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An analysis of plane wave reflection is developed for a two-layer sediment, the top layer consisting of a fine-grained material (mud) with an upward refracting linear sound speed profile. Beneath is a homogeneous basement, and above is homogeneous seawater. A rather curious, exact analytical expression for the reflection coefficient is derived, involving easy to evaluate integrals over finite limits, of the modified Bessel functions of low-integer order. The expression is generally valid for any linear profile with positive gradient in the surficial mud layer and for any sound speed in the basement, either greater than or less than that in the seawater. For “fast” basements, a critical angle always exists that is independent of the sound speed in the mud layer. With a “slow” basement, a quasi-angle of intromission may exist, which depends only weakly on both frequency and the gradient of the profile in the mud, a conclusion that may be relevant to the conditions of the Seabed Characterization Experiment (2017) performed over the New England Mud Patch. With both types of basement, fast and slow, the reflection coefficient, as a function of grazing angle, exhibits fluctuations that are strongly frequency dependent, associated with resonances and anti-resonances in the mud layer.

The Gold Medal is presented in the spring to a member of the Society, without age limitation, for contributions to acoustics. The first Gold Medal was presented in 1954 on the occasion of the Society's Twenty-Fifth Anniversary Celebration and biennially until 1981. It is now an annual award.

This paper reviews some of the highlights of selected topics in ocean acoustics during the thirty years that have passed since the founding of the Journal of Theoretical and Computational Acoustics. Advances in computational methods and computers helped to make computational ocean acoustics a vibrant area of research during that period. The parabolic equation method provides an unrivaled combination of accuracy and efficiency for propagation problems in which the bathymetry, sound speed, and other environmental parameters vary in the horizontal directions. The extension of this approach to cases involving layers that support shear waves has been an active area of research throughout the thirty year period. Interest in basin-scale and global-scale propagation was stimulated by the Heard Island Feasibility Test for monitoring climate change in terms of changes in travel time that occur as the temperature of the ocean rises. Diminishing ice cover in the Arctic, which is one of the consequences of climate change, has stimulated renewed interest in Arctic acoustics during the past decade. Reverberation is a challenging problem that was the topic of a major research program during the beginning of the thirty year period. An innovative approach for making it feasible to solve such problems was applied to data for reverberation from the seafloor and from schools of fish, and some of the findings were featured in Science and Nature. Source localization is one of the core problems in ocean acoustics. When applied on a 2-D array of receivers, an approach based on the eigenvectors of the covariance matrix is capable of separating the signals from different sources from each other, determining when this partitioning step is successful, and tracking sources that cross each other in bearing; one of the advantages of this approach is that it does not require environmental information or solutions of the wave equation. Geoacoustic inversion for estimating the layer structure, wave speeds, density, and other parameters of ocean bottoms has also been a topic of interest throughout the thirty year period.

An analysis of the plane wave reflection coefficient of the seabed, R, is developed for two upward-refracting sediment sound speed profiles: the two-parameter linear and the three-parameter inverse-square, both extending to infinite depth. For the linear profile, it turns out that | R| = 1, representing total reflection for all grazing angles and all frequencies, signifying that in this special case, | R| is insensitive to the gradient. The implication is that if | R| is to return information about the shape of a profile, the gradient must change with depth, either smoothly through the presence of second- and/or higher-order depth derivatives or discontinuously at, say, an interface between sediment layers. The inverse-square is an example of a profile with a smoothly varying gradient, for which a general, closed-form expression for R is derived, valid for all grazing angles and all frequencies. When the sound speed ratio is less than unity, representative of a fine-grained sediment (mud), | R| exhibits two frequency regimes, designated high and low, separated by a transition frequency, fT. In each of these regimes, | R| exhibits a frequency-dependent angle of intromission, which exhibits high- and low-frequency limiting values, differing by approximately 3.5°, depending on the geo-acoustic parameters of the sediment.

In the viscous grain shearing (VGS) theory of wave propagation in an unconsolidated sediment, the dispersion formulas for the phase speed and attenuation of the compressional and shear wave involve two parameters, the compressional modulus, γp, and the shear modulus, γs, which depend on the radius of the circle of contact between contiguous grains in the granular medium. The radius of contact itself depends on the overburden pressure, and hence depth, in the sediment. Based on these observations, the VGS theory is extended to create a geo-acoustic model of a horizontally stratified sediment in which each layer has a uniform porosity, bulk density, and mean grain size, all of which are assumed known from geological survey data. In a given layer, the overburden pressure consists of the contributions from all the higher layers. From the overburden pressure, the compressional and shear moduli are expressed as functions of depth throughout the layer, thereby allowing the frequency dependent phase speed and attenuation profiles of both types of wave to be computed from the VGS dispersion formulas. To illustrate the VGS geo-acoustic modeling technique, two examples are discussed, one of which represents the mud overlying sand sediment at the New England Mud Patch.

The autonomous passive-acoustic lander Deep Sound was deployed at five locations during the Office of Naval Research (ONR)-supported Seabed Characterization Experiment, a multi-institutional field effort held at the New England Mud Patch, where the seabed is known to consist of a thick layer of silt and clay overlying a medium and coarse sand. The five deployments of Deep Sound were up to 9 h long, during which time ambient noise data, taken over an acoustic bandwidth of 5 Hz–30 kHz, were collected on four hydrophones arranged in an inverted “T” shape. Local temperature and conductivity were also recorded continuously at each location. A wave number integral model of wind-driven noise in a fluid waveguide over a two-layered elastic seabed was used to calculate the dependence of the vertical noise coherence on the geoacoustic properties in the overlying silt and clay layer, as well as the subbottom sand half-space. The modeled noise coherence was fitted to the data over the band 100 Hz–12 kHz, returning the compressional- and shear-wave speeds and densities of both layers and the thickness of the top layer.

Marginal probability distributions for parameters representing an effective sound-speed structure of a fine-grained sediment are inferred from a data ensemble maximum entropy method that utilizes a sparse spatially distributed set of received pressure time series resulting from multiple explosive sources in a shallow-water ocean environment possessing significant spatial variability of the seabed. A remote sensing seabed acoustics experiment undertaken in March 2017 off the New England Shelf was designed so that multiple independent analyses could infer the statistical properties of the seabed. The current analysis incorporates the measured horizontal variability from interpretations of a subbottom profiling survey of the experimental area. An idealized range- and azimuth-dependent parameterization of the seabed is derived from identification of horizons within the seabed that define multiple sediment layers. A sparse set of explosive charges were deployed on circular tracks with radii of about 2, 4, and 6.5 km with an acoustic array at the center to correlate a set of random measurements to physical acoustic processes that characterize the seabed. The mean values of a surface sound speed ratio and a linear sound speed gradient for the fine-grained sediment layer derived from 12 data samples processed in the 25–275-Hz band provide an estimate of the effective sound-speed structure in a 130-km $^2$ area. The inferred sediment sound speed values are evaluated by predicting measured time series data not used in the statistical inference, and are also compared to historical measurements. Finally, the low-frequency maximum entropy estimate of the sediment sound speed along with physical measurements derived from piston core measurements are utilized to estimate the sediment grain bulk modulus.

Since HMS Challenger made the first sounding in the Mariana Trench in 1875, scientists and explorers have been seeking to establish the exact location and depth of the deepest part of the ocean. The scientific consensus is that the deepest depth is situated in the Challenger Deep, an abyss in the Mariana Trench with depths greater than 10,000 m. Since1952, when HMS Challenger II, following its namesake, returned to the Mariana Trench, 20 estimates (including the one from this study) of the depth of the Challenger Deep have been made. The location and depth estimates are as diverse as the methods used to obtain them; they range from early measurements with explosives and stop watches, to single- and multi-beam sonars, to submersibles, both crewed and remotely operated. In December 2014, we participated in an expedition to the Challenger Deep onboard Schmidt Ocean Institute’s R/V Falkor and deployed two free-falling, passive-acoustic instrument platforms, each with a glass-sphere pressure housing containing system electronics. At a nominal depth of 9,000 m, one of these housings imploded, creating a highly energetic shock wave that, as recorded by the other instrument, reflected multiple times from the sea surface and seafloor. From the arrival times of these multi-path pulses at the surviving instrument, in conjunction with a concurrent measurement of the sound speed profile in the water column, we obtained a highly constrained acoustic estimate of the Challenger Deep: 10,983 ± 6 m.

Summary Meal kits are popular for consumers seeking greater convenience in preparing meals at home. The market share for meal kit subscription services (MKSSs) is growing in developed nations including Australia, however, literature about their health promoting qualities, e.g. nutritional composition, is scarce. This study aimed to assess the characteristics and nutritional composition of meals offered from an MKSS over 12 months. Nutritional data were extracted from recipes available to order from HelloFresh in Australia from 1 July 2017 to 30 June 2018. In total, 346 (251 unique) recipes were retrieved. Per serve (median size 580 g), meals contained a median of 2840 kJ (678 kcal) of energy, 58 g carbohydrate (14 g sugar), 44 g protein, 28 g total fat (8 g saturated fat) and 839 mg sodium. Median energy from macronutrients was total fat (38%), carbohydrates (34%), protein (25%) and saturated fat (11%). This paper is the first to describe characteristics of recipes available from an MKSS over a 12-month period of time. With their growing popularity, meal kit delivery services have the capacity to influence consumer food behaviours, diets and subsequently population health. MKSSs may function to promote health though education, training, and enabling home cooking behaviours, and may be a powerful commitment device for home cooking behaviour change. However, it is important for health professionals, including dietitians and nutritionists, to understand the nutritional risks, benefits and suitability of this contemporary mealtime option before recommending them to clients and members of the public as part of health promotion. Lay summary Meal kit delivery services are growing in popularity in developed countries, complementing busy lifestyles with pre-measured ingredients and recipe instructions delivered to the home. These meal kits have the ability to influence consumer diets and population health, and may support health promoting diet behaviours, e.g. eating vegetables, and enable home cooking. In this study, we reviewed a years’ worth of recipes from a popular meal kit service. We report that a typical recipe contained approximately nine different ingredients, comprising three vegetables and required three ingredients from the home pantry. Meals took ∼35 min to prepare and were found to be relatively high in energy from fat and protein, and relatively low in energy from carbohydrates. The level of sodium varied widely and some meals exceeded the Australian Suggested Dietary Target for sodium (

The frequency bandwidth of the sound from a light helicopter, such as a Robinson R44, extends from about 13 Hz to 2.5 kHz. As such, the R44 has potential as a low-frequency sound source in underwater acoustics applications. To explore this idea, an experiment was conducted in shallow water off the coast of southern California in which a horizontal line of hydrophones detected the sound of an R44 hovering in an end-fire position relative to the array. Some of the helicopter sound interacted with seabed to excite the head wave in the water column. A theoretical analysis of the sound field in the water column generated by a stationary airborne source leads to an expression for the two-point horizontal coherence function of the head wave, which, apart from frequency, depends only on the sensor separation and the sediment sound speed. By matching the zero crossings of the measured and theoretical horizontal coherence functions, the sound speed in the sediment was recovered and found to take a value of 1682.42 ± 16.20 m/s. This is consistent with the sediment type at the experiment site, which is known from a previous survey to be a fine to very-fine sand.

Scientists and explorers have been searching to determine the exact location and depth of the deepest part of the ocean since the HMS Challenger made the first sounding of the Mariana Trench in 1875. The consensus is that the deepest abyss in the ocean is in the Challenger Deep, a portion of the Mariana Trench with depths greater than 10 000 m. Since the HMS Challenger II returned to the Mariana Trench in 1952, 14 estimates of the deepest depth of the ocean have been made. Estimates of the location and maximum depth are as diverse as the methods used including wire soundings, explosives, single and multibeam sonars, and remotely operated and manned submersibles. During an Office of Naval Research supported expedition to the Challenger Deep in 2014, two free falling passive acoustic instruments were deployed. The implosion of one instrument was recorded by the other when both were at depths greater than 8000 m. Multiple reflections from the seafloor and sea surface of the sound generated by the implosion were used to determine the depth of the Challenger Deep. The result was the most constrained estimate of the deepest part of the ocean, 10 991 ± 6 m.

The Viscous Grain Shearing (VGS) theory predicts the existence of a compressional wave and a shear wave in an unconsolidated marine sediment. Although it is known that, subject to certain constraints, the shear wave satisfies causality, the causal nature of the compressional wave is less well understood. In this paper, the VGS compressional-wave speed and attenuation are examined in three frequency regimes, where it is shown that they follow approximately frequency power laws. It is then proved that the VGS propagation factor, which is a combination of the phase speed and attenuation, is a causal transform: its inverse Fourier transform is zero for all times prior to the onset of the source. The derivation of this result, which is a necessary condition if the VGS compressional wave equation is to satisfy causality, includes the development of a technique for evaluating a class of previously unknown integrals. This integration procedure relies on a limiting argument combined with certain Fourier transforms, the latter taking the form of “improper” integrals, which, it is shown, can be expressed explicitly based on the properties of generalized functions. An expression for the impulse response of the VGS compressional wave is also developed and shown to satisfy causality, although the transition from zero to the peak level is abrupt, quite unlike the perfectly smooth behavior exhibited by the impulse response of the VGS shear wave, which is maximally flat everywhere in the medium at the instant the source is activated.

An attenuation obeying a frequency power law scales as | ω | β , where ω is angular frequency and β is a real constant. A recently developed dispersion formula predicts that the exponent β can take only certain values in well defined, disjoint intervals. It is shown here that these admissible values of β are consistent with the physical requirement, stemming from the second law of thermodynamics, that the work done during the passage of a wave must always be positive. Since the dispersion formula, which is derived from the strain-hardening wave equation, is a causal transform, it is expected that the associated Green's function should also satisfy causality for all the permitted values of β. Such is not the case, however: the Green's function is maximally flat at the time of source activation, and hence is causal, but only for values of β in the interval (0.5, 1). This restriction supersedes the weaker constraints on β derived from the dispersion formula alone. For the previously admissible values of β outside the interval (0.5, 1), although the dispersion formula satisfies causality, the Green's function is non-causal. Evidently, causality may be satisfied by the dispersion formula but violated by the Green's function.

The absorption of sound in seawater is due to the viscous and chemical relaxation of different compounds. Over the wind noise band of 1–10 kHz, the frequency dependence of the absorption is due to the mechanisms of chemical relaxation for magnesium sulfate (f > 3 kHz) and for boric acid (f 10 m/s), the ambient noise field is dominated by locally generated surface noise and has a depth-independent directionality and a weakly frequency and depth-dependent intensity, due to sound absorption. By comparing measurements with theory, estimates of ocean acidity can be made from the depth profiles of ambient noise. [Work supported by ONR.]The absorption of sound in seawater is due to the viscous and chemical relaxation of different compounds. Over the wind noise band of 1–10 kHz, the frequency dependence of the absorption is due to the mechanisms of chemical relaxation for magnesium sulfate (f > 3 kHz) and for boric acid (f 10 m/s), the ambient noise field is dominated by locally generated surface noise and has a depth-independent directionality and a w...

An attenuation scaling as a power of frequency, |ω|(β), over an infinite bandwidth is neither analytic nor square-integrable, thus calling into question the application of the Kramers-Kronig dispersion relations for determining the frequency dependence of the associated phase speed. In this paper, three different approaches are developed, all of which return the dispersion formula for the wavenumber, K(ω). The first analysis relies on the properties of generalized functions and the causality requirement that the impulse response, k(t), the inverse Fourier transform of -iK(ω), must vanish for t

A seven element, bi-linear hydrophone array was deployed over a coral reef in the Papahãnaumokuãkea Marine National Monument, Northwest Hawaiian Islands, in order to investigate the spatial, temporal, and spectral properties of biological sound in an environment free of anthropogenic influences. Local biological sound sources, including snapping shrimp and other organisms, produced curved-wavefront acoustic arrivals at the array, allowing source location via focusing to be performed over an area of 1600 m(2). Initially, however, a rough estimate of source location was obtained from triangulation of pair-wise cross-correlations of the sound. Refinements to these initial source locations, and source frequency information, were then obtained using two techniques, conventional and adaptive focusing. It was found that most of the sources were situated on or inside the reef structure itself, rather than over adjacent sandy areas. Snapping-shrimp-like sounds, all with similar spectral characteristics, originated from individual sources predominantly in one area to the east of the array. To the west, the spectral and spatial distributions of the sources were more varied, suggesting the presence of a multitude of heterogeneous biological processes. In addition to the biological sounds, some low-frequency noise due to distant breaking waves was received from end-fire north of the array.

This chapter provides a framework and roadmap for the book. It starts with a brief history of underwater acoustics from the time of the Greek philosopher Aristotle (384–322 BC) up to the post–World War II era. This is followed by a discussion of the international system of units used in the book and a discussion on the use of the decibel scale. Next, the chapter deals with the features of oceanography including sound speed profiles, thermoclines, arctic regions, deep isothermal layers, expressions for the speed of sound, surface waves, internal waves, bubbles from wave breaking, ocean acidification, deep-ocean hydrothermal flows, eddies, fronts and large-scale turbulence, and diurnal and seasonal changes. This is followed by a discussion of the sonar equation that is fundamental to underwater acoustics.

Although ambient biological underwater sound was first characterized more than 60 years ago, attributing specific components of ambient sound to their creators remains a challenge. Noise produced by snapping shrimp typically dominates the ambient spectra near tropical coasts, but significant unexplained spectral variation exists. Here, evidence is presented indicating that a discernible contribution to the ambient sound field over coral reef ecosystems in the Line Islands archipelago originates from the interaction of hard-shelled benthic macro-organisms with the coral substrate. Recordings show a broad spectral peak centered between 14.30 and 14.63 kHz, incoherently added to a noise floor typically associated with relatively "white" snapping shrimp sounds. A 4.6 to 6.2 dB increase of pressure spectral density level in the 11 to 17 kHz band occurs simultaneously with an increase in benthic invertebrate activity at night, quantified through time-lapse underwater photography. Spectral-level-filtered recordings of hermit crabs Clibanarius diugeti in quiet aquarium conditions reveal that transient sounds produced by the interaction between the crustaceans' carapace, shell, and coral substrate are spectrally consistent with Line Islands recordings. Coral reef ecosystems are highly interconnected and subtle yet important ecological changes may be detected quantitatively through passive monitoring that utilizes the acoustic byproducts of biological activity.

A series of shallow-water acoustic experiments has been conducted off La Jolla, California using a Robinson R44 helicopter as a low-frequency (≈13–2500 Hz) sound source. The sound speed of the sand sediment was recovered from the horizontal coherence of the head wave excited in the water column by the helicopter. Previously, on 14 December 2016, with a horizontal aperture of 3 m, this technique returned the sound speed of the sediment, from 800–2300 Hz, as 1682 ± 16 m/s, consistent with the known sediment type. An additional experiment was conducted on 6 February with larger horizontal apertures of 9, 12, and 15 m. The hydrophones, situated 0.5 m above the seabed, received the head-wave signals, allowing the coherence function to be formed over the bandwidth of the airborne source. The sediment sound speed was recovered by matching the zero crossings of the measured coherence function to those predicted by the theory of head-wave generation in shallow water. The dispersion in the sediment sound speed was estimated over a frequency range extending between 27 Hz, the lowest zero crossing of the coherence function, and 2.5 kHz, the bandwidth of the source. [Research supported by ONR, SMART(DOD), NAVAIR and SIO.]

Over recent years, ambient noise in the ocean has come to be recognized as a signal in its own right, containing a wealth of information about the ocean and ocean processes. Ambient noise has thus become a central pillar of acoustical oceanography. Since the attributes of ambient noise are based on straightforward physical principles, the noise field may be inverted to recover, for example, the sound speed in the seabed. Some selective examples of ambient noise oceanography will be reviewed, based on personal experiences gained during a career that includes research in the Arctic, the North Atlantic, the deep ocean trenches, and the shallow, continental shelf waters of the English Channel and the Pacific Ocean, off the coast of California. Much of this work was accomplished with the talented assistance of many students and colleagues; and it was made possible through the consistent support of our sponsors. It is a pleasure to acknowledge that, throughout, the Acoustical Society has provided a cordial environment where acoustical oceanographers could meet and are always made welcome. [Research supported by ONR.]

Passive acoustic monitoring of three protected coral reef habitats south of St. John Island in the US Virgin Islands was conducted in April, 2019. Four wideband Autonomous Passive Acoustic Monitoring (APAM) packages, each with 12-element hydrophone arrays, were deployed on the 10-m-deep seafloor and recorded continuously over the 9-day experiment. Previously published methods for robust feature extraction of individual biological sounds [Mellinger and Bradbury, 2007] have been applied to these data and compared with enhanced approaches to feature extraction. This talk presents results of quantitative evaluations of the performance of these methods. Feature extraction is categorized as a parameter estimation problem whose performance is quantified by the statistical distribution of estimates, typically summarized by the bias and variance of these distributions. Results for a simulated case first are presented, and then those from the APAM-recorded data. The enhanced approaches show significant improvement over the standard approaches for several of the extracted features.

Acoustic inferences from remote sensing of surface ship radiated noise in bottom-limited ocean environments are difficult due to a generally unknown geoacoustic structure of the seabed. The idea here is to first calibrate an acoustic sensing system by estimating geoacoustic parameter values by utilizing controlled sources with known levels. Then, the acoustic field that results from a surface ship is utilized to estimate the ship source levels where the transmission loss is constructed based on the previous estimate of the seabed parameterization and measurements of the sound speed profile at the time that the ship noise measurements were made. This concept was tested with acoustic data collected on two vertical line arrays (VLAs) during the Seabed Characterization Experiment in the New England Mudpatch during April 2017, in 75 m of water. The acoustic field was produced with a controlled source radiating in the 1.5–4 kHz band. A maximum entropy method provided estimates of viscous grain shearing (VGS) model parameter values. Then, using this VGS parameterization, ship source levels as a function of aspect and frequency out to about 3 kHz were extracted for the RV Endeavor and several merchant ships passing near the VLAs. [Work supported by ONR N00014-16-C-3065.]

During the Philippine Sea experiment in May 2009, Deep Sound, a free-falling instrument platform, descended to a depth of 5.1 km and then returned to the surface. Two vertically aligned hydrophones monitored the ambient noise continuously throughout the descent and ascent. A heavy rainstorm passed over the area during the deployment, the noise from which was recorded over a frequency band from 5 Hz to 40 kHz. Eight kilometers from the deployment site, a rain gauge on board the R/V Kilo Moana provided estimates of the rainfall rate. The power spectral density of the rain noise shows two peaks around 5 and 30 kHz, elevated by as much as 20 dB above the background level, even at depths as great as 5 km. Periods of high noise intensity in the acoustic data correlate well with the rainfall rates recovered from the rain gauge. The vertical coherence function of the rain noise has well-defined zeros between 1 and 20 kHz, which are characteristic of a localized source on the sea surface. A curve-fitting procedure yields the vertical directional density function of the noise, which is sharply peaked, accurately tracking the storm as it passed over the sensor station.

Ambient acoustic noise fields in the ocean are generally three dimensional in that they exhibit vertical and horizontal directivity. A model of spatially homogeneous noise is introduced in which the directionality is treated as separable, that is, the overall directionality of the field is the product of the individual directivities in the horizontal and vertical. A uni-modal von Mises circular distribution from directional statistics is taken to represent the noise in the horizontal, whilst the vertical component is consistent with a surface distribution of vertical dipoles. An analysis of the coherence and cross correlation of the noise at two horizontally aligned sensors is developed. The coherence function involves a single integral over finite limits, whilst the cross-correlation function, derived on the assumption that the noise has been pre-whitened, is given by an integral with limits that depend on the correlation delay time. Although the cross-correlation function does not exhibit delta functions that could be identified with the Green's function for propagation between the two sensors in the field, it does drop abruptly to zero at numerical time delays equal to the travel time between the sensors. Hence the noise could be used to recover the sound speed in the medium.

During the Seabed Characterization Experiment, a multi-institutional field effort held at the New England mud patch, the autonomous passive acoustic lander Deep Sound made a series of ambient noise measurements from the seafloor. The instrument platform carried four hydrophones, arranged in an inverted ‘T’ shape with three spaced in the horizontal and two in the vertical, and landed on the seafloor with the bottom phones 30 cm above the interface. Pressure time series, vertical and horizontal noise coherence (directionality), were recorded continuously for periods of 9 hours over the acoustic bandwidth of 5 Hz to 30 kHz, along with the local temperature, conductivity, and depth. An analytical Pekeris waveguide noise model was fitted to the data in order to determine the bulk sound speed, sheer speed, density, and frequency dependent attenuation in the bottom fluid half-space. Acoustic properties of the mud were determined by comparing the data to the output of a range independent noise model, featuring a realistic multi-layered seabed. [Research supported by ONR.]During the Seabed Characterization Experiment, a multi-institutional field effort held at the New England mud patch, the autonomous passive acoustic lander Deep Sound made a series of ambient noise measurements from the seafloor. The instrument platform carried four hydrophones, arranged in an inverted ‘T’ shape with three spaced in the horizontal and two in the vertical, and landed on the seafloor with the bottom phones 30 cm above the interface. Pressure time series, vertical and horizontal noise coherence (directionality), were recorded continuously for periods of 9 hours over the acoustic bandwidth of 5 Hz to 30 kHz, along with the local temperature, conductivity, and depth. An analytical Pekeris waveguide noise model was fitted to the data in order to determine the bulk sound speed, sheer speed, density, and frequency dependent attenuation in the bottom fluid half-space. Acoustic properties of the mud were determined by comparing the data to the output of a range independent noise model, featuring a ...

An attenuation obeying a frequency power law scales as |ω|^β, where ω is angular frequency and β is a real constant. According to the strain-hardening shear-wave equation in the grain-shearing theory, the attenuation of the shear wave supported by a marine sediment follows a frequency power law. The associated dispersion formula, which is a causal transform, predicts that the phase speed is also a power law and that the product of the phase speed and the attenuation divided by ω is a constant, independent of frequency. From the dispersion formula, along with the conditions that the phase speed and attenuation must both be positive and the propagation factor must exhibit conjugate symmetry, it follows that the exponent β can take only certain values that fall in well-defined intervals extending indefinitely with no upper or lower limit. However, to satisfy the requirement that Green’s function be causal, β is further constrained to lie in the interval [0.5 1), under which condition the Green’s function is maximally flat at the time the source is activated. With other values of β the Green’s function is non-causal, exhibiting non-zero values at times preceding the onset of the source. [Research supported by ONR.]An attenuation obeying a frequency power law scales as |ω|^β, where ω is angular frequency and β is a real constant. According to the strain-hardening shear-wave equation in the grain-shearing theory, the attenuation of the shear wave supported by a marine sediment follows a frequency power law. The associated dispersion formula, which is a causal transform, predicts that the phase speed is also a power law and that the product of the phase speed and the attenuation divided by ω is a constant, independent of frequency. From the dispersion formula, along with the conditions that the phase speed and attenuation must both be positive and the propagation factor must exhibit conjugate symmetry, it follows that the exponent β can take only certain values that fall in well-defined intervals extending indefinitely with no upper or lower limit. However, to satisfy the requirement that Green’s function be causal, β is further constrained to lie in the interval [0.5 1), under which condition the Green’s function is ...

Chotiros and Isakson [J. Acoust. Soc. Am. 127, 2095–2098 (2010)] raised three main issues concerning the grain-shearing and viscous-grain-shearing (VGS) theories of wave propagation in saturated marine sediments. (1) They introduced the R-ratio as a test of the two theories, (2) they then used the R-ratio to compare the theories with published measurements of compressional and shear wave properties of laboratory sediments under high confinement pressures, and (3) they pointed out that the VGS theory overestimates the shear attenuation measured during the Sediment Acoustics Experiment 1999 (SAX99) by about an order of magnitude. With regard to the R-ratio, it provides an incomplete test of the theories and, moreover, it returns ambiguous results. As for the tests against measurements made under high confinement pressures, they are invalid because the theories are not applicable under such conditions. The third point is correct, but a minor modification to the VGS theory resolves the difficulty.

A series of shallow-water acoustic experiments has been conducted off the coast of southern California using a Robinson R44 helicopter as a low-frequency (≈ 13–3500 Hz) sound source. The aim of the experiments was to recover the sound speed of a fine to very-fine sand sediment from the horizontal coherence of the head wave excited in the water column by the helicopter. Two hydrophones, separated horizontally by approximately 15 m and situated 0.5 m above the seabed, received the head-wave signals, allowing the coherence function to be formed over the bandwidth of the airborne source. The sediment sound speed was recovered by matching the zero crossings of the measured coherence function to those predicted from a recently developed theory of head-wave generation in shallow water. Using this technique, the dispersion in the sediment sound speed can be estimated over a frequency range extending between 27 Hz, the lowest zero crossing of the coherence function, and 3.5 kHz, the bandwidth of the source. In the middle of the frequency band, the sound speed of the sediment was estimated to be 1682 ± 16 m/s, consistent with the known sediment type. [Research supported by ONR, SMART(DOD), NAVAIR, and SIO.]A series of shallow-water acoustic experiments has been conducted off the coast of southern California using a Robinson R44 helicopter as a low-frequency (≈ 13–3500 Hz) sound source. The aim of the experiments was to recover the sound speed of a fine to very-fine sand sediment from the horizontal coherence of the head wave excited in the water column by the helicopter. Two hydrophones, separated horizontally by approximately 15 m and situated 0.5 m above the seabed, received the head-wave signals, allowing the coherence function to be formed over the bandwidth of the airborne source. The sediment sound speed was recovered by matching the zero crossings of the measured coherence function to those predicted from a recently developed theory of head-wave generation in shallow water. Using this technique, the dispersion in the sediment sound speed can be estimated over a frequency range extending between 27 Hz, the lowest zero crossing of the coherence function, and 3.5 kHz, the bandwidth of the source. In the...

Ambient noise in the deep ocean is traditionally monitored using bottom-mounted or surface-suspended hydrophone arrays. An alternative approach has recently been developed in which an autonomous, untethered instrument platform free falls under gravity from the surface to a preassigned depth, where a drop weight is released, allowing the system to return to the surface under buoyancy. Referred to as Deep Sound, the instrument records acoustic, environmental, and system data continuously during the descent and ascent. The central component of Deep Sound is a Vitrovex glass sphere, formed of two hemispheres, which houses data acquisition and storage electronics, along with a microprocessor for system control. A suite of sensors on Deep Sound continuously monitor the ambient noise, temperature, salinity, pressure, and system orientation throughout the round trip from the surface to the bottom. In particular, several hydrophones return ambient noise time series, each with a bandwidth of 30 kHz, from which the noise spectral level, along with the vertical and horizontal coherence, are computed as functions of depth. After system recovery, the raw data are downloaded and the internal lithium ion batteries are recharged via throughputs in the sphere, which eliminates the need to separate the hemispheres between deployments. In May 2009, Deep Sound descended to a depth of 6 km in the Philippine Sea and successfully returned to the surface, bringing with it a unique data set on the broadband ambient noise within and below the deep sound channel. The next deep deployment is planned for November 2009, when Deep Sound will descend almost 11 km, to the bottom of the Challenger Deep at the southern end of the Mariana Trench. If successful, it will return with continuous acoustic and environmental recordings taken from the sea surface to the bottom of the deepest ocean on Earth.

Acoustic wave propagation in a dispersive medium may be described by a wave equation containing one or more dissipation terms. Three such equations are examined in this article: van Wijngaarden's equation (VWE) for sound propagating through a bubbly liquid; Stokes' equation for acoustic waves in a viscous fluid; and the time-dependent diffusion equation (TDDE) for waves in the interstitial gas in a porous solid. The impulse-response solution for each of the three equations is developed and all are shown to be strictly causal, with no arrivals prior to the activation of the source. However, the VWE is nonphysical in that it predicts instantaneous arrivals, which are associated with infinitely fast, propagating Fourier components in the Green's function. Stokes' equation and the TDDE are well behaved in that they do not predict instantaneous arrivals. Two of the equations, the VWE and Stokes' equation, satisfy the Kramers-Kronig dispersion relations, while the third, the TDDE, does not satisfy Kramers-Kronig, even though its impulse-response solution is causal and physically realizable. The Kramers-Kronig relations are predicated upon the (mathematical) existence of the complex compressibility, a condition which is not satisfied by the TDDE because the Fourier transform of the complex compressibility is not square-integrable.

A theory is developed for the acoustic field in a three-layer waveguide, representing the atmosphere, shallow ocean and sediment. The unaccelerated source is moving horizontally in the atmosphere. Two solutions are presented. The first, for a line source normal to the direction of travel, is a single wavenumber integral yielding the two-dimensional (2-D) field in each layer; and the second, for a point source, is a double wavenumber integral for the 3-D field in each layer. In both cases, the moving-source dispersion relationship for the three-layer environment is derived. From the 2-D dispersion relation, asymmetries fore and aft of the source, due to source motion, are shown to exist in the field in all three layers. In the water column, complex Doppler effects modify asymmetrically the effective depth of the channel and hence also the mode shapes. Evidence of the fore-aft modal asymmetry appears in the high-resolution spectrum of the field in the channel, which exhibits several sharp peaks on either side of the unshifted frequency, each associated with an up- or downshifted mode. A numerical evaluation of the 3-D solution provides a graphic illustration of the asymmetrical character of the field in all three layers.

Measurements are presented of multi-frequency underwater acoustic backscattering from suspensions of glass spheres and sands. The data were collected in a sediment tower, specifically designed for such measurements and capable of generating a homogeneous suspension over a distance of approximately 1 m. The glass sphere data were collected to assess the capability of the system and for calibration. The measurements on suspensions of sands were obtained as part of on-going studies into the measurement of nearbed sediment transport processes using acoustics. Utilizing the backscattered sound from sand suspensions, both the form function and total scattering cross section of the sediments have been measured for a range of sediments and particle sizes. Interpretation of the observations has been carried out within a framework of sphere scattering. The results show enhanced scattering for suspensions of sand grains, relative to that of similar size spherical scatterers and the enhancement can be described by a ...

When the bulk and shear moduli of the mineral frame are set to zero, the full Biot theory of wave propagation in a porous medium such as a marine sediment reduces to Williams’ “effective density fluid” (EDF) model [J. Acoust. Soc. Am. 110, 2276–2281 (2001)]. Although eight material variables appear in the EDF model, it is in fact tightly constrained, possessing just three degrees of freedom: the phase speeds in the limits of low and high frequency, c0 and c∞, respectively, and a transition frequency, fT, separating the low- and high-frequency regimes. In this paper, an algebraic approximation to the EDF model is formulated, which is termed the “modified viscous fluid” (MVF) model, involving only the three parameters (c0,c∞,fT). Expressions are developed for (c0,c∞,fT) in terms of the eight material properties; and a comparison of the MVF and EDF dispersion curves is performed, showing that they are essentially identical at all frequencies. Apart from its computational simplicity, the MVF model provides in...

Based on a one-dimensional model, a wave-theoretic analysis of the sound field from a moving, harmonic source in a viscous medium is developed. When the source is inbound to the receiver, the field consists of an attenuated propagating wave with Doppler up-shifted frequency. A similar wave is present when the source is outbound from the receiver but with down-shifted frequency. Also present on the outbound run is an evanescent wave that appears at the instant the source passes the receiver. The evanescent wave is very highly attenuated and exists only in the presence of both source motion and dissipation. Expressions are formulated for the frequency and attenuation coefficient of the two propagating waves and the evanescent wave. The attenuation of the propagating waves scales with the square of the frequency, which is a characteristic of viscous dissipation; and the attenuation is strongly asymmetrical, being significantly higher on approach than departure. The asymmetry in the attenuation arises partly from the upward and downward Doppler shifts in the frequency on approach and departure, respectively. In addition, the attenuation is skewed by the factor (1 +/- beta)(-1), where the lower (upper) sign applies on approach (departure) and beta is the Mach number of the source. At a Mach number of 0.85, the ratio of the inbound to outbound attenuation is 2000.

Experiments were performed to investigate the nearfield sound from an axisymmetric conical bubble plume formed by a continuous vertical freshwater jet as it penetrates the surface of a pool of fres...

The sound from a light aircraft in flight is generated primarily by the propeller, which produces a sequence of harmonics in the frequency band between about 80 Hz and 1 kHz. Such an airborne sound source has potential in underwater acoustics applications, including inversion procedures for determining the wave properties of marine sediments. A series of experiments has recently been performed off the coast of La Jolla, California, in which a light aircraft was flown over a sensor station located in a shallow (approximately 15 m deep) ocean channel. The sound from the aircraft was monitored with a microphone above the sea surface, a vertical array of eight hydrophones in the water column, and two sensors, a hydrophone and a bender intended for detecting shear waves, buried 75 cm deep in the very-fine-sand sediment. The propeller harmonics were detected on all the sensors, although the s-wave was masked by the p-wave on the buried bender. Significant Doppler shifts of the order of 17%, were observed on the microphone as the aircraft approached and departed from the sensor station. Doppler shifting was also evident in the hydrophone data from the water column and the sediment, but to a lesser extent than in the atmosphere. The magnitude of the Doppler shift depends on the local speed of sound in the medium in which the sensor is located. A technique is described in which the Doppler difference frequency between aircraft approach and departure is used to determine the speed of sound at low-frequencies (80 Hz to 1 kHz) in each of the three environments, the atmosphere, the ocean and the sediment. Several experimental results are presented, including the speed of sound in the very fine sand sediment at a nominal frequency of 600 Hz, which was found from the Doppler difference frequency of the seventh propeller harmonic to be 1617 m/s.

During the Sediment Acoustics Experiment in 1999 (SAX99), the in Situ Sediment geoAcoustic Measurement System (ISSAMS), transmitting tone bursts containing an integer number of cycles, was used to measure the speed and attenuation of compressional waves in a weakly dispersive, medium-sand sediment in the Gulf of Mexico. ISSAMS was deployed at seven stations and operated mostly at a frequency of 38 kHz, but at two of the sites, a succession of pulses was transmitted with frequencies extending from 25 to 100 kHz, in 5-kHz increments, yielding the phase speed, the group speed and the attenuation as a function of frequency. An analysis of a tone-burst transmission in a dispersive medium illustrates that several subtle factors, including the narrow bandwidth of the source, along with dispersion and attenuation in the medium, have the potential for introducing significant errors into travel-time measurements. It is concluded that, in general, the timing is best performed between two receivers rather than between the source and a receiver, the difficulty in the latter case being that the output from a narrow-band source is not a replica of the input. A correlation applied to the arrivals at the two receivers yields the travel time, from which a good approximation to the group speed is immediately available. Alternatively, a Fourier decomposition yields the phase speed as a function of frequency, which would be an advantage in a highly dispersive medium. The two techniques return almost identical wave speeds when applied to the ISSAMS tone-burst data from the weakly dispersive SAX99 sediments: at 38 kHz, the mean wave speed from the six primary stations is 1778 m/s. Attenuation was also estimated from receiver-to-receiver travel paths, using three different techniques: the ratio of the mean-square values of the arrivals, the ratio of the Fourier magnitudes of the arrivals and transposition. All three methods yield similar results when applied to the SAX99 data, returning a mean attenuation from the six stations of 12 dB/m at 38 kHz, which is comparable with previously reported measurements of attenuation in marine sands. From the broadband measurements, between 25 and 100 kHz, the dispersion is found to be weak but detectable and the attenuation scales almost linearly with frequency, which corresponds to a nearly constant Q.

The Grain-Shearing (GS) model of wave propagation in unconsolidated sediments is embodied in two sets of dispersion relations, one for the compressional wave and the other for the shear wave. Besides frequency, these expressions for the wave speed and attenuation depend on the physical properties of the sediment, notably the bulk density and porosity. They also involve a material exponent, n, and grain shearing coefficients that are associated with the sliding of grains against one another, which is a non-linear, stick-slip type of process that is controlled by micro-asperities on the surface of the grains. Bioturbation is known to affect both the bulk density and porosity of sediments, while biogenic coatings of mineral grains modify the surface roughness, which alters the grain-shearing coefficients. The magnitude of the effects of bioturbation and biogenic coatings on the wave speeds and attenuations predicted by the GS theory will be discussed, based on available biological information in the literatu...

The autonomous passive acoustic lander Deep Sound was deployed five times during the Seabed Characterization Experiment and collected ambient noise data on four hydrophones, arranged in a inverted “T” shape, with three spaced in the horizontal and two in the vertical. The lander was deployed with the bottom-most phones approximately 30 cm above the seafloor, recording over an acoustic bandwidth of 5 Hz–30 kHz. Pressure time series, vertical and horizontal noise coherence (directionality), and the local temperature and conductivity were recorded continuously for periods of 9 hours. Wind-driven surface ambient noise coherence was used to estimate bulk acoustic seabed properties. An analytical Pekeris-waveguide noise model was fitted to the data in order to determine the bulk sound speed, density, and frequency dependent attenuation in the bottom fluid half-space. [Research supported by ONR.]

Based on the pioneering work of David Farmer, it is now is well recognized that the layer immediately beneath the sea surface is a highly dynamic, two-phase region, where bubbles created by wave breaking form an upward refracting sound speed profile that acts as an acoustic waveguide. The bottom boundary, although less dynamic than the sea surface, possesses its own unique complexities that are no less challenging to understand than those of the near-surface bubble layer. For instance, a growing body of experimental evidence indicates that the acoustic attenuation in a marine sediment obeys a frequency power law, extending over a wide bandwidth, in which the exponent takes a value close to unity. A long-standing problem has been to identify the frequency dispersion in the sound speed associated with such a power-law attenuation. Several solutions to this problem have been proposed over recent decades but are in fact unphysical in that they fail to obey the Kramers-Kronig dispersion relations. An alternati...

A series of underwater acoustic experiments using a Robinson R44 helicopter and an underwater receiver station has been conducted in shallow (16.5 m) water. The receiver station consisted of an 11-element nested hydrophone array with a 12 m aperture configured as a horizontal line (HLA) 0.5 m above the seabed. A microphone was located immediately above the surface. The main rotor blades of the helicopter produce low-frequency harmonics, the fundamental frequency being ~13 Hz. The tail rotor produces a sequence of harmonics six times higher in frequency. An analytical solution for the horizontal coherence for the head wave has been developed using a 3-layer (atmosphere-ocean-sediment) acoustic propagation model. By comparing the theoretical coherence with the coherence function from the data the sediment sound speed is recovered. The results from the theoretical model and an experiment conducted north of Scripps Pier off the coast of southern California are presented. [Research supported by ONR, SMART(DOD)...

In September 2012, the free-falling, deep-diving instrument platform Deep Sound III descended to the bottom of the Tonga Trench, where it resided at a depth of 8515 m for almost 3 h, recording ambient noise data on four hydrophones arranged in a vertical L-shaped configuration. The time series from each of the hydrophones yielded the power spectrum of the noise over the frequency band 3 Hz to 30 kHz. The spatial coherence functions, along with the corresponding cross-correlation functions, were recovered from all available hydrophone pairs in the vertical and the horizontal. The vertical coherence and cross-correlation data closely follow the predictions of a simple theory of sea-surface noise in a semi-infinite ocean, suggesting that the seabed in the Tonga Trench is a very poor acoustic reflector, which is consistent with the fact that the sediment at the bottom of the trench consists of very-fine-grained material having an acoustic impedance similar to that of seawater. The horizontal coherence and cross-correlation data are a little more complicated, showing evidence of (a) bathymetric shadowing of the noise by the walls of the trench and (b) highly directional acoustic arrivals from the research vessel supporting the experiment.

Chotiros and Isakson [J. Acoust. Soc. Am. 135, 3264–3279 (2014)] contend that the physics-based grain-shearing (GS) theories of wave propagation in granular materials are not consistent with one particular shear-attenuation data set for water-saturated angular sand that has appeared in the literature. This provides them with the rationale for developing their own model, an extension of the empirical Biot-Stoll model, which they designate the Extended Biot (EB) model. In this article, the EB model and the grain-shearing theories are briefly reviewed, and it is demonstrated that, in fact, the original GS theory accurately matches the frequency-dependent trends of all the shear attenuation data sets that are currently available, including those for saturated angular sands after random fluctuations are suppressed by averaging over several realizations of the medium. It is also pointed out that Chotiros and Isakson's treatment of the available shear-attenuation data is highly selective, and that the format in which they present the selected data makes their comparisons with theoretical models difficult to interpret. Thus, their attempts at validating the EB model and their conclusions concerning alternative theories should be treated with caution.

A recently developed theoretical model of the airborne acoustic field from an explosive volcanic eruption of the Strombolian type is described in this article. The magma column is assumed to be a circular cylinder, which is open to the atmosphere at the top, and which opens into a large magma chamber below. The magma itself is treated as a fluid, and the surrounding bedrock is taken to be rigid. An explosive source near the base of the magma column excites the natural resonances of the conduit. These resonances result in displacement of the magma surface, which acts as a piston radiating sound into the atmosphere. The source is modeled in much the same way as an underwater explosion from a high-explosive chemical such as TNT, although in the case of the volcano the detonation mechanism is the ex-solution of magmatic gases under extremely high hydrostatic pressure. The new theory shows compelling agreement with airborne acoustic signatures that were recorded in July 1994 at a distance of 150 m from the western vent of Stromboli volcano, Italy. The theoretical and observed power spectra both display the following features: (1) four energetic peaks below 20 Hz, identified as the first four longitudinal resonances of the magma column; (2) a broad minimum around 30 Hz, interpreted as a source-depth effect, occurring because the source lay close to nulls in the fifth and sixth longitudinal resonances and thus failed to excite these modes; and (3) radial resonance peaks between 35 and 65 Hz. On the basis of the theory, an inversion of the acoustic data from Stromboli yields estimates of the depth (≈100 m) and radius (≈16 m) of the magma column as well as the depth (≈83 m), spectral shape and peak shock wave pressure (≈1 GPa) of the explosive source. Most of the parameters estimated from the acoustic inversion compare favorably with the known geometry and source characteristics of Stromboli.

A recently introduced theoretical model of wave propagation in an unconsolidated, sandy marine sediment is discussed in this article. Essentially, the model consists of four analytical expressions, which specify four wave properties of the sediment, namely the speed and attenuation of the compressional and the shear wave. These expressions contain just three unknown constants, which must be evaluated from data. A technique is described in which these constants are determined from measured values of the compressional wave speed, the shear wave speed, and the shear wave attenuation. This technique is applied to preliminary data from O.N.R.s SAX'99 recent experiment on a sandy sediment in the Gulf of Mexico. From the fully specified equations, the fourth wave property, the attenuation of the compressional wave, is computed and found to lie within 0.5 dB/m of the measured value. Based on this limited evidence, it appears that the wave properties of an unconsolidated sediment are highly correlated and predictable. According to the theory, the causal connections between the wave properties originate in the sliding of one micro/asperity against another on the surfaces of contact between contiguous grains in the medium.

A 1-km/sup 2/ area located 2 km off the Florida Panhandle (30/spl deg/22.6'N; 86/spl deg/38.7'W) was selected as the site to conduct high-frequency acoustic seafloor penetration, sediment propagation, and bottom scattering experiments. Side scan, multibeam, and normal incidence chirp acoustic surveys as well as subsequent video surveys, diver observations, and vibra coring, indicate a uniform distribution of surficial and subbottom seafloor characteristics within the area. The site, in 18-19 m of water, is characterized by 1-2-m-thick fine-to-medium clean sand and meets the logistic and scientific requirements specified for the acoustic experiments. This paper provides a preliminary summary of the meteorological, oceanographic, and seafloor conditions found during the experiments and describes the important physical and biological processes that control the spatial distribution and temporal changes in these characteristics.