I stray into Nick's bailiwick here!

The "S" wave is in rock, not air.

Body waves (those that travel through the rock):

"P" wave = primary wave, or longitudinal, compressional, wave, ~6 km/s
"S" wave = secondary wave, or shear wave, transverse wave, ~4km/s, don't travel through liquid, or the earth's core

Surface Waves:
"L" wave = Love wave (after the mathematician who modeled them),
"R" wave = Rayleigh Wave

The medium through which these waves passes also affects their speed. Helps in defining rock types, rheologic properties, etc.

(I transposed some of these in the earlier post, sorry Nick, trying to not embarrass myself too much here...)

This is a pretty good explanation:
What is seismology and what are seismic waves?

This is interesting: Seismic waves generated by Aircraft Impacts and Building Collapses at WTC, NY. It shows how P and S waves arrive at different times from this event. Would be a useful comparison to the OK explosion seismic signature.

Of course there is this from the USGS: Glossary of earthquake terms

Or this from the Colorado School o' Mines: Seismic Waves

I've not taken the time to track down the seismic record from this event, if someone has a link, I'd like to see it. I'm not really qualified to read it (only in the simplest way), but I'd like to see it.

~jms~