Focusing aspects of the parabolic Radon transform

Abstract

From a geometrical point of view, the parabolic Radon transform of a common shotpoint gather is a focusing technique where the “focal length” is determined by the velocity field. When the traveltime curves at small offset are approximated by hyperbolas, the reciprocal of the curvature of an “image” is related to the square of the curvature at zero offset of the corresponding traveltime curve. Each event on a common‐shotpoint gather will be separated by the parabolic Radon transform, and the position of the foci associated with peg‐leg multiples can be predicted. Examples on synthetic common‐shotpoint gathers illustrate the merits of the analysis.