Two point raytracing for reflection off a 3D plane

A Postscript

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.