Focus projection of the parabolic radon transform and multiple waves separator, elimination

Abstract

Based on the scalar wave equation, making use of the ray approximation of the reflected seismic data (CMP or CSP gathers), the authors derive respectively the projection function of the primary waves and multiple waves at the near-offset (CMP or CSP gathers) in the parabolic Radon transform (PRT) domain. From the geometric point, the authors prove that the energy of the reflection still distributes along hyperbola which has higher curvature in the PRT domain and becomes some energy masses. So the primary waves and the multiple waves which interweave each other in (x, t) domain can be completely separated, which helps the multiple waves eliminated by filtering or muting. It is important for the analysis of velocity and the separator and elimination of multiple waves.

Keywords

parabolic Radon transform / multiple waves / projection / focus