Theoretical study of the penetration of highly directional acoustic beams into sediments

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Abstract
Recently Muir et al. [J. Sound Vib. 64, 539–551 (1979)] presented results of an experimental study of the penetration of directional acoustic beams into bottom sediments. We consider here the linearized theory of the refracted sound field produced by a highly directional beam in a bottom sediment. Simplified equations, valid for ka large (k, k′, wavenumbers in sediment and water, respectively; a, width of the incident beam at the interface; qi, angle of the acoustic axis with the normal to the interface) are derived and solved analytically, subject to the nondissipative boundary condition at the interface. The radiation field is found to be similar to that of a phase shaded and infinitely compliant piston source. The solution is valid whenever the characteristic length of the diffraction effects is small compared to the attenuation length in the sediment; this is the case in the experiment referred to. Results are in good agreement with the Muir et al. experiment. The reflected sound field is also considered.

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