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Revealing hidden information with quadratic products of acoustic field amplitudes
Phys. Rev. Fluids 3, 110506 – Published 21 November, 2018
DOI: https://doi.org/10.1103/PhysRevFluids.3.110506
Abstract
Acoustic waves are omnipresent in modern life and are well described by the linearized equations of fluid dynamics. Once generated, linear acoustic waves carry and collect information about their source and the environment through which they propagate, and this information may be retrieved by analyzing recordings of these waves. Because of this, acoustics is the primary means for imaging and remote sensing in otherwise opaque environments, such as the Earth's oceans and crust and the interior of the human body. For these information-retrieval tasks, acoustic fields are nearly always interrogated within their recorded frequency range or bandwidth. However, this frequency-range restriction is not general; acoustic fields may also carry hidden information at frequencies outside their bandwidth that can be revealed by analyzing the quadratic products of a pair of complex frequency-domain field amplitudes having different frequencies. The two unique quadratic field products, known as the frequency-difference and frequency-sum autoproducts, can be utilized for remote sensing at the difference and sum of the two constituent frequencies, respectively, even if these difference and sum frequencies lie outside the recorded field's bandwidth. Despite some fundamental limitations, forming and analyzing the autoproducts enables a variety of acoustic remote sensing applications that were long thought to be impossible. In particular, analysis of the frequency-difference autoproduct allows the detrimental effects of sparse-array recordings, random scattering, and other unknown source-to-receiver propagation effects to be suppressed when the recorded acoustic field has sufficient bandwidth. Examples and applications from laboratory and ocean propagation experiments are provided that involve frequencies from a few Hertz to more than 100 kHz and propagation distances from tens of centimeters to more than 100 km.
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2018 Invited Papers
Physical Review Fluids publishes a collection of papers associated with the invited talks presented at the 70th Annual Meeting of the APS Division of Fluid Dynamics.
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