Underwater acoustics: radiated noise and pile driving

Underwater sound is referenced to 1 µPa (not the 20 µPa of airborne acoustics), and its exposure to 1 µPa²·s. This page covers the ISO 18405 reference levels realised as the shared primitives, the ISO 17208 ship radiated noise level and equivalent monopole source level, and the ISO 18406 percussive pile-driving single-strike, peak and cumulative sound exposure. Every quantity is an exact closed form, verified analytically.

1. Reference levels (ISO 18405)

Three primitives, referred to 1 µPa, are computed from a captured pressure signal (in Pa):

$$\mathrm{SPL}=10\lg \frac{⟨p^2⟩}{p_0^2},\mathrm{SEL}=10\lg \frac{\int p^{2}dt}{E_0},L_{p,\mathrm{pk}}=20\lg \frac{\max |p|}{p_0},$$

with p₀ = 1 µPa and E₀ = 1 µPa²·s. The sound pressure level is the mean-square level (ISO 18406 Formula 7); the sound exposure level integrates the squared pressure over the record (Formulae 3–4); the peak level is the zero-to-peak value.

from phonometry import underwater

spl = underwater.sound_pressure_level(pressure)        # dB re 1 µPa
sel = underwater.sound_exposure_level(pressure, fs)     # dB re 1 µPa²·s
pk = underwater.peak_sound_pressure_level(pressure)     # dB re 1 µPa

To re-reference a level between the underwater (1 µPa) and airborne (20 µPa) conventions (a 20·lg(20) ≈ 26.02 dB shift, not an energy/intensity equivalence), use underwater_to_in_air_spl / in_air_to_underwater_spl. For background-noise subtraction, reuse the ISO 3744 background_noise_correction (K1) helper.

2. Ship radiated noise and source level (ISO 17208-1/-2)

A surface ship measured in deep water is described first by its radiated noise level and then by an equivalent monopole source level:

$$L_{\mathrm{RN}}=20\lg \frac{p_{\mathrm{rms}}}{p_0}+20\lg \frac{r}{r_0}\mathrm{dB}\mathrm{re}1\mu \mathrm{Pa}\cdot \mathrm{m},L_s=L_{\mathrm{RN}}+\Delta L,$$

where the Lloyd’s-mirror surface correction (ISO 17208-2 Formula 3) for a nominal source depth d_s = 0.7·D (D = mean draught) and u = k·d_s, k = 2πf/c, is

$$\Delta L=-10\lg \frac{2u^4+14u^2}{14+2u^2+u^4}\mathrm{dB}.$$

ΔL diverges at low u (grazing / low frequency) and tends to −10·lg(2) = −3.01 dB as u → ∞. The reported source level is an equivalent monopole broadside value and must be quoted with its source depth.

Show the code for this figure

import numpy as np
from phonometry import underwater

freqs = np.array([20, 25, 31.5, 40, 50, 63, 80, 100, 125, 160, 200, 250, 315,
                  400, 500, 630, 800, 1000, 1250, 1600, 2000, 2500, 3150,
                  4000, 5000, 6300, 8000, 10000, 12500, 16000, 20000.0])
rnl = 175.0 - 12.0 * np.log10(freqs / 20.0)
res = underwater.monopole_source_level(rnl, freqs, draught=6.0)
res.plot()

from phonometry import underwater

lrn = underwater.radiated_noise_level(2e-6, 100.0)   # p_rms = 2 µPa, r = 100 m
res = underwater.monopole_source_level(lrn, 200.0, draught=6.0)
print(res.source_level, res.surface_correction, res.source_depth)
res.plot()   # RNL, Ls and ΔL vs frequency (needs matplotlib)

hydrophone_depths gives the three ISO 17208-1 measurement depths from the 15°/30°/45° depression angles, and source_level_uncertainty the tabulated expanded uncertainty (5 dB ≤100 Hz, 3 dB 125 Hz–16 kHz, 4 dB >16 kHz).

What turns these closed forms into a comparable number is the measurement discipline ISO 17208-1 wraps around them. The ship transits a straight course past a vertical string of three hydrophones at a closest point of approach of 100 m or one ship length, whichever is greater, in water at least 150 m or 1.5 ship lengths deep so the bottom stays out of the picture (Clauses 5.2, 5.4). Only the data window of ±30° about the CPA is scored: the averaging runs while the ship crosses a window of length $2d_{CPA}\tan 30°$ (about 1.15 CPA distances), centred on the beam aspect the radiated noise level is defined for (Clause 3, Figure 3). Four runs are required, two per side; each run’s three hydrophone levels are power-averaged (Formula 8), the runs are then arithmetically averaged (Formula 9), and port and starboard are also reported separately, because a real ship does not radiate symmetrically (Clause 6.5). Background noise is measured at the start and end of each test period and the ISO 3744-style correction applied per band; the recommended wind limit is 20 kn for ships above 100 m (Clause 5.3). Skip any of this and the number you quote is a level, but not an ISO 17208 radiated noise level.

3. Pile-driving sound (ISO 18406)

Percussive pile driving radiates one impulsive pulse per hammer strike. Each strike has a single-strike sound exposure level SEL_ss; over a driving sequence the exposures add to a cumulative sound exposure level:

$$\mathrm{SE}{\mathrm{L}}_{\mathrm{cum}}=10\lg \sum _{n}10^{{\mathrm{SEL}}_n/10},\text{and for }N\text{ identical strikes }=\mathrm{SE}{\mathrm{L}}_{\mathrm{ss}}+10\lg N.$$

Show the code for this figure

import numpy as np
from phonometry import underwater

fs = 48000
t = np.arange(int(0.3 * fs)) / fs
envelope = np.where(t < 0.01, t / 0.01, np.exp(-(t - 0.01) / 0.04))
pressure = 8000.0 * envelope * np.sin(2 * np.pi * 180.0 * t)
res = underwater.pile_strike_metrics(pressure, fs)
res.plot()

from phonometry import underwater

sel_ss = underwater.single_strike_sel(strike_pressure, fs)   # dB re 1 µPa²·s
sel_cum = underwater.cumulative_sel_identical(sel_ss, 2000)   # 2000 strikes
res = underwater.pile_strike_metrics(strike_pressure, fs)
print(res.single_strike_sel, res.peak_spl, res.pulse_duration)
res.plot()   # waveform + cumulative energy (needs matplotlib)

pile_strike_metrics bundles the single-strike SEL, the peak sound pressure level, the SPL/Leq and the 90 %-energy pulse duration for one recorded strike; cumulative_sel sums a sequence of differing per-strike SELs.

These are the metrics that regulation is written in. ISO 18406 exists because offshore wind-farm, oil-and-gas and bridge foundations are consented under environmental impact frameworks that require the radiated sound to be monitored, and its scope is drawn accordingly: percussive driving in 4 to 100 m of water, with vibro- and sheet-piling excluded (Clause 1). The minimum campaign is one measurement position as close as possible to 750 m from the pile, recording the entire driving sequence and reporting the actual range; the standard is explicit that 750 m is chosen for comparability with the large body of existing measurements, not because any regulator’s limit lives there, and that a single-range level has no predictive value for other sites (Clause 6.1.2, Notes 1–2). Impact criteria for marine fauna are phrased in exactly the quantities of this section, a cap on the single-strike or cumulative SEL and on the peak level at a stated range, which is why pile_strike_metrics reports them together and cumulative_sel follows the strike-by-strike energy sum of Formulae 8–9.

What this guide covers

Covered. ISO 18405:2017 for the reference levels re 1 µPa and 1 µPa²·s: sound_pressure_level, sound_exposure_level and peak_sound_pressure_level. ISO 17208-1:2016 and ISO 17208-2:2019 for the ship radiated noise level and the equivalent monopole source level: radiated_noise_level and monopole_source_level, with the Lloyd’s-mirror surface correction (Formula 3) and the 0.7·draught source depth (Formula 1), the three-hydrophone geometry (hydrophone_depths) and the tabulated source-level uncertainty (source_level_uncertainty). ISO 18406:2017 for the pile-driving metrics of section 3: the single-strike SEL (Formulae 3-4), the mean-square SPL (Formula 7) and the cumulative SEL (Formulae 8-9), which single_strike_sel, cumulative_sel, cumulative_sel_identical and pile_strike_metrics compute.

Not covered. ISO 17208-1’s measurement discipline itself is not implemented: the four-run, three-hydrophone power and arithmetic averaging (Formulae 8-9), the CPA and water-depth geometry checks, the ±30° data-window scoring and the ISO 3744-style background-noise correction described in section 2 above are left to the reader; the library only supplies the closed-form radiated_noise_level and monopole_source_level formulae. ISO 18406 itself excludes vibro- and sheet-piling from its scope (Clause 1), so continuous pile-driving noise has no closed form here or elsewhere in phonometry.

See also

• API reference: underwater.acoustics, underwater.pile_driving_noise and underwater.ship_radiated_noise.
• General underwater propagation modelling (ray, normal mode, parabolic equation) is covered in Underwater sound propagation.

References

• Ainslie, M. A. (2010). Principles of sonar performance modelling. Springer. https://doi.org/10.1007/978-3-540-87662-5The systematic treatment of underwater acoustical quantities in the line that ISO 18405 standardised; supports the reference levels and the source level of sections 1-2.
• International Organization for Standardization. (2016). Underwater acoustics — Quantities and procedures for description and measurement of underwater sound from ships — Part 1: Requirements for precision measurements in deep water used for comparison purposes (ISO 17208-1:2016). The radiated noise level, the deep-water three-hydrophone geometry and the tabulated source-level uncertainty of section 2.
• International Organization for Standardization. (2017). Underwater acoustics — Measurement of radiated underwater sound from percussive pile driving (ISO 18406:2017). The single-strike (Formulae 3–4), peak and cumulative (Formulae 8–9) sound exposure of section 3, and the mean-square sound pressure level (Formula 7) of section 1.
• International Organization for Standardization. (2017). Underwater acoustics — Terminology (ISO 18405:2017). The 1 µPa sound-pressure and 1 µPa²·s sound-exposure references and the definitions of sound pressure level, sound exposure level and peak sound pressure level.
• International Organization for Standardization. (2019). Underwater acoustics — Quantities and procedures for description and measurement of underwater sound from ships — Part 2: Determination of source levels from deep water measurements (ISO 17208-2:2019). The equivalent monopole source level via the Lloyd's-mirror surface correction (Formula 3) for a 0.7·draught source depth.
• Urick, R. J. (1983). Principles of underwater sound (3rd ed.). McGraw-Hill. Reprinted 1996 by Peninsula Publishing. ISBN 978-0-932146-62-5. Open Library record (https://openlibrary.org/books/OL9317725M). The classic treatment of underwater sound levels and of ship radiated noise behind the reference conventions of sections 1-2.