Attenuation and group velocity of normal mode in shallow water

Proceedings from the eigenvalue equation of the normal modes in homogeneous shallow water, we derive several formulae for calculating the mode attenuation and group velocity, and compare their accuracy by means of numerical results. Especially discussed are the attenuation and group velocity of the critical mode in a Perkeris channel and it is shown that, in general, the attenuation and the group velocity of the critical mode, respectively, are less than the absorption and the sound speed in the bottom. Therefore, the Kornhauser, Raney, Weston and Tindle conclusions that the attenuation and the group velocity of the critical mode are exactly equal to the absorption and the sound speed in the bottom, respectively, are modified.