underwater.sources.ship_radiated_noise

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

A surface ship measured in deep water is characterised by its radiated noise level and then by an equivalent monopole source level referred to a point source below the sea surface:

• radiated_noise_level — $L_{\mathrm{RN}}=20{\log }_{10}(p_{\mathrm{rms}}/p_0)+20{\log }_{10}(r/r_0)$ dB re 1 µPa·m (ISO 17208-1), the level of the product of the far-field RMS pressure and the source distance.
• monopole_source_level — converts LRN to the source level $L_{\mathrm{s}}=L_{\mathrm{RN}}+\Delta L$ with the Lloyd’s-mirror surface correction $\Delta L$ of ISO 17208-2 Formula 3, for a nominal source depth $d_{\mathrm{s}}=0.7D$ (Formula 1).

Supporting helpers give the ISO 17208-1 three-hydrophone measurement depths (hydrophone_depths) and the ISO 17208-2 tabulated source-level uncertainty (source_level_uncertainty). The conversion assumes an ideal pressure-release sea surface and ignores wind; the reported source level is an equivalent monopole broadside value and must be quoted with its source depth.

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hydrophone_depths

hydrophone_depths(
    cpa_distance: float,
    angles: tuple[float, ...] = (15.0, 30.0, 45.0),
) -> NDArray[np.float64]

Hydrophone depths for the ISO 17208-1 deep-water geometry.

At the closest point of approach the three hydrophones sit at depression angles from the sea surface seen from the ship reference point; at a horizontal range equal to cpa_distance the depth of each is $d=d_{\mathrm{CPA}}\tan (\mathrm{angle})$.

Parameters

Name	Description
cpa_distance	Horizontal distance at the closest point of approach, in m ($d_{\mathrm{CPA}}=\max (100\text{m},\text{ship length})$).
angles	Depression angles, in degrees (default 15°, 30°, 45°).

Returns: The hydrophone depths, in m.

Raises

Exception	When
ValueError	If the distance or any angle is out of range.

monopole_source_level

monopole_source_level(
    rnl: float | NDArray[np.float64] | list[float],
    frequency: float | NDArray[np.float64] | list[float],
    draught: float,
    *,
    c: float = 1500.0,
) -> ShipSourceLevelResult

Equivalent monopole source level from radiated noise level (ISO 17208-2).

$L_{\mathrm{s}}=L_{\mathrm{RN}}+\Delta L$ with the surface correction

$$\Delta L=-10{\log }_{10}\frac{2u^4+14u^2}{14+2u^2+u^4}\text{\hspace{1em}(Formula 3)}$$

where $u=k{d}_{\mathrm{s}}$, $k=2\pi f/c$ and the nominal source depth is $d_{\mathrm{s}}=0.7D$ (Formula 1).

Parameters

Name	Description
rnl	Radiated noise level per frequency, in dB re 1 µPa·m (scalar or array; array length must match frequency).
frequency	Frequency or frequencies, in Hz.
draught	Ship draught D (mean of bow and stern), in m.
c	Speed of sound in sea water, in m/s (default 1500).

Returns: A ShipSourceLevelResult.

Raises

Exception	When
ValueError	If the inputs are invalid or the shapes mismatch.

radiated_noise_level

radiated_noise_level(rms_pressure: float, distance: float) -> float

Radiated noise level LRN (ISO 17208-1), dB re 1 µPa·m.

$L_{\mathrm{RN}}=20{\log }_{10}(p_{\mathrm{rms}}/p_0)+20{\log }_{10}(r/r_0)$ — the level of the product of the far-field RMS sound pressure and the source distance, referred to 1 µPa·m.

Parameters

Name	Description
rms_pressure	Far-field RMS sound pressure p_rms, in Pa.
distance	Distance r from the ship reference point, in m.

Returns: Radiated noise level, in dB re 1 µPa·m.

Raises

Exception	When
ValueError	If the pressure or distance is not positive.

ShipSourceLevelResult

ShipSourceLevelResult(
    frequencies: NDArray[np.float64],
    radiated_noise_level: NDArray[np.float64],
    surface_correction: NDArray[np.float64],
    source_level: NDArray[np.float64],
    source_depth: float,
    sound_speed: float,
)

Equivalent monopole source level of a ship (ISO 17208-2).

Attributes

Name	Description
frequencies	Frequencies, in Hz.
radiated_noise_level	Input RNL per frequency, in dB re 1 µPa·m.
surface_correction	Lloyd’s-mirror correction $\Delta L$ per frequency, dB.
source_level	Equivalent monopole source level $L_{\mathrm{s}}=L_{\mathrm{RN}}+\Delta L$, in dB re 1 µPa·m.
source_depth	Nominal source depth $d_{\mathrm{s}}=0.7D$, in m.
sound_speed	Speed of sound used, in m/s.

ShipSourceLevelResult.plot()

ShipSourceLevelResult.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Plot RNL, source level and the ΔL surface correction vs frequency.

source_level_uncertainty

source_level_uncertainty(frequency: float) -> float

Tabulated expanded source-level uncertainty (ISO 17208-2 §5), in dB.

5 dB for the low-frequency bands (the standard lists 10 Hz-100 Hz; values below 10 Hz reuse it), 3 dB for the mid-frequency bands (125 Hz-16 kHz) and 4 dB for the high-frequency bands. Part 2 prints its high band as ”> 20 000 Hz”, which leaves the 20 kHz band itself unassigned; Part 1, from which the values are taken, prints ”>= 20 000 Hz”. This implementation follows Part 1, so the 4 dB high-band value applies from the 20 kHz band upwards (the cut is written at 16 kHz because no one-third-octave band lies between the two). These are representative values, not exact.

Parameters

Name	Description
frequency	One-third-octave band centre frequency, in Hz.

Returns: The representative expanded uncertainty, in dB.

Raises

Exception	When
ValueError	If the frequency is not positive.