The Ray Paths of Trapped Waves Over The Submerged Ridge

Abstract

Due to refraction, the oceanic ridge acts as a waveguide forcing long-period waves to propagate along the topography. For the slowly varying depth and small amplitude compared to the water depth, the linear ray theory can be used to describe the refraction and its related phenomena in detail. The present study considers a special case of a symmetrical hyperbolic-cosine squared submerged ridge and derive analytical solutions for wave paths to reveal the ray path of wave propagation over the ridge. As all the contour of the ocean ridge are parallel to the ridge, the well-known Snell’s law can be used to describe the wave propagation angle and the wavenumber, which govern the wave path. Consider the seismic source located at the top of the ridge and tsunami waves radiate out uniformly in all directions. As all ocean ridges have finite width, whether the ray can be trapped is not only related to its propagation angle at the origination but also to the ridge width. The relationship of the caustic lines and wave frequency and wavenumber is obtained. This work is hoped to improve the understanding of the exciting mechanism.