How does scientists know earth has a solid core surrounded by mantle when we have never dug so deep? How do that happens when IMO 12 km is the deepest we have dug?
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There are two main types of vibrations produced by earthquakes, P-waves and S-waves. They move through solids and liquids very differently. Networks of seismographs on the surface can reveal the patterns of movement, even through the center of the core. These patterns can be analyzed to show the state of matter deep inside earth. ( very similar to the software that enables CAT scan xrays to show images of your insides)
The Wikipedia article on this is excellent, with great diagrams:
https://en.m.wikipedia.org/wiki/Seismic_wave
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