seismic waves in EarthWatch
a) the speed of the wave is constantly changing as the wave is being refracted
b) there are areas of different densities
The speed of the wave depends heavily on density. In general when it comes to crystalline materials and whatnot like a lot of rocks and metals, the harder it is, the faster waves travel in it, to my awareness.
Refraction implies a density boundary for the wave, i.e. high to low, low to high. That changes the speed based on the density argument above. Like glass and air are optically dense and rare, with light being slower in glass than air, a rock is "acoustically" rarer for sound than dirt, which is denser. Using density here in terms of the wave properties. Anyway, rare means that the wave travels faster in it. That's the basis for refraction so I assume using it in that sense is fine.
b) That sounds correct, but don't take my word for it. If the density of the rocks in the Earth were all the same, or similar, scientists wouldn't notice big differences in wave speed as they travel through the different layers of Earth.