The group velocity of normal modes

A simple, general formula for normal mode group velocities provides an intuitive grasp of the factors influencing group velocity, especially for shallow water environments associated with strong seabed interaction. This is demonstrated using some hypothetical shallow water environments, and by comparing mode shapes at different frequencies. The formula is especially convenient to implement in normal mode computer codes which already perform similar calculations for mode normalization and attenuation coefficients. Using the WKB approximation to the normal mode functions, the formula is identified with the average horizontal speed of the ray equivalent to the mode. For a shallow water environment with bottom interaction, the group velocity formula is shown to include the beam and the time displacement effects of modified ray theory. This result strenghthens the ray/mode analogy which is used in analyzing ocean acoustics problems.