underwater.sonar_equation

The sonar equation (passive and active), in decibels.

Combines the sonar performance terms — source level SL, transmission loss TL, noise level NL, directivity index DI, detection threshold DT, target strength TS and reverberation level RL — into the signal excess SE, the signal-to-noise ratio and the figure of merit (the maximum allowable transmission loss at the detection limit SE = 0):

• passive_sonar_equation — SE = SL − TL − (NL − DI) − DT.
• active_sonar_equation — monostatic, noise-limited SE = SL − 2·TL + TS − (NL − DI) − DT or, when a reverberation level is given, reverberation-limited SE = SL − 2·TL + TS − RL − DT.

All quantities are in dB (levels re a plane wave of 1 µPa rms; the terms are spectrum levels, i.e. referred to a 1 Hz band). Source: Urick, Principles of Underwater Sound, via Etter (2003), Table 10.2.

Auto-generated from the source docstrings by scripts/generate_api_docs.py (make api-docs). Do not edit by hand.

active_sonar_equation

active_sonar_equation(
    source_level: float,
    transmission_loss: NDArray[np.float64] | list[float] | float,
    target_strength: float,
    noise_level: float,
    *,
    directivity_index: float = 0.0,
    detection_threshold: float = 0.0,
    reverberation_level: float | None = None,
) -> SonarEquationResult

Monostatic active sonar equation with a two-way transmission loss.

Noise-limited: SE = SL − 2·TL + TS − (NL − DI) − DT. When reverberation_level is given, reverberation-limited: SE = SL − 2·TL + TS − RL − DT (DI does not apply to reverberation).

Parameters

Name	Description
source_level	Source level SL, in dB.
transmission_loss	One-way transmission loss TL, in dB (scalar or array); the equation applies 2·TL.
target_strength	Target strength TS, in dB.
noise_level	Background noise level NL, in dB.
directivity_index	Receiver directivity index DI, in dB.
detection_threshold	Detection threshold DT, in dB.
reverberation_level	Reverberation level RL in dB; when given, the case is reverberation-limited.

Returns: A SonarEquationResult.

Raises

Exception	When
ValueError	If an input is not finite.

passive_sonar_equation

passive_sonar_equation(
    source_level: float,
    transmission_loss: NDArray[np.float64] | list[float] | float,
    noise_level: float,
    *,
    directivity_index: float = 0.0,
    detection_threshold: float = 0.0,
) -> SonarEquationResult

Passive sonar equation SE = SL − TL − (NL − DI) − DT.

Parameters

Name	Description
source_level	Source level SL (of the target), in dB.
transmission_loss	One-way transmission loss TL, in dB (scalar or array).
noise_level	Background noise level NL, in dB.
directivity_index	Receiver directivity index DI, in dB.
detection_threshold	Detection threshold DT, in dB.

Returns: A SonarEquationResult.

Raises

Exception	When
ValueError	If an input is not finite.

SonarEquationResult

SonarEquationResult(
    mode: str,
    signal_excess: NDArray[np.float64],
    snr: NDArray[np.float64],
    figure_of_merit: float,
    transmission_loss: NDArray[np.float64],
    source_level: float,
    noise_level: float,
    directivity_index: float,
    detection_threshold: float,
    target_strength: float | None,
    reverberation_limited: bool,
)

Sonar-equation solution.

Attributes

Name	Description
mode	"passive" or "active".
signal_excess	Signal excess SE per transmission loss, in dB (detection when SE >= 0).
snr	Signal-to-noise (or signal-to-reverberation) ratio, in dB (SE + DT).
figure_of_merit	Maximum allowable (one-way) transmission loss at the detection limit SE = 0, in dB.
transmission_loss	The transmission-loss values, in dB.
source_level	Source level SL, in dB.
noise_level	Background noise level NL input, in dB. The masking term is NL − DI, except when reverberation_limited is true, where the reverberation level RL masks instead.
directivity_index	Receiver directivity index DI, in dB.
detection_threshold	Detection threshold DT, in dB.
target_strength	Target strength TS, in dB (None for passive).
reverberation_limited	Whether the active case is reverberation-limited.

SonarEquationResult.plot()

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

Plot signal excess versus transmission loss with the detection limit.