Sound Travel in the SOFAR Channel

In the deep ocean at mid-latitudes, the slowest sound speed occurs at a depth of about 800 to 1000 meters. This is called the sound speed minimum. The sound speed minimum creates a sound channel in which sound waves can travel long distances. Sound is focused in the sound channel because the sound waves are continually bent, or refracted, towards the region of lower sound speed. Sound that travels upward from a source at the sound speed minimum is bent back towards the minimum. Similarly, sound that travels down from the source is bent back up toward the minimum.

The following figure has two parts. On the left is a plot of sound speed as a function of depth. The sound speed minimum at a depth of 1000 meters is called the deep sound channel or, more historically, the SOFAR channel. SOFAR stands for SOund Fixing And Ranging. On the right are the paths followed by sound waves as they travel away from the source. These waves are continually refracted toward the sound speed minimum.

Graph showing sound speed and path of travel through the water column. On the left is a plot off sound speed as a function of depth. On the right are the paths followed by sound waves as they travel away from a sound source located at a depth of 1000 m, on the sound channel axis. Only rays that do not hit the ocean surface or seafloor are shown. Adapted from Figure 2.3 in Munk et al., 1995.

Vertical distances in this figure are greatly exaggerated compared to horizontal distances. This causes the angles from the horizontal at which sound waves travel to look much steeper than they really are. The steepest paths shown in this figure are only about 12° from the horizontal and are in reality nearly horizontal.

Only certain sound waves stay in the sound channel without hitting the ocean surface or seafloor. Sound waves traveling upward from the source at angles of less than about 12° are refracted back toward the sound speed minimum before ever reaching the surface. Similarly, sound waves traveling downward from the source at angles of less than about 12° will be refracted back toward the minimum before ever reaching the seafloor. Sound waves that start upward from the source at steeper angles are still refracted, but not sharply enough to avoid hitting the ocean surface. Similarly, sound waves that start downward from the source at steeper angles will not be refracted sharply enough to avoid hitting the seafloor.

Sound loses energy whenever it hits the ocean surface or seafloor. Whenever sound reflects from the rough ocean surface or seafloor, some sound energy is scattered and lost. A sound wave that hits the ocean surface or seafloor many times will be too weak to be detected.

Sound that does not hit the ocean surface or seafloor will still lose energy to absorption. Low-frequency sounds lose very little energy to absorption, however. The result is that low-frequency sounds that do not interact with the ocean surface or seafloor can be detected after traveling long distances through the ocean.

The amount of absorption increases as the frequency of the sound increases, and higher frequency sounds are therefore only detectable at shorter distances. The distances at which sounds can be detected depend on the frequency, how loud the source is, and how loud the background (ambient) noise is.

Sound waves traveling in the sound channel follow many different paths. When the sound source and receiver are located at the depth of the sound speed minimum, called the SOFAR or sound channel axis, sound waves travel nearly straight down the axis and cycle above and below the axis, almost reaching both the surface and bottom.

Sound channel axis. On the left, sound speed profile from mid-latitudes. On the right are shown only the paths sound travels from a source at 1000m depth to a receiver at 1000m depth that is 210km away from the source. Contrast this image with the image toward the top of the page where all paths a sound travels from a sound source are shown. Adapted from Figure 1.1 of Munk et al., 1995.

Although sound travels away from a sound source in all directions, only sound traveling away from a source on paths that leave the source at specific angles will reach a receiver at a specific location. The sound waves traveling on these different paths have slightly different travel times. A single explosive source will therefore be heard as a number of separate arrivals, leading to the characteristic signature of a SOFAR transmission building up to its climax:

The final pulse of sound is typically the loudest and comes from the sound wave that travels nearly on the sound channel axis. Although this sound wave travels the shortest distance, it travels in the region near the sound speed minimum where the sound speed is lowest.

The paths that sound will take for a source near the ocean surface are quite different. If the deep sound channel extends up to the surface, rays that depart from the source nearly horizontally will not hit the ocean surface or seafloor. Sounds that travel on these paths can be detected at long ranges, just as is true for sounds traveling away from a deep source that do not interact with the ocean surface or seafloor. Sound paths from a source near the surface come together, or converge, creating regions of higher sound pressure at about the same depth as the source every 50-60 km away from it. These regions of higher sound pressure are called convergence zones. In between the convergence zones, there are regions of lower sound pressure called shadow zones.

On the left is a plot of sound speed as a function of depth. On the right are the paths followed by sound waves as they travel away from a sound source located at a depth of 50 m. Only rays that do not hit the ocean surface or seafloor are shown. The rays come back together near the surface at a range of about 55 km, forming a convergence zone. The rays do not reach the region near the surface between the source and the convergence zone, forming a shadow zone.

Additional Links on DOSITS

• Sound Speed Minimum
• Sound Channel Variability
• History of the SOFAR Channel

References

• Munk, W., Worcester, P., & Wunsch, C. (1995). Ocean acoustic tomography. Cambridge, England: Cambridge University Press. ISBN: 0-521-11536-1