I know you’ve been answered in terms of earthquakes, and I’ll reiterate that part briefly, but there is actually more to our understanding of Earth’s interior, which I’ll get to.
So, about earthquakes: Every time they occur, scientists can look at the way the shock waves (aka seismic waves) from these earthquakes move through the planet — both the speed of the waves and how the waves bounce off of denser parts inside the planet (the inner and outer cores). It’s essentially this way that we have determined the physical state of Earth’s separate layers:
**Crust**: solid rock
**Mantle**: solid rock (apart from a few melty bits near the top of the mantle which make magma and feed volcanoes). The mantle convects veeeeery slowly like a super-thick liquid despite being solid.
**Outer core**: liquid metal (mostly iron) which convects vigorously.
**Inner core**: solid metal (mostly iron) because the pressure becomes too high for the metal to be molten.
We have determined where the boundaries for these layers are based on seismic ‘discontinuities’ – sudden jumps in the speed that the seismic waves travel. Check out a [scaled diagram](https://i.imgur.com/NNaNTQ2.jpg) to illustrate how thick these layers are. On average, the crust is actually similar in thickness relative to the whole Earth as the skin of an apple is to the whole apple. Also, it’s not usually made explicit when just giving an overview of Earth’s insides, but Earth’s core is pretty damn big, even by planetary standards. If you were to tunnel down and reach the edge of the outer core, you’re still not halfway to the centre of the Earth.
So all the seismic stuff is the most fruitful approach there’s been to figuring out physical properties of Earth’s interior, but this is all backed up and complimented by a few other lines of thought:
• The Earth has a magnetic field, so must have a metallic core, at least some of which is fluid and circulating in order to generate the magnetic field. This is consistent with (1) the types of seismic waves which do and do not pass through the outer and inner cores respectively; and (2) the fact that some meteorites which fall to Earth are an iron-nickel alloy — these represent the cores of baby planets in the early solar system which got big enough to separate into bodies with a core and mantle, but then smashed apart to set free their innards.
• Even before we knew all that, early measurements of the Earth’s total mass meant that we knew their must be much denser material somewhere inside the Earth, as the rock of the crust was not dense enough to account for all the mass of the planet. Iron is a good fit for all the density, stellar physics tells us it’s relatively common in the universe, and there is obviously some natural process which can concentrate iron into pretty pure lumps of the stuff based on those metallic meteorites.
• With regards to the mantle, we do have certain pieces of mantle rock which get entrained into magma and eventually erupted as part of lavas which these still solid chunks of mantle rock within. (Many people think of the whole mantle as lava/magma, but it’s almost entirely solid rock with localised melty bits here and there). The chunks of mantle that occasionally get brought up to the surface are known as ‘mantle xenoliths’ and [they are a wonderful dark to striking green colour due to the mineral olivine.](https://i.imgur.com/Jhc2kiu.jpg).
• There are also high-pressure high-temperature experiments that some scientists run on [specialist lab equipment](https://en.wikipedia.org/wiki/Diamond_anvil_cell), this tells us what sort of rock exists in the deeper mantle. Essentially, when upper mantle materials are subjected (in stuff like diamond anvil cells) to the appropriate temps and pressures that exist closer to the core they turn into the kinds of minerals that make up the lower mantle, or at least give us big clues as to what’s down there when we observe how their squishiness or how the packing of their atoms changes.
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