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.
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References
Thorson J, Claerbout J. Velocity stack and slant stochastic inversion[J]. Geophysics, 1985, 50(12): 2727–2741.
Beylkin G. Discrete Radon transform[J]. IEEE Tans ASSP, 1987, 35(1): 162–172.
Foster D, Mosher. Suppression of multiple reflections using the Radon transform[J]. Geophysics, 1992, 57(2): 386–395.
Zhou B, Greenhalgh S. Linear and parabolic τ-p transforms revisited[J]. Geophysics, 1994, 59(4): 1133–1149.
Sacchi M, Ulrych T. High-resolution velocity gathers and offset space reconstruction [J]. Geophysics, 1995, 60 (4): 1169–1177.
Hampson D. Inverse velocity stacking for multiple elimination [J]. J Can Soc Expl Geophys, 1986, 22(1): 44–55.
Yilmaz O. Velocity stack processing [J]. Geophys Posp, 1989, 37(4): 357–382.
Maeland. Focusing aspects of the parabolic Radon transform [J]. Geophysics, 1998, 63(6): 1708–1715
Bickel S H. Focusing aspects of the hyperbolic Radon transform[J]. Geophysics, 2000, 65(2): 652–655.
Peacock K, Treitel S. Predictive deconvolution—Theory and practice[J]. Geophysics, 1969, 34(1): 155–169.
Verschour D, Berkhout A. Adaptive surface-related multiple elimination[J]. Geophysics, 1992, 57(6): 1166–1177.
Dragoset W, Jericevic Z. Some remarks on surface multiple attenuation[J]. Geophysics, 1998, 63(3): 772–789.
Landa E, Belfer I. Multiple attenuation in the parabolic τ-p domain using wavefront characteristics of multiple generating primaries[J]. Geophysics, 1999, 64(6): 1806–1815.
Song Shougen, Zhang Rongfeng. High resolution wavefield reconstruction in seismic migration for viscoelastic media [J]. Journal of Seismic Exploration, 2000, 9(1): 1–18.
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Foundation item: The Key Program of 9th Five-Year Plan of China (No. 96-111-08-05) and The Cross-Century Human Resources Development of Education Ministry (No. 1999-02).
Biography of the first author: ZHANG Jian-gui, doctoral candidate, born in 1972, majoring in the high-resolution imaging of geophysics.
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Zhang, Jg., Song, Sg. & Yuan, Xg. Focus projection of the parabolic radon transform and multiple waves separator, elimination. J Cent. South Univ. Technol. 9, 30–35 (2002). https://doi.org/10.1007/s11771-002-0007-1
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DOI: https://doi.org/10.1007/s11771-002-0007-1