Background
Variable refraction
Earthquake waves are refracted at the boundaries between the different layers of the Earth. This is because there is a change in speed at the boundary between layers. However, they are also refracted within each layer, because the density of the rock increases with depth as the rock is more compressed. Pressure waves travel faster in the denser rock because the particles are closer together. Therefore the waves speed up as they go deeper into the Earth.
This makes them continually bend. However, there isn't a clear boundary at which we can imagine a normal. Instead, we have to think of lots of small layers (like the skins of an onion). The normal at each layer will be along a radius. So the waves are constantly bending away from a radius as they go deeper. Eventually they will start coming back towards the surface. Travelling in this direction, they bend towards a radius.
There is a similar situation in optical fibres. A simple optical fibre has a core with a high refractive index with a casing around it with a lower refractive index. The light travels faster in the casing and is totally internally reflected at the boundary between the two regions. However, to reduce dispersion, fibres can be made with a variable refractive index, which gets lower towards the edge so that the light speeds up. It is no longer totally internally reflected as there is no boundary. Instead it curves around in the variable-index region. In the same way, earthquake waves curve through the variable index of the Earth's rocks. The P shadow zone
As well as bending in the variable index of the layers inside the Earth, the waves are refracted at the boundaries between layers. In particular, they bend at the boundary between the mantle and the liquid outer core. The P waves travel more slowly in the liquid and are bent towards the normal. The liquid core behaves like a spherical lens. The P waves are partially focused into a region on the surface directly opposite the epicentre, where their intensity is increased. Around this region there is a ring on the Earth's surface that feels no P waves because they have been focused away from it. This ring is the P shadow zone.
