Modeling air-to-water sound transmission using standard numerical codes of underwater acoustics

Recently, it was shown that a normal mode underwater acoustic propagation code can be modified to model air-to-water sound transmission simply by altering the mode excitation coefficients [D. M. F. Chapman and P. D. Ward, J. Acoust. Soc. Am. 87, 601–618 (1990)]. Herein, it is shown that if the height of the source above the surface is sufficiently small, then the air-to-water transmission problem can be modeled by replacing the source in air with a source in water at a depth d≪λ below the surface, where λ is the acoustic wavelength in water. For a distant receiver in water, both the true source in air and the effective source in water exhibit nearly identical dipole radiation patterns, although the source strengths are different. The correct transmission loss from the source in air can be recovered by adding the quantity 20 log10(kad), where ka is the wave number in air. Using this approach, numerical results for three standard underwater acoustic models (normal mode, multipath expansion, parabolic equation) are compared to benchmark results provided by the SAFARI model for a generic air-to-water transmission example.