Ocean Acoustic Tomography Simulator: Map Temperature with Sound

simulator intermediate ~10 min
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Δt = −0.90 ms — travel time anomaly from warming

A 0.5°C temperature anomaly along a 1000 km path speeds up sound by about 2 m/s, arriving 0.90 milliseconds early. This precision timing allows oceanographers to measure basin-averaged temperature changes with unprecedented accuracy.

Formula

t₀ = L / c₀ (baseline travel time)
Δt = −L × δc / c₀² ≈ −L × 4ΔT / c₀² (travel time perturbation)
δT = c₀² × Δt / (4 × L) (temperature from travel time)

Listening to Ocean Temperature

Ocean acoustic tomography exploits a simple physical fact: sound travels faster in warmer water. By precisely timing acoustic pulses sent between pairs of transceivers separated by hundreds or thousands of kilometers, oceanographers can measure the path-averaged temperature of the intervening ocean. The technique, proposed by Walter Munk and Carl Wunsch in 1979, represents one of the few methods capable of monitoring the ocean interior at basin scales.

Ray Paths as Thermometers

Sound between a source and receiver travels along multiple ray paths, each sampling different depth ranges as it refracts through the ocean's sound speed profile. A steep ray that loops to near the surface measures upper-ocean temperature, while an axial ray near the SOFAR channel reports deep-water conditions. Identifying and timing each ray arrival creates a set of depth-resolved temperature measurements from a single source-receiver pair.

Tomographic Inversion

With multiple source-receiver pairs arranged in a network, the intersecting ray paths create a grid of constraints on the ocean's temperature field. Solving the resulting inverse problem — mathematically analogous to medical CT scanning — yields a three-dimensional temperature map. The resolution improves with more paths and more crossing angles, making network geometry a critical design parameter.

Climate Monitoring at Scale

Acoustic tomography offers unique advantages for climate science: it inherently averages over large volumes (suppressing mesoscale noise that plagues point measurements), operates continuously in all weather, and reaches the deep ocean that satellites cannot see. The ATOC experiment demonstrated that basin-averaged temperature trends can be measured to millidegree precision — sufficient to track the oceanic heat uptake that dominates Earth's energy imbalance.

FAQ

What is ocean acoustic tomography?

Ocean acoustic tomography is a technique that uses the travel times of sound pulses between multiple source-receiver pairs to reconstruct the ocean's temperature structure. Just as medical CT scans use X-ray paths to image the body, acoustic tomography uses intersecting sound paths to image the ocean interior. It was proposed by Walter Munk and Carl Wunsch in 1979.

How does temperature affect sound travel time?

Sound speed in the ocean increases by approximately 4 m/s per degree Celsius of warming. Over a 1000 km path, a 0.5°C warming shortens travel time by about 0.9 milliseconds. Modern ocean acoustic systems can measure travel times to sub-millisecond precision, enabling millidegree temperature resolution.

What is the ATOC experiment?

The Acoustic Thermometry of Ocean Climate (ATOC) experiment, conducted from 1996 to 2006, transmitted low-frequency (75 Hz) sound from a source near Hawaii to receivers across the North Pacific. It successfully measured basin-averaged temperature changes consistent with satellite and float observations, demonstrating the feasibility of acoustic climate monitoring.

How is tomographic inversion performed?

Each identified ray path between source and receiver samples a different region of the ocean. By measuring travel time perturbations on multiple paths and using knowledge of the ray geometries, an inverse problem is solved (similar to medical CT) to reconstruct the spatial distribution of sound speed anomalies, which are then converted to temperature.

Sources

Embed

<iframe src="https://homo-deus.com/lab/ocean-acoustics/acoustic-tomography/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub