Directional response of the short vertical line array for the distance source in deep ocean

The arrival signals of the vertical line array (VLA) in the waveguide are not plane waves. The direction of maximum array output will not be the exact direction of the source. The acoustic pressure field can be expressed in terms of a normal mode expansion. The output of the VLA for a distance source in the waveguide is then constructed by summing up contributions of array response to each of the modes weighted in accordance to the normal mode amplitude. The low and high order modes arrive at shallow and steep grazing angles, respectively. In deep ocean, a source away from the sound channel axis couples strongly with high order modes while weakly with low order modes. The direction of maximum output of a short VLA deviates significantly from the horizontal direction.