also, very importantly: shearing waves do not propagate in liquids (quakes create both pressure and shearing waves). you can tear a solid, such as a sheet of paper, but trying to do the same to a liquid doesn't make sense. whereas pressure waves, like sound, propagate in both solids and liquids

so it's very obvious that (at least an outer layer of) the core is liquid because it's "dark" when looked at using shearing waves