We did a online lab on seismic waves to help detrmain how we know what the inside of the Earth looks like. What I learned is that we use earthquakes.
The way we determine if the layer is a solid or a liquid is P and S waves from earthquakes. A S wave can’t go through liquid and that is how we know that the outer core is the S waves stop when they get there. The way we know that the inner core is a solid is that when the P wave go through the liquid, they slow down but they speed up when they get to a solid again. The way we know that the crust and mantel are a solid is that both P and S waves go through them.