Source: https://jmrplens.github.io/phonometry/underwater/marine-mammal-exposure/ # Marine-mammal noise exposure: audiograms, auditory weighting and injury criteria A marine mammal does not hear every frequency equally, so an underwater noise assessment cannot compare a broadband level against a single number. Regulatory practice instead **weights** the spectrum with a filter shaped like the hearing group's sensitivity, sums the weighted energy, accumulates it over the whole activity and compares the result against a published onset criterion. This page covers the three pieces the library provides for that chain: the hearing curves themselves, the weighting functions and criteria of the current guidance, and the end-to-end assessment of a piling campaign. Levels are in dB re 1 µPa (sound pressure), dB re 1 µPa²·s (sound exposure) or, for the two in-air carnivore groups, dB re 20 µPa and dB re (20 µPa)²·s. The underwater reference conventions themselves are in [Underwater acoustics](https://jmrplens.github.io/phonometry/underwater/underwater-acoustics/). ## 1. Hearing groups (and why the names collide) Every current criteria set sorts marine mammals into hearing groups and gives each one a filter. The **group codes are not portable between guidance versions**, and the collision is a real trap: | Southall et al. (2019) / NMFS 2024 | NMFS 2018 | Typical genera | |---|---|---| | LF cetaceans | LF | baleen whales | | HF cetaceans | **MF** | sperm, beaked and most delphinid whales | | VHF cetaceans | **HF** | porpoises, *Cephalorhynchus*, *Kogia* | | PCW / PW | PW | phocid seals in water | | OCW / OW | OW | otariids, in water | | SI, PCA, OCA | — | sirenians and carnivores in air | `hearing_groups(guidance)` lists the codes a version defines, and passing a code from the wrong version raises rather than silently returning the wrong filter. ```python from phonometry import underwater print(underwater.hearing_groups("nmfs-2024")) # ('LF', 'HF', 'VHF', 'PW', 'OW', 'PA', 'OA') print(underwater.hearing_groups("nmfs-2018")) # ('LF', 'MF', 'HF', 'PW', 'OW') ``` ## 2. Group audiograms `group_audiogram` evaluates the band-pass fit of Southall et al. (2019), Equation (1), after Finneran (2016): $$ T(f) = T_0 + A \log_{10}\!\left(1 + \frac{F_1}{f}\right) + (f/F_2)^{B}, $$ with $f$ in kilohertz. `normalized=False` (the default) uses the Table 2 parameters, fitted to the absolute median behavioural thresholds; `normalized=True` uses the Table 3 refit on thresholds normalised to each individual's best value. The article publishes **no fitted audiogram for LF cetaceans** (no audiometric data exist and $F_1$ is never printed), so that group is deliberately absent rather than reconstructed by guesswork. ```python import numpy as np from phonometry import underwater freqs = np.logspace(2, 5.3, 400) audiogram = underwater.group_audiogram(freqs, "VHF") print(audiogram.best_frequency, audiogram.best_threshold) audiogram.plot() # threshold vs frequency (needs matplotlib) print(underwater.AUDIOGRAM_GROUPS) # ('HF', 'VHF', 'SI', 'PCW', 'OCW', 'PCA', 'OCA') ``` For a species rather than a group, `orca_audiogram` implements the killer-whale curve of Wensveen & Van Roij (2007) as printed in Ainslie (2010), Equation (11.159), a three-branch power law over 0.5 to 80 kHz. Its minimum is 39.0 dB re 1 µPa at 22.6 kHz, and 51.2 dB re 1 µPa at 50 kHz. That second value needs the **third** branch: evaluating the second one there returns 50.5 dB instead, which is why both published points are pinned by the tests. ```python from phonometry import underwater print(underwater.orca_audiogram(50e3).threshold[0]) # 51.20 dB re 1 uPa ``` That value is the hearing threshold in Ainslie's orca-versus-salmon example: with a source level of 198.2 dB re 1 µPa²·m² and a salmon target strength of −29.0 dB re m², the hearing-limited figure of merit is $(SL + TS - HT)/2 = 59.0$ dB re m². ## 3. Auditory weighting and exposure functions All three current criteria sets use the same generic band-pass filter (NMFS 2018 Equation 1, Southall et al. Equation 2): $$ W(f) = C + 10 \log_{10} \frac{(f/f_1)^{2a}} {\left[1+(f/f_1)^2\right]^{a}\left[1+(f/f_2)^2\right]^{b}} , $$ with $f$ in kilohertz. $C$ is fixed by putting the peak of $W$ at 0 dB, so the companion **exposure function** $E(f) = K + C - W(f)$ has its minimum at the weighted TTS-onset threshold $T_\mathrm{w} = K + C$. Below $f_1$ the filter falls at $20a$ dB/decade and above $f_2$ at $20b$ dB/decade. Only the parameter table changes between versions, so the version is an explicit argument and is carried on the result: - **`"nmfs-2024"`** (the default): NOAA Fisheries *Updated Technical Guidance* v3.0, October 2024. It supersedes the 2018 revision, sets $b = 5$ for every group, adopts the Southall group names and replaces "PTS onset" with "auditory injury (AUD INJ) onset". - **`"nmfs-2018"`**: the 2018 revision v2.0, still cited by assessments already in flight. - **`"southall-2019"`**: the peer-reviewed criteria, numerically identical to NMFS 2018 on the five shared groups and adds sirenians and both in-air carnivore groups.

Show the code for this figure

```python import matplotlib.pyplot as plt import numpy as np from phonometry import underwater freqs = np.logspace(1, 5.4, 700) fig, ax = plt.subplots() for group in ("LF", "HF", "VHF", "PW", "OW"): res = underwater.auditory_weighting(freqs, group, guidance="nmfs-2024") crit = underwater.exposure_criteria(group, guidance="nmfs-2024", impulsive=True) ax.semilogx(res.frequencies, res.weighting, label=f"{group} (AUD INJ {crit.injury_sel:.0f} dB)") ax.set(xlabel="Frequency [Hz]", ylabel="Weighting amplitude W(f) [dB]", ylim=(-75, 5)) ax.legend() ax.grid(True, which="both", alpha=0.3) plt.show() ```

```python from phonometry import underwater res = underwater.auditory_weighting(1000.0, "LF", guidance="nmfs-2018") print(res.weighting[0]) # -0.06 dB, the published Appendix D value print(res.weighted_tts_onset) # Tw = K + C params = underwater.weighting_parameters("OW", guidance="nmfs-2024") print(params.a, params.b, params.f1_khz, params.f2_khz, params.c_db) ``` > NMFS 2024 prints $C = 1.37$ dB for the otariid in-water group and states in > the same table's footnote that the value should be 1.36 dB. The library > implements 1.36 (recomputing $C$ from the peak of $W$ gives 1.3643) and keeps > the printed digit as `c_db_as_printed`. Southall's Table 7 carries four > peak-SPL misprints corrected by the journal's own errata, and the corrected > values are the ones implemented. Both are recorded in > [Errata found in published sources](https://jmrplens.github.io/phonometry/reference/errata/). ## 4. Onset criteria `exposure_criteria` returns the published TTS and injury onset criteria of a group. Impulsive noise carries a **dual metric**: a weighted sound exposure level *and* an unweighted ("flat") peak sound pressure level, and the criterion that produces the larger isopleth governs. ```python from phonometry import underwater crit = underwater.exposure_criteria("VHF", guidance="nmfs-2024", impulsive=True) print(crit.injury_label) # 'AUD INJ' print(crit.tts_sel, crit.injury_sel) # 144, 159 dB re 1 uPa2 s (weighted) print(crit.tts_peak_spl, crit.injury_peak_spl) # 196, 202 dB re 1 uPa (flat) print(crit.source) ``` The tables are internally consistent in ways the library pins as tests: the non-impulsive injury level is always TTS + 20 dB, the published weighted TTS onset is always the rounded $K + C$, and in Southall's impulsive table the SEL criteria run TTS + 15 dB and the peak criteria TTS + 6 dB. Only the auditory-effect criteria are implemented: the behavioural-disturbance thresholds (the step-function and dose-response criteria used for harassment take estimates) are out of scope. ## 5. A worked pile-driving assessment Percussive pile driving is the canonical impulsive case. The chain runs from the recorded strike to the verdict: 1. `strike_sel_spectrum` splits the single-strike sound exposure of the record into fractional-octave bands (the band energies sum back to the broadband `single_strike_sel` of [Underwater acoustics](https://jmrplens.github.io/phonometry/underwater/underwater-acoustics/), by Parseval); 2. `weighted_exposure` applies $W(f)$ band by band, sums the weighted energy, accumulates it over the number of strikes (the ISO 18406 $+10\log_{10} N$) and compares the result with the criteria, unweighted peak SPL included. ```python import numpy as np from phonometry import underwater # One recorded strike (here a synthetic 200 Hz decaying burst). fs = 48_000 t = np.arange(int(0.2 * fs)) / fs strike = 50.0 * np.exp(-t / 0.06) * np.sin(2 * np.pi * 200.0 * t) spectrum = underwater.strike_sel_spectrum(strike, fs, fraction=3) peak = underwater.peak_sound_pressure_level(strike) res = underwater.weighted_exposure( spectrum.frequencies, spectrum.band_sel, "LF", guidance="nmfs-2024", impulsive=True, n_events=3000, peak_spl=peak, ) print(res.unweighted_sel, res.weighted_sel, res.cumulative_sel) print(res.sel_margin, res.peak_margin) # positive means the criterion is exceeded print(res.exceeds_injury, res.exceeds_tts) res.plot() # weighted spectrum against the criteria (needs matplotlib) ``` A 200 Hz hammer sits inside the low-frequency cetacean passband and far outside the very high-frequency one, so the same campaign weights tens of decibels lower for a porpoise than for a baleen whale, which is the whole point of weighting, and the reason a single unweighted cumulative SEL is not an assessment. Three things the chain leaves to you. The library does not choose a hearing group or an accumulation period: both are assessment decisions, made per species and per activity. It does not model the animal's movement relative to the source, so the cumulative SEL it reports is the stationary-receiver worst case. And it does not check that the supplied spectrum spans the group's passband: a record that stops short of $f_2$ is weighted as given and under-reports the exposure. The natural companion is the sonar-equation chapter of [Underwater sound propagation](https://jmrplens.github.io/phonometry/underwater/underwater-propagation/): the same figure of merit machinery that gives a sonar detection range gives the range at which a piling campaign's weighted exposure falls below a criterion. ## See also - [Underwater acoustics: radiated noise and pile driving](https://jmrplens.github.io/phonometry/underwater/underwater-acoustics/): the ISO 18405 reference levels and the ISO 18406 pile-driving exposure that feed this page. - [Underwater sound propagation](https://jmrplens.github.io/phonometry/underwater/underwater-propagation/): the propagation loss and figure-of-merit machinery that turns a criterion into a range. - API reference: [`underwater.bioacoustics.weighting`](https://jmrplens.github.io/phonometry/reference/api/underwater/weighting/) and [`underwater.bioacoustics.audiograms`](https://jmrplens.github.io/phonometry/reference/api/underwater/audiograms/). ## References - National Marine Fisheries Service (2018). *2018 Revision to: Technical Guidance for Assessing the Effects of Anthropogenic Sound on Marine Mammal Hearing (Version 2.0)*. NOAA Technical Memorandum NMFS-OPR-59. [NOAA Fisheries](https://www.fisheries.noaa.gov/s3/2023-05/TECHMEMOGuidance508.pdf). The Table 3 weighting parameters, the Table ES3 PTS onset thresholds and the Appendix D worked example (W at 1 kHz for the five groups) used as the numeric oracle of section 3. - National Marine Fisheries Service (2024). *2024 Update to: Technical Guidance for Assessing the Effects of Anthropogenic Sound on Marine Mammal Hearing (Version 3.0)*. NOAA Technical Memorandum NMFS-OPR-71. [NOAA Fisheries](https://www.fisheries.noaa.gov/s3/2024-11/Tech_Memo-Guidance_-3.0-_OCT-2024-508_OPR1.pdf). The current guidance and the default of `guidance`: Table 5 parameters, Table ES3 AUD INJ criteria and the Navy Phase 4 Table A.E-2 impulsive TTS. - Southall, B. L., Finneran, J. J., Reichmuth, C., Nachtigall, P. E., Ketten, D. R., Bowles, A. E., Ellison, W. T., Nowacek, D. P., & Tyack, P. L. (2019). Marine mammal noise exposure criteria: Updated scientific recommendations for residual hearing effects. *Aquatic Mammals*, 45(2), 125-232. [doi:10.1578/AM.45.2.2019.125](https://doi.org/10.1578/AM.45.2.2019.125). The group audiograms of section 2 (Equation 1, Tables 2 to 4) and the weighting and threshold tables of sections 3 and 4 (Tables 5 to 7); the errata, *Aquatic Mammals* 45(5), 569-572, [doi:10.1578/AM.45.5.2019.569](https://doi.org/10.1578/AM.45.5.2019.569), corrects four peak-SPL values of Table 7. - Finneran, J. J. (2016). *Auditory weighting functions and TTS/PTS exposure functions for marine mammals exposed to underwater noise*. Technical Report 3026, SSC Pacific. The band-pass filter form and the audiogram equation both criteria sets adopt. - Ainslie, M. A. (2010). *Principles of Sonar Performance Modelling*. Springer/Praxis. [doi:10.1007/978-3-540-87662-5](https://doi.org/10.1007/978-3-540-87662-5). The orca audiogram of section 2 (Equation 11.159, after Wensveen & Van Roij 2007) and the orca-versus-salmon worked example. - ISO 18405:2017. *Underwater acoustics — Terminology*. [ISO page](https://www.iso.org/standard/62406.html). The symbols and references the guidance documents adopt for their criteria ($L_{p,\text{0-pk}}$ and $L_{E,p}$ re 1 µPa and 1 µPa²·s). ## Standards & sources - Auditory weighting and exposure criteria: NMFS (2024) v3.0 (default), NMFS (2018) v2.0 and Southall et al. (2019) with its published errata. - Group audiograms: Southall et al. (2019), Equation (1) with Tables 2 and 3. - Orca audiogram: Wensveen & Van Roij (2007) via Ainslie (2010) Eq. (11.159). - Pile-driving sound exposure: ISO 18406:2017, via [Underwater acoustics](https://jmrplens.github.io/phonometry/underwater/underwater-acoustics/).