This is my research field, but I’m about to teach a class so I’ll edit this post with citations and more details later. — Update: added links.
Early suspicions of liquid water ocean came from [Voyager](https://en.wikipedia.org/wiki/Voyager_program) data which showed almost no craters and very little elevation change, suggesting that the ice crust had no solid support underneath. Supporting evidence came from Europa’s size, mass, shape and gravitational field, which showed that it has an overall density less than rock, but is much denser in the center than near the surface, so it’s probably rock on the inside and either ice or water near the surface.
But that’s not enough on its own to prove liquid water, it could just be ice. (Ice flows like a very thick liquid on geological scales: see glaciers and ice caps on Earth.)
“Proof” of a salty *liquid* ocean came from [Galileo](https://en.wikipedia.org/wiki/Galileo_(spacecraft)) [magnetic field data](https://www.nature.com/articles/27394), which showed that Europa responds to Jupiter’s changing magnetic field the same way an electrically conductive sphere would. So either Europa has a layer of copper metal under its surface (no way), or there’s a continuous layer of salt water down there. And no, a metal core wouldn’t explain the observations, nor would little pockets of water in an ice shell.
[Additional studies](https://www.sciencedirect.com/science/article/pii/S0019103507000656) have used more precise magnetic field modeling to roughly constrain *how* salty it is (saltier than soup, maybe as salty as the Dead Sea) and [chemical modeling](https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2000je001413) shows that if you get the rocks we guess Europa is made of wet, they will release lots of salt.
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