Reddit reviews An Introduction to Seismology, Earthquakes and Earth Structure

A couple of things...

The second is tomographic inversion of a huge number of earthquake arrival datasets to essentially CAT-scan the earth. But strictly speaking that isn't necessary.

The first is this (briefly). There are two fundamental body waves - P waves and S waves. There are also surface waves (travel only along interfaces, e.g. surface of Earth). Lets ignore those for now.

So... wave velocity is related to material and density. Waves follow paths through the earth, and on hitting an interface, can transform. So a P wave goes to the core-mantle boundary and splits into a bunch of waves - a P reflected, an S reflected, a P transmitted, and no S transmitted (because the outer core is liquid). An S wave does the same. There is a complex nomenclature for wave arrivals that identifies what phase arrived (SKS, SCS, PKP, etc. etc. etc.). Since the P and S wave velocities are different, and since there are so many phases that follow different paths, we end up being able to solve fairly simply for some material properties on a generalized basis. The answer is sort-of non unique. Certain phases do and do not show up certain places, which allows us to pin the size of the inner core, for example (because as Lehman demonstrated, there is a shadow zone...) (see http://en.wikipedia.org/wiki/Shadow_zone )

Next, we have totally different and complementary ways of knowing the gross structure (e.g. spin of Earth moments) which also constrain the density structure. Simultaneously solving different systems gives us a pretty good model of the structure (e.g. the PREM - preliminary reference earth model)...

If we don't go for a generalized model, but instead solve specific paths in 3d (rather than the generalized spherically symmetric case) then we are in the second case - tomography - and we can image structure on the core-mantle boundary and large scale density anomalies in the mantle. Forex, one interesting thing is that some hotspots (non-plate-boundary mafic volcanoes like the Hawaii-Emporer chain) source at the core mantle boundary, others do not...

Finally, there is a third case that doesn't apply to the core, but is damned interesting. If you look at an S wave coming up from a distant source, and so coming up at you pretty much vertically, the wave may split into two components (shear wave splitting) that partition because the upper mantle is anisotropic (has faster velocity in one direction due to crystal alignment). So we can indirectly examine what we infer to be flow fields in the mantle (plastic flow, not liquid...).

A good but kind of advanced book on this stuff is:

http://www.amazon.com/Introduction-Seismology-Earthquakes-Earth-Structure/dp/0865420785/ref=sr_1_1?s=books&ie=UTF8&qid=1319660379&sr=1-1

(no affiliation with me... I just dig the book).