What leads astronomers to believe that some large moons associated with the giant planets have compositions that are roughly half water?

Astronomers are able to determine facts about the composition of these moons by examining the nature of light that is reflected from their surfacy using a method called spectroscopy. This process works because different materials tend to reflect light at different wavelengths So, by observing at which wavelengths a planetary body reflects light, astronomers are able to estimate its composition.