PIERCE A D . Acoustics: an introduction to its physical principles and applications [M ] . New York, NY, US : AIP , 1981 : 134 - 135 .

BREKHOVSKIKH L M , GODIN O A . Acoustics of layered media I: plane and quasi-plane waves [M ] . Berlin : Springer , 1992 : 19 - 24 .

YOUNG R W . Sound pressure in water from a source in air and vice versa [J ] . Journal of the Acoustical Society of America , 1973 , 53 ( 6 ): 1708 - 1716 . DOI: 10.1121/1.1913524 http://doi.org/10.1121/1.1913524 https://pubs.aip.org/jasa/article/53/6/1708/661717/Sound-pressure-in-water-from-a-source-in-air-and https://pubs.aip.org/jasa/article/53/6/1708/661717/Sound-pressure-in-water-from-a-source-in-air-and Sound-pressure level Lp at a depth d, in water, due to a point source in air at a distance h above the water surface, may be calculated from Lp = [Ls −7 +20 log(cosθ)]−20 log(r/rs), where Ls the source level is the sound-pressure level in air at distance rs from the source, r is the straight-line distance to the receiving hydrophone from a virtual sound source situated under the actual source at height h′ = (c1/c2) h above the surface; c1 and c2 are the respective speeds of sound in air and water; θ is the angle between the vertical and the line of length r. Comparisons with various published results obtained by more sophisticated ray-theory show agreement within 1 dB, except at shallow depths and far sidewise from the sound source; agreement within 2 dB is found for new experimental data here presented for sound bursts of frequency 500, 1000, and 2000 Hz, and h = 3.5 m. For sound originating in water at depth d below the surface, the sound-pressure level received in air is to be calculated from Lp = Ls − 52 + 40 log(cosθ) − 20 log(r/rs), where Ls is the source level, at rs, in the water. Experimental data obtained with a sound source in the water at depth d = 5.6 m, and frequencies of 500, 1000, or 2000 Hz, are in agreement with this equation, mostly within 2 dB, for receiving positions in air 1 or 2 m above the water and offsets as great as 3 m.

GODIN O A . Anomalous transparency of water-air interface for low-frequency sound [J ] . Physical Review Letters , 2006 , 97 ( 16 ): 164301 . DOI: 10.1103/PhysRevLett.97.164301 http://doi.org/10.1103/PhysRevLett.97.164301 https://link.aps.org/doi/10.1103/PhysRevLett.97.164301 https://link.aps.org/doi/10.1103/PhysRevLett.97.164301

GODIN O A . Transmission of low-frequency sound through the water-to-air interface [J ] . Acoustical Physics , 2007 , 53 ( 3 ): 305 - 312 . DOI: 10.1134/S1063771007030074 http://doi.org/10.1134/S1063771007030074 http://link.springer.com/10.1134/S1063771007030074 http://link.springer.com/10.1134/S1063771007030074

GODIN O A . Low-frequency sound transmission through a gas-liquid interface [J ] . Journal of the Acoustical Society of America , 2008 , 123 ( 4 ): 1866 - 1879 . DOI: 10.1121/1.2874631 http://doi.org/10.1121/1.2874631 Typically, sound speed in gases is smaller and mass density is much smaller than in liquids, resulting in a very strong acoustic impedance contrast at a gas-liquid interface. Sound transmission through a boundary with a strong impedance contrast is normally very weak. This paper studies the power output of localized sound sources and acoustic power fluxes through a plane gas-liquid interface in a layered medium. It is shown that, for low-frequency sound, a phenomenon of anomalous transparency can occur where most of the acoustic power generated by a source in a liquid half-space can be radiated into a gas half-space. The main physical mechanism responsible for anomalous transparency is found to be an acoustic power transfer by inhomogeneous (evanescent) waves in the plane-wave decomposition of the acoustic field in the liquid. The effects of a liquid's stratification and of guided sound propagation in the liquid on the anomalous transparency of the gas-liquid interface are considered. Geophysical and biological implications of anomalous transparency of water-air interface to infrasound are indicated.

GODIN O A . Wave refraction at an interface: snell’s law versus Chapman’s law [J ] . Journal of the Acoustical Society of America , 2009 , 125 ( 4 ): EL117 . DOI: 10.1121/1.3082003 http://doi.org/10.1121/1.3082003 https://pubs.aip.org/asa/jasa/article/125/4/EL117-EL122/925636 https://pubs.aip.org/asa/jasa/article/125/4/EL117-EL122/925636

LIU Y K , WANG Y . Low-frequency sound transmission through water-air interface: a comparison between ray and wave theory[C]//Proceedings of OCEANS 2014-TAIPEI . Taipei, China : IEEE , 2014 .

PARVIZ G , ALIREZA B , MOHAMMAD A F C , et al. Numerical investigation of transmission of low frequency sound through a smooth air-water interface [J ] . Journal of Marine Science and Application , 2015 , 14 ( 3 ): 334 - 342 . DOI: 10.1007/s11804-015-1315-9 http://doi.org/10.1007/s11804-015-1315-9 http://link.springer.com/10.1007/s11804-015-1315-9 http://link.springer.com/10.1007/s11804-015-1315-9

MCDONALD B E , CALVO D C . Enhanced sound transmission from water to air at low frequencies [J ] . Journal of the Acoustical Society of America , 2007 , 122 ( 6 ): 3159 - 3161 . DOI: 10.1121/1.2793709 http://doi.org/10.1121/1.2793709 Excitation of acoustic radiation into the air from a low-frequency point source under water is investigated using plane wave expansion of the source spectrum and Rayleigh reflection/transmission coefficients. Expressions are derived for the acoustic power radiated into air and water as a function of source depth and given to lowest order in the air/water density ratio. Near zero source depth, the radiation into the water is quenched by the source's acoustic image, while the power radiated into air reaches about 1% of the power that would be radiated into unbounded water.

陶智 , 冯博 . 低频球面声波在水-空界面传播特性的研究 [J ] . 舰船电子工程 , 2015 , 35 ( 5 ): 133 - 137 .

TAO Z , FENG B . Spherical sound transmission through water-air surfaceat lowfrequency [J ] . ShipElectronic Engineering , 2015 , 35 ( 5 ): 133 - 137 . (in Chinese)

GLUSHKOV E V , GLUSHKOVA N V , GODIN O A . The effect of anomalous transparency of the water-air interface for a volumetric sound source [J ] . AcousticalPhysics , 2013 , 59 ( 1 ): 6 - 15 .

WOODS D C , STUART BOLTON J , RHOADS J F . On the use of evanescent plane waves for low-frequency energy transmission across material interfaces [J ] . Journal of the Acoustical Society of America , 2015 , 138 : 2062 - 2078 . DOI: 10.1121/1.4929692 http://doi.org/10.1121/1.4929692 The transmission of airborne sound into high-impedance media is of interest in several applications. For example, sonic booms in the atmosphere may impact marine life when incident on the ocean surface, or affect the integrity of existing structures when incident on the ground. Transmission across high impedance-difference interfaces is generally limited by reflection and refraction at the surface, and by the critical angle criterion. However, spatially decaying incident waves, i.e., inhomogeneous or evanescent plane waves, may transmit energy above the critical angle, unlike homogeneous plane waves. The introduction of a decaying component to the incident trace wavenumber creates a nonzero propagating component of the transmitted normal wavenumber, so energy can be transmitted across the interface. A model of evanescent plane waves and their transmission across fluid-fluid and fluid-solid interfaces is developed here. Results are presented for both air-water and air-solid interfaces. The effects of the incident wave parameters (including the frequency, decay rate, and incidence angle) and the interfacial properties are investigated. Conditions for which there is no reflection at the air-solid interface, due to impedance matching between the incident and transmitted waves, are also considered and are found to yield substantial transmission increases over homogeneous incident waves.

VOLOSHCHENKO A P , TARASOV S P . Effect of anomalous transparency of a liquid-gas interface for sound waves [J ] . Acoustical Physics , 2013 , 59 ( 2 ): 163 - 169 . DOI: 10.1134/S1063771013020127 http://doi.org/10.1134/S1063771013020127 http://link.springer.com/10.1134/S1063771013020127 http://link.springer.com/10.1134/S1063771013020127

VOLOSHCHENKO A P , TARASOV S P . Experimental study of the transmission of low-frequency acoustic waves through a water-air interface [J ] . Journal of the Acoustical Society of America , 2019 , 145 ( 6 ): 143 - 148 . DOI: 10.1121/1.5085774 http://doi.org/10.1121/1.5085774 https://pubs.aip.org/jasa/article/145/1/143/638644/Experimental-study-of-the-transmission-of-low https://pubs.aip.org/jasa/article/145/1/143/638644/Experimental-study-of-the-transmission-of-low The effect of the anomalous transparency of the water–air interface on low-frequency acoustic waves is investigated. The effect is an abnormal increase in the amount of energy that passes from water to air. This effect is manifested if the source of the acoustic waves is located at a distance less than the wavelength from the water–air interface. According to the mathematical models of Godin and Brekhovskikh, this effect is based on the properties of inhomogeneous plane waves. The results of the measurement of the pressure transmission coefficient for a spherical source are given in this article, and the conditions of the laboratory experiment are briefly described. Graphs showing the dependence of the transmission coefficient on the frequency of source radiation are provided. Oscillograms that indirectly confirm the presence of inhomogeneous plane waves are also provided. The results of the experiments are in good agreement with the theoretical calculations of Godin and Brekhovskikh. The article briefly discusses possible ways of applying the anomalous transparency effect in two real problems: transferring information from a submarine to an aircraft and monitoring underwater seismic activity.

VOLOSHCHENKO A P . Analysis of the anomalous transparency effect of the water-air interface [J ] . Acoustical Physics , 2020 , 66 ( 3 ): 220 - 227 . DOI: 10.1134/S1063771020020141 http://doi.org/10.1134/S1063771020020141

邓怡情 , 陶建成 , 邱小军 . 水下运动低频声源的异常声透射 [J ] . 声学技术 , 2011 , 30 ( 6 ): 83 - 84 .

DENG Y Q , TAO J C , QIU X J . Anomalous transparency of an underwater moving source [J ] . Technical Acoustics , 2011 , 30 ( 6 ): 83 - 84 . (in Chinese)

DENG Y Q , TAO J C , QIU X J . Sound radiation into air by a point source moving underwater [J ] . Journal of Sound and Vibration , 2012 , 331 ( 20 ): 4481 - 4487 . DOI: 10.1016/j.jsv.2012.04.030 http://doi.org/10.1016/j.jsv.2012.04.030 https://linkinghub.elsevier.com/retrieve/pii/S0022460X1200346X https://linkinghub.elsevier.com/retrieve/pii/S0022460X1200346X

CALVO D C , NICHOLAS M , ORRIS G J . Experimental verification of enhanced sound transmission from water to air at low frequencies [J ] . Journal of the Acoustical Society of America , 2013 , 134 ( 5 ): 3403 - 3408 . DOI: 10.1121/1.4822478 http://doi.org/10.1121/1.4822478 Laboratory measurements of enhanced sound transmission from water to air at low frequencies are presented. The pressure at a monitoring hydrophone is found to decrease for shallow source depths in agreement with the classical theory of a monopole source in proximity to a pressure release interface. On the other hand, for source depths below 1/10 of an acoustic wavelength in water, the radiation pattern in the air measured by two microphones becomes progressively omnidirectional in contrast to the classical geometrical acoustics picture in which sound is contained within a cone of 13.4° half angle. The measured directivities agree with wavenumber integration results for a point source over a range of frequencies and source depths. The wider radiation pattern owes itself to the conversion of evanescent waves in the water into propagating waves in the air that fill the angular space outside the cone. A ratio of pressure measurements made using an on-axis microphone and a near-axis hydrophone are also reported and compared with theory. Collectively, these pressure measurements are consistent with the theory of anomalous transparency of the water-air interface in which a large fraction of acoustic power emitted by a shallow source is radiated into the air.

GILLOT G , DEREC C , GENEVAUX J M . A new insight on a mechanism of airborne and underwater sound of a drop impacting a liquid surface [J ] . Physics of Fluids , 2020 , 32 : 062004 . DOI: 10.1063/5.0010464 http://doi.org/10.1063/5.0010464 https://pubs.aip.org/aip/pof/article/1068116 https://pubs.aip.org/aip/pof/article/1068116

LEE T , IIZUKA H . Sound propagation across the air/water interface by a critically coupled resonant bubble [J ] . Physical Review B , 2020 , 102 : 104105 . DOI: 10.1103/PhysRevB.102.104105 http://doi.org/10.1103/PhysRevB.102.104105 https://link.aps.org/doi/10.1103/PhysRevB.102.104105 https://link.aps.org/doi/10.1103/PhysRevB.102.104105

WEHNER D , SVENSSON U P , LANDRØ M . Acoustic signals in air and water generated by very shallow marine seismic sources: an experimental study [J ] . Journal of the Acoustical Society of America , 2020 , 147 ( 2 ): 1092 - 1103 . DOI: 10.1121/10.0000691 http://doi.org/10.1121/10.0000691 When a marine seismic source, like an airgun, is fired close to the water surface the oscillating bubble interacts with the water-air interface. The main interest for seismic applications is how this effect impacts the acoustic signal propagating into the water. It is known that the sound transmission into air is abnormally strong when the sound source is very close to the sea surface relative to the emitted wavelength. Detailed insight into how the acoustic signal changes when the source depth is changed is useful in seismic data analysis and processing. Two experiments are conducted in a water tank with two different types of seismic sources. In experiment A the source is a small cavity that is sufficiently far away from the water-air interface so that it can be assumed that no interaction between the cavity and water surface occurs. In experiment B the source is a larger air bubble that is very close to the water-air interface, and hence interaction between the bubble and water surface occurs. The effects on the water surface, oscillating bubble, and emitted acoustic pressure into air are discussed. It is demonstrated that the moving surface contributes significantly to the acoustic signal measured in air.

BOLGHASI A , GHADIMI P , FEIZI CHEKAB M A . Low-frequency sound transmission through rough bubbly air-water interface at the sea surface [J ] . Journal of Low Frequency Noise, Vibration and Active Control , 2017 , 36 ( 4 ): 319 - 338 . DOI: 10.1177/1461348417744295 http://doi.org/10.1177/1461348417744295 http://journals.sagepub.com/doi/10.1177/1461348417744295 http://journals.sagepub.com/doi/10.1177/1461348417744295 Transmission of a sound generated by a localized point source in the air through a realistic sea surface is studied by the use of the Kirchhoff-Helmholtz integral. An earlier approach had been based on the Kirchhoff-Helmholtz integral which only considered the effects of rough surface. In the current study, not only the effect of the rough surface is taken into account but also the effects of subsurface bubbles are included in modeling the real phenomenon more accurately. In order to include the effects of subsurface bubble population, the classic relations of the Kirchhoff-Helmholtz integral are reformulated. Accordingly, a three-phase region of air, water, and bubbly water at the sea surface is analyzed, and the rough interface of bubbly water–air is discretized. Through considering an element area Ai, the transmission coefficient [Formula: see text], incident angle [Formula: see text], transmitted angle [Formula: see text], and local surface acoustical roughness Ri are investigated for each individual element. Also, the effects of subsurface bubbles, transmission change as a function of frequency f, wind speed W, incident angle [Formula: see text], source/receiver position ratio (D/H), surface acoustical roughness, and subsurface bubble population are examined. Results of the modified Kirchhoff-Helmholtz integral method display good agreement against available experimental data.

郭业才 , 连晨方 , 张秀再 , 等 . 环境因素对海-气界面低频异常声透射的影响研究 [J ] . 物理学报 , 2015 , 64 ( 14 ): 144301 .

GUO Y C , LIAN C F , ZHANG X Z , et al. Influences of environmental factors on low frequency abnormal sound transmission through sea-air interface [J ] . Acta Physica Sinica , 2015 , 64 ( 14 ): 144301 . (in Chinese) DOI: 10.7498/aps http://doi.org/10.7498/aps https://wulixb.iphy.ac.cn/ https://wulixb.iphy.ac.cn/

BREKHOVSKIKH L M , GODIN O A . Acoustics of layered media I: plane and quasi-plane waves [M ] . Berlin : Springer , 1992 : 17 - 18 .

LIU R Y , LI Z L . Effects of rough surface on sound propagation in shallow water [J ] . Chinese Physics B , 2019 , 28 ( 1 ): 14302 . DOI: 10.1088/1674-1056/28/1/014302 http://doi.org/10.1088/1674-1056/28/1/014302 https://iopscience.iop.org/article/10.1088/1674-1056/28/1/014302 https://iopscience.iop.org/article/10.1088/1674-1056/28/1/014302