Finally, whether or not a particular acoustic signal can be detected in the ocean is a factor of the level of the signal of interest relative to the background noise level of the ocean, or ambient noise. This is normally expressed as a "signal to noise ratio" (SNR), where any value greater than 1 implies that the signal is detectable above the noise, while a number below 1 implies that the signal is "buried" in the noise.  For rough, "back of the envelope" calculations of SNR, ambient noise level (NL) is  subtracted from the sound intensity level:

SNR = SIL - NL

A number greater than 0 dB implies we could detect the signal from background noise, while a number less than 0 dB would imply we could not hear the signal. In the above example of the vocalizing humpback, could we hear this animal above background noise at this distance ? (assume NL at 120 Hz is about 70 dB)

SNR = 90 - 70 dB

= 20 dB

This whale vocalization is about 20 dB above ambient noise level, and we are likely to hear it!

In practice, this basic concept becomes much more complicated. First, the ambient noise field of the ocean is quite variable with respect to time, location, and frequency. Effects can be seasonal, for example the presence of absence of a storm track that introduces loud wave noise, or hourly, such as the passing of a ship. Also, the propagation properties of the water column vary widely with location, depending on the physical oceanographic properties, local bathymetry, and bottom properties. Sophisticated numerical models have been developed over the last several decades to provide improved prediction of acoustic environmental properties. Finally, natural sound sources such as marine mammals and earthquakes may have significant variability in their source level making the calculation of signal-to-noise ratio even more difficult.