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

References

[1] ThorsonJ, ClaerboutJ. Velocity stack and slant stochastic inversion[J]. Geophysics, 1985, 50(12): 2727-2741

[2] BeylkinG. Discrete Radon transform[J]. IEEE Tans ASSP, 1987, 35(1): 162-172

[3] FosterD, Mosher. Suppression of multiple reflections using the Radon transform[J]. Geophysics, 1992, 57(2): 386-395

[4] ZhouB, GreenhalghS. Linear and parabolic τ-p transforms revisited[J]. Geophysics, 1994, 59(4): 1133-1149

[5] SacchiM, UlrychT. High-resolution velocity gathers and offset space reconstruction [J]. Geophysics, 1995, 60(4): 1169-1177

[6] HampsonD. Inverse velocity stacking for multiple elimination [J]. J Can Soc Expl Geophys, 1986, 22(1): 44-55

[7] YilmazO. Velocity stack processing [J]. Geophys Posp, 1989, 37(4): 357-382

[8] Maeland. Focusing aspects of the parabolic Radon transform [J]. Geophysics, 1998, 63(6): 1708-1715

[9] BickelS H. Focusing aspects of the hyperbolic Radon transform[J]. Geophysics, 2000, 65(2): 652-655

[10] PeacockK, TreitelS. Predictive deconvolution—Theory and practice[J]. Geophysics, 1969, 34(1): 155-169

[11] VerschourD, BerkhoutA. Adaptive surface-related multiple elimination[J]. Geophysics, 1992, 57(6): 1166-1177

[12] DragosetW, JericevicZ. Some remarks on surface multiple attenuation[J]. Geophysics, 1998, 63(3): 772-789

[13] LandaE, BelferI. Multiple attenuation in the parabolic τ-p domain using wavefront characteristics of multiple generating primaries[J]. Geophysics, 1999, 64(6): 1806-1815

[14] SongShougen, ZhangRongfeng. High resolution wavefield reconstruction in seismic migration for viscoelastic media [J]. Journal of Seismic Exploration, 2000, 9(1): 1-18