We have a combination of 3 different phenomenae.
1. Scientists can be really smart.
2. Different materials transmit waves in different ways. We are able to understand what the telltale signs of different materials would be.
3. Earthquake are very good at making waves.
So you end up with earthquakes that are analyzed, and the results of that analysis shows that there’s a layer where earthquake waves bounce. That’s something that happens when you go between something solid to something liquid. So we can understand that to mean there is a liquid layer of the Earth.
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