Why blue whales don't have mobile phones.

I had a thought - I can turn the tables on underwater noise modelling. Make the animals make the sound and then model that. How far could a theoretical blue whale communicate with other blue whales? Turns out trans-Atlantic is no problem!

The blue whale makes some of the loudest sounds ever recorded (source.pdf). Albeit they are not as loud as sperm whale clicks that can reach SPL's over 200 dB re 1 µPa (up to 236 dB re 1 µPa). These sounds are very short pulses though, and not sustained sounds like the calls of the blue whale. 
One thing besides volume that makes the call of the blue whale especially far-reaching is its very low frequency. Low frequencies travel further because they are not absorbed or scattered as easily.
Recording of blue whale call from the south pacific recorded by NOAA 
The frequencies in this call are centred around 25 Hz, but the call I had access to for my modelling peaks at just 16 Hz (to low for humans to hear).

Further helping the range of their calls is the fact that sound speeds are usually not uniform throughout the water column. Sound will be refracted towards areas of lower sound speed, so sounds travel a lot further in this "channel" because it is no longer spread out as much.
Ray tracing in an ocean of varying speed of sound (from DOSITS). Sound waves are redirected towards areas of lower sound speed, this creates a zone of effective sound conduction.
I've tried to plot this in dBSea. Below here is the result. Whale "A" outputs 186 dB re 1 µPa, and whale "B" receives this signal at ~70 dB. The attentive reader will think, hang on, that can't be right 2500 km! And no it is not correct, I need to take into account that the ocean is not quiet. This will add 60-115 dB to background noise (source), and so whale B will not be able to pick out the call, unless it moves to a "blue" zone in the picture below.

Communication between two imaginary whales across the Atlantic ridge. Notice the presence of a sound channel, in which the sound travels particularly well. 
I'd be excited to get my hands on some real life data on this (and then add that to dBSea), as I have made some BIG assumptions here due to lack of blue whale data. 
  1. I've based blue whale hearing on data from minke whale CT scans (in its own right worth a read!)
  2. There's no noise in my ocean, an important part of this kind of model.
Anyway there's a new version of dBSea out - check it out at: http://www.dbsea.co.uk/download/