Estimating the height of a tsunami wave propagating over a parabolic bottom in the ray approximation

In this paper, the kinematics of tsunami wave rays and wavefronts propagating over an uneven bottom is considered. Formulas to determine the wave height along a ray tube are obtained. An exact analytical solution for the trajectory of a wave ray over a parabolic bottom is derived. In the wave-ray approximation, this solution makes it possible to analytically determine the heights of tsunami waves over an area with a sloping bottom. The distribution of wave-height maxima over an area with a parabolic bottom is compared with that obtained by numerical computation with a shallow-water model.