Source: https://jmrplens.github.io/phonometry/guides/underwater-acoustics/ # Underwater acoustics: radiated noise and pile driving (ISO 18405 / 17208 / 18406) 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): $$ \mathrm{SPL} = 10\lg\frac{\langle p^2\rangle}{p_0^2}, \qquad \mathrm{SEL} = 10\lg\frac{\int p^2\,dt}{E_0}, \qquad L_{p,\mathrm{pk}} = 20\lg\frac{\max|p|}{p_0}, $$ 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. ```python 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**: $$ L_{\mathrm{RN}} = 20\lg\frac{p_{\mathrm{rms}}}{p_0} + 20\lg\frac{r}{r_0} \ \ \mathrm{dB\ re\ 1\ \mu Pa\!\cdot\! m}, \qquad L_s = L_{\mathrm{RN}} + \Delta L, $$ 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.

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```python 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() ```

```python 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 `2·d_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**: $$ \mathrm{SEL_{cum}} = 10\lg\sum_{n} 10^{\mathrm{SEL}_n/10}, \qquad\text{and for } N \text{ identical strikes } = \mathrm{SEL_{ss}} + 10\lg N. $$

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```python 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() ```

```python 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. ## References - 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. - Ainslie, M. A. (2010). *Principles of sonar performance modelling*. Springer. [doi:10.1007/978-3-540-87662-5](https://doi.org/10.1007/978-3-540-87662-5). The 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. ## Standards ISO 18405:2017, *Underwater acoustics — Terminology*: 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. ISO 17208-1:2016 and ISO 17208-2:2019, *Underwater acoustics — Quantities and procedures for description and measurement of underwater sound from ships*: the radiated noise level, the deep-water three-hydrophone geometry, the tabulated source-level uncertainty and the equivalent monopole source level via the Lloyd's-mirror surface correction (Formula 3) for a `0.7·draught` source depth. ISO 18406:2017, *Underwater acoustics — Measurement of radiated underwater sound from percussive pile driving*: the single-strike (Formulae 3–4), peak and cumulative (Formulae 8–9) sound exposure. All quantities are verified against exact analytic oracles. General underwater propagation modelling (ray, normal mode, parabolic equation) is out of scope here.