Investigations of the acoustic-field autoproducts in three dimensions

Abstract

Acoustic remote sensing tasks, such as remote unknown source localization, are commonly completed via signal processing schemes that are implemented in the bandwidth of the acoustic recordings. Interestingly, many such schemes can also be implemented at frequencies outside of the bandwidth of the recorded field—despite their absence from the recordings—by using the frequency-difference and frequency-sum autoproducts [Worthmann and Dowling, J. Acoust. Soc. Am., 141 (2017) 4579–4590]. Recent acoustic-field autoproduct studies have involved beamforming and source localization in shallow- and deep-ocean environments, and have addressed the impacts of refraction, shadow zones, rough surface scattering, and noise. These previous efforts primarily explored the properties of the autoproducts when the sound field primarily varies in two spatial dimensions. This presentation provides the results of a study of the autoproducts formed from the simple but fully three-dimensional acoustic fields arising from an isolated source placed in a uniform-sound-speed environment bounded by reflecting surfaces that are not parallel. This study indicates the extent to which the autoproduct properties associated with two dimensional acoustic-field variations extend to three dimensional acoustic-field variations. The results from theory and simulations are presented, and from laboratory water-tank measurements if time allows.