Time-frequency analysis of the bistatic acoustic scattering from a spherical elastic shell

The development of low-frequency sonar systems, using, for instance, a network of autonomous systems in unmanned vehicles, provides a practical means for bistatic measurements (i.e., when the source and receiver are widely separated) allowing for multiple viewpoints of the target of interest. Time-frequency analysis, in particular, Wigner-Ville analysis, takes advantage of the evolution time dependent aspect of the echo spectrum to differentiate a man-made target, such as an elastic spherical shell, from a natural object of the similar shape. A key energetic feature of fluid-loaded and thin spherical shell is the coincidence pattern, also referred to as the mid-frequency enhancement (MFE), that results from antisymmetric Lamb-waves propagating around the circumference of the shell. This article investigates numerically the bistatic variations of the MFE with respect to the monostatic configuration using the Wigner-Ville analysis. The observed time-frequency shifts of the MFE are modeled using a previously derived quantitative ray theory by Zhang et al. [J. Acoust. Soc. Am. 91, 1862-1874 (1993)] for spherical shell's scattering. Additionally, the advantage of an optimal array beamformer, based on joint time delays and frequency shifts is illustrated for enhancing the detection of the MFE recorded across a bistatic receiver array when compared to a conventional time-delay beamformer.