Deep sound channel

Why does a whale call fade within kilometres near the surface yet cross an ocean at a certain depth?

A fin whale calls at around twenty hertz. Near the surface that call is lost within a few kilometres. Made at the right depth, the same call — same animal, same frequency, same power — can be picked up an ocean away.

Nothing about the sound has changed, and the water is the same water. So whatever is doing the work belongs to the place. But depth by itself does not carry sound. What does depth change?

Sound in seawater travels at roughly fifteen hundred metres per second, and that figure is not a constant — it depends on temperature, pressure and salinity. Salinity varies little in the open ocean. Temperature and pressure do the work, and both, independently, make sound faster.

Now descend. Below the wind-stirred surface layer the temperature falls steeply through the thermocline. Keep going and it stops falling: the deep ocean is nearly uniformly cold, a couple of degrees, all the way to the bottom. Pressure does something quite different. It rises steadily with depth and never stops.

Put those two together and ask what their sum must look like. Near the surface the collapsing temperature dominates and sound speed falls. Deeper down, temperature has flattened out and the pressure term is unopposed, so sound speed climbs again. A quantity that falls and then rises has a minimum somewhere between — and that minimum is not a coincidence or a feature of any particular sea. It is forced by two competing terms, one of which runs out. (The depth of the crossing is often put at about a kilometre in mid-latitudes, but it genuinely varies with basin, latitude and season, so I will not quote a number for it.)

What does a minimum in speed do to a ray of sound? Refraction gives the answer: a wave crossing a gradient always bends toward the slower side. So a ray setting off upward from the minimum enters faster water and is curved back down. A ray setting off downward also enters faster water, and is curved back up. Neither can leave; the ray oscillates about that depth indefinitely.

Notice what we never needed: a boundary. No mirror, no wall, no interface. The confinement is done by a gradient spread continuously through hundreds of metres of open water.

Why does that matter so much? Two reasons, both large. First, the loss budget. Sound reaching the sea surface is scattered by the wave field; sound reaching the seabed is absorbed and scattered by sediment. A near-surface call spends its short life bouncing between those two lossy faces, while a trapped ray touches neither — so the dominant loss terms simply switch off. Second, geometry. Energy from a point source in open water spreads over an expanding sphere, so intensity falls with the square of range. Confined between an upper and a lower turning depth, it can only spread sideways — over a cylinder — and intensity falls with the first power. Across a thousand kilometres that is not a refinement; it is the whole story. Add that seawater absorbs low frequencies far less strongly than high ones, and a twenty-hertz call has almost nothing working against it.

Does this account predict anything odd enough to be worth testing? It does. Steep rays swing far above and below the axis, spending most of their journey in the faster water at the extremes. The ray that hugs the axis travels the shortest path — through the slowest water. So which arrives first? The steep ones, on the longer path, because speed beats distance here; the axial ray arrives last. An explosive pulse should therefore be heard at range not as a bang but as a rising rumble that stops abruptly at its loudest instant. That is exactly the signature of a channel arrival, and it was the basis of the wartime location scheme Ewing and Worzel proposed in the 1940s.

The refuting observation is equally direct. Lower a probe, measure the profile, and predict where sound will be trapped: at the profile's minimum, wherever that happens to be. Go poleward and the warm surface layer thins away, so the profile becomes an almost monotonic rise from the surface down — the minimum is the surface itself. The prediction is that the channel follows it up, and in polar seas the long-range duct is indeed near-surface. If instead a mid-depth channel persisted in a column whose measured minimum sat at the top, this account would be finished.

The most tempting mistake is to file this alongside an optical fibre. They are not the same trick. A fibre has a step in refractive index at a real boundary, and light is turned back by total internal reflection at that surface. The ocean has no boundary anywhere in the channel; the turning is gradual, done by a gradient, and a ray follows a smooth curve rather than a corner. What the two share is an acceptance angle: only rays launched within a limited angle of the horizontal turn before reaching the surface or the bottom. Sound aimed steeply down from the axis escapes however well placed the source is. The channel selects by angle, not by depth alone.

Two honest qualifications. Ray tracing is an approximation, and at twenty hertz the wavelength is about seventy-five metres, comparable to the scale over which the profile curves — so the careful treatment is in terms of modes rather than rays, and near the axis the ray picture is being pushed. And the channel is indifferent to who uses it: low-frequency shipping noise is funnelled and preserved by exactly the same mechanism, which is one reason the deep ocean's background noise at those frequencies has risen with traffic.

• How the travel time of a channel arrival can be used to measure the average temperature of an entire ocean basin.

Every term the collection defines is gathered in the glossary.