Ocean Acoustic Monitoring Simulator

Sound source

Water & array

Sound speed (surface layer) 1500 m/s

Thermocline depth 70 m

Hydrophones in array 5

Localization error

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TDOA spread

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Next pulse in

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How it works

Every pulse leaves the source and crosses the water at a speed set mostly by temperature — warmer, shallower water carries sound faster than the cold layer below the thermocline. Each hydrophone on the seafloor hears the pulse at a slightly different moment because it sits a different distance away; those arrival-time differences are the raw data of underwater acoustic monitoring.

v(T) ≈ 1449 + 4.6·T − 0.055·T² + 1.34·(S−35) + 0.017·D
Δt_ij = (|S−H_i| − |S−H_j|) / v

To find the source, pick a reference hydrophone (the first to hear the pulse) and write, for every other hydrophone i, a range-difference equation R_i = v·(t_i − t_ref). Squaring and subtracting the reference equation turns the hyperbolic system into a linear one in the source's (x, z) position and its unknown range r₀ to the reference — solved here by least squares from ≥4 hydrophones:

2x(x_ref−x_i) + 2z(z_ref−z_i) − 2r₀R_i = R_i² − (x_i²+z_i²) + (x_ref²+z_ref²)

Sound speed — the reference speed the array assumes is uniform, exactly as real sonar processing does; raise or lower it to see the whole estimate shift.
Thermocline depth — where the fast surface layer gives way to the slower deep layer. A pulse's real travel time is a distance-weighted blend of both layers, but the solver still assumes one uniform speed — the deeper the thermocline sits relative to source and array, the bigger that mismatch, and the further the triangulated fix drifts from the true source.
Hydrophones — more receivers over-determine the system and average out noise in the fix; four is the minimum for a 2D least-squares solve.
Source type — a whale call is a slow, deep-diving low-frequency pulse train; a ship stays near the surface and pulses faster, mimicking continuous engine/propeller noise.

Real-world relevance: this is exactly how passive acoustic monitoring networks track whales for conservation and how naval hydrophone arrays localize surface vessels — a moored array plus a stopwatch, no active pinging required.

Hydrophone Sound source Estimated fix Arrival flash

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