Recommendations on bioacoustical metrics relevant for regulating exposure to anthropogenic underwater sound^a)

The effects of sound on marine life are a growing global concern. To predict the possible effects of a sound producing activity (or sound source) on marine fauna, it is essential to quantitatively predict the generated sound field.

Underwater noise regulations permit certain human-generated sounds while setting acceptable exposure limits for marine fauna. However, assessing these impacts requires estimating the scope and severity of anthropogenic sound exposure on marine life. This involves quantifying the sound field around the source and using biologically relevant metrics for impact predictions. However, this process requires two separate disciplines for quantifying and assessing anthropogenic sound exposure: physics for the sound field quantification and biology for assessing the predicted sound impacts on marine organisms. These disciplines use overlapping but not always congruent metrics and sometimes lack sufficient understanding and knowledge of each other's capabilities and limitations. Acoustic metrics describe the physical characteristics of sound, whereas bioacoustic metrics, a subset of acoustic metrics, are scientifically determined sound properties that affect marine life.

To be “bioacoustically “relevant, metrics must bridge the outputs of sound source-modeling and sound propagation-modeling with the marine fauna potentially impacted by the sound. Several well-established metrics, most of which are biologically relevant, are currently used by industry and regulators to assess underwater noise exposure to marine fauna. However, recent advances in understanding the cause-effect relationships for certain marine taxa, particularly fishes and invertebrates, suggest that additional metrics are necessary to correctly describe and quantify the sound fields (van Geel , 2022).

Impact assessment of underwater noise exposure and relevant regulations are currently constrained by a lack of quantitative information on the sensitivity and susceptibility of marine fauna to sound exposure. Although the growing body of research is gradually improving the baseline understanding, it is clear that in addition to new and emerging metrics, more refined approaches for assessing noise-induced effects and setting safe exposure limits within national regulations for underwater noise are needed.

Effective communication requires a shared understanding of the terminology used (Ainslie , 2022). We adhere to international standard terminology (ISO, 2017, 2020) supplemented by ADEON terminology in Ainslie (2020a).

Several metrics have been established for sound source-modeling and sound propagation-modeling and are currently used to regulate underwater noise exposure to marine fauna (Tables I and II). However, a temporal observation window (TOW) and a frequency weighting function (or frequency band) should be reported in all cases but often are not. These metrics (i.e., TOW and the weighting functions) are posited to be scientifically relevant and should be considered in future underwater noise regulations.

Currently, regulations primarily focus on marine mammals and fishes, which is based on limited data sets of auditory and behavioral effects to sound exposure in these animals. There is even less data on the effects of anthropogenic sound on invertebrates and other taxonomic groups. Additionally, other aspects of exposure to anthropogenic sound, such as masking effects and nonauditory effects, have not been considered in any of the taxonomic groups. The metrics listed in Tables I and II are also limited to the most common sound sources such as seismic airguns, pile driving, and vessel operations.

All fishes and aquatic invertebrates are thought to be primarily sensitive to particle motion based on their known auditory sense organs (e.g., otolithic end organs in fishes and statocysts in invertebrates). This particle motion sensitivity has been confirmed in tested species, but it remains unexamined in many other fish and marine invertebrate groups. Moreover, the mechanism and thresholds for sound detection in fishes and aquatic invertebrates are largely unknown, given the more than 36 000 species of fishes (Fricke , 2024) and the greater than 240 000 species of marine invertebrates that have been formally described (Bouchet , 2023).

Particle motion is typically characterized using vector quantities measured in all three planes (x, y, and z). Although the scientific data do not definitively identify the most relevant derivative of particle motion (displacement, velocity, acceleration, jerk, etc.), we suggest that the sensitivities of the auditory sense organs of fishes and invertebrates are best described in terms of acceleration. Kalmijn (1988) argued that describing particle motion sensitivity in terms of acceleration level at threshold is more useful as the mass-loaded auditory sense organs are driven by the inertial forces on the otoliths or statocysts, resulting from the linear or angular accelerations of the head or body. Furthermore, while auditory hair cells are displacement detectors at the receptor level, the otolith organs and statocysts function as acceleration-sensitive devices at the organ and system levels (Kalmijn, 1988). We also support the conclusions and recommendations of Nedelec (2021), particularly those advocating for interdisciplinary and multidisciplinary collaboration, standardized data analysis, and the consistent reporting of particle motion sensitivity data for fish and invertebrate species.

In terms of relevant bioacoustic metrics for assessing noise exposure, kurtosis and its derivates (see Table III) are emerging as significant sound properties in the context of noise impact assessments. Additionally, the importance of kurtosis has yet to be acknowledged within the regulatory framework for underwater noise exposure (see overview by van Geel , 2022).

Defining the metrics relevant for assessing effects of underwater sound is a multifactorial challenge. The relevant factors are the differences in

• sound sources;

• taxonomic groups; and

• types of effects, ranging from stress to behavioral responses, auditory effects, injury, and nonauditory effects.

The metrics required for assessing noise effects based on these factors can overlap, but each noise effect can also require a different set of metrics. The most significant challenge is the lack of empirical data on many aspects related to effects of underwater sound on marine fauna. There is insufficient information to characterize potential physiological and behavioral responses across different species. Additionally, the functional processes leading to effects caused by noise (or particle motion) remain unclear for some taxa. This deficiency hampers our ability to accurately assess and mitigate the impacts of anthropogenic underwater sound on marine fauna.

For fishes, it is clear that their inner-ear otolithic end organs are designed to detect particle acceleration (Sisneros and Rogers, 2016; Schulz‐Mirbach , 2019) and although not commonly reported, this biologically relevant metric of auditory sensitivity needs to be included in scientific studies on fish and invertebrate species (Krysl , 2012; Schilt , 2012; Popper and Hawkins, 2018).

An important issue in the regulation and risk assessment of anthropogenic sound exposure is the lack of a clear and consistent metric for defining impulsive sound. This ambiguity complicates the accurate assessment of noise-induced effects. The application of kurtosis to received sounds is an emerging metric that offers a novel approach for defining signal impulsiveness. We highlight the relevance of kurtosis and provide a rationale for its importance in improving the accuracy and effectiveness of noise regulation.

We also emphasize the importance of applying and reporting on several types of filter (or weighting) functions in the context of modeling sound fields and assessing noise-induced effects in marine fauna as this information is often neglected in impact assessments and noise regulation.

A TOW is the time window over which squared sound pressure is integrated for calculating sound exposure and mean square sound pressure. Thus, TOW is a necessary defined quantity for obtaining unambiguous sound exposure level (SEL) and sound pressure level (SPL) values for sound exposure estimates.

An acoustic measurement is the output of a data acquisition system, which typically acts as a bandpass filter, that introduces an undesirable dependence of the resulting sound pressure or particle motion time series on the characteristics of this system filter (SF). The SF depends on the system used, which means that two sets of measurements can only be compared if they are made with the same system-frequency filtering or frequency weighting is applied to override the system's frequency response. For example, the undesirable dependence on system characteristics can be addressed by applying auditory frequency weighting (AFW), e.g., when calculating weighted sound exposure (Southall , 2007; NMFS, 2018a; Southall , 2019). For this reason, AFW should always be applied and reported.

Kurtosis can be thought of in the same way because the frequency weighting function is an input to frequency-weighted SEL, and kurtosis is an input to the calculation of the kurtosis-adjusted SEL. In addition, kurtosis has been proposed as an input for calculating the SPL of airgun pulses (Müller , 2023). The benefit of using kurtosis in this (second) way is that it results in a stable SPL metric.

Impulsive or “pulsed” sounds can be described as discrete sounds (e.g., single pulses) produced by sources such as seismic airguns and pile driving. These sounds, sometimes also termed transients, are typically brief acoustic signals consisting of a high peak in sound pressure with a rapid rise time and rapid decay (NIOSH, 1998). There are currently no quantitative metrics specified to identify and define the impulsiveness of acoustic signals, which makes it problematic to characterize and report the impulsiveness of anthropogenic sound. The quantity “pressure impulse” (ISO, 2017, entry 3.1.5.2) quantifies the potential of sound to impart momentum and is used as a metric for some types of sound, but impulse is not a measure of impulsiveness.

Auditory research on humans and rodents has exposed that impulsive sound can damage the auditory system more than non-impulsive sound (e.g., Taylor , 1984; Hamernik and Qiu, 2001). Similar differences in susceptibility of the hearing system to noise-induced effects were shown to exist in marine mammals (Finneran, 2015). There are substantial differences in the threshold levels promulgated by regulatory guidance of underwater noise exposure for marine mammals because they commonly include the two mutually exclusive categories: impulsive and non-impulsive sounds (e.g., NMFS, 2018a). However, the definitions used to classify sounds (and sound sources) as impulsive or non-impulsive are ambiguous and can result in misclassified sounds. With permanent threshold shift (PTS) thresholds for evaluating potential effects differing by 13–18 dB (depending on hearing group; NMFS, 2018a), misclassification of the received sound could result in underestimating auditory effects or overestimating effects when none might occur. It is, therefore, essential to either define impulsiveness in a way that is applicable from a physical perspective and meaningful in biological terms or to use existing and already defined quantities (which would be the best option in this context).

To better gauge their potential impacts on hearing, several quantitative definitions have been suggested to classify signals as impulsive or non-impulsive. Harris (1998) suggested an impulse factor that is easily calculated as the sound level measured using impulse weighting (35 ms decay constant) minus the sound level measured with either fast or slow time weighting (0.125 or 1 s decay constants, respectively) on standard airborne sound level meters. A difference of ≥3 dB in measurements between these settings would constitute an impulse, whereas non-impulsive sounds are characterized by a difference of <3 dB. As pointed out by Guan (2022), however, the Harris approach introduces subjectivity because time-gating of the signals is sensitive to bias if the signal-to-noise ratio is low as a result of reverberation within a very short inter-pulse interval.

Several impulsive metrics have been suggested to discern between impulsive and non-impulsive sounds, which are airborne and in water. Non-impulsive sounds produced by anthropogenic sound sources, such as ships and marine vibrator signals, can be intermittent or continuous. Non-impulsive sounds have a longer duration than impulsive sounds, and they usually lack the high peak sound pressure and rapid rise and decay times that are characteristic of impulsive sounds (NIOSH, 1998). However, especially with respect to their auditory effects on marine fauna, the term non-impulsive does not imply long duration signals.

ISO (2016a) gives this technical definition of impulsive sound: “sound characterized by brief bursts of sound pressure and the duration of a single impulsive sound is usually less than 1 s.”

Based on these definitions, classifying most sounds into the two sound types may seem straight forward and noncontroversial. However, problems arise with classifying types of sound sources that contain impulsive and non-impulsive structures [e.g., down-the-hole pile installation sounds that have hammer striking (impulsive) and debris pumping (non-impulsive) structures; Guan and Miner, 2020; Guan , 2022], and animals in the wild are often exposed to noise from different sound types (e.g., concurring impact and vibratory pile driving or impact pile driving from a barge operating dynamic positioning systems). Sounds with widely varied spectral and temporal signal characteristics, such as commercial sonars and echosounders, are equally difficult to classify. The existing definitions of impulsiveness identify them as either impulsive or non-impulsive sounds and do not allow for an unequivocal classification and regulation of these devices.

Moreover, with increasing distance from the sound source, sound propagation effects can change the temporal and spectral structure of an impulsive sound. For distant receivers, pulsed sounds may, therefore, lack the characteristics described above. This is mostly caused by reverberations, which lead to signal lengthening, thereby changing the structure of an impulsive sound to a non-impulsive sound. This is corroborated by the finding by Guan (2022) related to down-the-hole pile installation, which suggests that a simple dichotomy of classifying sounds as impulsive or non-impulsive may be overly simplistic for assessing auditory effects (in marine mammals) as it does not apply for all sound sources, over distance, and in complex sound fields. It would be desirable to find a metric that accounts for the transitory effects of sound over distance and its potential effects on the hearing of marine animals. Unless the concept of “impulsiveness” is quantified, it should be supplemented by quantitative metrics such as kurtosis.

Safe levels for noise exposure in humans are defined based on the hypothesis that hearing loss is a function of total exposure energy, independent of the temporal characteristics of the fatiguing sound (NIOSH, 1998; ISO, 2013). Thus, the equal energy hypothesis (EEH) assumes that the auditory effect of noise exposure is proportional to the duration of exposure multiplied by the energy intensity of the exposure (Zhang , 2021).

Although the EEH holds in situations when exposed to continuous non-impulsive sounds (as in the case of occupational noise exposure), controlled laboratory studies on terrestrial animals (Henderson , 1982; Ahroon , 1993), dolphins (Finneran , 2010), and fishes (Halvorsen , 2011; 2012), however, have shown that the EEH is inapplicable in multiple cases. Exposure to impulsive and/or complex sounds results in greater hearing threshold shift than that for non-impulsive sound of the same cumulative SEL (Hamernik , 2007; Qiu , 2007). In a study on chinchillas, Hamernik (2003) investigated how the amplitude distribution of received sound affected hearing loss. While keeping the total sound energy and spectra the same, Hamernik (2003) presented noises with Gaussian-distributed amplitudes and non-Gaussian-distributed amplitudes, which were produced by inserting high-amplitude transients into otherwise Gaussian-distributed noise. The non-Gaussian noise with high-amplitude transients produced greater hearing loss in chinchillas.

A more appropriate approach (alternative or additional) is required for overcoming the inadequacy of current definitions of impulsiveness. Such an approach will be necessary to account for the complexity related to the effects of impulsive sound propagation over distance on the impulsiveness of sound and the complexity of physiological aspects of auditory effects due to noise exposure.

Erdreich (1986) presented kurtosis as an indicator of impulsiveness and demonstrated that it was a sensitive discriminator of the impulsiveness of noise. Sound pressure kurtosis (⁠ $βp$⁠; ISO, 2017; Müller , 2020) is a measure of the outliers in a given distribution (or time series) that has been successfully used to predict hearing loss from exposure to sounds with differing amounts of transients (Qiu , 2020).

A signal with a kurtosis of three constitutes a signal with Gaussian-distributed sound pressure, which serves as a baseline and is the expectation for a non-impulsive signal. Qiu (2020) found that signals with a kurtosis >3 are associated with greater hearing loss than signals with a kurtosis ≤3, and the amount of additional hearing loss in terrestrial animals asymptotes for signals with a kurtosis >40. A sound signal that has a kurtosis of ≤3 could be classified as non-impulsive, whereas a sound signal with a kurtosis >40 could be classified as impulsive.

Normandeau Associates (2012) proposed kurtosis as a metric to distinguish impulsive sounds in the studies of fishes and invertebrates. Martin (2020) compared various types of impulsive and non-impulsive sounds in terms of their kurtoses, and the results support using kurtosis for quantifying impulsiveness. Future assessments and revised underwater noise regulations for marine mammals would be improved by adopting and applying a conversion factor between impulsive and non-impulsive sounds based on their kurtosis value. However, as Goley (2011) point out, kurtosis is an energy-independent parameter and, therefore, cannot be used as a noise metric by itself, It can, however, be incorporated with SPL or SEL to create a new noise metric.

Kurtosis is an established criterion in human audiometry and has recently been applied in auditory studies on a marine mammal species (Kastelein , 2017; von Benda-Beckmann , 2022). Further investigation of kurtosis, however, is needed for different underwater scenarios and more species/taxa. Research on human hearing (Gee , 2018) suggests that the statistics of the derivative of the pressure signal, rather than the statistics of the signal itself, are important for predicting the perception of crackle sounds. In the absence of extant studies in marine life that separate out the statistics of the pressure waveform and the statistics of the derivative, a definitive answer to which of the two is responsible for either perceptual or auditory consequences cannot be given.

The use of a binary classification scheme for regulating exposure to underwater sounds (impulsive and non-impulsive) creates a complicated situation. Some sources produce various sounds, and the question arises if all their sounds should be classified in the same way. Additionally, and conversely, the question of whether similar sounds that are classified differently because they come from different sources should be assessed using different thresholds arises.

Von Benda-Beckmann (2022) tested Goley's approach in a controlled study on a harbor porpoise (Phocoena phocoena), providing the first empirical data involving kurtosis as an adjustment factor. Although they concluded that a scaling factor adjustment is required for this species to predict the dose-response relationship more accurately, their results indicate that using kurtosis as an adjustment factor in determining the impact risk of underwater sound for marine mammals is justifiable. In the absence of more species-specific data, it seems prudent to develop an adjustment factor at a higher taxonomical level such as marine mammal hearing groups. Such a hearing group-specific adjustment factor should, ideally, be applicable to the existing noise regulations to be effective in current risk assessments.

To evaluate the potential of a sound to cause PTS in, e.g., VHF cetaceans, the process would be (1) calculate the kurtosis of the received sound, β; (2) use the equation to find the adjusted SEL; and (3) compare the adjusted SEL to the non-impulsive SEL threshold for PTS (173 dB). In this way, there is no need to determine (arbitrarily) whether a sound is “impulsive” and, hence, no need for a separate threshold for impulsive sounds. Applying a kurtosis adjustment factor means that there would be one criterion and one threshold for all sounds (see Fig. 1).

Only the non-impulsive threshold (SEL 173 dB re 1 μPa² s for VHF) is needed because adding to the SEL is equivalent to reducing the threshold. In other words, scaling the metric by the kurtosis adjustment precludes the need to scale the threshold by the impulsiveness of the signal. Signals with a kurtosis of three would receive no adjustment to SEL, hence, their effective threshold is equal to the non-impulsive threshold (SEL 173 dB re 1 μPa² s for VHF). Pulsed signals with kurtosis ≥40 would have an effective PTS threshold equal to the impulsive PTS threshold (SEL 155 dB re 1 μPa² s for VHF). Sounds with kurtoses between 3 and 40 would have effective thresholds between the non-impulsive and impulsive PTS thresholds. In this way, there is a smooth transition between signal types. Signals of an intermediate kurtosis will incur some penalty in the form of a reduced threshold [via Eq. (2)] but would not necessarily be considered impulsive. The benefit of the kurtosis adjustment factor proposed here is its applicability to existing regulatory criteria.

Acoustic signals are filtered for many reasons, including signal conditioning, noise removal, and extracting desired information. Filter functions are a broad category of mathematical functions used for signal processing and conditioning. Filter functions enhance or dampen specific frequency components from a signal either by passing or attenuating those components (e.g., low-pass, high-pass, bandpass, etc.). Frequency weighting functions quantify the effectiveness of a filter as specified by the magnitude of the filter's transfer function. Auditory frequency weighting functions (AFWFs) are a specific type of weighting function and are designed to account for the frequency-dependent hearing sensitivity or susceptibility to auditory injury of a listener. The terms frequency weighting function and AFWF are defined by ISO (2017).

Recording systems have a finite bandwidth and specific frequency response that are often not specified, and act as a frequency filter before any frequency weighting is applied. Thus, the frequency characteristics of each system need to be accounted for. System components operate in their own frequency bands or range of best sensitivity, which imposes frequency limitations on recordings caused by the system's frequency response. This is often the source of signals being filtered unwittingly and with unknown frequency limits.

One reason frequency weighting functions are needed is a biological driver; when designing an exposure study, the range of frequencies relevant to the animal is a critical feature. Each tested frequency will have a correlated response, and it is those biological responses that create the structure of an AFWF, and it is determined from and for a biological perspective and application. As researchers, we want to understand what sound the animal receives, which requires filtering in a biologically relevant frequency range.

Physics and calculation of metrics requires that variables be specified; in particular, the start and end frequencies to be used for calculations of comparative metrics, such as sound pressure. When standard decidecade bands (IEC 61260-1:2014) are applied, it is sufficient to identify the standard band (often by reporting the band's nominal center frequency). For any non-standard band, the start and end frequency should be reported and harmonized to facilitate quantitative comparisons.

The potential for underwater noise to impact marine fauna depends, in part, on whether the noise occurs at frequencies that an animal can hear well. The importance of particular sound's frequencies can be scaled by auditory frequency weighting to account for an animal's sensitivity to those frequencies. When hearing sensitivity is plotted versus frequency, this is called an audiogram. An AFWF is based on hearing sensitivity and, by default, is frequency specific. An AFWF is used to capture the frequency-dependent nature of noise effects (see review by Houser , 2017). As species are not equally sensitive to noise at all frequencies, the AFWFs are specific to a receiver (i.e., fauna). Therefore, AFWFs, which are mathematical functions, are used to emphasize the frequencies in which animals are more susceptible to noise exposure and de-emphasize those frequencies in which animals are less susceptible. The functions are frequency-dependent filters applied to a noise exposure before calculating a weighted SEL value.

The first marine mammal frequency weighting functions were developed by Southall (2007) and were based on the shape of the “C-weighting” function for humans with adjusted parameters such that the frequency weighting function shape better matched the known or suspected hearing range for each hearing group. The suite of resulting frequency weighting functions is referred to as the “M-weighting” functions (Southall , 2007) and formed the basis for a more advanced set of AFWFs (Finneran , 2017; Southall , 2019). These current marine mammal AFWFs are an integral part of the noise criteria and risk assessments for auditory effects (e.g., NMFS, 2018a; Danish Energy Agency, 2022).

Using Eq. (3) in Eq. (4) ensures that the maximum of $Wν=0 dB$⁠. For the marine mammal frequency weighting functions published by Southall (2019), the value of $ν$ is between 1.64 (LF: low-frequency, LF cetaceans) and 39.8 kHz (VHF cetaceans; Ainslie , 2022).

Some taxonomic groups, such as fishes and invertebrates, have only been minimally studied with regard to their hearing sensitivity, and most quantitative information is based on a few species (Popper, 2023). However, there is sufficient information to recommend a simplistic approach. The proposed AFWFs reflect the limitations of empirical data but, by being conservative, account for the complexity and uncertainty regarding the factors contributing to the onset of noise-induced auditory effects.

Marine mammal frequency weighting functions are the weighting functions that our field is accustomed to; these are usually related to risk of auditory injury (Southall , 2007, 2019). No comparable weighting functions exist for fishes or invertebrates. However, there remains a need for fish and invertebrate frequency weighting functions. Proposals for these are made in Sec. IV C.

Traditional weighting functions consider only the magnitude of the corresponding transfer function. The magnitude is sufficient to quantify the weighted energy spectral density and, therefore, suitable for determining weighted sound exposure but not weighted sound pressure, which requires knowledge of the phase. Applications requiring weighted sound pressure for aquatic mammals are considered in Sec. IV D.

Knowledge of the effects of sound on fishes and invertebrates is currently at a stage similar to the understanding of effects on aquatic mammals as documented by Richardson (1995). This indicates that research on fishes and invertebrates is approximately 30 years behind the research on mammals. Since its introduction by Southall (2007), researchers have been using AFWF for marine mammals. Of particular concern is the identification of the frequency bands that are most important to fishes and invertebrates regardless of their sound detection systems (e.g., inner ear, otolithic end organs, and statocyst). Most fish and invertebrate taxa operate in the acoustic space below a few kilohertz (specific ranges are detailed in Table V). Defining these frequency bands is crucial for measuring the sound field consistently and facilitating quantitative comparisons between studies. Additionally, scientific focus is expanding to include the study of the production, propagation, and reception of substrate-borne vibrations by organisms and their effects on behavior. This nascent field of biotremology holds promise for uncovering an often-overlooked mode of animal communication and its environmental interaction. Given its similarities with in-water acoustics, biotremology may progress more rapidly by applying insights gained from research on fishes and invertebrates.

The importance of understanding how sound impacts fishes and invertebrates will continue to grow, along with the need to better understand the acoustic ecology of fishes and invertebrates and how these animals perceive the low-frequency sounds present in their natural environment. To have lasting value, research aimed at increasing knowledge on the effects of anthropogenic sound on fishes and invertebrates needs to be grounded in the best available science and develop standardized protocols to facilitate quantitative inter-study comparisons. An example of these notions is observed in behavioral response studies on aquatic mammals (Southall , 2012; Southall , 2021).

In general, most fishes and aquatic invertebrates have auditory sense organs broadly tuned and sensitive to relatively low frequencies. For fishes, these frequencies typically range from less than 100 to 6000 Hz, although this varies significantly by species and group (see fish groups described in Table V). For invertebrates, the sensitivity is generally between less than 500 to 3000 Hz, based on limited data for crustaceans and cephalopods (Dijkgraaf, 1960; Lovell , 2005; Mooney , 2010; Popper , 2019). Based on current literature, we propose a generalized AFWF in the form of a low-pass filter with a broad roll-off rate of 12 dB per octave beyond the recommended roll-off frequencies for fishes and invertebrates (detailed below; see Table VI). We recommend using a low-pass frequency filter with a broad roll-off for an AFWF for fishes and invertebrates to preserve a biologically relevant frequency band (i.e., frequencies < 100 Hz), which remains largely unexplored due to technological limitations.

To date, most studies have been unable to generate stable acoustic signals below 100 Hz as a result of various technical and physical limitations. Most off-the-shelf underwater projectors are not large enough to efficiently produce low-frequency sounds (<100 Hz) with long wavelengths; for example, a 100 Hz sound in water has a wavelength of approximately 15 m. Producing such long wavelengths requires large transducers that are capable of significant diaphragm movement (excursion) within the transducer. However, most underwater speakers are mechanically limited in how far the diaphragm can move and too small to displace a sufficient amount of water to produce stable low-frequency sounds. Furthermore, generating low-frequency sounds below 100 Hz demands considerable power, and most underwater projectors are not equipped to handle the high power required without introducing distortion. As a result, the lowest tested frequency in fish and invertebrate hearing studies is often only as low as 100 Hz. These limitations stem from the constraints and capabilities of the testing equipment and not the hearing capabilities of the animal subjects.

The otolithic end organs of fishes exhibit high sensitivity to acceleration, responding to gravity (0 Hz) and sinusoidal motions from less than 1 Hz up to several hundred hertz (Buerkl, 1969; Chapman and Sand, 1974; Sand and Karlsen, 1986). Behavioral particle acceleration audiograms for Atlantic cod (Gadus morhua) show that cod maintain very high sensitivity to particle acceleration down to frequencies as low as 0.1 Hz (infrasound; Sand and Karlsen, 1986). Similarly, the statocysts of cephalopods can detect sinusoidal motions from 30 up to 500 Hz, as shown using a shaker table system for particle acceleration stimulation (Mooney , 2010). Despite these findings, there is very limited data on the particle motion sensitivity of fishes and no data for invertebrates at frequencies below 20 Hz in the infrasound range. Consequently, future studies are needed to examine the hearing capabilities of fishes and invertebrates in the infrasound range to fill these significant gaps in our understanding.

The extreme low-frequency end of the spectrum, which includes infrasound frequencies (<20 Hz), presents numerous challenges due to the constraints and capabilities of current testing equipment (Nedelec , 2021). These limitations necessitate immediate and focused attention as of 2024. We propose that AFWF be adaptable and evolve as new information becomes available, similar to the approach demonstrated for marine mammals by Southall (2019). Delaying progress would be a disservice to fishes and invertebrates as there are sufficient and reliable data to suggest a generic AFWF for these groups (Fay, 1988; Dijkgraaf, 1960; Lu, 2004, Lovell , 2005, Mooney , 2010).

Implementing a generic AFWF for fishes and invertebrates is feasible based on the current state of knowledge, even without a complete understanding of all the sensory mechanisms across or within taxa. The use of AFWF enables comparisons between studies, facilitating a more efficient and coherent understanding of how animals perceive very low frequencies and are affected by anthropogenic sounds within their hearing range. By standardizing these comparisons, researchers can better assess and mitigate the impacts of human-made noise on aquatic life.

Particle motion detection is considered to be an ancestral trait, whereas sound pressure detection in fishes is regarded as a more recently derived characteristic of their auditory systems (Fay and Popper, 1980). All fishes can use their otolithic end organs (inner ear) as inertial accelerometers to detect linear acceleration and respond to direct displacement by local particle motion (Dijkgraaf, 1960; Sand and Enger, 1973; Fay, 1984; Kalmijn, 1988; Sand and Karlsen, 2000).

We recognize the three fish hearing groups identified by Popper (2014), categorized based on the degree of influence of their swim bladder on hearing sensitivity. However, it is essential to also account for organisms that primarily sense acoustic acceleration. We propose a refinement and restructuring of these categories to include invertebrates, providing them with a dedicated subcategory. Furthermore, we suggest restructuring the grouping based on the ability to detect acceleration only (category A) and sound pressure (category P) as detailed in Table IV. Category A has four hearing groups: A1, invertebrates; A2, cartilaginous fish; A3, bony fishes without a swim bladder; and A4, bony fishes with a swim bladder not involved in hearing. Category P, representing bony fishes with a swim bladder involved in hearing and known for their “pressure sensitivity,” has three hearing groups: P1, without adaptation; P2, mechanical connection of swim bladder to inner ear; and P3, ultrasonic adaptation. Within Table IV and described in the text, we provide examples of taxa which are abridged and intended as a guide to select the most appropriate weighting function. These categories are designed to be flexible, accommodating new findings, with each hearing group explained in further detail below. They are based on our expert recommendations and comprehensive review of available data, particularly from Fay (1988) and a key review by Ladich and Fay (2013). As new information emerges, we recommend modifying and updating these interim recommendations accordingly.

Taxa assigned to this category are sensitive to acoustic acceleration (i.e., particle motion). Examples of taxa are provided, but it is not an exhaustive list for any of the following hearing groups.

Due to the paucity of hearing data for invertebrates as well as the similarity of statocysts to otolithic organs as biological accelerometers with low-pass filtering, we propose that invertebrates be included in this category of animals primarily sensitive to particle motion. Limited hearing data are available for cephalopods and crustaceans. Mooney (2010) demonstrated that longfin squid (Loligo pealeii) are most sensitive to particle accelerations between 100 and 200 Hz, with measurable response between 30 and 500 Hz. Another study by Putland (2023) showed that the hummingbird bobtail squid (Euprymna berryi) is most sensitive to particle accelerations between 300 and 500 Hz and can detect frequencies from 100 Hz to 1 kHz. Based on these limited data, cephalopods may be sensitive to particle acceleration at frequencies as high as 1 kHz and are included in hearing group A1.

Data on crustaceans are even more limited. Lovell (2005) show that the prawn (Palaemon serratus) was acoustically most sensitive to 100 Hz with an upper detection range up to 3 kHz. However, this study only measured sound pressure and not particle motion. It is posited that the statocysts of crustaceans are sensitive primarily to particle acceleration rather than sound pressure. Despite this, Lovell (2005) mention that the hearing acuity of the prawn is similar to that of a fish with a typical hearing range between 100 and 1000 Hz, captured here in hearing group P1. More studies are needed to comprehensively test the hearing sensitivity of invertebrates, particularly, in terms of particle motion sensitivity.

This group of fishes has a skeleton composed primarily of cartilage rather than bone, unlike most other fishes. The fishes lack a swim bladder or other gas-filled vesicle that could provide sound pressure sensitivity and increase the range of audible frequencies. These fishes exhibit a range of sensitivity and frequency detection capabilities, generally, most sensitive to frequencies below 100 Hz to 1 kHz. Fishes in this category include elasmobranchs (sharks, skates, and rays) and chimaeras (ratfish or ghost sharks).

This group of fishes lack a swim bladder or gas-filled vesicle. The fishes exhibit a diverse range of sensitivity and frequency detection capabilities, generally, being most sensitive to frequencies below 100 Hz to 1 kHz. Fishes in this category include flatfish, gobies, lungfishes, marlins, tunas, swordfish, and some deep-sea fishes (Nelson , 2016). These fishes have evolved various adaptations to maintain buoyancy, a primary function of the swim bladder, enabling them to navigate their environments effectively without it.

This group of fishes possesses a swim bladder, but based on our review of audiogram data, the swim bladder does not seem to enhance hearing sensitivity. Examples include salmon, sturgeon, and deep-sea lanternfishes. The swim bladder is situated too far from the inner ears to provide significant acoustic enhancement for hearing. Generally, this group is most sensitive to frequencies below 400 Hz to 1 kHz (Fay, 1988; Halvorsen , 2009; Hawkins and Popper, 2020). Their hearing sensitivity is more aligned with the acceleration-sensing group rather than the acoustic pressure sensing group; therefore, this group is assigned to hearing group A4.

Taxa assigned to category P are known to have acoustic pressure sensitivity. This group represents a continuum of adaptations, ranging from fishes with swim bladders directly connected to the inner ear to those with swim bladders located close to the ear. These varying proximities and structural adaptations result in different degrees of enhanced hearing sensitivity, as the presence of a gas bladder near the inner ear significantly improves sound detection.

This group consists of fishes with swim bladders that are close to but not directly connected to the inner ear, such as the Atlantic cod (Hawkins and Popper, 2020). Ladich and Fay (2013) conducted a comprehensive survey of more than 100 studies that used the auditory evoked potential recording technique to determine the hearing sensitivity of over 110 species of fishes from 51 families. They generalized that all known species with a swim bladder near or in close contact with the inner ears were sensitive to frequencies as high as 3 kHz. This observation underscores the significant role of the swim bladder's proximity to the inner ear in enhancing the auditory capabilities by re-radiating sound pressure information to the ears of various fish species.

This group of fishes have evolved modified vertebrae known as Weberian ossicles, which connect the anterior part of the swim bladder to the inner ear for enhanced hearing (<6 kHz; Braun and Grande, 2008). Weberian ossicles are a phenotypic trait found in all Otophysan fishes (superorder Ostariophysi). These ossicles form a direct physical connection between the swim bladder and inner ear, and the swim bladder acts as a crude “ear drum” that captures sound pressure energy and transduces it to the inner ear via the otophysic connection. Otophysan fishes include several orders of fishes, such as Cypriniformes (carps, goldfish, zebrafish, and minnows), Characiformes (characins and piranhas), Siluriformes (catfishes), and Gymnotiformes (electric eels and knifefishes). Weberian ossicles enhance sound pressure sensitivity, allowing fishes with this adaptation to detect a wider range of frequencies. For instance, Cypriniformes fishes, such as carps, zebrafish, and minnows, are most sensitive to sound pressure from approximately 300–800 Hz and have detection limits up to approximately 4 kHz (Kenyon , 1998; Higgs , 2002; Higgs , 2003; Wysocki and Ladich, 2005; Gutscher , 2011; Zeng , 2021). Siluriforme fishes, such as catfishes, are most sensitive to sound pressure from approximately 500–1000 Hz with detection limits up to approximately 6 kHz (Ladich, 2023).

Fishes in the family Clupeidae, such as herring, shads, sardines, and menhadens, possess an air-filled bulla adjacent to the utricle that enables them to detect sound pressure detection in the ultrasonic frequency range (>20 kHz). This adaptation aids in detecting ultrasonic signals produced by marine mammal predators, such as dolphins and porpoises. The ability to detect these ultrasonic signals can trigger startle responses (antipredator behavior) to evade predation. Clupeid fishes are most sensitive to sound pressure from approximately 100–800 Hz, and some can detect and respond to ultrasound frequencies in the range between 20 and 90 kHz (Ladich and Fay, 2013). One species of clupeid fish, the American shad (Alosa sapidissima), has been shown to respond to ultrasonic frequencies up to 180 kHz (Mann , 1997).

In the following, we distinguish between the roll-off frequency [the value of $f2$ in Eq. (7)], the cut-off frequency [the frequency at which the weighting function, $10W/10 dB$⁠, is equal to 0.5, such that $W≈−3.01 dB$], and the upper frequency limit (frequency above which the hearing threshold of a hearing group exceeds its minimum hearing threshold by at least 40 dB).

We choose $b=2$⁠, corresponding to a second-order filter with a low (precautionary) roll-off rate of approximately 12 dB/oct, which is analogous to a damped harmonic oscillator (Kalmijn, 1988). An exception is made for hearing group P3, for which we propose b = 1 to account for the exceptionally wide hearing frequency band associated with this group (Mann , 1997).

The remaining variable is the upper roll-off frequency, $f2$⁠, which can be determined from the cut-off frequency (3 dB loss of sensitivity) observed in audiograms. Following Sec. IV, we choose $fc=800 Hz$ (b = 2) for hearing category A (hearing groups A1–A4), f_c = 1500 Hz and f_c = 3000 Hz (b = 2) for hearing groups P1 and P2, respectively, and $fc=1000 Hz$ (b = 1) for hearing group P3 (clupeid family). The chosen cut-off frequencies for each group, along with the upper frequency limit (calculated from using the hearing group filter function) are shown in Table V. The corresponding roll-off frequencies (f₂) and equation order (b) needed to calculate the filter functions are displayed in Table VI, and the filter functions are illustrated in Fig. 2.

The dynamic range of a fish's ear or invertebrate's acoustic sensing apparatus is not fully understood. Here, we assume a useful range of 40 dB to calculate the upper hearing frequency limit based on the proposed filter functions. This means that the range from threshold of sensation to saturation is 40 dB, with sounds exceeding this range not perceived as louder than those at the 40-dB threshold. When applying the filter functions, sounds entirely outside of the 40-dB passband may be discounted due to reduced sensitivity. The upper frequency limit is where the filter function reaches –40 dB, as shown in Fig. 2 (abscissa) as well as the frequencies listed in Table V.

The need to account for the detection limitations of the auditory system is evident because it is limited in bandwidth. This limitation is already acknowledged in risk assessments and regulation of auditory effects from underwater noise exposure for marine mammals. The same rationale, however, applies in the context of noise-induced behavioral effects on animals because sounds are less likely to disturb an animal if the sounds are at frequencies above their sensory detection limits. Applying frequency weighting functions in the context of behavioral responses of marine fauna to underwater sound is complicated by the fact that exposure-response probability of marine mammals depends on context (Ellison , 2012; Southall , 2021; Pirotta , 2022). There are no behavioral response studies designed to derive frequency-specific responses to different sound types and develop behavioral-based filters. Moreover, the available AFWFs for marine mammals are based on temporary threshold shift (TTS) data (or proxy), thus, representing an animal's susceptibility to excessive noise exposure and not at biologically relevant sound levels that might affect normal behavior.

This renders applying a more narrow frequency filter approach using criteria described by Southall (2019) unjustifiable for assessing the risk of eliciting behavioral responses. For marine mammals, an intermediate approach between AFWF and the bandpass filter functions (or no frequency weighting function at all) involves use of the M-weighting functions, which are deliberately broad in frequencies (Southall , 2007). Such a simplified and deliberately broad approach is intended to mitigate the risk of illogical conclusions related to animals responding to signals entirely outside of their hearing ranges while avoiding an overly prescriptive approach.

It is recognized that previous behavioral response criteria that have lacked any means of relating frequency content of noise sources to perceptual capabilities may, in some instances, be wildly misleading. The approach of using M-weighting here (Southall , 2007), which has been applied in some regulatory contexts for marine mammal noise criteria, is proposed as a compromise.

Behavioral effects assessments from exposure to anthropogenic sound should consider the temporal response of an animal's auditory system to sound in addition to its frequency response. To this end, behavioral response criteria are most often expressed in terms of SPL, which is, by definition, derived from the sound pressure waveform, a time-domain quantity. When suitably weighted, SPL is generally understood to reflect the perceived loudness of a sound (to first approximation). The SPL captures the temporal response of the auditory system in two distinct ways:

1. Through temporal averaging of mean square sound pressure, which is meant to reflect the integration time of the auditory system (Plomp and Bouman, 1959; Madsen , 2006; MacGillivray , 2014); and

2. through linear filtering of the sound pressure, which is meant to reflect the phase (i.e., lag) response of the auditory system to pressure stimulus.

Often overlooked, the second point is an essential consideration when computing the SPL. This is because phase distortion (i.e., a delay between the stimulus time and response time) is present in all physical systems that have a nonuniform frequency response, whether mechanical or biological. Thus, for computing SPL, it is necessary to move from an AFWF to an auditory transfer function.

A complete filter specification must be given as the (complex) sound pressure transfer function, $H(f)$⁠, which specifies the amplitude and phase response versus frequency. Because we have not specified the phase (i.e., temporal) response of the filter, there are an infinite number of linear filters that meet this specification. These include filters that are unphysical and, worse, filters that would misrepresent the SPL of a sound stimulus (Fig. 3 and Table VII).

If we are given only an AFWF, as is commonly the case, then we must choose an appropriate phase response based on reasonable assumptions about the responses of auditory systems to external stimuli. Although audiogram testing has yielded a large body of frequency sensitivity data, on which AFWF curves may be based (Southall , 2007; Southall , 2019), no similar data set exists for constructing phase response curves for auditory systems. At least two possible assumptions regarding the phase response have been put forward in the past:

1. The zero-phase assumption, as in Tougaard and Beedholm (2019), where the filter involved in calculating SPL is assumed to have zero-phase response [ $argH(f)=0$] at all frequencies; and

2. the minimum phase assumption, as in Martin (2020), where the filter involved in calculating SPL is designed such that it minimizes the causal time delay of all signals passing through the filter.

Which choice is best? Fortunately, the theory of linear systems (Oppenheim and Schafer, 1999) provides two useful design criteria for realizable filters that must, likewise, apply to any realistic model of auditory system response:

1. Causality: The response of the auditory system must only depend on inputs received at the present time and in the past; and

2. stability: The response of the auditory system must be bounded (i.e., not become infinite) in response to all finite inputs.

The minimum phase assumption satisfies both criteria (i.e., causal and stable), whereas the zero-phase assumption satisfies only the second criterion (and, then, only if the Fourier transform is convergent). Furthermore, the minimum phase filter is unique for a given AFWF. Thus, the minimum phase assumption provides a better model of auditory response and should be preferred over the zero-phase assumption when computing hearing weighted SPL.

This raises another strong reason to prefer a minimum phase filter over a zero-phase filter: only the former is suitable for implementing in real-time sound measurement systems. Real-time monitoring of sound is often a requirement for noise management and mitigation plans (Van Parijs , 2021). For a real-time monitoring system to be implemented in practice, the measurement of SPL at some time should not depend on signals measured at a future time. The impulse response for a minimum phase filter is strictly zero for negative time delays and, hence, always meets this causality requirement.

The sound pressure time series is needed to determine the zero-to-peak sound pressure, which is considered relevant to the risk of auditory injury (Southall , 2007, 2019). Although Southall et al. do not mention any weighting, any measured sound pressure is (inevitably) filtered by the frequency response of the data acquisition system and, thus, inappropriately weighted. Assuming that the data acquisition system has a flat response within the frequency range of interest, application of the fish frequency weighting function removes the inappropriate dependence on the characteristics of the data acquisition system, instead, replacing it by a band of frequencies appropriate to the scientific question that is asked.

The signal duration influences its detectability by marine mammals, fishes, and aquatic invertebrates. The (mammalian) ear acts as an energy integrator, collecting acoustic energy over time. The auditory integration time differs across species and is frequency dependent.

Integration times in marine mammals are on the order of tens to hundreds of milliseconds (except for echolocating marine mammals, which can perceive echolocation clicks with integration times less than 1 ms; Au , 1988). Auditory thresholds for short-duration signals decrease with increasing signal duration up to a certain value. Increasing the signal duration beyond this value does not further improve a listener's ability to hear a given signal. Longer integration times are required for generally lower-frequency signals, and shorter times are required for higher-frequency signals.

Erbe (2016) recommended that while auditory hearing integration times show substantial variation (Table VIII), the tone level (SPL) of an acoustic signal, if predicting an animal's ability to detect a signal of interest, should be computed over a fixed window of a few hundred milliseconds length for marine mammals (and selected according to the integration time corresponding to the subject species), rather than the potentially shorter pulse duration, before comparing to the audiogram. For ambient sound monitoring studies with no particular species in mind, what matters for the purpose of comparability is uniformity of the averaging time across studies. To facilitate comparability between studies, we recommend a fixed TOW duration. The precise value is arbitrary, and we propose the nearest round number in the range from a few tens to a few hundreds of milliseconds, namely, 100 ms.

In principle, the TOW can be selected to match the auditory integration time of a few hundred milliseconds. There are practical reasons, mainly applicable to ambient sound monitoring, why a larger TOW value might be preferred, including the following.

Increasing uncertainty in band level with decreasing TOW duration (⁠ $TTOW$⁠) and decreasing band frequency (Ward , 2021). (ANSI (2004) recommends a TOW duration of 30 s for accurate amplitude representation of the 10 Hz decidecade band (Ward , 2021). A more general rule is $fc TTOW$> 300, where f_c is the decidecade band center frequency. For example, $TTOW$ > 3 s at 100 Hz.

Ambient sound monitoring typically involves modeling of the sound radiated by ships and wind-generated breaking waves. To compare a measurement with a model prediction, or even to use the model prediction directly, one needs to use an averaging time that is commensurate with the inputs to the model. Standard ship source level measurements are averaged over 10–30 s (ISO, 2016b), whereas wind source level depends on reported wind speed (Chapman , 2024), for which the averaging time is rarely less than 600 s, suggesting an averaging time for ambient sound monitoring between 10 and 600 s. A TOW duration of 60 s is widely used in soundscape studies (Miksis-Olds , 2013; Miksis-Olds and Nichols, 2016; Harris , 2019; Park , 2023) and is recommended by the International Quiet Ocean Experiment (IQOE, 2019). To facilitate comparability between studies, we recommend a TOW duration of precisely 60 s.

When dealing with airgun pulses or similar sounds, it is common practice to use a temporal averaging window corresponding to 90% of the pulse energy (the 90% energy signal duration, “T90”; Madsen, 2005), with recent examples including Buehler (2015), Finneran (2017), NMFS (2018), Blackstock (2018), and Sidorovskaia and Li (2022). However, the use of T90 can lead to undesirable step changes in the SPL, resulting from small (even infinitesimal) changes in amplitude (Ainslie , 2020b). T90 can focus on the weaker parts of a pulse instead of the stronger parts, effectively measuring the root mean square sound pressure during nulls between peaks instead of the peaks themselves (Müller , 2023). Instead, a fixed TOW is preferred.

To meet the physics and biology needs, a dual-value approach is suggested with two separate TOW values, 0.1 and 60 s. The following are recommended:

• Use TOW = 0.1 s with a sliding window [per Eq. (10)] to characterize the sound field for relevance to the hearing integration time; this averaging window is suitable, e.g., for characterizing a single airgun pulse; and

• use TOW = 60 s to characterize the sound field averaged for a stable metric of greater physical significance; this longer averaging window is suitable for ambient sound monitoring or characterizing multiple pulses and is consistent with IQOE (2019).

In addition, the distribution of the sound level should be reported to allow assessing variations (i.e., showing outliers) that may be significant in terms of effects to marine life.

For the purpose of soundscape characterization, the arithmetic mean (of the squared sound pressure) should be used as it is a robust metric that is independent of TOW and facilitates comparability between studies, as recommended by IQOE (2019). If metrics other than the arithmetic mean are used to characterize a soundscape, such as the median, TOW durations of 0.1 and 60 s are recommended.

This section provides a worked example of computing biologically relevant metrics using real hydrophone data, following the approaches recommended in Secs. II–IV. For this example, we use a 100-s sample of sound pressure data from a marine seismic airgun array, recorded by a hydrophone in the Chukchi Sea. This is the unweighted sound pressure waveform, $pt$⁠, displayed in Fig. 4. For our example, we choose to evaluate sound level metrics for beluga whales (Delphinapterus leucas), which are classified as mid-frequency cetaceans by Southall (2007) and high-frequency cetaceans by Southall (2019). We begin by computing metrics for assessing behavioral responses and soundscape characterization, followed by metrics for auditory injury, indicating the weighting functions by means of the subscripts “MF07” and “HF19,” respectively.

The steps involved in our worked example are as follows:

1. Start by calculating the weighted sound pressure waveform for behavioral responses and soundscape characterization metrics [ $pMF07(t)$], using the minimum phase AFWF filter of Eq. (12). M-weighting AFWF coefficients are given by the mid-frequency cetacean hearing group from Southall (2007) (⁠ $a=2,b=2,f1=0.15 kHz, f2=160 kHz, C=0 dB$⁠). To perform this calculation in the frequency domain,² take the discrete Fourier transform (DFT) of $pt$⁠, multiply it by the minimum phase transfer function $Hf$ for both positive and negative frequencies, and take the inverse DFT to obtain $pMF07(t)$⁠. A small amount of zero padding (0.1 s) should be applied to the end of $pt$⁠, before taking the DFT, to avoid wraparound errors.

2. For assessing behavioral responses, compute the weighted SPL versus time (⁠ $Lp,MF07,0.1s$⁠) by applying a 0.1-s boxcar filter to the square of the weighted sound pressure [ $pMF072(t)$] and taking the decibel value (Fig. 5). Evaluate behavioral responses against the maximum value of the weighted SPL over the exposure period, equal to 160.7 dB [see Eq. 10)].

3. For soundscape characterization, compute the weighted SPL versus time (⁠ $Lp,MF07,60s$⁠) by applying a 60-s boxcar filter to the square of the frequency-weighted sound pressure and taking the decibel value (Fig. 5).

4. Next, calculate the weighted sound pressure waveform for auditory injury metrics [ $pHF19(t)$]. This calculation proceeds as in step (1) but with AFWF coefficients given by the high-frequency cetacean hearing group from Southall (2019) (⁠ $a=1.6,b=2,f1=8.8 kHz, f2=110 kHz, C=1.20 dB$⁠).

5. Compute the sound pressure kurtosis from $pHF19(t)$⁠. The kurtosis of $pHF19(t)$ in Fig. 4 is $βp$=155.2.

6. Compute the weighted SEL (⁠ $LE,HF19$⁠) from the time integral of the square of the frequency-weighted sound pressure [ $pHF192(t)$], taking the decibel value. The SEL of $pHF19(t)$ in Fig. 4 is $LE,HF19$=127.4 dB.

7. Compute the kurtosis-adjusted SEL (⁠ $LE,HF19′$⁠) according to Eq. (2), with appropriately chosen constants. From Fig. 1, the $λ$ value for the high-frequency hearing group is 11.56 dB and the maximum adjustment value is 13 dB. Because the sound pressure kurtosis is greater than 40, the kurtosis-adjusted SEL is $LE,HF19′$=140.4 dB.

Finally, we consider the dependence of the zero-to-peak sound pressure on the choice of frequency band. If the “unweighted” (i.e., system-filtered) sound pressure is used, the peak sound pressure is 710 Pa. Although there is a clear need to remove the characteristics of the SF, it is not obvious what frequency weighting function to replace it with. As an illustrative example, the corresponding MF07-weighted value is 388 Pa. The benefit of applying frequency weighting in this way is that the result is independent of the system response while retaining the frequency range relevant to the animal's hearing.

The main conclusions follow.

Using a clear terminology is essential for effective communication about underwater acoustics. Adhering to standards such as ISO (2017) helps prevent misunderstandings.

The dichotomy in the regulatory classification of sound types can be addressed by incorporating kurtosis as an additional parameter and applying a kurtosis-based conversion factor. This allows kurtosis-adjusted sound levels to be used without altering existing regulations.

The common practice of using the 90% energy signal duration, T90, as a temporal averaging window can lead to unstable and misleading results (Sec. IV). Instead, a fixed TOW is recommended. The proposed dual-value approach provides the required accuracy while meeting the needs of sound field characterization and the biological considerations of animals' hearing systems.

Detection limitations of the auditory system should be acknowledged in risk assessments and regulation of auditory effects from underwater noise exposure for marine mammals, taking into account noise-induced behavioral effects on animals. The proposed behavioral AFWFs, applied conservatively, include marine mammals, fishes, and aquatic invertebrates.

Reporting of technical acoustical parameters should include information on AFWFs and TOWs. Minimum phase filters are recommended for calculating weighted sound pressure. The phase response of an AFWF must be specified; otherwise, the computed SPL is ill-defined. Minimum phase filters are suitable for real-time monitoring systems.

The primary use of the proposed AFWFs for fishes and invertebrates is to assess potential impacts of underwater noise to animals in a regulatory context, including harmonized measurement of dose-response curves. In the absence of more complete information, weighting functions for regulation should be precautionary, excluding only those acoustic frequencies that fishes and invertebrates are known not to sense. These weighting functions are expected to be refined as more data become available.

The following specific recommendations are made:

• Follow the international standard ISO (2017) for underwater acoustical terminology;

• avoid ambiguous terms such as impulsive to characterize sounds;

• use a fixed TOW (0.1 or 60 s).

• apply appropriate AFWFs for all aquatic fauna, not just marine mammals, and sound pressure and sound exposure; and

• when calculating weighted sound pressure, use a minimum phase filter.

This work is an outcome of an expert workshop held in summer of 2022 in Cambridge, United Kingdom, aimed at reducing uncertainty in predictions of sound fields related to offshore exploration and production (E and P) activities (Ainslie , 2023). The workshop was supported by the E and P Sound and Marine Life Joint Industry Programme under Contract No. JIP22 III-17-01. We would like to especially thank Darlene Ketten for her valuable contributions on the topic of bioacoustical metrics during the workshop.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

We can determine the properties of such a filter by inspecting its transfer equation and locating the poles and zeros in the complex s-plane. This filter has one zero, at $s=0$⁠, and four poles, at $s=±2πf1$ and $s=±2πf2$⁠. This filter is stable because the region of convergence (⁠ $−2πf1<s<2πf1$⁠) includes the imaginary axis (implying that the Fourier transform converges). However, this filter is neither causal nor has minimum phase because it has a zero on the imaginary axis (⁠ $s=0$⁠) and two poles to the right of the imaginary axis (⁠ $s=2πf1$ and $s=2πf2$⁠). For a filter to be causal, stable, and minimum phase, all the poles and zeros of its transfer equation must be to the left of the imaginary axis in the s-plane [i.e., $Re(s)<0$].

For practical implementations, we set $ε$ to zero to obtain a filter that remains causal and stable and is only infinitesimally different from a minimum phase filter. We substitute $s=i2πf$ into Eq. (A2) to obtain the Fourier transform for the AFWF filter of Eq. (12). The same method may be applied to similar types of AFWFs, such as those given by Southall (2007) and NMFS (2016).