Double beamforming with a vertical receiver array and a ship of opportunity

Double beamforming leverages two vertical arrays (at the source and receiver) and a matrix of Green's functions to estimate acoustic launch and reception angles of eigenrays in the ocean. This study extends the technique to a more practical configuration involving a vertical receiver array and an unknown broadband source, such as a passing ship. The proposed method consists of two main steps: (1) blind deconvolution to estimate the Green's function between the vertical receiver array and the source, and (2) extrapolation of this function to neighboring ranges using waveguide invariant theory to synthesize a horizontal array centered on the source. Experimental results using broadband noise (200-900 Hz) from a ship of opportunity in shallow water demonstrate the viability of this approach. The estimated launch and reception angles closely match model-based eigenray predictions, with errors under 1°.