Humpback High Season

I found out through Whale Watch Cork that Christmas and New Years is the season for humpback whale sightings in Ireland. They're not spotted that often in Irish waters as they pass by en-route between the Azores and the Arctic. That got me wondering. If we assume that they are indeed there could we use Passive Acoustic Monitoring (PAM) to detect them even though we're not out at sea to see them? But where should we place the listening stations?
Below I'm outlining a guess for a migration route for an imaginary humpback (some clearly go a different way, Kennedy et al. 2013).

Figure 1. This route is my best guess (one of many), based on the fact that some of the whales are seen close to the Irish coast on their route. 

There's a couple of assumptions/decisions that need to be made for this kind of modelling. I've set our whale at 50 metres depth and it's only calling at the points on the map. I've assumed that there is a sound duct at 500 meters depth (sound speed = 1480 m/s). The seabed is sandy and the weather is calm (so shallow areas confine sound energy between bottom and surface). Also I'm counting on the calls of the whale to omni-directional or at least random in direction. The real detection ranges will be smaller than these predictions.

Figure 2. The extent of our whale's call in an otherwise quiet ocean. Notice the ducting in shallow waters on the continental shelf.

Figure 3. Within the coloured area in the figures an acoustic logger should be able to detect our whale (given an otherwise quiet ocean). In the right-hand illustration, the noise floor of the hydrophone is applied. Loggers in red areas would not detect the whale.

The self noise of the hydrophone (an SM2M from WildlifeAcoustics) is 78 dB re 1 μPa, and thus the minimal detectable sound has to be louder than this. What is interesting here is not finding that by placing a logger in the yellow area in Figure 3, we would expect to detect the whale. The interesting bit is the locations where we would not expect to detect it, even though the whale is quite close (Figure 3 red areas). 
The modelling also allows us to predict that placing loggers in the deeper waters will give my loggers way more success in detecting our whale.

Thank you for reading, please feel free to comment if you have thoughts/questions!

Literature

Kennedy AS, Zerbini AN, Vasquez OV, Gandilhon N, Clampham PJ & Adam O. (2014). Local and migratory movements of humpback whales (Megaptera novaeangliae) satellite-tracked in the North Atlantic Ocean. Canadian Journal of Zoology, 92:9-18.

Thompson PO, Cummings WC & Ha SJ. (1986). Sounds, source levels, and associated behavior of humpback whales, Southeast Alaska. Journal of Acoustical Society of America, 80(3):735-740.