Abstract

The trapping effect of oceanic ridge plays an important role on the far-field tsunami propagation pattern though the trapping mechanism is still unknown. Based on the linear shallow water equations, the trapped modes over a symmetric parabolic-profile submerged ridge are obtained analytically. The spatial energy distribution pattern for each mode is discussed. The wave amplitude gets the maximum at the top of ridge and decays gradually towards both sides, and the decaying rate is gentler with higher modes. A first-order approximation is derived to simplify the transcendental equation of dispersion relationship, which is useful to describe tsunami waves trapped over some shallowly submerged oceanic ridges in reality. The trapped wave length with the same period over the steep-profile and deep-submerged ridges is longer than that over the gentle and shallow ridges.

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