Chris,

While someone once might have computed a synthetic seismogram with singularities at those distances, that is not how real seismic waves look.

IRIS has web tools with which one can look at seismic sections. I'd bet against there existing many examples, of larger ground motions at 50 degrees or more than at 10 degrees distance for the same event. Especially more than 100 degrees. Maybe very strong directivity might do that occasionally, but that is primarily an azimuth-dependent, not distance-dependent effect.

Sorry to be a spoil sport. No other explanations for the rings?

John