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This paper presents an atmospheric propagation model, based on ray acoustics, that accounts for realistic weather conditions in the evaluation of the noise footprint of an aircraft. Noise sources, obtained using the Ffowcs Williams and Hawkings acoustic analogy applied to scale-resolved flow simulation data, are stored on a hemisphere surrounding the vehicle. These noise sources are propagated using a propagation model that takes into account the vertical variability of air temperature and wind velocity. The electric vertical takeoff and landing aircraft, presented by Casalino, van der Velden, and Romani [(2019). in Proceedings of the AIAA Scitech 2019 Forum, January 7-11, San Diego, CA, pp. 1834-1851], is used as a case study; noise footprints, obtained considering various vertically varying temperature and wind velocity distributions, are compared. It is shown that weather conditions in the acoustic wave propagation can contribute to mismatch up to 4 dBA in the illuminated zone and a significant drop in the refractive shadow zone caused by the vertical air temperature and wind velocity gradients. This work constitutes the first accomplishment in including realistic atmospheric effects in aircraft community noise prediction based on scale-resolved flow simulations.

Scale-model tank experiments offer a controlled environment in which to make underwater acoustic propagation measurements that can provide high-quality data for comparison with numerical models. This paper presents results from a scale model experiment for a translationally invariant wedge with a 10° slope fabricated from closed-cell polyurethane foam to investigate three-dimensional (3-D) propagation effects. A computer controlled positioning system accurately located a receiving hydrophone in 3-D space to create a dense field of synthetic vertical line arrays, which are subsequently used to mode filter the measured pressure field. The resulting mode amplitudes show the modal propagation zone, the modal shadow zone, and the classical intra-mode interference pattern resulting from rays launched up and along the slope. The observed features of the measured data are compared to three different propagation models: an exact, closed-form solution for a point source in wedge with pressure release boundaries, a 3-D ray trace model, and an adiabatic model. Examination of the mode amplitudes produced by the models reveals how the effects of vertical mode coupling can be observed in the measured data.

This article aims to investigate if the proportion of the rotor area of a wind turbine that is in the refractive shadow zone according to a ray tracing algorithm coupled to meteorological forecast data is correlated to sound levels and amplitude modulation. The acoustic station is situated 950 m from a wind farm in Northern Sweden and the measurement period is seven months. On average, 1.9 dBA lower sound levels are measured when the part of the rotor disk of the closest turbine is in the refractive shadow zone. A higher probability of amplitude modulations are observed when around half of the turbine rotor is within the refractive shadow zone compared to conditions with no shadow zone present.

Underwater noise from impact pile driving of 512 -m-long conductor casings was measured at a deep-water offshore oil platform in the Santa Barbara Channel. Beamforming measurements, obtained with a vertical array, confirmed that the primary wave front generated by hammering the conductor casing was a Mach cone propagating at an angle of 17.6° below the horizontal. Analysis of the processed array data also revealed the presence of high-frequency secondary waves at angles steeper than 45° below the horizontal. These secondary waves, which appeared to be generated near the sea-surface, dominated the acoustic spectrum of the pulses at frequencies above 1 kHz. Shallow hydrophone measurements outside the Mach cone showed clear evidence of a surface shadow zone, which was caused by the strong downward directivity of the source. Although reflected waves, diffraction, and secondary waves still produced sound inside the surface shadow zone, sound levels were 10-15 dB lower in this region. Long-term hydrophone measurements showed that there was little difference (±1 dB) in mean sound levels from impact hammering of different conductors installed at the same platform over three months.

Ocean acoustic tomography depends on a suitable reference ocean environment with which to set the basic parameters of the inverse problem. Some inverse problems may require a reference ocean that includes the small-scale variations from internal waves, small mesoscale, or spice. Tomographic inversions that employ data of stable shadow zone arrivals, such as those that have been observed in the North Pacific and Canary Basin, are an example. Estimating temperature from the unique acoustic data that have been obtained in Fram Strait is another example. The addition of small-scale variability to augment a smooth reference ocean is essential to understanding the acoustic forward problem in these cases. Rather than a hindrance, the stochastic influences of the small scale can be exploited to obtain accurate inverse estimates. Inverse solutions are readily obtained, and they give computed arrival patterns that matched the observations. The approach is not ad hoc, but universal, and it has allowed inverse estimates for ocean temperature variations in Fram Strait to be readily computed on several acoustic paths for which tomographic data were obtained.

The mesoscale eddies are the most common mesoscale phenomena in the ocean. The cold and warm water carried by the mesoscale eddies can significantly change the structure of the sound speed field, which is the key factor affecting long range deep-water sound propagation. In this presentation, a deep-sea analytical eddy model [Henrick et al., JASA 62, 860–870(1977) ] is used to determine the sound speed distributions produced by cold eddy in the southwest of the South China Sea. The statistical characteristics of the influence of eddies on the acoustic propagation are investigated with a range-dependent parabolic equation (PE) model to asses the effects of the relative position of sound sources and eddies, the frequency sensitivity, the acoustic energy deviation of the convergence zone and the shadow zone for long-range (600 km) low frequency (50 Hz) sound propagation in this ocean model. Specific features of the induced sound propagation variability such as the travel time deviation and the standard deviation of ensemble intensity Will be quantified. Finally, the refraction due to mesoscale eddies on large scale low-frequency propagation is discussed using the full three-dimensional parabolic (FOR3D) and explaining by the full three-dimensional ray theory (Bellhop3D).

Modeling of acoustic field metrics for transient seismic signals in ocean environments is required for the regulatory and resource management purposes. The validation by calibrated measurements is a critical step to assess model’s accuracy. The talk discusses acoustic metrics derived from the field data collected in the Northern Gulf of Mexico. The purpose of the experiment was to characterize 3-dimemsional field of the industrial seismic exploration array. Received Sound Pressure Levels of direct arrivals showed a large variability (up to 50 dB re 1 μPa) for a fixed distance between source and receiver indicating that the distance cannot be used as a single parameter to derive meaningful exposure thresholds. However, the far-field primary acoustic field variations with distance along the true acoustic path for a narrow angular bin are accurately predicted using a simplified model of the theoretical monopole source in free space. The source level of a monopole depends on radiation direction. The different acoustic metrics show robust relationships. As distance between source and receiver increases, the direct arrival may not be present (shadow zone). In this case more comprehensive propagation modeling is required. [Research funded by the Sound and Marine Life Joint Industry Programme.]Modeling of acoustic field metrics for transient seismic signals in ocean environments is required for the regulatory and resource management purposes. The validation by calibrated measurements is a critical step to assess model’s accuracy. The talk discusses acoustic metrics derived from the field data collected in the Northern Gulf of Mexico. The purpose of the experiment was to characterize 3-dimemsional field of the industrial seismic exploration array. Received Sound Pressure Levels of direct arrivals showed a large variability (up to 50 dB re 1 μPa) for a fixed distance between source and receiver indicating that the distance cannot be used as a single parameter to derive meaningful exposure thresholds. However, the far-field primary acoustic field variations with distance along the true acoustic path for a narrow angular bin are accurately predicted using a simplified model of the theoretical monopole source in free space. The source level of a monopole depends on radiation direction. The different...

Deep seafloor (~5000 m) observations of seismoacoustic arrivals are presented from the Aloha Cabled Observatory (ACO), Hawaii-2 Observatory (H20), and Ocean Seismic Network-1 (OSN1). Acoustic observations of local earthquakes from the ACO 24 kHz hydrophone show extraordinarily high frequencies up to 165 Hz at distances to ~200 km—a unique window into earthquake source dynamics. Combined seismic and hydrophone observations show that the traditional T wave propagates as a seismoacoustic polarized interface wave “Ti” coupled to the seafloor. Seismoacoustic Ti waves propagating at the sound speed of water are routinely observed over megameter distances at H2O between Hawaii and California, even though the seafloor site is within the shadow zone for acoustic wave propagation. Internal waves or thermohaline covariation may or may not be sufficient to scatter acoustic energy from the SOFAR channel to the deep seafloor. Ti has also been observed on seismometers SSW of Oahu at the OSN1 site at the seafloor and within an ODP borehole 242 m into the basalt basement. The observation of Ti from an earthquake in Guatemala at OSN1, whose path is blocked by the Island of Hawaii, is consistent with scattering from the vicinity of the Cross Seamount.

A weather balloon filled with carbon dioxide gas is used as a positive spherical acoustic lens. High frequency but audible sound from a circular loudspeaker ensonifies the balloon and produces increased sound pressure levels in a region along the principal axis according to a ray acoustics model. This enhancement was measured experimentally and was found to agree with theory. The possibility that interference from reflected sound off walls or the floor could mask or mimic the expected focusing was countered by calculating and measuring within a "shadow zone" in which only direct rays or rays refracted by the balloon exist by the method of Fresnel volumes. The experiment described in this paper would be a suitable learning experience for junior high and high school students showing how rays and Snell's law apply to sound as well as light and giving them a measurable predicted focal region for enhanced sound pressure levels.

The sound field temporal correlation and spatial correlation, which are the foundation of the investigation of underwater signal space-time high-order characteristics, have important value in the underwater acoustic application. The spatial correlation is studied based on the shallow water acoustic propagation experiment data acquired in the northern South China Sea in 2017, and the deep water acoustic propagation experiment data acquired in the western Pacific in 2013. As for the explosive sound signals in shallow water, time domain waveform cross-correlation coefficients between signals from different propagation distance are calculated. In contrast, the linear frequency modulated signals in deep water need additional matched filtering. The signal processing results shows that, the overall spatial correlation is poor and the correlation radius is relatively small in shallow water, the convergence zone has an obviously better spatial correlation than the shadow zone for the deep water situation. The processing result is verified by simulation and analysis.

It is difficult to distinguish between surface and underwater targets in passive detecting with a single sensor or a horizontal linear array in deep water. It is noticed that targets in different depths have different characteristics in time delay difference of rays. This paper takes advantage of this feature to discriminate targets' depths in direct-arrival zone and shadow zone in deep water. And the relation between judgment boundary and depth of sensor is analyzed. The simulation result shows that when the depth of sensor is 50m, the boundary which can distinguish between surface and underwater targets can be set to 10m. And the depth of the boundary decreases with the increase of the depth of sensor.

Receptions, from a ship-suspended source (in the band 50-100 Hz) to an ocean bottom seismometer (about 5000 m depth) and the deepest element on a vertical hydrophone array (about 750 m above the seafloor) that were acquired on the 2004 Long-Range Ocean Acoustic Propagation Experiment in the North Pacific Ocean, are described. The ranges varied from 50 to 3200 km. In addition to predicted ocean acoustic arrivals and deep shadow zone arrivals (leaking below turning points), "deep seafloor arrivals," that are dominant on the seafloor geophone but are absent or very weak on the hydrophone array, are observed. These deep seafloor arrivals are an unexplained set of arrivals in ocean acoustics possibly associated with seafloor interface waves.

Multimegameter-range acoustic data obtained by bottom-mounted receivers show significant acoustic energy penetrating several hundred meters into geometric shadow zones below cusps (caustics) of timefronts computed using climatological databases [B. D. Dushaw et al., IEEE J. Ocean. Eng. 24, 202-214 (1999)]. This penetration is much larger than predicted by diffraction theory. Because these receivers are horizontal arrays, they do not provide information on the vertical structure of the shadow-zone arrivals. Acoustic data from two vertical line array receivers deployed in close proximity in the North Pacific Ocean, together virtually spanning the water column, show the vertical structure of the shadow-zone arrivals for transmissions from broadband 250-Hz sources moored at the sound-channel axis (750 m) and slightly above the surface conjugate depth (3000 m) at ranges of 500 and 1000 km. Comparisons to parabolic equation simulations for sound-speed fields that do not include significant internal-wave variability show that early branches of the measured timefronts consistently penetrate as much as 500-800 m deeper into the water column than predicted. Subsequent parabolic equation simulations incorporating sound-speed fluctuations consistent with the Garrett-Munk internal-wave spectrum at full strength accurately predict the observed energy level to within 3-4-dB rms over the depth range of the shadow-zone arrivals.

Combined seismic and hydrophone observations show that the traditional T wave propagates as a seismoacoustic polarized interface wave (Ti) coupled to the seafloor. Seismoacoustic Ti waves propagating at the sound speed of water are routinely observed over megameter distances at the deep (4979 m) seafloor Hawaii-2 Observatory (H2O) between Hawaii and California, even though the seafloor site is within a shadow zone for acoustic wave propagation. Ti has also been observed on seismometers 225 km SSW of Oahu at the OSN1 site at the seafloor and within an ODP borehole into the basalt basement. Analyses of timing, apparent velocity, energy, and polarization of these interface waves are presented. At low frequency (approximately 5 Hz) Ti propagates dominantly in the sediments and is consistent with higher-mode Rayleigh waves. At higher frequencies the observed Ti waves dominantly propagate acoustically with characteristics suggesting local scattering. The observation of Ti from an earthquake in Guatemala at OSN1, whose path is blocked by the Island of Hawaii, is consistent with scattering from the vicinity of the Cross Seamount.

The formalism of D. Chu [J. Acoust. Soc. Am. 86, 1883–1896 (1989)] is used to perform an investigation of the spatial and time domain variations of the scattered field of a penetrable isovelocity wedge. The direct, reflected, and diffracted field components are considered, and the relationships between them are investigated. The density contrast surface is an appropriate model for many water–seafloor interfaces and, since diffractions often dominate scattering from rough surfaces, an emphasis is placed on achieving an improved description and understanding of these waves. Particular emphasis is placed on a detailed study of the wave phenomena and transition behavior around the forward scattering shadow boundary, where the causal relationship between the direct incident field and the diffracted field is specifically examined. At the apex the two fields coincide, and their propagational effects here, and also above and below the geometrical shadow zone, lead to complicated temporal and azimuthal variations of the field. The origin and behavior of diffractions associated with specular reflections of the source in the faces of the wedge is also studied. [Work supported by ONR.]

Geometrical acoustics predicts the amplitude of sonic booms only within the carpet. Inside the geometrical shadow zone, a nonlinear, geometrical theory of diffraction in the time domain is proposed. An estimation of magnitude orders shows that nonlinear effects are expected to be small for usual sonic booms. In the linear case, the matching to geometrical acoustics yields an analytical expression for the pressure near the cutoff. In the shadow zone, it can be written as a series of creeping waves. Numerical simulations show that the amplitude decay of the signal compares favorably with Concorde measurements, while the magnitude order of the rise time is correct. The ground impedance is shown to influence the rise time and peak amplitude of the signal mostly close to the cutoff. In the case of a weakly refractive atmosphere (low temperature gradient or downwind propagation), the transition zone about the cutoff is large, the transition is smooth, and the influence of ground absorption is increased.

In this work, receiver-to-receiver path losses calculated from measurements of underwater explosions in shallow water (water depth ∼15 m) off the coast of Virginia Beach, VA will be presented. Within the approximate frequency range of 40 to 70 Hz, these data have path losses that suggest energy increasing with range by up to 10 dB. Above this frequency range, these data show energy decreasing with range as expected. An analytical model [Frisk, George V., “Determination of sediment sound speed profiles using caustic range information,“ Bottom-Interacting Ocean Acoustics. Springer, US, 1980, 153–157] and numerical propagation models will be used to show that these path losses can be attributed to an upward refracting sound speed gradient in the sediment. This upward refraction of sound waves propagating in the seabed results in the formation of caustics that define shadow zone boundaries. Below the cutoff frequency of the waveguide, receivers in the shadow zone will exhibit lower sound levels than receivers...

The frequency-difference and frequency-sum autoproducts are quadratic products of nonzero-bandwidth frequency-domain acoustic fields at different frequencies but the same spatial location. The autoproducts have been shown to mimic genuine lower- or higher-frequency, out-of-band, acoustic fields within some limitations (Worthmann and Dowling, 2017, JASA 141, 4579–4590). Previous analysis of the autoproducts considered only spatial regions of the environment that were well-ensonified by the in-band acoustic field, which itself is well-described by the ray-approximation. In this presentation, the necessity of this well-ensonified restriction is analyzed by comparing autoproduct fields with their out-of-band analogues in and near acoustic shadow zones created by refraction. The results presented are derived from exact or asymptotic solutions of the Helmholtz equation. The propagation environment chosen for this study is a horizontal, range-independent, stratified, unbounded, truncated-n 2-parabolic waveguide, which creates acoustic shadow zones in some regions of the acoustic field. By analyzing the autoproducts near the transition from well-ensonified region to shadow zone, the potentially detrimental effects of diffraction on the autoproducts’ mimicry of out-of-band acoustic fields can be analyzed and quantified. [Sponsored by ONR and NSF.]

Water depth has significant effects on sound propagation in underwater. A deep-water propagation experiment along two different tracks with the flat and uneven bottoms was conducted in the South China Sea in 2014. Some different propagation phenomena and horizontal-longitudinal correlations oscillation patterns were observed. Due to the reflection-blockage effects by a sea hill with height less than 1/10 water depth, transmission losses increase up to about 8 dB in the reflection area of the sea hill than that of flat bottom. Moreover, there is an inverted-triangle shadow zone with a maximal depth of 1500 m below the sea surface. The horizontal-longitudinal correlations in the reflection area of the sea hill do not show an obvious cyclical oscillation any longer as that in flat bottom environment. The differences of the transmission losses and the horizontal-longitudinal correlations oscillation patterns are explained by using the ray theory. [Work supported by the National Natural Science Foundation of China under Grant Nos. 11434012, 41561144006, and 11404366.]

Each summer, large-scale detonations are carried out at the Utah Test and Training Range (UTTR) west of Salt Lake City. In 2016, acoustic sensors were placed at ranges up to 90 km east of the UTTR test site. The frequencies of the recorded signals indicate that they are infrasonic waves. The travel times imply that they are direct arrivals although the sensors lie within a shadow zone. Finally, the signal amplitudes indicate that acoustic propagation is nonlinear near the source. Consequently, numerical simulations that account for diffraction, and the effects of strong shocks are required to accurately map infrasound propagation into this region. A finite difference time-domain infrasound propagation method is applied to these signals. The algorithm relies on the assumption that the environmental model is azimuthally symmetric about the source location, allowing for efficient numerical computation of acoustic propagation from a spherical source. For each detonation, numerical computations are performed a...

The paper deals with the reduction of the sound energy in the shadow region behind barriers by means of an attached body at the edge of the screen. The reflecting attributes of the barrier’s headpiece are described by a locally reacting impedance. Diffraction at ideal soft and hard bodies demonstrates the basic principle of tangential power transport parallel to their surface: the impedance must be chosen so that the tangential intensity near the edge is lowered, turning the incoming power in harmless directions. The differences due to finite impedances are then discussed. The physical principles are demonstrated in frozen pictures of the sound field for the different cases. Theoretical computations show considerably improved levels in the shadow zone for larger angles of diffraction. These are compared with empirical results, and practical applications are discussed.

Small-scale laboratory experiments have been conducted to study the propagation of sound over a curved, rough, rigid, convex surface in the range kR=275–550, and ke=0.09–0.18, where k is the wave number, R the radius of curvature, and e the characteristic roughness length scale of steep-sloped, densely packed scatterers. Experimental results are presented at 6, 8, and 12 kHz, with the receiver successively on the surface, along the line of sight behind the surface, and along a vertical axis in the shadow zone. At low frequencies (f=6 kHz, ke=0.09), a boundary wave caused by coherent multiple scattering develops near the surface, creeps into the deep shadow zone, and increases the sound-pressure levels measured in the deep shadow zone by up to 8 dB as compared to the levels measured in the absence of surface roughness. At high frequencies (f=12 kHz, ke=0.18), surface roughness causes incoherent scattering and decreases the measured sound-pressure levels by about 10 dB on the surface, in the shadow zone, an...

Sound generally reaches the shadow zone behind a noise barrier by diffraction, or scattering, from the edge at the top of the barrier. By redirecting the incident sound into the shadow zone, the edge acts as a line source. For the traditional straight-edge barrier, the line source is coherent. Since a crooked line source is less coherent, we propose to improve barrier performance by making the edge randomly jagged. Laboratory model experiments to compare insertion loss of straight- and jagged-edge barriers are reported here. A spark was used as a point source, the barriers were thin (compared to a wavelength), and ground and meteorological effects were not important. After preliminary measurements showed that a jagged edge can produce significantly more insertion loss at high frequency, a three level full factorial experiment was done. The results led to an empirical equation for insertion loss of a jagged-edge barrier. Improvement over the straight barrier was found to increase with jaggedness. An unexplained result was the poorer performance of the jagged-edge barrier at low frequency.

Measurements made by Havelock et al. show that above a few hundred Hertz, the sound levels in a refractive shadow zone are weakly dependent on frequency. Parabolic equation calculations made recently by Di and Gilbert indicate that the weak frequency dependence is consistent with scattering from small‐scale turbulence governed by a Kolmogorov spectrum. In this paper a theoretical analysis is presented using the distorted‐wave Born approximation (DWBA) to show why the Kolmogorov spectrum leads to the observed weak frequency dependence. Using DWBA, the problem of scattering by turbulence is formulated in terms of a sampling function that shows the physical origin of the frequency dependence by showing what part of the turbulence spectrum contributes in a typical measurement of levels in a refractive shadow. Results from the DWBA analysis are compared with the data of Havelock et al. and with parabolic equation calculations. [Work supported by the Army Research Laboratory and the Applied Research Laboratory.]

The present study formulates a consistent method to simulate the outdoor, near-surface sound propagation through realistic refractive conditions. The correlated atmospheric stratification and turbulence properties are derived from standard meteorological quantities through flux-profile similarity relationships. The propagation of a monochromatic sound field is simulated in presence of the turbulence and stratification effects and an impedance ground. The propagation model uses a numerical solution of a second-order moment parabolic equation, which is introduced and evaluated. The so-formed coupled atmospheric-acoustic model is used to systematically investigate the sound levels in near-surface refractive shadows. In an illustrative propagation scenario, the shadow zone sound levels are predicted to show significant variations with the meteorological conditions. Specifically, the sound levels decrease with the adverse wind, as a consequence of enhanced mean upward refraction. Conversely, they increase with the absolute value of the surface heat flux, as a consequence of enhanced turbulence scattering. Implications for the assessment of the sound levels in shadow zones are discussed.

Interacting low‐frequency acoustic propagation effects of range‐dependent oceanographic sound‐speed profiles and range varying topography, with a fluid sediment layer, are modeled in the Gulf Stream region using a parabolic approximation to the Helmholtz equation. Oceanographic frontal effects, monotonically upsloping and downsloping topographic effects are identified in propagation between reciprocally chosen points on either side of the Gulf Stream at frequencies of 25, 50, and 100 Hz. For propagation from Slope to Sargasso water, surface shadow zone formation is documented, and ensonification of the shadow zone due to low‐frequency diffraction. In propagation from Sargasso to Slope water, increased surface ensonification results. Topographic effects include truncation/reflection of deep propagation paths for upsloping topography, and increased depth for water column refraction for downsloping topography. Frequency and source depth‐dependent oceanographic and topographic interaction effects are document...

Field experiments and numerical simulation show that due to scattering from internal-wave-induced sound speed perturbations, the sound energy at megameter ranges penetrates well below the unperturbed timefront, i.e., into the geometric shadow. Shadow zone arrivals form continuations of cusps of the timefront. In the present paper, this effect is analyzed using a stochastic ray theory derived for statistical description of chaotic rays. Probability density functions for parameters of perturbed rays, including those penetrating into the shadow zone, are evaluated analytically. This made it possible to derive analytical estimates for a vertical extent of shadow zone arrivals and for a coarse-grained distribution of sound energy in the shadow zone. It is shown that the lengths of cusp extensions into the shadow zone grow with range r as r(1/2). A known estimate for the spread of timefront segments in the presence of internal waves is applied for obtaining a criterion of nonoverlapping of the cusp continuations. These results are derived for steep rays whose grazing angles at the sound channel axis exceed 5°.

The radiation pattern of a focused transducer is reexamined. The radiation field is divided into an illuminated zone and a shadow zone. A numerically convergent solution of the pressure distribution in terms summations of Bessel functions is provided. This solution is computationally more advantageous than earlier results where a double or single integral in the complex plane is required. The pressure amplitude differs from earlier reports slightly for off-axis locations at low frequency. This difference may have significance for backscatter coefficient determination where scatterers are assumed present over a time-gated volume. The solution for a flat disk radiator is obtained as a limiting case.

Surface ducts are formed by wind mixing at the sea surface and are a common feature in many of the world’s oceans. These surface ducts have the effect of channeling acoustic energy for long ranges. This paper, however, focuses on the energy that leaks out of the surface duct—paths that are typically neglected by ray models. It is found that the leakage energy at lower frequencies can be surprisingly strong so that a receiver in a ray‐theory shadow zone is actually well insonified. Furthermore, the leakage energy is refracted back into the duct where it may dominate the ducted paths. Inside the duct, these two arrivals add up constructively or destructively resulting in anomalously high or low acoustic levels in the surface duct relative to a prediction that neglects the leaky arrival. Thus, a full‐wave model is needed; however, certain types of parabolic equations (PEs) fail for these problems because they scramble the phases of the two dominant arrivals. The same mechanism that causes the PEs to fail makes the problem very sensitive to environmental data. For instance, a change in the mean duct speed of 0.5 m/s can also produce large changes in the acoustic levels.

Previous work on sound propagation past curved rough rigid surfaces demonstrated substantial changes in the insertion loss in the shadow zone due to the roughness ranging from +6 to -20 dB from their smooth counterparts. These previous data also lead to new propagation modeling efforts to incorporate the effects of roughness via an impedance model but the data and modeling efforts were limited to a narrow range of roughness and hill sizes. The current effort was designed to expand the range of roughness and hill sizes in order to explore the range of influence of the roughness. The work presented here confirms the effects of surface roughness as observed in previous work and indicates where the effects of roughness begin to emerge as well as where they transition between decreasing the insertion loss to increasing the insertion loss.

A 1960 experiment is examined in which sound from three underwater explosions near Perth, Australia, was detected near Bermuda. A recent attempt [Munk et al., J. Phys. Ocean. 18, 1876 (1988)] to calculate propagation paths for this event included rotational flattening of the Earth and horizontal refraction determined from the vertical sound speed minimum. That calculation left Bermuda in a shadow zone. The current work invokes adiabatic mode theory to include refraction due to horizontal variations in the vertical mode structure. These results include separate horizontal rays for each of the first few vertical modes, using an archival data set of 230 ocean sound profiles to generate the modes numerically. Where appropriate, interaction with bathymetry is included. This solution possesses two eigenray groups: Group A passes just south of the Cape of Good Hope, at which point group B is almost 1000 km to the south. Intermediate rays are blocked by islands. Group A proceeds unimpeded to Bermuda for a total t...

A recursive solution procedure is developed to analyze the acoustical scattering by multilayer concentric circular cylindrical scatterers. The procedure is based on multiple scattering in the single-scatterer methodology originally proposed by one of the authors. The solution for a scatterer having an arbitrary number of layers is solved by recursively using the solution for a dual-layer scatterer. The solution procedure and its implementation are extensively validated. Computational characteristics, including potential pitfalls and their avoidance, are explored. The solution procedure can be used to analyze scatterers with continuously varying properties in the radial direction by approximating such a scatterer as a multilayer system. A comprehensive numerical example shows an interesting phenomenon: when a planar wave impinges onto a cooling tube in air, instead of forming a shadow zone, a strongly collimated beam is formed behind the cooling tube. This phenomenon can be explained as due to the gradient-index acoustical lens that is created around the cooling tube, which bends the sound and collimates it in the forward direction.

Detailed experimental impulse‐propagation results measured in a refractive atmosphere over grassland at distances up to 200 m from the source are compared with two residue‐series forms of creeping‐wave theory. Results are compared both prior to and inside the meteorological shadow zone. Although the theory, derived assuming a linear sound‐speed gradient, correctly accounts for changes in source–receiver geometry and ground impedance, it consistently underpredicts levels deep within the shadow zone. An empirical method for including the effects of a nonlinear gradient is also considered.

Experimental measurements were conducted around a right-angle wall to investigate the effect of this obstacle on sound propagation outdoors. Using small explosions as the source of the acoustic waves allowed reflected and diffracted arrivals to be discerned and investigated in detail. The measurements confirm that diffraction acts as a low-pass filter on acoustic waveforms in agreement with simple diffraction theory, reducing the peak pressure and broadening the waveform shape received by a sensor in the shadow zone. In addition, sensors mounted directly on the wall registered pressure doubling for nongrazing angles of incidence in line-of-sight conditions. A fast two-dimensional finite difference time domain (FDTD) model was developed and provided additional insight into the propagation around the wall. Calculated waveforms show good agreement with the measured waveforms.

There is an effort to develop metamaterials for cloaking objects in a way that eliminates backscattering and fills in the shadow zone. The development of this cloaking material for spherical and other shapes would inhibit the acoustic detection of objects, such as mines, torpedoes, UUV's, and, ultimately, submarines by a means which would make them invisible to acoustic waves. It has, however, been pointed out that this form of inactive cloaking could cover a target in a way that shields the target from using its own acoustic sonar means for detecting the source, unless the cloaking could be turned off. We address this issue by presenting an active cloaking transducer system which effectively cloaks the target and yet can also be used as an acoustic sonar system. Equivalent circuits and finite element models are used to demonstrate transducer cloaking. This would have been a good transducer project for Kim Benjamin to implement and I believe he would have enjoyed the challenge and developed one of the best cloaking transducer arrays possible.

Fast field programs are known to produce spurious oscillations for sound level predictions deep within a shadow zone. These oscillations are actually a Gibbs phenomenon, and can be reduced by applying an appropriate window function prior to Fourier transformation of the radial wave‐number spectrum. Errors caused by finite sampling of the wave‐number spectrum are also discussed.

The estuarine environment often hosts a salt wedge-a layer of denser seawater advected by the rising tide under fresh water discharged by the river. The nature of the stratification is a function of the tide's range and speed of advance, river discharge volumetric flow rate and river mouth morphology. The competing effects of temperature and salinity on sound speed present the question: Is the salt wedge acoustically observable? Using temperature and salinity profiles collected in situ, numerical results show that the salt wedge can impact acoustic propagation. Acoustically, this environment can be approximated by two isospeed layers separated by a thin gradient. While this three-layer very shallow water acoustic waveguide is typically dominated by high angle multipath propagation, refraction occurring in the gradient layer allows low-angle energy from near-surface sources to be trapped above the gradient and creates a shadow zone below the gradient. Energy from near-bottom sources is refracted to higher angles and attenuated more quickly. Acoustic fluctuations observed at an upstream/downstream receiver depend upon the presence/absence of bedforms and the interaction between the advancing/receding tide and the river discharge, which can include the presence of internal waves propagating along the top of the salt wedge.

JASCO Applied Sciences performed acoustic modeling and measurements to calculate marine mammal exclusion zones for Chevron Canada Limited’s 2012 Sirluaq 3-D seismic program in the Canadian Beaufort Sea. The Sirluaq survey was located in deep water (>650 m), on and beyond the continental slope, and presented unique challenges from both modeling and measurement standpoints. The modeling was performed with JASCO’s Marine Operations Noise Model (MONM), which uses a parabolic-equation-based algorithm to accurately predict N×2-D sound propagation in ocean environments. Sound levels were measured with five calibrated Autonomous Multichannel Acoustic Recorder (AMAR) systems at distances of 50–50 000 m from the airgun array, in water depths ranging from 50 to 1500 m. The sensors were laid out to capture sound levels in both the broadside (perpendicular to survey line) and endfire (along the survey line) directions. The high-resolution digital recordings of seismic sounds were analyzed to determine peak and rms sound pressure levels (SPL), and sound exposure levels (SEL) as functions of range from the airgun array. The model estimates were generally conservative; however, the model predictions at the specific depth of the receivers accurately predicted the existence of a shadow zone and the overall transmission loss trend.

The seismo-acoustic field in a range dependent fluid-elastic environment can be computed from elastic coupled modes. Range dependence breaks the strict mathematical orthogonality of the modes causing energy to be exchanged among the elements of the modal spectrum. The original theory is from Maupin (1988). Range-dependent propagation effects are illustrated for a 2-D model including a seamount. The mode coupling is directly proportional to the bathymetric slope of the range dependence. While the range-dependent environmental model is composed of vertical slices, no iteration is required to solve for both the transmitted and the reflected seismo-acoustic field, which is found by solving a matrix Riccati equation for the modal reflection and transmission matrices. A particular feature of the elastic coupled modes is the automatic inclusion of the interface Scholte wave modes, which are absent from any all-fluid environmental propagation model. The excitation of the Scholte modes may be important for observed deep shadow zone acoustic arrivals. The coupled mode results will be compared to the results from an elastic parabolic equation (PE). [Work supported by ONR.]

In this research project, Finite Element Numerical Modeling Method is used to compute the low frequency acoustical insertion losses of barriers with different edge shapes. Rectangular, Round Edge and Couple Round Edge barriers are included. The coupled round edge barrier is a hollowed round edge barrier with a slit on the round edge and a tube with a slit placed at the center of the hollow space of the round edge. The result shows that the coupled round edge barrier can produce a higher insertion loss on a specific range of low frequency noise in shadow zone. The shadow zone is also enlarged at the same time. The performance of the barrier is improved by the slit on the coupled round edge barrier under the dual resonator effect.

Besides numerical models, another way to model complex environments is using physical reduced‐scale models. This project used scale models to study several factors which may influence the performance of roadside noise barriers. One is the barrier absorption. Making the barrier sound absorptive decreases reflections and may decrease amplification between parallel barriers. The other is tree foliage growing near the barrier. Tree foliage may scatter sound into the shadow zone behind the barrier, increasing noise levels and decreasing the insertion loss. Tree foliage may also attenuate sound that would normally be diffracted into the shadow zone, actually increasing the insertion loss. A 1:31.5 scale model was created in an anechoic chamber to test the effects of these two factors. Excess attenuation measurements were performed to choose scale model materials, which accurately represent full scale surfaces. Parallel barriers were modeled with a reflective surface and their IL's were measured for different configurations of absorptive covering. IL's of single barriers were measured both with and without scale model trees placed either in front or behind them. The results are compared to previously performed field test measurements.

Receptions of long‐range acoustic transmissions by deep hydrophone arrays in the Pacific and Atlantic often have ‘‘ray‐like’’ arrivals that occur in the shadow zone of the predicted time front. These ‘‘ray‐like’’ arrivals can frequently be identified with the cusps of the predicted time front, but the receivers are up to 750 m below the depth of the cusps. Preliminary calculations show that the observed acoustic energy is not accounted for by errors in the sound speed, leakage of acoustic energy below the cusps as predicted by the full wave equation, or scattering due to internal waves. Data obtained during experiments in the Atlantic and Pacific will be reviewed. Experiments that have been conducted with receivers of vertical line arrays have not had receivers deep enough to observe this phenomena. The effect is seen when bottom‐mounted or midwater acoustic sources are used. These data present a number of problems: If the ray paths are wandering all over the water column, why are predictions of ray travel times usually accurate? How does the energy loss associated with these data increase the attenuation of very long‐range acoustic transmissions? Without knowing the forward problem, how can these data be used to determine oceanographic information?

Minimization of the sound pressure field within the shadow zone of a noise barrier is achieved by reducing the pressure gradient along a line, at the top of a barrier, via active noise control. The noise control effectiveness of a barrier is increased by this strategy, especially for specific system configurations. The proposed method was evaluated by numerical simulation. Results indicate that system orientation has little effect on minimizing the pressure gradient at the top of the barrier when the error sensors are invisible to the primary noise disturbance. Highly effective control within the shadow zone and close to the barrier is possible when the system is oriented at an angle where two or more error sensors are in line with the first diffracting edge and the primary noise disturbance. Increasing the spatial extent of the quiet zone is possible by increasing the number of control sources, where the error sensors have a line of sight with the primary noise disturbance. [Work supported by a fellowship (CRH) and grant (SKL) from the University of Nebraska ‐ Lincoln.]

In preparation for a field experiment, a numerical study of impulse propagation over a hill has been carried out. The near side of the hill corresponds to downward refraction with the associated ducted propagation. The far side of the hill corresponds to upward refraction with the associated shadow zone. Thus conditions corresponding to nighttime propagation (downward refraction) and daytime propagation (upward refraction) can be studied in the same experiment. Of particular interest is the propagation of surface waves over the hill and into the shadow zone on the far side of the hill. For selected values of hill curvature and ground impedance, numerical predictions are presented and discussed in relation to the envisioned experiment. [Research supported by the U.S. Army TACOM‐ARDEC at Picatinny Arsenal, New Jersey]

Two highly instrumented homes have been ensonified by low‐amplitude sonic booms. The resulting measurements have been analyzed (1) to gain insight to the dominant physical acoustics associated with sonic booms heard indoors and (2) to rank order the mechanisms needed for high‐quality auralizations. The mechanisms turn out to be both clear and elegant. Diffraction loading on the exterior surface is as expected with an enhancement around on the incident side of the home and a strong shadow zone at higher non‐dimensional frequencies. The resulting pressure loading induces modal vibration of the walls, ceiling, and windows; each of which show their first flexural modes at frequencies below 20 Hz. The walls themselves appear to break up into multi‐layered wave bearing structures around 100 Hz, above which the nonlinear contact and sliding mechanisms take on a dominant role in the signature. These insights have been combined to motivate a low‐dimensional tool for auralizing the complete audio bandwidth of booms heard indoors.

An unexplained set of arrivals has been observed on ocean bottom seismometers (OBSs) during the NPAL04 long‐range ocean acoustic propagation experiment in the North Pacific. The observed intensity pattern of the OBS arrivals is significantly more complex than the waterborne arrivals seen on the deep vertical line array (DVLA). These “deep seafloor” arrivals occur later than the first PE predicted arrival; their arrival time is not predicted by acoustic PE propagation models, they do not correspond to decay from shallower turning points (as is the case for deep shadow zone arrivals), and they are not readily observed on the DVLA hydrophone just 750 m above the seafloor. The arrival structure in the observed data, in time and amplitude, varies substantially between three OBSs that are separated by less than 4 km. Could these unexplained arrivals be scattering or horizontal multi‐path from persistent ocean thermal structure?

An isolated building, a fundamental case of urban acoustics, has recently been the subject of an experimental effort to characterize the building’s influence on propagating sound [Alberts and Noble, J. Acoust. Soc. Am. 121, 3064 (2007)]. As a precursor to modeling efforts involving finite‐difference time‐domain simulations, two common diffraction models, the frequency domain model of Pierce and Medwin’s extension of Biot and Tolstoy’s time‐domain model, have been utilized to estimate the sound pressure at various locations in the building’s acoustic shadow. The discussion will include the models used and comparisons between calculated and measured data, demonstrating reasonable agreement between measured and calculated spectra in limited cases at some frequencies.

To gain insight into the physical mechanisms responsible for deep shadow zone arrivals in long range ocean acoustic propagation we have characterized some key features of the replica correlated signals observed on an ocean bottom seismometer (OBS) deployed on the 2004 long‐range ocean acoustic propagation experiment. We compare the vertical seismometer data from an OBS at 4973‐m depth beneath the deep vertical line array (DVLA) with the deepest hydrophone on the DVLA at 4270 m depth. The results of the preliminary analysis show (1) that the vertical geophone channel has more arrivals than the deep DVLA hydrophone channels, (2) that the first arrivals on the OBS geophone and DVLA deep hydrophones correspond to energy in the first deep arriving path predicted by the parabolic equation solution, (3) that the later arrivals which are much larger in amplitude are not explained by the parabolic equation method, and (4) that it is the later arrivals that contribute to the long range (up to 3200 km) shadow zone “receptions.” Possible mechanisms for the later arrivals and some consequences of the observation are discussed. [This work was supported by the Office of Naval Research.]

Qualitative observations from bottom‐mounted US Navy SOSUS receiving stations in the North Pacific reveal anomalously deep acoustic arrivals at travel times directly corresponding with timefronts expected to have turned much higher in the water column. The vertical structure of these shadow zone arrivals was studied during SPICEX, a long‐range propagation experiment conducted from June to November 2004 in the North Pacific, utilizing moored sources 500 and 1000 km distant from two vertical line array receivers, which together virtually spanned the full ocean depth. Comparison of the measured absolute intensities of shadow zone arrivals with Monte Carlo parabolic equation simulations suggest that the amount of internal wave scattering associated with the standard Garrett‐Munk (GM) internal wave spectrum is not adequate to account for the extent of scattering into the acoustic shadow evident in the experimental data, suggesting either that the GM spectrum is not an appropriate representation of the internal...

The classical geometrical acoustics theory predicts the amplitude of sonic booms only within the carpet. Inside the geometrical shadow, the sound field is known to emanate from rays shed by creeping waves propagating along the ground. A new, nonlinear, time‐domain formulation of diffraction effects inside the shadow zone is given. The resulting equation is analogous to an unsteady, two‐dimensional, transonic equation. In the linear case, it can be solved, so that the dispersion equation for creeping waves is recovered. If only the least attenuated one is taken into account, an approximate equation of Burgers‐type describing the nonlinear propagation of the creeping wave can be deduced. A dimensional study indicates that nonlinear effects are small, except for small sound‐speed gradients. A numerical simulation shows that the amplitude decay of the signal compares favorably with Concorde measurements made by ISL at Biscarosse in 1973, at least sufficiently deep within the shadow zone. [Work supported by Aerospatiale Aeronautique–Toulouse.]