Kathy and Debbie
Compressional or P (for primary)
Transverse or S (for secondary)
P and S are called body waves because they travel or propagate throught the body of Earth. The latter two are called surface waves they travel along the Earth's surface and amplitude decreases with depth into the Earth.
First two, P and S are within the earth as compressions (longitudinal waves) and transverse waves.
Second two, Love and Rayleigh are surface wave.
Love waves are transverse waves that vibrate the ground in the horizontal direction perpendicular to the direction that the waves are traveling They are formed by the interaction of S waves with Earth's surface and shallow structure and are dispersive waves. Only can be measured on seismomaters that measure the horizontal ground motion.
Rayleigh waves are the slowest of all the seismic waves and the most complicated. The are dispersive so the particular speed at which they travel depends on the wave period and the near-surface geologic structure. Particle movement is eliptical and decreases with depth.
The LIGO interferometer mirrors can be affected by seismic waves and must be separated out. All the different earth shaking...hurricanes, earth quakes, etc. are background information that needs to be filtered out.