Source: https://jmrplens.github.io/phonometry/underwater/ # Underwater acoustics Underwater acoustics runs on the same physics as airborne acoustics but on a different scale and a different reference: levels are expressed re **1 µPa** (not 20 µPa), exposure re 1 µPa²·s, and the medium itself, with its depth-dependent sound speed, refracts sound into channels that carry it for kilometres. This section covers the discipline along the source-path-receiver chain of the rest of the library. That reference difference is the commonest trap for a reader arriving from airborne acoustics, and it is worth settling before anything else. The same pressure expressed re 1 µPa is **26 dB larger** than expressed re 20 µPa, which is arithmetic. On top of that, the same pressure in water carries far less intensity than in air, because sea water's characteristic impedance is some 3 700 times that of air. An underwater 120 dB and an airborne 120 dB therefore describe entirely different physical situations, and the two must never be compared. The rule this section follows is simple: every level carries its reference explicitly, a conversion between the two conventions is pure re-referencing and never an energy equivalence, and the only place the airborne reference appears here at all is for the two in-air carnivore hearing groups on the exposure page. The **source** stage, in [Underwater acoustics: radiated noise and pile driving](https://jmrplens.github.io/phonometry/underwater-acoustics/), sets up the ISO 18405 terminology (SPL, SEL and peak levels and their references) and applies it to two regulated measurement cases: ships, with the radiated noise level of ISO 17208-1 and the equivalent monopole source level of ISO 17208-2 via the Lloyd's-mirror surface correction, and percussive pile driving, with the single-strike, peak and cumulative sound exposure of ISO 18406. The **path** stage spans two pages. [Underwater sound propagation](https://jmrplens.github.io/phonometry/underwater-propagation/) predicts what the sea does to that sound in closed form: geometrical spreading plus volume absorption (Francois-Garrison, Ainslie-McColm or Thorp), Weston's four shallow-water regimes with their transition ranges, the speed of sound in sea water by four formulations, the passive and active sonar equation with its detection-range inversion, Rayleigh seabed reflection loss, and the Wenz ambient-noise spectrum with JOMOPANS-ECHO ship traffic. When refraction and boundaries decide the answer, [Underwater propagation solvers](https://jmrplens.github.io/phonometry/underwater-solvers/) computes the field instead: the normal-mode expansion, ray tracing and the split-step Fourier parabolic equation, with the guidance for choosing between them and the closed forms. A **receiver** stage closes the loop. [Marine-mammal noise exposure](https://jmrplens.github.io/phonometry/marine-mammal-exposure/) takes the level a source and a path produce and asks what it does to the animals that hear it: the group audiograms of Southall et al., the regulatory auditory weighting functions of the NMFS guidance, the TTS and injury onset criteria, and the weighted cumulative exposure of a piling campaign measured against them. Read the pages in that order: the reference levels come first because every propagation result is expressed in them, and the exposure criteria come last because they consume both. Unusually for this site, the theory for these pages lives inline with the guides rather than in the theory reference. ## Pages in this section - [Underwater acoustics: radiated noise and pile driving](https://jmrplens.github.io/phonometry/underwater-acoustics/): ISO 18405 reference levels, ISO 17208 ship radiated noise and monopole source level, and ISO 18406 pile-driving sound exposure. - [Underwater sound propagation](https://jmrplens.github.io/phonometry/underwater-propagation/): propagation loss, sound speed, the sonar equation, seabed reflection and ocean ambient noise, in closed form. - [Underwater propagation solvers](https://jmrplens.github.io/phonometry/underwater-solvers/): the normal-mode, ray-tracing and parabolic-equation solvers of the stratified waveguide, each validated against an exact closed form, and how to choose a propagation model. - [Marine-mammal noise exposure](https://jmrplens.github.io/phonometry/marine-mammal-exposure/): group audiograms, the regulatory auditory weighting functions with the guidance version selectable, the TTS and injury onset criteria, and a worked pile-driving assessment. ## What this section does not cover **The measurement discipline is not implemented, only its arithmetic.** ISO 17208-1's four-run, three-hydrophone averaging, its closest-point-of-approach and water-depth geometry checks, its ±30° data-window scoring and its background-noise correction are the operator's; the library supplies the closed-form radiated-noise and monopole source levels that follow. ISO 18406 itself excludes vibro- and sheet-piling from its scope, so continuous pile-driving noise has no closed form here or anywhere in the library. **The seabed is thin.** The closed-form page models it as a lossless fluid-fluid Rayleigh reflection, so sediment attenuation is out of scope, and all three solvers assume a **range-independent** water column with no absorbing or elastic bottom and no real bathymetry — which rules out range-dependent problems entirely. The ray solver returns paths and travel times but not amplitudes (no ray-tube intensity, no caustic correction), and the parabolic equation is the standard small-angle Tappert form rather than a wide-angle Padé variant. For the elastic seabed physics these fluid solvers leave out, the [elastic wave solver](https://jmrplens.github.io/phonometry/simulation/elastic-waves/) is the nearest thing the library has. **The exposure page rates hearing, not behaviour.** Only the auditory-effect criteria are implemented; behavioural-disturbance thresholds, the ones a harassment take estimate turns on, are out of scope. Nothing chooses a hearing group or an accumulation period for you, and nothing models the animal moving relative to the source, so the cumulative exposure reported is the stationary-receiver worst case. There is no audiogram for low-frequency cetaceans, because the source publication does not print one of its parameters. Two smaller boundaries: the ambient-noise spectrum leaves out the low-frequency turbulence band and has no built-in distant-shipping model — supply a shipping spectrum yourself — and the active sonar equation is monostatic only. ## Before and after these pages Every level here is a level re 1 µPa computed from a hydrophone record, so the calibration, weighting and spectral estimation behind it are in [Signal analysis](https://jmrplens.github.io/phonometry/signals/), and [Build a sound level meter](https://jmrplens.github.io/phonometry/signals/sound-level-meter/) runs that chain end to end on one runnable page, in air but with the same functions. The underwater theory is deliberately not in the theory reference: it lives inline with the four guides above, where the quantity system of ISO 18405 is introduced with them. If you arrived here from a search and want the shape of the whole library, [What do you need to measure?](https://jmrplens.github.io/phonometry/start/tasks/) indexes it by the job and [All guides](https://jmrplens.github.io/phonometry/) lists every page with a line on each.