Dynamic acoustic imaging of a surface wave propagating at an air-water interface is a complex task that is investigated here at the laboratory scale through an ultrasonic experiment in a shallow water waveguide. Using a double beamforming algorithm between two source-receiver arrays, the authors isolate and identify each multi-reverberated eigenbeam that interacts with the air-water and bottom interfaces. The waveguide transfer matrix is recorded 100 times per second while a low-amplitude gravity wave is generated by laser-induced breakdown at the middle of the waveguide, just above the water surface. The controlled, and therefore repeatable, breakdown results in a blast wave that interacts with the air-water interface, which creates ripples at the surface that propagate in both directions. The amplitude perturbations of each ultrasonic eigenbeam are measured during the propagation of the gravity-capillary wave. Inversion of the surface deformation is performed from the amplitude variations of the eigenbeams using a diffraction-based sensitivity kernel approach. The accurate ultrasonic imaging of the displacement of the air-water interface is compared to simultaneous measurements with an optical camera, which provides independent validation.
Ocean acoustic tomography is traditionally performed using the travel-time variations of an acoustic path between a source and a receiver. In the context of shallow-water tomography and multipath propagation, the different acoustic paths can be correctly identified if the source and the receiver are arrays of transducers. Here, a double-beamforming algorithm can be applied to extract a collection of eigenbeams from the raw acoustic dataset. In this study, four observables can be measured for each eigenbeam: the travel-time, the amplitude, and the emitting and receiving angles. In this study, the sensitivity kernel (SK) formulation is used to establish a quantitative relation between a perturbation of the surface of an ultrasonic waveguide and the emitting and receiving angles of each eigenbeam. This theoretical relation is experimentally demonstrated using a forward model experiment designed to measure the SK. The SK formulation is then used in a second experiment to quantitatively and dynamically image the propagation of a surface wave traveling across the surface of the waveguide. The inversion results show that the quality of the joint inversion of the emitting and receiving angles is higher than previous results based on amplitude or travel-time observables. V
The dynamic imaging of a gravity wave propagating at the air-water interface is a complex task that requires the sampling of every point at this interface during the gravity wave propagation. Using two source-receiver vertical arrays facing each other in a shallow water environment, we manage to isolate and identify each multi-reverberated eigenbeam that interacts with the air-water interface. The travel-time and amplitude variations of each eigenbeam are then measured during the crossing of the gravity wave. In this work, we present an ultrasonic experiment in a 1 m-long, 5 cm-deep waveguide at the laboratory scale. The waveguide transfer matrix is recorded 100 times per second at a sample rate of 1.1 MHz between two source-receiver arrays while a low-amplitude gravity wave is generated by a laser-induced breakdown at the middle of the waveguide above the water surface. The controlled and therefore repeatable breakdown causes a blast wave that interacts with the air-water interface and penetrates into the water, creating ripples at the surface that propagate in both directions. The surface deformation induced by these two wave packets is also measured by two cameras which allows for independent validation of the ultrasonic inversion. The ultrasonic inversion performed from a few thousand eigenbeams lead to accurate quantitative imaging of the dynamic of the air-water interface, using either the travel-time or the amplitude variation of the ultrasonic arrivals.
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