The scattered light carries with it information about the energy of the waves, from which the interaction strength and sound velocity can be calculated. Pressure waves are stronger than shear waves. Think about the atomic picture. It is much easier to push atoms together than it is to pull them sideways. Pressure waves can propagate from one medium to another.
Shear waves have a very hard time doing that.
So, when seismic waves are detected through the Earth on the opposite side, the shear waves don't survive the transit and only pressure waves are detected. In general, shear waves don't survive transit from one layer to the next like pressure waves. By looking at the sound velocities of the waves and transit of shear waves, seismologists can determine what the wave must have travelled through, the depth of layers, and how many layers.