A fast preliminary estimation model for transoceanic tsunami propagation

Abstract

A simplified one-dimensional method is proposed to estimate the height of the leading wave of transoceanic tsunamis by means of a directivity function applied to the one-dimensional finite difference model based on the shallow water equations. The numerical modeling of the October 4, 1994 Shikotan tsunami, and the analysis of its deep-ocean signature observed at a distance of ~6300 km from the source, as well as the analysis of the linear shallow water equations (non-dispersive theory) and of the Boussinesq equations (dispersive theory), shows that the frequency dispersion mechanism, as prescribed by Boussinesq equations, is a necessary and sufficient condition to simulate the transoceanic propagation of tsunamis. The analytical results from non- dispersive equations, as compared with those obtained using dispersive theory, overestimate significantly the height of the leading wave of large and medium size tsunamis. The results confirm that the linear shallow water equations solved by an explicit central finite difference method are appropriate to simulate the tsunami propagation from the source area to the far field. This is due to the fact that the inherent frequency dispersion in the numerical method mimics the frequency dispersion prescribed by Boussinesq equations (Imamura et al., 1990; Liu et al., (1995).