SOFAR Channel Simulator: How Sound Travels Across Oceans

simulator intermediate ~10 min
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c_min = 1481 m/s at 800 m depth — SOFAR axis

With 18°C surface temperature and 35 PSU salinity, the sound speed minimum of 1481 m/s occurs at the SOFAR axis (800 m depth), creating an acoustic waveguide that can trap sound energy for thousands of kilometers.

Formula

c(z) = 1449 + 4.6T − 0.055T² + 0.0003T³ + (1.39−0.012T)(S−35) + 0.017z
θ_max = arccos(c_min / c_surface) (maximum trapped ray angle)
r_CZ ≈ π × R_E × θ_max (convergence zone range)

The Ocean's Acoustic Waveguide

The SOFAR channel is one of nature's most remarkable waveguides. Discovered during World War II by Maurice Ewing and Joe Worzel, it arises from the competing effects of temperature and pressure on sound speed. Temperature decreases with depth (lowering sound speed) while pressure increases (raising it). The resulting sound speed minimum, typically between 600 and 1200 meters depth, acts as a lens that continuously refracts acoustic energy back toward the axis.

Sound Speed Profile

The Mackenzie equation calculates sound speed from temperature, salinity, and depth. Near the surface, warm water yields high sound speed (~1520 m/s in the tropics). Through the thermocline, speed drops rapidly. Below, in the cold isothermal deep ocean, increasing pressure steadily raises speed again. The minimum — the SOFAR axis — is where temperature's downward pull exactly balances pressure's upward push.

Trapping and Propagation

Sound rays launched near the SOFAR axis oscillate up and down about the minimum, never reaching the surface or bottom. This eliminates reflection losses and reduces geometric spreading from spherical (1/r²) to cylindrical (1/r). Combined with the ocean's extremely low absorption at frequencies below 100 Hz, this allows signals to traverse entire ocean basins — a phenomenon exploited by blue whales whose calls can be heard across the Pacific.

Modern Applications

Acoustic thermometry uses the SOFAR channel to measure basin-averaged ocean temperatures to millidegree precision by timing signals across thousands of kilometers. Changes in travel time reveal warming trends with unprecedented sensitivity. The same channel supports submarine communication, earthquake detection via T-phase arrivals, and autonomous underwater vehicle navigation using acoustic positioning networks.

FAQ

What is the SOFAR channel?

The SOFAR (Sound Fixing and Ranging) channel is a natural acoustic waveguide in the ocean, centered on the depth of minimum sound speed (typically 600-1200 m). Sound speed decreases with temperature (which drops with depth) but increases with pressure (which rises with depth). The resulting minimum traps acoustic energy, allowing sounds to propagate thousands of kilometers.

Why does sound speed vary with depth in the ocean?

Sound speed depends on temperature, salinity, and pressure. In the upper ocean, temperature dominates: the thermocline causes sound speed to decrease with depth. Below the thermocline, pressure takes over: sound speed increases with depth. The competition creates a minimum — the SOFAR channel axis — where acoustic energy is naturally focused.

How far can sound travel in the SOFAR channel?

Under favorable conditions, low-frequency sounds (10-100 Hz) can propagate across entire ocean basins — over 20,000 km. This remarkable range is possible because the waveguide prevents geometric spreading loss in the vertical direction, and absorption at low frequencies is extremely small.

What are SOFAR channel applications?

Originally developed for locating downed aircraft and submarines during WWII, the SOFAR channel now supports acoustic thermometry (measuring ocean temperature changes over basin scales), submarine communication, tsunami warning systems, and marine mammal research — many whale species exploit the SOFAR channel for long-range communication.

Sources

Embed

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