Measurements of the ambient sound generated by breaking waves over the range 40–20 000 Hz reveal well-defined spectral peaks [D. M. Farmer and S. Vagle, J. Acoust. Soc. Am. 86, 1897–1908 (1989)], suggesting the modulation of the ambient sound by the waveguide formed by the ocean-surface bubbles. The measurements show that the sound-speed profile in such a waveguide may be modeled by an exponential form. The theory of the waveguide propagation of the ambient sound is considered. It is shown that the sound propagation in the ocean-surface waveguides bears analogy with that in the optical waveguides formed by diffusion and can be solved analytically in a simple form. The cutoff frequencies of such waveguides are determined by a simple equation that incorporates only the waveguide parameters. Theoretical predictions of the spectral peaks, which seem to be associated with the modal cutoff frequencies, are compared favorably to the observations. Moreover, the present results are compared to the previous theory base on the model of inverse square sound-speed profiles in great details. It is shown that, although the two profiles are almost the same shape in the cases considered here, the sound propagation in the two waveguides is rather different. It is shown that the normal-mode propagation in the inverse square model is very sensitive to both source and receiver positions in addition to the waveguide parameters, and different modes can overlap, thereby making data fitting difficult. On the other hand, in the exponential model, the sound spectral function depends mainly on the waveguide parameters, e.g., sound-speed anomaly at the surface and the e-folding depth. Therefore the distinct spectral peaks observed are a stable prediction from the exponential waveguide model. The simplicity and the stability of the results can help solve the inverse problem, that is, "given an observed distribution of spectral peaks, can the bubble distribution be inferred?"
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机译：对由40–20 000 Hz范围内的碎波产生的环境声音进行的测量显示出明确定义的频谱峰值[D。 M. Farmer和S. Vagle，J。Acoust。 Soc。上午。 86，1897–1908（1989）]，提出了由海面气泡形成的波导对环境声音的调制。测量表明，这种波导中的声速分布可以通过指数形式建模。考虑了环境声的波导传播理论。结果表明，海面波导中的声音传播与通过扩散形成的光波导中的声音传播类似，并且可以以简单的形式通过解析来解决。这种波导的截止频率由一个仅包含波导参数的简单方程式确定。频谱峰值的理论预测似乎与模态截止频率相关，因此可以很好地与观测值进行比较。此外，将当前结果与基于逆平方声速剖面模型的先前理论进行了比较详细的比较。结果表明，尽管在这里考虑的情况下，两个轮廓几乎是相同的形状，但是在两个波导中的声音传播却大不相同。结果表明，除了波导参数之外，逆平方模型中的正常模式传播对源和接收器位置都非常敏感，并且不同的模式可能会重叠，从而使数据拟合变得困难。另一方面，在指数模型中，声谱函数主要取决于波导参数，例如表面的声速异常和电子折叠深度。因此，根据指数波导模型，观察到的独特光谱峰是稳定的预测。结果的简单性和稳定性可以帮助解决反问题，即“给定观察到的光谱峰分布，可以推断出气泡分布吗？”
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