# Hydrophone arrays, FTW!

We do a lot of things out here on the CalCurCEAS cruise – we play cribbage, we eat cookies, we ride the stationary bicycle – but mostly we do these two things, A LOT:

1) Look for whales and dolphins.
2) Listen for whales and dolphins.

Part 1, the “Look” part, is within the realm of the visual team, who stand bravely in wind and cold and rain (and sometimes gorgeous, balmy sunshine) and scan the surface of the ocean for animals that might pop up to say hi and or take a quick breath of air.

Part 2, the “Listen” part, exists because, well, it’s pretty difficult to see what animals are doing once they dip down beneath the waves. And we all know that’s where the fun stuff happens (synchronized swimming practice? underwater tea parties? you never know!).

Since I’m on the acoustics team, I thought I’d give a little overview of how our operation works.  We eavesdrop on the animals using a pair of hydrophones, which are basically underwater microphones. If we just used one hydrophone, it would be okay, we could hear the animals. But adding a second allows us to not only hear them, but figure out where they are.

The pair of hydrophones are built into the end of a cable that is spooled onto a winch on the back deck. Every morning we head out there, don our life jackets, hard hats, and boots, and reel out the cable until the hydrophones are 300 meters behind us. The hydrophones are spaced one meter apart, and once the vessel is up to speed, they are roughly at the same depth.

The upper part of Figure 2 (blue) shows a cartoon schematic of the hydrophone setup. Here’s what it all means:

$H_1$ and $H_2$ – hydrophones #1 and #2

Known quantities:

$d_h$ – distance between $H_1$ and $H_2$. For our array this distance is 1 meter

$c_w$ – measured sound speed in water (approximately 1500 m/s, but depends on temperature and salinity)

Measured/derived quantities:

$\Delta t$ – time delay between when the signal arrives at $H_1$ and $H_2$

$d'$ – distance associated with the time delay $\Delta t$, derived using $c_w$

Unknown quantity:

$\theta$ – angle between the incoming ray path and the array baseline. This is what we’re solving for!

OK, that seems complicated. But feel free to ignore the math, of course. The basic idea is that depending on where the sound comes from, it can arrive at the hydrophones at different times. For example, in the image above, it hits hydrophone 1 first, and after some amount of time, it hits hydrophone 2. The signals from each of the hydrophones are sent upstairs to the acoustics lab (see bottom part of Figure 2). The call shows up at slightly different times on each of the hydrophone channels, and we can measure that time delay $\Delta t$ very precisely.

Using the time delay $\delta t$ and the measured sound speed $c_w$, we can obtain distance $d'$ using:

$d' = c_w * \Delta t$

So now we’ve got a right triangle where we know the hypotenuse and one other side, and you know what that means – trigonometry time!! Everyone’s favorite time! We finally have what we need to solve for the angle $\theta$.

$\theta = acos( \frac{d'}{d_h})$

We now know what angle the dolphin is at relative to the array. Huzzah! But wait. There are just a couple of little details that you need to remember (see Figure 3). First: you don’t know how far away the dolphin is. Second: there’s this pesky thing called “left-right ambiguity” *.

From the perspective of the array, there’s no difference between an animal calling from an angle $\theta$ to the left and an animal calling from an angle $\theta$ to the right.

These are fundamental limitations of the method, but we can (sort of) overcome them. As the vessel moves along, and we estimate angles at different locations, we end up with a location where most of the bearing lines intersect. If the vessel is traveling in a straight line, we can get a good idea of range – how far the animal is from the trackline. We just won’t know which side of the trackline it’s on. But if the vessel makes a turn, the new bearings estimated after the turn will resolve which side of the line it’s on!

At this point you might be wondering, Michelle, what assumptions are you making when you do these calculations? So here they are:

Assumptions**:

• The array is horizontal
• The animals are calling at the surface
• The animals are staying in approximately the same location for the duration of the measurements

So there you have it. That’s how we locate animals underwater with a towed, 2-element hydrophone array.

* Yin, one of the amazing visual observers on the cruise, thinks “Left-right ambiguity” would be a great name for a band, and I agree.

** assumptions are made to be broken

## 10 thoughts on “Hydrophone arrays, FTW!”

1. Alexis says:

Michelle. This is amazing.

2. How long after you get back does it take you to publish the results of your study? What baseline populations are you using so you know if there’s less/more of a given species?

I’ve been following the plight of the blue whales and the issue with ship[ strikes for over a decade. It seems the populations are decreasing primarily due to ship strikes. And it seems ship strikes could be greatly reduced if the container ships slowed down by a few knots. Since you’re on the water and seeing what’s going on is that viable, or necessary?

1. This is not actually my study – I’m volunteering on one leg (3.5 weeks) of a 5 month research cruise. I wrote a short blog post summarizing the project, you can read it here: bit.ly/calcurceas.

3. Sheyka says:

Thank you so much for the post, Michelle. Really love the way you explain your research. It makes acoustic study sounds exciting! (I always love detective game). Anyway, I’m just wondering about the assumptions; Will the result be different if the animals are calling from underwater/certain depth? And how long is your duration of measurement!

4. Hi Sheyka! With just two hydrophones, we don’t really have enough information to solve for the depth of the animal. The assumption that the animals are calling at the surface allows us to work in 2 dimensions rather than 3 – our world reduces to just a horizontal plane which allows us to at least get an approximate location. I hope that helps!

5. JD Lee says:

I found your blog while prepping a class about SONAR, and it’s both hilarious and very helpful. I hope you don’t mind my using your sketch of the hydrophone overhead view in my lecture, of course you’ll be cited. It’s much better than my drawing would have been! Plus dolphins make it fun.

1. You can definitely use the sketch in a lecture. Thanks for the feedback! 🙂