Linear array beamforming in harbor environments.

The use of linear arrays of sources to focus low‐frequency sound on a target zone of limited spatial extent in a very shallow water environment is a topic of current interest for applications such as harbor defense. While linear array beamforming provides a starting point, the analytical expressions for beam response of a line array found in standard acoustics texts are developed for arrays of compact simple sources in a free‐fieldenvironment. In contrast, the typical harbor environment is characterized by very shallow water depths, varying bottom conditions, irregular vertical boundaries, and the presence of multiple scattering bodies. In addition to environmental conditions, the size and cost of low‐ frequency sources limit the validity of the simple source assumption and impose practical limits on the number of sources and maximum aperture length. Standard beamforming calculations are compared to measured data from a June 2008 harbor acoustic propagation experiment to quantify limitations of the linea...