Estimation of Tsunami Initial Displacement of Water Surface Using Inversion Method with a Priori Information

Abstract

Up to now, because the tsunami initial displacement of water surface cannot be observed directly, the approach of presuming it from the fault model of the earthquake has been taken. Thanks to Yamashita and Sato (1974), it is established that an amount of the water level change in the surface of the sea is equal to the amount of the perpendicular ground change in the bottom of the sea caused by the earthquake. And, thanks to Aida (1969), the style of a present tsunami numerical calculation is established. The analytical solution proposed by Mansinha and Smylie (1971) is widely used, in order to presume the amount of the perpendicular ground change in bottom of the sea from the fault model. Still, for the risk evaluation of the tsunami, magnitude scales of earthquakes and those locations are assumed, the earthquake fault model is presumed, and a tsunami numerical calculation is done by the method as the above-mentioned. On the other hand, the research on the estimation process of the tsunami initial displacement of water surface, that is the initial-value problem of the tsunami, includes pioneering research of Aida (1969). Here, the coefficient that becomes each amount of the change is requested by the least squares method, when setting up the unit source of wave in the sea area where the initial water level distribution is expected. However, it is necessary to note that the location of the unit source of wave is assumed from earthquake information beforehand. In the research on the tsunami inversion, the research of Satake (1986) is typical. Here the tsunami record of the tidal station is used by the research. However, Satake only used the tsunami record of the tidal station, not to have done the tsunami inversion in order to presume the tsunami initial displacement of water surface, but in order to examine no homogeneity of the fault movement. Actually, the amount of slip of each small fault that divides the fault model into some models is chosen as an unknown parameter of the inverse problem. Therefore, it can be said that the style that essentially assumes the fault model and calculates the numerical value of the tsunami will not have changed. However, Koike et al. (2003) proposed a new method. Here, the tsunami initial displacement of water surface is presumed directly by the tsunami inversion. It is devised to reduce the number of the unknown parameters by using the base of wavelet in order to evade nonappropriateness of the inverse problem, and to solve the inverse problem by the least squares method uniquely. But, at the present stage theoretically setting the standard of the