One of the references I allude to in the introduction was the classic
posthumous publication of Slotnick (1959). In that tome, I found
the proposition, a consequence of Apollonius' Theorem (see, e.g.,
Godfrey and Siddons (1908) pages 20-21),
that for a fixed
source location and with receivers placed diagonally opposite each other
at equal distances from the source, the sum of the squares of the two
source to receiver traveltimes is independent
of source-receiver azimuth. This result, analogous on the face of it to
the updip-downdip refraction shooting method,
appears to have been used fairly routinely
to estimate moveout velocities before the advent of the common midpoint
gather but is no longer taught to students or industry professionals.
I think it, or some modern recasting of it, may well provide uplift to
both academia and industry seismic processing and analysis.