Dr. Ilia Mindlin
Applied Mathematics State Technical University of Nizhny Novgorod, Rus IAPSO
A numerable set of specific basic waves on the sea surface are found analytically. It is shown that any
tsunami is a combination (not superposition: the waves are nonlinear) of the basic waves, 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. In this way, 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. Twoparametric
model is discussed thorouhly. 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
occurred in Japan are considered. For each of the tsunamis, the tsunami energy, the duration of the
tsunami source formation, the maximum water elevation in the wave originating area, dimensions of the
area, and the average magnitude of the sea surface displacement at the margin of the wave originating
area are estimated on the basis of data recorded by tide gauges. The results are compared (and, in the
author's opinion, are in line) with the data known from the literature. It should be mentioned that,
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 earlier works [1, 2]
very closely and extends their theoretical results. Example. The following notations are used below: E
for tsunami energy (in Joules), H for the maximum water elevation in the wave originating area (in
metres), R for the mean radius of the wave origin, h for the averaged magnitude of the sea surface
displacement at the margin of the wave origin (in centimetres), T for the duration of the tsunami source
formation (in seconds). Variant a): estimates obtained using a model of tsunami generated by initial
free surface displacement; variant b): estimates obtained using a model of tsunami triggered by a
sudden change in the velocity field of initially still water. The asterisk shows that the value of the
parameter is known in the available literature. The Hiuganada earthquake of 1968, April, 1, 9h 42m (J.
S. T.) A tsunami of moderate size arrived at the coast of the south-western part of Shikoku and the
eastern part of Kyushu. a) E=1.91·1012, H=3.43, R=22, h=17.2; b) E=8.78·1012, H=1.38, R=20.4,
h=9.2, T=16.4; E*=1.3·1013 ([3], attributed to Hatori), E*=(1.4 2.2)·1012 ([3], attributed to Aida),
R*=21.2, h*=20 [4] (variant a) since was obtained by means of inverse refraction diagram.) 1. Mindlin
I.M. Integrodifferential equations in dynamics of a heavy layered liquid. Moscow: Nauka*Fizmatlit, 1996
(Russian). 2. Mindlin I.M. Nonlinear waves in two-dimensions generated by variable pressure acting on
the free surface of a heavy liquid. J. Appl. Math. Phys. (ZAMP), 2004, vol.55, pp. 781 - 799. 3. Soloviev
S.L., Go Ch.N. Catalogue of tsunami in the West of Pacific Ocean. Moscow, 1974 (Russian). 4. Hatory
T., A study of the wave sources of the Hiuganada tsunamis. - Bull. Earthq. Res. Inst., Tokyo Univ.,
1969, vol. 47, pp. 55-63.