Nonlinear optimization for beamforming a geometrically deficient vertical line array: Application to sediment tomography

Abstract

The 1996 Shelfbreak PRIMER experiment included broadband acoustic transmissions in the vicinity of a shelfbreak front collected using a geometrically deficient vertical line array (VLA). The broadband signals were used to tomographically image sediment sound speed and attenuation. The VLA spanned the lower half of the water column. Hence, the orthonormal properties of the underlying normal modes cannot be guaranteed for any replica vector based on the local modal structure. This produces modal sidelobes in the output of the geometrically deficient VLA. Various methods of extracting the normal modes from VLA data have been developed including a generalized least squares method shown to improve the performance of a geometrically deficient VLA processing phase encoded tomography signals [Chiu et al., IEEE J. Ocean. Eng. 22, 522–533 (2005)]. The present study seeks to enhance the modal resolution for the reception of high-amplitude, impulsive signals transmitted over a wide variety of source receiver paths in shallow water where ensemble averaging is not an option. The method uses nonlinear optimization techniques to compute a set of array element coefficients that enhance suppression of modal sidelobes, while maintaining adequate spatial matching with the desired mode. [Work supported by Office of Naval Research.]