Source level of wind-generated ambient sound in the oceana)

Inference of source levels for ambient ocean sound from local wind at the sea surface requires an assumption about the nature of the sound source. Depending upon the assumptions made about the nature of the sound source, whether monopole or dipole distributions, the estimated source levels from different research groups are different by several decibels over the frequency band 10-350 Hz. This paper revisits the research issues of source level of local wind-generated sound and shows that the differences in estimated source levels can be understood through a simple analysis of the source assumptions.

Modelling sound particle motion in shallow watera)

Fish species and aquatic invertebrates are sensitive to underwater sound particle motion. Studies on the impact of sound on marine life would benefit from sound particle motion models. Benchmark cases and solutions are proposed for the selection and verification of appropriate models. These include a range-independent environment, with and without shear in the sediment, and a range-dependent environment, without sediment shear. Analysis of the acoustic impedance illustrates that sound particle velocity can be directly estimated from the sound pressure field in shallow water scenarios, except at distances within one wavelength of the source, or a few water depths at frequencies where the wavelength exceeds the water depth.

On definitions of signal duration, evaluated on close-range airgun signals

In impact assessments for underwater noise, the duration of a transient signal is often expressed by the 90%-energy signal duration τ90 %. Consequently, the rms sound pressure is computed over this duration. Using a large set of measurements on marine-seismic airgun signals, it is shown that τ90 % is often very close to the interval between the primary and secondary pulse (the bubble period) or a small integer multiple thereof. In this situation τ90 % is a measure of the duration of the relative silence between primary and secondary peaks, which is not the intended measure. Rarely, τ90 % quantifies the duration of the main peak, leading to a much lower value of τ90 %. Since the number of peaks included in τ90 % is sensitive to the nature of the signal, relatively small differences in the signal lead to large differences in τ90 %, causing instability in any metric based on τ90 %, e.g., the rms sound pressure. Alternative metrics are proposed that do not exhibit these weaknesses. The consequences for the interpretation of sound pressure level of a transient signal, and the benefits of using a more stable metric than τ90 % are demonstrated.

Measuring vessel underwater radiated noise in shallow water

Performing reproducible vessel source level (SL) measurements is complicated by seabed reflections in shallow water. In deep water, with a hydrophone far from the seabed, it is straightforward to estimate propagation loss (PL) and convert sound pressure level (SPL) into SL using the method codified in the international standard ISO 17208-2 [International Organization for Standardization (ISO), Geneva, Switzerland (2019)]. Estimating PL is more difficult in shallow water because of the way that sound reflects from the seabed such that multiple propagation paths contribute to SPL. Obtaining reproducible SL measurements in shallow water requires straightforward and robust methods to estimate PL. From May to July 2021, a field experiment evaluated different methods of measuring vessel SL in shallow water. The same vessels were measured many times in water depths of 30, 70, and 180 m. In total, 12 079 SL measurements were obtained from 1880 vessel transits and 16 hydrophones, distributed across 3 moored vertical line arrays and 2 moored horizontal line arrays. The experiment confirmed that it is possible to obtain reproducible vessel SL estimates in shallow water comparable to within ±2.5 dB of ISO-compliant measurements in deep water and repeatable to within ±1.5 dB.

International harmonization of procedures for measuring and analyzing of vessel underwater radiated noise

The habitat of the endangered southern resident killer whale (SRKW) overlaps major international shipping lanes near the Port of Vancouver, British Columbia. Shipping is a dominant source of underwater noise, which can hinder SRKW key life functions. To reduce environmental pressure on the SRKWs, Vancouver Fraser Port Authority offers incentives for quieter ships. However, the absence of a widely accepted underwater radiated noise (URN) measurement procedure hinders the determination of relative quietness. We review URN measurement procedures, summarizing results to date from two Canadian-led projects aimed at improving harmonization of shallow-water URN measurement procedures: One supports the International Organization for Standardization (ISO) in the development of a URN measurement standard; the other supports the alignment of URN measurement procedures developed by ship classification societies. Weaknesses in conventional shallow-water URN metrics are identified, and two alternative metrics proposed. Optimal shallow-water measurement geometry is identified.

Characterization of the acoustic output of single marine-seismic airguns and clusters: The Svein Vaage dataset

The acoustical output of marine-seismic airguns is determined from recordings of the sound pressure made on hydrophones suspended below a floating barge from which the airguns are also deployed. The signals from multiple types of airguns are considered and each type is operated over a range of deployment depths and chamber pressures. The acoustical output is characterized in terms of a "source waveform" with dimensions of the pressure-times-distance and in an infinite idealized medium, could be divided by the source-receiver distance to give the sound pressure at that receiver. In more realistic environments, the source waveform may be used to predict the pressure at any arbitrary receiver position simply by the application of a time-domain transfer function describing the propagation between the source and receiver. The sources are further characterized by metrics such as the peak source waveform and energy source level. These metrics are calculated in several frequency bands so that the resulting metrics can be used to characterize the acoustical output of the airguns in terms of their utility for seismic image-processing or possible effects on marine life. These characterizations provide reference data for the calibration of models that predict the airguns' acoustical output. They are validated via comparisons of the acoustic pressure measured on far-field hydrophones and predicted using the source waveforms. Comparisons are also made between empirically derived expressions relating the acoustic metrics to the chamber volume, chamber pressure, and deployment depth and similar expressions from the literature.

Temperature-driven seasonal and longer term changes in spatially averaged deep ocean ambient sound at frequencies 63-125 Hz

The soundscape of the Northeast Pacific Ocean is studied with emphasis on frequencies in the range 63-125 Hz. A 34-year (1964-1998) increase and seasonal fluctuations (1994-2006) are investigated. This is achieved by developing a simple relationship between the total radiated power of all ocean sound sources and the spatially averaged mean-square sound pressure in terms of the average source factor, source depth, and sea surface temperature (SST). The formula so derived is used to predict fluctuations in the sound level in the range 63-125 Hz with an amplitude of 1.2 dB and a period of 1 year associated with seasonal variations in the SST, which controls the amount of sound energy trapped in the sound fixing and ranging (SOFAR) channel. Also investigated is an observed 5 dB increase in the same frequency range in the Northeast Pacific Ocean during the late 20th century [Andrew, Howe, Mercer, and Dzieciuch (2002). ARLO 3, 65-70]. The increase is explained by the increase in the total number of ocean-going ships and their average gross tonnage.

Modeling potential masking of echolocating sperm whales exposed to continuous 1-2 kHz naval sonar

Modern active sonar systems can (almost) continuously transmit and receive sound, which can lead to more masking of important sounds for marine mammals than conventional pulsed sonar systems transmitting at a much lower duty cycle. This study investigated the potential of 1-2 kHz active sonar to mask echolocation-based foraging of sperm whales by modeling their echolocation detection process. Continuous masking for an echolocating sperm whale facing a sonar was predicted for sonar sound pressure levels of 160 dB re 1 μPa², with intermittent masking at levels of 120 dB re 1 μPa², but model predictions strongly depended on the animal orientation, harmonic content of the sonar, click source level, and target strength of the prey. The masking model predicted lower masking potential of buzz clicks compared to regular clicks, even though the energy source level is much lower. For buzz clicks, the lower source level is compensated for by the reduced two-way propagation loss to nearby prey during buzzes. These results help to predict what types of behavioral changes could indicate masking in the wild. Several key knowledge gaps related to masking potential of sonar in echolocating odontocetes were identified that require further investigation to assess the significance of masking.

Effects of a seismic survey on movement of free-ranging Atlantic cod

Geophysical exploration of the seabed is typically done through seismic surveys, using airgun arrays that produce intense, low-frequency-sound pulses¹ that can be heard over hundreds of square kilometers, 24/7.^2,3 Little is known about the effects of these sounds on free-ranging fish behavior.^4-6 Effects reported range from subtle individual change in activity and swimming depth for captive fish^7,8 to potential avoidance⁹ and changes in swimming velocity and diurnal activity patterns for free-swimming animals.¹⁰ However, the extent and duration of behavioral responses to seismic surveys remain largely unexplored for most fish species.⁴ In this study, we investigated the effect of a full-scale seismic survey on the movement behavior of free-swimming Atlantic cod (Gadus morhua). We found that cod did not leave the detection area more than expected during the experimental survey but that they left more quickly from 2 days to 2 weeks after the survey. Furthermore, during the exposure, cod decreased their activity, with time spent being "locally active" (moving small distances, showing high body acceleration) becoming shorter, and time spent being "inactive" (moving small distances, having low body acceleration) becoming longer. Additionally, diurnal activity cycles were disrupted with lower locally active peaks at dusk and dawn, periods when cod are known to actively feed.^11,12 The combined effects of delayed deterrence and activity disruption indicate the potential for seismic surveys to affect energy budgets and to ultimately lead to population-level consequences.¹³.

Application of kurtosis to underwater sound

Regulations for underwater anthropogenic noise are typically formulated in terms of peak sound pressure, root-mean-square sound pressure, and (weighted or unweighted) sound exposure. Sound effect studies on humans and other terrestrial mammals suggest that in addition to these metrics, the impulsiveness of sound (often quantified by its kurtosis β) is also related to the risk of hearing impairment. Kurtosis is often used to distinguish between ambient noise and transients, such as echolocation clicks and dolphin whistles. A lack of standardization of the integration interval leads to ambiguous kurtosis values, especially for transient signals. In the current research, kurtosis is applied to transient signals typical for high-power underwater noise. For integration time (t₂-t₁), the quantity (t₂-t₁)/β is shown to be a robust measure of signal duration, closely related to the effective signal duration, τ_eff for sounds from airguns, pile driving, and explosions. This research provides practical formulas for kurtosis of impulsive sounds and compares kurtosis between measurements of transient sounds from different sources.

Application of damped cylindrical spreading to assess range to injury threshold for fishes from impact pile driving

Environmental risk assessment for impact pile driving requires characterization of the radiated sound field. Damped cylindrical spreading (DCS) describes propagation of the acoustic Mach cone generated by striking a pile and predicts sound exposure level (L_E) versus range. For known water depth and sediment properties, DCS permits extrapolation from a measurement at a known range. Impact assessment criteria typically involve zero-to-peak sound pressure level (L_p,pk), root-mean-square sound pressure level (L_p,rms), and cumulative sound exposure level (L_E,cum). To facilitate predictions using DCS, L_p,pk and L_p,rms were estimated from L_E using empirical regressions. Using a wind farm construction scenario in the North Sea, DCS was applied to estimate ranges to recommended thresholds in fishes. For 3500 hammer strikes, the estimated L_E,cum impact ranges for mortal and recoverable injury were up to 1.8 and 3.1 km, respectively. Applying a 10 dB noise abatement measure, these distances reduced to 0.29 km for mortal injury and 0.65 km for recoverable injury. An underlying detail that produces unstable results is the averaging time for calculating L_p,rms, which by convention is equal to the 90%-energy signal duration. A stable alternative is proposed for this quantity based on the effective signal duration.

Source specific sound mapping: Spatial, temporal and spectral distribution of sound in the Dutch North Sea

Effective measures for protecting and preserving the marine environment require an understanding of the potential impact of anthropogenic sound on marine life. A crucial component is a proper assessment of the anthropogenic soundscape: which sounds are present where, when and how strong? We provide an extensive case study modelling the spatial, temporal and spectral distribution of sound radiated by several anthropogenic sources (ships, seismic airguns, explosives) and a naturally occurring one (wind) in the Dutch North Sea. We present the results as a series of sound maps covering the whole of the Dutch North Sea, showing the spatial and temporal distribution of the energy from these sources. Averaged over a two year period, shipping is responsible for the largest amount of acoustic energy (∼1800 J), followed by seismic surveys (∼300 J), explosions (∼20 J) and wind (∼20 J) in the frequency band between 100 Hz and 100 kHz. Our study shows that anthropogenic sources are responsible for 100 times more acoustic energy (averaged over 2 years) in the Dutch North Sea than naturally occurring sound from wind. The potential impact of these sounds on aquatic animals depends not only on these temporally averaged and spatially integrated broadband energies, but also on the source-specific spatial, spectral and temporal variation. Shipping is dominant in the southern part and along the coast in the north, throughout the years and across the spectrum. Seismic surveys are relatively local and spatially and temporally dependent on exploration activities in any particular year, and spectrally shifted to low frequencies relative to the other sources. Explosions in the southern part contribute wide-extent high energy bursts across the spectrum. Relating modelled sound fields to the temporal and spatial distribution of animal species may provide a powerful tool for understanding the potential impact of anthropogenic sound on marine life.

Predicting acoustic dose associated with marine mammal behavioural responses to sound as detected with fixed acoustic recorders and satellite tags

To understand the consequences of underwater noise exposure for cetaceans, there is a need for assessments of behavioural responses over increased spatial and temporal scales. Bottom-moored acoustic recorders and satellite tags provide such long-term and large spatial coverage of behaviour compared to short-duration acoustic-recording tags. However, these tools result in a decreased resolution of data from which an animal response can be inferred, and no direct recording of the sound received at the animal. This study discusses the consequence of the decreased resolution of data from satellite tags and fixed acoustic recorders on the acoustic dose estimated by propagation modelling and presents a method for estimating the range of sound levels that animals observed with these methods have received. This problem is illustrated using experimental results obtained during controlled exposures of northern bottlenose whales (Hyperoodon ampullatus) exposed to naval sonar, carried out near Jan Mayen, Norway. It is shown that variability and uncertainties in the sound field, resulting from limited sampling of the acoustic environment, as well as decreased resolution in animal locations, can lead to quantifiable uncertainties in the estimated acoustic dose associated with the behavioural response (in this case avoidance and cessation of foraging).

Modelling the broadband propagation of marine mammal echolocation clicks for click-based population density estimates

Passive acoustic monitoring with widely-dispersed hydrophones has been suggested as a cost-effective method to monitor population densities of echolocating marine mammals. This requires an estimate of the area around each receiver over which vocalizations are detected-the "effective detection area" (EDA). In the absence of auxiliary measurements enabling estimation of the EDA, it can be modelled instead. Common simplifying model assumptions include approximating the spectrum of clicks by flat energy spectra, and neglecting the frequency-dependence of sound absorption within the click bandwidth (narrowband assumption), rendering the problem amenable to solution using the sonar equation. Here, it is investigated how these approximations affect the estimated EDA and their potential for biasing the estimated density. EDA was estimated using the passive sonar equation, and by applying detectors to simulated clicks injected into measurements of background noise. By comparing model predictions made using these two approaches for different spectral energy distributions of echolocation clicks, but identical click source energy level and detector settings, EDA differed by up to a factor of 2 for Blainville's beaked whales. Both methods predicted relative density bias due to narrowband assumptions ranged from 5% to more than 100%, depending on the species, detector settings, and noise conditions.

Pile driving acoustics made simple: Damped cylindrical spreading model

Sound produced by marine pile driving activities poses a possible risk to marine life. The assessment and mitigation of this risk requires a precise prediction of the expected levels. An analytical approach to estimate the radiated sound exposure levels is presented, based on the axial symmetry of the problem, resulting in damped cylindrical spreading. The approach is verified against numerical results from the recently held COMPILE benchmark workshop and validated with data from three different wind farm construction sites in the North Sea. In addition, found to yield more accurate estimates of the sound exposure level than an empirical decay formula sometimes used to evaluate the impact of marine pile driving.

Temporary hearing threshold shift in a harbor porpoise (Phocoena phocoena) after exposure to multiple airgun sounds

In seismic surveys, reflected sounds from airguns are used under water to detect gas and oil below the sea floor. The airguns produce broadband high-amplitude impulsive sounds, which may cause temporary or permanent threshold shifts (TTS or PTS) in cetaceans. The magnitude of the threshold shifts and the hearing frequencies at which they occur depend on factors such as the received cumulative sound exposure level (SELcum), the number of exposures, and the frequency content of the sounds. To quantify TTS caused by airgun exposure and the subsequent hearing recovery, the hearing of a harbor porpoise was tested by means of a psychophysical technique. TTS was observed after exposure to 10 and 20 consecutive shots fired from two airguns simultaneously (SELcum: 188 and 191 dB re 1 μPa²s) with mean shot intervals of around 17 s. Although most of the airgun sounds' energy was below 1 kHz, statistically significant initial TTS_1-4 (1-4 min after sound exposure stopped) of ∼4.4 dB occurred only at the hearing frequency 4 kHz, and not at lower hearing frequencies tested (0.5, 1, and 2 kHz). Recovery occurred within 12 min post-exposure. The study indicates that frequency-weighted SELcum is a good predictor for the low levels of TTS observed.

Sonar equations for planetary exploration

The set of formulations commonly known as "the sonar equations" have for many decades been used to quantify the performance of sonar systems in terms of their ability to detect and localize objects submerged in seawater. The efficacy of the sonar equations, with individual terms evaluated in decibels, is well established in Earth's oceans. The sonar equations have been used in the past for missions to other planets and moons in the solar system, for which they are shown to be less suitable. While it would be preferable to undertake high-fidelity acoustical calculations to support planning, execution, and interpretation of acoustic data from planetary probes, to avoid possible errors for planned missions to such extraterrestrial bodies in future, doing so requires awareness of the pitfalls pointed out in this paper. There is a need to reexamine the assumptions, practices, and calibrations that work well for Earth to ensure that the sonar equations can be accurately applied in combination with the decibel to extraterrestrial scenarios. Examples are given for icy oceans such as exist on Europa and Ganymede, Titan's hydrocarbon lakes, and for the gaseous atmospheres of (for example) Jupiter and Venus.

The effect of sound speed profile on shallow water shipping sound maps

Sound mapping over large areas can be computationally expensive because of the large number of sources and large source-receiver separations involved. In order to facilitate computation, a simplifying assumption sometimes made is to neglect the sound speed gradient in shallow water. The accuracy of this assumption is investigated for ship generated sound in the Dutch North Sea, for realistic ship and wind distributions. Sound maps are generated for zero, negative and positive gradients for selected frequency bands (56 Hz to 3.6 kHz). The effect of sound speed profile for the decidecade centred at 125 Hz is less than 1.7 dB.

Offshore Dredger Sounds: Source Levels, Sound Maps, and Risk Assessment

The underwater sound produced during construction of the Port of Rotterdam harbor extension (Maasvlakte 2) was measured, with emphasis on the contribution of the trailing suction hopper dredgers during their various activities: dredging, transport, and discharge of sediment. Measured source levels of the dredgers, estimated source levels of other shipping, and time-dependent position data from a vessel-tracking system were used as input for a propagation model to generate dynamic sound maps. Various scenarios were studied to assess the risk of possible effects of the sound from dredging activities on marine fauna, specifically on porpoises, seals, and fish.

Controlled Sonar Exposure Experiments on Cetaceans in Norwegian Waters: Overview of the 3S-Project

In mitigating the risk of sonar operations, the behavioral response of cetaceans is one of the major knowledge gaps that needs to be addressed. The 3S-Project has conducted a number of controlled exposure experiments with a realistic sonar source in Norwegian waters from 2006 to 2013. In total, the following six target species have been studied: killer, long-finned pilot, sperm, humpback, minke, and northern bottlenose whales. A total of 38 controlled sonar exposures have been conducted on these species. Responses from controlled and repeated exposure runs have been recorded using acoustic and visual observations as well as with electronic tags on the target animal. So far, the first dose-response curves as well as an overview of the scored severity of responses have been revealed. In this paper, an overview is presented of the approach for the study, including the results so far as well as the current status of the ongoing analysis.

Assessing the Effectiveness of Ramp-Up During Sonar Operations Using Exposure Models

Ramp-up procedures are used to mitigate the impact of sound on marine mammals. Sound exposure models combined with observations of marine mammals responding to sound can be used to assess the effectiveness of ramp-up procedures. We found that ramp-up procedures before full-level sonar operations can reduce the risk of hearing threshold shifts with marine mammals, but their effectiveness depends strongly on the responsiveness of the animals. In this paper, we investigated the effect of sonar parameters (source level, pulse-repetition time, ship speed) on sound exposure by using a simple analytical model and highlight the mechanisms that limit the effectiveness of ramp-up procedures.

Mapping Underwater Sound in the Dutch Part of the North Sea

The European Union requires member states to achieve or maintain good environmental status for their marine territorial waters and explicitly mentions potentially adverse effects of underwater sound. In this study, we focused on producing maps of underwater sound from various natural and anthropogenic origins in the Dutch North Sea. The source properties and sound propagation are simulated by mathematical methods. These maps could be used to assess and predict large-scale effects on behavior and distribution of underwater marine life and therefore become a valuable tool in assessing and managing the impact of underwater sound on marine life.

How effectively do horizontal and vertical response strategies of long-finned pilot whales reduce sound exposure from naval sonar?

The behaviour of a marine mammal near a noise source can modulate the sound exposure it receives. We demonstrate that two long-finned pilot whales both surfaced in synchrony with consecutive arrivals of multiple sonar pulses. We then assess the effect of surfacing and other behavioural response strategies on the received cumulative sound exposure levels and maximum sound pressure levels (SPLs) by modelling realistic spatiotemporal interactions of a pilot whale with an approaching source. Under the propagation conditions of our model, some response strategies observed in the wild were effective in reducing received levels (e.g. movement perpendicular to the source's line of approach), but others were not (e.g. switching from deep to shallow diving; synchronous surfacing after maximum SPLs). Our study exemplifies how simulations of source-whale interactions guided by detailed observational data can improve our understanding about motivations behind behaviour responses observed in the wild (e.g., reducing sound exposure, prey movement).

A depth-dependent formula for shallow water propagation

In shallow water propagation, the sound field depends on the proximity of the receiver to the sea surface, the seabed, the source depth, and the complementary source depth. While normal mode theory can predict this depth dependence, it can be computationally intensive. In this work, an analytical solution is derived in terms of the Faddeeva function by converting a normal mode sum into an integral based on a hypothetical continuum of modes. For a Pekeris waveguide, this approach provides accurate depth dependent propagation results (especially for the surface decoupling) without requiring complex calculation methods for eigenvalues and corresponding eigenfunctions.

Modeling effectiveness of gradual increases in source level to mitigate effects of sonar on marine mammals

Ramp-up or soft-start procedures (i.e., gradual increase in the source level) are used to mitigate the effect of sonar sound on marine mammals, although no one to date has tested whether ramp-up procedures are effective at reducing the effect of sound on marine mammals. We investigated the effectiveness of ramp-up procedures in reducing the area within which changes in hearing thresholds can occur. We modeled the level of sound killer whales (Orcinus orca) were exposed to from a generic sonar operation preceded by different ramp-up schemes. In our model, ramp-up procedures reduced the risk of killer whales receiving sounds of sufficient intensity to affect their hearing. The effectiveness of the ramp-up procedure depended strongly on the assumed response threshold and differed with ramp-up duration, although extending the duration of the ramp up beyond 5 min did not add much to its predicted mitigating effect. The main factors that limited effectiveness of ramp up in a typical antisubmarine warfare scenario were high source level, rapid moving sonar source, and long silences between consecutive sonar transmissions. Our exposure modeling approach can be used to evaluate and optimize mitigation procedures.

Dose-response relationships for the onset of avoidance of sonar by free-ranging killer whales

Eight experimentally controlled exposures to 1-2 kHz or 6-7 kHz sonar signals were conducted with four killer whale groups. The source level and proximity of the source were increased during each exposure in order to reveal response thresholds. Detailed inspection of movements during each exposure session revealed sustained changes in speed and travel direction judged to be avoidance responses during six of eight sessions. Following methods developed for Phase-I clinical trials in human medicine, response thresholds ranging from 94 to 164 dB re 1 μPa received sound pressure level (SPL) were fitted to Bayesian dose-response functions. Thresholds did not consistently differ by sonar frequency or whether a group had previously been exposed, with a mean SPL response threshold of 142 ± 15 dB (mean ± s.d.). High levels of between- and within-individual variability were identified, indicating that thresholds depended upon other undefined contextual variables. The dose-response functions indicate that some killer whales started to avoid sonar at received SPL below thresholds assumed by the U.S. Navy. The predicted extent of habitat over which avoidance reactions occur depends upon whether whales responded to proximity or received SPL of the sonar or both, but was large enough to raise concerns about biological consequences to the whales.

Neglect of bandwidth of Odontocetes echo location clicks biases propagation loss and single hydrophone population estimates

Passive acoustic monitoring with a single hydrophone has been suggested as a cost-effective method to monitor population density of echolocating marine mammals, by estimating the distance at which the hydrophone is able to intercept the echolocation clicks and distinguish these from the background. To avoid a bias in the estimated population density, this method relies on an unbiased estimate of the detection range and therefore of the propagation loss (PL). When applying this method, it is common practice to estimate PL at the center frequency of a broadband echolocation click and to assume this narrowband PL applies also to the broadband click. For a typical situation this narrowband approximation overestimates PL, underestimates the detection range and consequently overestimates the population density by an amount that for fixed center frequency increases with increasing pulse bandwidth and sonar figure of merit.

Echo and reverberation in a Pekeris waveguide by convolution and by the product rule

The detection performance of an active sonar depends on the intensity of the signal (target echo) relative to that of a background of reverberation plus noise. The echo is calculated for a standard test problem by convolving the time-domain impulse response at the target position with itself. The same approach is applied to a closely related test problem for reverberation by integrating over scatterers at all ranges. The result is compared with a widely used rule whereby the reverberation intensity is approximated by integrating the product of the source, propagation, and scattering factors over grazing angle. The error resulting from this approximation, which increases with increasing grazing angle and tends to infinity as the upper limit of integration tends to π/2, can be corrected by including a simple trigonometric multiplying factor in the integrand.

Validation of finite element computations for the quantitative prediction of underwater noise from impact pile driving

The acoustic radiation from a pile being driven into the sediment by a sequence of hammer strikes is studied with a linear, axisymmetric, structural acoustic frequency domain finite element model. Each hammer strike results in an impulsive sound that is emitted from the pile and then propagated in the shallow water waveguide. Measurements from accelerometers mounted on the head of a test pile and from hydrophones deployed in the water are used to validate the model results. Transfer functions between the force input at the top of the anvil and field quantities, such as acceleration components in the structure or pressure in the fluid, are computed with the model. These transfer functions are validated using accelerometer or hydrophone measurements to infer the structural forcing. A modeled hammer forcing pulse is used in the successive step to produce quantitative predictions of sound exposure at the hydrophones. The comparison between the model and the measurements shows that, although several simplifying assumptions were made, useful predictions of noise levels based on linear structural acoustic models are possible. In the final part of the paper, the model is used to characterize the pile as an acoustic radiator by analyzing the flow of acoustic energy.

Review of scattering and extinction cross-sections, damping factors, and resonance frequencies of a spherical gas bubble

Perhaps the most familiar concepts when discussing acoustic scattering by bubbles are the resonance frequency for bubble pulsation, the bubbles' damping, and their scattering and extinction cross-sections, all of which are used routinely in oceanography, sonochemistry, and biomedicine. The apparent simplicity of these concepts is illusory: there exist multiple, sometimes contradictory definitions for their components. This paper reviews expressions and definitions in the literature for acoustical cross-sections, resonance frequencies, and damping factors of a spherically pulsating gas bubble in an infinite liquid medium, deriving two expressions for "resonance frequency" that are compared and reconciled with two others from the reviewed literature. In order to prevent errors, care is needed by researchers when combining results from different publications that might have used internally correct but mutually inconsistent definitions. Expressions are presented for acoustical cross-sections associated with forced pulsations damped by liquid shear and (oft-neglected) bulk or dilatational viscosities, gas thermal diffusivity, and acoustic re-radiation. The concept of a dimensionless "damping coefficient" is unsuitable for radiation damping because different cross-sections would require different functional forms for this parameter. Instead, terms based on the ratio of bubble radius to acoustic wavelength are included explicitly in the cross-sections where needed.

The effect of wind-generated bubbles on sea-surface backscattering at 940 Hz

Reliable predictions of sea-surface backscattering strength are required for sonar performance modeling. These are, however, difficult to obtain as measurements of sea-surface backscattering are not available at small grazing angles relevant to low-frequency active sonar (1-3 kHz). Accurate theoretical predictions of scattering strength require a good understanding of physical mechanisms giving rise to the scattering and the relative importance of these. In this paper, scattering from individual resonant bubbles is introduced as a potential mechanism and a scattering model is derived that incorporates the contribution from these together with that of rough surface scattering. The model results are fitted to Critical Sea Test (CST) measurements at a frequency of 940 Hz, treating the number of large bubbles, parameterized through the spectral slope of the size spectrum for bubbles whose radii exceed 1 mm, as a free parameter. This procedure illustrates that the CST data can be explained by scattering from a small number of large resonant bubbles, indicating that these provide an alternative mechanism to that of scattering from bubble clouds.

Fixed time versus fixed range reverberation calculation: analytical solution

Reverberation is commonly calculated by estimating the propagation loss to and from an elementary area, defined by transmitted pulse length and beam width, and treating the resulting backscatter from the area as a function of its range. In reality reverberation is strictly a function of time and contributions for a given time come from many ranges. Closed-form solutions are given for reverberation calculated both at fixed range and at fixed time isovelocity water and some variants of Lambert's law and linear reflection loss with an abrupt critical angle. These are derived by considering the shape of the two-way scattered multipath pulse envelope from a point scatterer. The ratio of these two solutions is shown to depend on the dominant propagation angle spread for the particular range or time. The ratio is largest at intermediate ranges (though typically less than 1 dB) and depends explicitly on the critical angle. At longer ranges mode-stripping reduces the propagation angle spread and the ratio reduces ultimately to unity. At short range the ratio is also close to unity although interpreting it requires care.

Near resonant bubble acoustic cross-section corrections, including examples from oceanography, volcanology, and biomedical ultrasound

The scattering cross-section sigma(s) of a gas bubble of equilibrium radius R(0) in liquid can be written in the form sigma(s)=4piR(0) (2)[(omega(1) (2)omega(2)-1)(2)+delta(2)], where omega is the excitation frequency, omega(1) is the resonance frequency, and delta is a frequency-dependent dimensionless damping coefficient. A persistent discrepancy in the frequency dependence of the contribution to delta from radiation damping, denoted delta(rad), is identified and resolved, as follows. Wildt's [Physics of Sound in the Sea (Washington, DC, 1946), Chap. 28] pioneering derivation predicts a linear dependence of delta(rad) on frequency, a result which Medwin [Ultrasonics 15, 7-13 (1977)] reproduces using a different method. Weston [Underwater Acoustics, NATO Advanced Study Institute Series Vol. II, 55-88 (1967)], using ostensibly the same method as Wildt, predicts the opposite relationship, i.e., that delta(rad) is inversely proportional to frequency. Weston's version of the derivation of the scattering cross-section is shown here to be the correct one, thus resolving the discrepancy. Further, a correction to Weston's model is derived that amounts to a shift in the resonance frequency. A new, corrected, expression for the extinction cross-section is also derived. The magnitudes of the corrections are illustrated using examples from oceanography, volcanology, planetary acoustics, neutron spallation, and biomedical ultrasound. The corrections become significant when the bulk modulus of the gas is not negligible relative to that of the surrounding liquid.

Observable parameters from multipath bottom reverberation in shallow water

Multipath ocean reverberation originating from the seabed in shallow isovelocity water, with particular attention to its information content in the cylindrical spreading and mode stripping regions, is considered. The reverberation is evaluated using Weston's flux integral method, both analytically with various simplifying approximations and numerically with all but one of these approximations rescinded. The functional form of the analytical solution is used to infer which physical seabed parameters can be extracted from measurements of reverberation. Coarse- and fine-grained sediments (sand and clay) are both considered. The main purpose of the numerical solutions is to check the accuracy of the analytical approximations; they also serve as a convenient surrogate for measured reverberation.

The sonar equation and the definitions of propagation loss

A rigorous application of the traditional definition of sonar equation terms leads to the appearance of an unexpected factor, not routinely included, equal to the ratio of the characteristic impedance at the receiver to that at the source. An omission of this factor can lead to non-negligible errors for realistic conditions. It is further argued that a gradual change in the de facto definition of propagation loss occurred between 1965 and 1980. Two alternatives to the traditional sonar equation are suggested, each using one of the two propagation loss definitions and both eliminating the unwanted impedance ratio.