Anomalous reflection from a two-layered marine sediment.

This paper concerns the theory of acoustic reflection from a two-layered marine sediment, the upper layer of which consists of a fine-grained material (mud). The seawater above and basement below the layer are treated as homogeneous half-spaces. Within the mud layer, the density is taken to be constant, and three sound speed profiles are considered: uniform, linear, and inverse-square. The reflection coefficient exhibits a background component that is similar in all three cases, exhibiting only a weak sensitivity to the gradient of the profile, the frequency, and the depth of the layer. Additionally, the two profiles with a non-zero gradient, linear and inverse-square, exhibit a sequence across grazing angle of narrow spikes of total reflection. The angular distribution of this acoustic glint is highly sensitive to the frequency and depth of the layer, and mildly so to the gradient. As the gradient approaches zero, the glint vanishes and the reflection coefficient reduces identically to the form of a uniform sound speed profile. If it were detectable, the angular distribution of the glint, observed at several frequencies, could constitute a unique, sensitive set of "fingerprints," allowing the depth and sound speed gradient of the mud layer to be inferred.

On plane-wave reflection from a two-layer marine sediment: A surficial layer with linear sound speed profile overlying an iso-speed basement.

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.

On acoustic reflection from a seabed exhibiting a non-uniform sound speed profile, with relevance to fine-grained sediments.

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.

Are meal kits health promoting? Nutritional analysis of meals from an Australian meal kit service.

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 (<2000 mg). Meal kit recipes were found to have health promoting qualities, frequently including vegetable ingredients, however, improvements to recipes would make these meal kits more health promoting. Current diet intakes and the nutritional composition of meal kits recipes should be reviewed before being recommended by health professionals.

Wave speed and attenuation profiles in a stratified marine sediment: Geo-acoustic modeling of seabed layering using the viscous grain shearing theory.

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 dispersion formula and the Green's function associated with an attenuation obeying a frequency power law.

An attenuation obeying a frequency power law scales as |ω|ß , where ω is angular frequency and ß is a real constant. A recently developed dispersion formula predicts that the exponent ß can take only certain values in well defined, disjoint intervals. It is shown here that these admissible values of ß 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 ß. 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 ß in the interval (0.5, 1). This restriction supersedes the weaker constraints on ß derived from the dispersion formula alone. For the previously admissible values of ß 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.

Estimating the sound speed of a shallow-water marine sediment from the head wave excited by a low-flying helicopter.

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.

Wave-speed dispersion associated with an attenuation obeying a frequency power law.

An attenuation scaling as a power of frequency, |ω|(ß), over an infinite bandwidth is neither analytic nor square-integrable, thus calling into question the application of the Kramers-Krönig 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 < 0. Second, a wave equation is introduced that yields the phase-speed dispersion associated with a frequency-power-law attenuation. Finally, it is shown that, with minor modification, the Kramers-Krönig dispersion relations with no subtractions (the Plemelj formulas) do in fact hold for an attenuation scaling as |ω|(ß), yielding the same dispersion formula as the other two derivations. From this dispersion formula, admissible values of the exponent ß are established. Physically, the inadmissible values of ß, which include all the integers, correspond to attenuation-dispersion pairs whose Fourier components cannot combine in such a way as to make the impulse response, k(t), vanish for t < 0. There is no upper or lower limit on the value that ß may take.

Cross-correlation, triangulation, and curved-wavefront focusing of coral reef sound using a bi-linear hydrophone array.

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.

Analysis of shear-wave attenuation in unconsolidated sands and glass beads.

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.

On the spatial properties of ambient noise in the Tonga Trench, including effects of bathymetric shadowing.

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.

The origins of ambient biological sound from coral reef ecosystems in the Line Islands archipelago.

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.

Theory of the directionality and spatial coherence of wind-driven ambient noise in a deep ocean with attenuation.

Acoustic attenuation in seawater usually has little effect on the spatial statistics of ambient noise in the ocean. This expectation does not hold, however, at higher frequencies, above 10 kHz, and extreme depths, in excess of 6 km, an operating regime that is within the capabilities of the most recently developed acoustic instrument platforms. To quantify the effects of attenuation, theoretical models for the vertical directionality and the spatial coherence of wind-generated ambient noise are developed in this paper, based on a uniform distribution of surface sources above a semi-infinite, homogeneous ocean. Since there are no bottom reflections, all the noise is downward traveling; and the angular width of the directional density function becomes progressively narrower with increasing frequency because sound from the more distant sources experiences greater attenuation than acoustic arrivals from overhead. This narrowing of the noise lobe modifies the spatial coherence, shifting the zeros in the horizontal (vertical) coherence function to higher (lower) frequencies. In addition, the attenuation modifies the amplitudes of the higher-order oscillations in the horizontal and vertical coherence functions, tending to suppress the former and enhance the latter. These effects are large enough to be detectable with the latest deep-diving sensor technology.

The depth-dependence of rain noise in the Philippine Sea.

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.

Depth dependence of wind-driven, broadband ambient noise in the Philippine Sea.

In 2009, as part of PhilSea09, the instrument platform known as Deep Sound was deployed in the Philippine Sea, descending under gravity to a depth of 6000 m, where it released a drop weight, allowing buoyancy to return it to the surface. On the descent and ascent, at a speed of 0.6 m/s, Deep Sound continuously recorded broadband ambient noise on two vertically aligned hydrophones separated by 0.5 m. For frequencies between 1 and 10 kHz, essentially all the noise was found to be downward traveling, exhibiting a depth-independent directional density function having the simple form cos θ, where θ ≤ 90° is the polar angle measured from the zenith. The spatial coherence and cross-spectral density of the noise show no change in character in the vicinity of the critical depth, consistent with a local, wind-driven surface-source distribution. The coherence function accurately matches that predicted by a simple model of deep-water, wind-generated noise, provided that the theoretical coherence is evaluated using the local sound speed. A straightforward inversion procedure is introduced for recovering the sound speed profile from the cross-correlation function of the noise, returning sound speeds with a root-mean-square error relative to an independently measured profile of 8.2 m/s.

Cross-correlation in band-limited ocean ambient noise fields.

Observations of ambient noise in the ocean are generally band limited, because of the natural spectral shape of the noise or the restricted bandwidth of the detection system. Either way, the noise may be regarded as white noise to which a band-limiting filter has been applied. An analysis of the two-point cross-correlation function of such filtered noise is presented for two cases, isotropic and surface-generated noise. The most pronounced effects occur with high-pass and bandpass filters when the low-frequency cut-off falls well above the first few zeros in the coherence function. In this situation, the sensor separation is very many times the longest acoustic wavelength (associated with the lowest frequency) in the passband. The filtering then produces sharp pulses at correlation delays equal to the numerical value of the acoustic travel time between the sensors. Although these pulses are narrow, they have a finite width, within which a fine structure appears in the form of multiple rapid oscillations, due to the differentiating action of the filter. The number of such oscillations increases as the low-frequency roll-off of the filter becomes steeper. This fine structure is evident in several recently published experimental determinations of the cross-correlation function of band-limited ocean ambient noise.

Spatial coherence and cross correlation of three-dimensional ambient noise fields in the ocean.

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.

On the two-point cross-correlation function of anisotropic, spatially homogeneous ambient noise in the ocean and its relationship to the Green's function.

It is well established that the free-space Green's function can be recovered from the two-point cross-correlation function of a random noise field if the noise is white and isotropic. Ambient noise in the ocean rarely satisfies either of these conditions. However, a non-uniform spectrum could be pre-whitened by the application of a suitable filter but anisotropy cannot be so readily eliminated. To investigate the effects of vertical anisotropy, three azimuthally uniform, spatially homogeneous noise fields are analyzed, two of which are idealized, while the third is representative of ambient noise in the deep ocean. In each case, the coherence function, the cross-correlation function, and the derivative of the latter with respect to the correlation delay, are derived for vertical and horizontal alignments of the sensor pair. With vertical sensors, any step-function discontinuity in the directional density function is mapped into a delta function at an appropriate time delay in the derivative (with respect to time delay) of the cross-correlation function. No such mapping occurs with horizontal sensors. In this case, only horizontally traveling noise can generate delta functions in the derivative of the cross-correlation function, and these always appear at the retarded time on either side of the origin.

On the transient solutions of three acoustic wave equations: van Wijngaarden's equation, Stokes' equation and the time-dependent diffusion equation.

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.

On pore-fluid viscosity and the wave properties of saturated granular materials including marine sediments.

The grain-shearing (GS) theory of wave propagation in a saturated granular material, such as a marine sediment, is extended to include the effects of the viscosity of the molecularly thin layer of pore fluid separating contiguous grains. An equivalent mechanical system consisting of a saturating, strain-hardening dashpot in series with a Hookean spring represents the intergranular interactions. Designated the VGS theory, the new model returns dispersion curves that differ mildly from those of the GS theory at lower frequencies, below 10 kHz, where effects due to the viscosity of the pore fluid may be non-negligible. At higher frequencies, the VGS dispersion curves approach those of the GS theory asymptotically. The VGS theory is shown to match the SAX99 dispersion curves reasonably well over the broad frequency band of the measurements, from 1 to 400 kHz. This includes the frequency regime between 1 and 10 kHz occupied by Schock's chirp sonar data, where the viscosity of the pore fluid appears to have a discernible effect on the dispersion curves.