Love waves are just a subset of S waves. However, they are surface waves, so their amplitude varies with depth.
When an S or P wave interacts with a surface, boundary conditions require that it reflects as a *coherent* combination of S *and* P wave. These combined SP waves are Rayleigh waves, and the fact that S and P are coherent violates the assumption in Eq. 5 in Vuk's note, where S and P are assumed to be uncorrelated. Further, the fraction of power that gets converted from S into P and vice versa is O(1). The good news is that there's a very predictable phase relationship between S and P in Rayleigh waves.
wave speed changes with depth for both S and P waves. This refraction causes wavefronts to change orientation as they travel through the Earth. Waves bouncing off the surface curve away from the center of the Earth and head back to the surface. Seismologists refer to the “turning depth” as the depth at which waves curve back to the surface. The value of turning depth depends on frequency and geological composition.
Inhomogeneities. Any features characterized by a size of lambda/4 can probably be safely ignored. At 1 Hz, Victor thinks this corresponds to a length scale of ~700m, and the rock should appear very uniform at that length scale. However, at 10 Hz, Victor thinks that the length scale will be ~20m (note v depends on f in rock), and we might see significant inhomogeneity at this scale.