It's quiet here - close to the source!?

Sometimes reality is curious, sometimes it gets quieter as you go towards the noise source, and louder as you move away. This counter-intuitive fact is caused by some nifty effects of how the sound speed changes with depth and temperature (calculator) in our oceans (similar to the SOFAR channel).

The other day I read up on the regulations and guidelines for seismic testing in the sea, and the guidelines all rely on animal logic for justification - I'll explain:

The guidelines (e.g. the JNCC guidelines) state that all noisy procedures should be started by emitting a less powerful version of the testing sound, slowly ramping up the volume (over 30 minutes), until full sound power level is reached. This makes intuitive sense as it gives the animals a change to swim away, provided the animals will react with swimming away, and not go to investigate the novel sound in their environment. But even then, the sound surely gets more intense as they approach the source.

...that is the assumption at least...

But, a big "but"...
Due to the nature of varying sound speeds in water, sound can get refracted i.e. "bend" from its path, and no longer travel straight. It also happens in air, and it is the reason you can hear people from far away over a cold lake. The air immediately over the lake is colder than the air further up, meaning that the sound is moving slower close to the surface of the lake, and faster further up, refracting the sound downwards, forming a sound "channel". In water a similar effect can cause the sound field to be anything but what you might expect.

Figure 1: The source emits sound horizontally (±30 degrees) and the sound speed profile causes the sound to be refracted towards a zone of sound speed minimum, here the speed minimum is at half the maximum depth. Notice how sound level is by no means uniform in spreading from the source.

Notice the area with no/low sound intensity in the left image of the above figure. It is exaggerated, but a zone of less intense sound is there. I've added a little whale (excuse my paint skills), for which it would get quieter if it moved towards the source. It could end up very close to the source during the ramping up of noise levels.
(The authors of the JNCC report are well aware of this and they discuss it in the report. I have no intend of discussing their work, I merely look at the interesting mechanics involved.)

Figure 2: A simple explanation of how sound is refracted, from: hyperphysics.

Figure 3: Animation of refraction of waves travelling from fast medium to slow medium, from: University of Southampton.

In the two above figures (that are not my creations) the refraction of waves between media is explained. In water, even though clines can seem very sudden they are nothing like the sharp borders depicted in Figure 2 & 3, rather they are gradual changes (10 cm to 10 m) in e.g. temperature or salinity. Together with pressure they determine the sound speed in the sea. In dBSea the solution to this propagation problem is to approximate the gradual changes by calculating refraction between hundreds of layers, in a process called ray tracing, where single ray-paths are followed and computed as they migrate through the water. Do this many times over, and you get a complete picture of the sound pathways. Below is an animation of a few waves:

Figure 4: Ray tracing with few rays, with sound speed minimum at ~1km depth. From Wikipedia

Enjoy your weekend.