Half awake

It is amazing how over time scientists and researchers discover or can explain things that we think we already know.
I was intrigued to read that researchers have discovered that on our first day in a new and unfamiliar location (eg. a hotel room, camping, having a sleep over, ...) at night when asleep, one side of our brain remains alert to what is happening around us. It is always the left side of the brain.
For humans it is called the first-night phenomenon.
It had been known that dolphins and whales sleep with half of their brain alert and is known as unihemispheric sleep.
The theory is that it is an ancient survival mechanism.

It makes sense. I recall broken sleep (alerted by something) on that first night in an unfamiliar place.

My only curiosity is that given the study of humans involved brain scans while people were asleep, how did they verify that dolphins and whales have unihemispheric sleep?