Effective vertical beam patterns for ocean acoustic reverberation calculations

A description is given of a concept for using effective vertical beam patterns to perform reverberation calculations in underwater acoustics when the source or receiver has both horizontal and vertical directivity. The concept involves integrating the 3-D beam pattern B (θ, φ) over azimuthal angles φ to obtain an effective vertical beam pattern that depends only on the vertical angle θ and gives the same reverberation response as the 3-D beam pattern. These effective vertical beam patterns have both computational and conceptual advantages. By precomputing the effective beam patterns, sonar models that normally handle only vertical directivity can be readily extended to handle general beam patterns. The concept is also very useful to the sonar engineer. The effective beam patterns are essentially equivalent to the gain against reverberation as a function of vertical angle; alternatively, they are a measure of the horizontal beamwidth of the array, as a function of vertical angle. To illustrate the concept, effective vertical beam patterns are calculated for several steering directions of a horizontal line array receiver, and bottom reverberation calculations are interpreted using these effective beam patterns