基于抛物线拉东变换的地震道重构
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摘要
研究了一种基于抛物线拉东变换(PRT)的地震道外推和内插方法,该方法根据部分NMO校正后的CMP(Common Middle Point,共中心点)道集中地震同相轴的抛物线假设,在待重建道的位置用零值道代替,然后采用迭代方式,通过带限抛物线拉东正变换和最小平方抛物线拉东反变换进行数据重构.结果表明,该方法可用于叠前道集中缺失道的重建、外推、内插以及数据重采样和数据规则化等方面.模型数据和实际数据应用还表明本方法是有效的和稳健的,它不需要精确的NMO速度,具有很强的抗噪能力,且能进行中间偏移距道和远偏移距道的处理,对于多次波的消除、AVO分析、DMO处理和某些三维叠前偏移成像方法都将是有益的.
Based on the parabolic Radon transform, a method for missing seismic traces reconstruction was put forward. This method is based on the parabolic assumption of the seismic events after a partial NMO correction in the CMP gathers. A forward band-limited parabolic Radon transform is taken for the data containing zero traces at the missing offset locations. After inverse transform, the originally zero traces are partially filled with useful information. By several iterations of the forward and inverse transform, the zero traces are almost fully reconstructed. This method can be used for offset interpolation, extrapolation and resampling of pre-stack CMP gathers. Examples on synthetic as well as on field data demonstrate its validity and robustness. With great antinoise capability, the method does not require precise NMO velocity information, and can reconstruct near-offset as well as intermediate-offset and far-offset traces, which will favor multiple attenuation, AVO analysis and DMO processing.
Based on the parabolic Radon transform, a method for missing seismic traces reconstruction was put forward. This method is based on the parabolic assumption of the seismic events after a partial NMO correction in the CMP gathers. A forward band-limited parabolic Radon transform is taken for the data containing zero traces at the missing offset locations. After inverse transform, the originally zero traces are partially filled with useful information. By several iterations of the forward and inverse transform, the zero traces are almost fully reconstructed. This method can be used for offset interpolation, extrapolation and resampling of pre-stack CMP gathers. Examples on synthetic as well as on field data demonstrate its validity and robustness. With great antinoise capability, the method does not require precise NMO velocity information, and can reconstruct near-offset as well as intermediate-offset and far-offset traces, which will favor multiple attenuation, AVO analysis and DMO processing.
引文
[1] Bardan V. Trace interpolation in seismic data processing [J]. Geophysical Prospecting, 1987, 35(3) : 343-358．
[2] 国九英,周兴元,俞寿朋.F-X域等道距道内插[J].石油地球物理勘探,1996,31(1) :28-34．
[3] Darche G. Spatial interpolation using a fast parabolic transform [A]. 60th SEG meeting, Expanded Abstracts [C]. Tulsal: Soc Expl Geophys, 1990． 1647-1650．
[4] Larner K, Gibson B, Rothman D. Trace interpolation and the design of seismic surveys[J]. Geophysics,1981, 46(4) : 407．
[5] Spitz S. Seismic trace interpolation in F-X domain [J]. Geophysics, 1991, 56 (6) : 785-794．
[6] Deregowski S M. What is DMO? [J]. First Break,1986, 4 (1) : 7-24．
[7] Verschuur, D. Surface-related multiple elimination,an inversion approach[D]. Delft: Delft University of Technology, 1991．
[8] Kostov C. Toeplitz structure in slant-stack inversion [A]. 60th SEG meeting, Expanded Abstracts[C].Tulsal: Soc Expl Geophys, 1990． 1618-1621．
[9] Beylkin G. Discrete Radon Transform [J]. IEEE Transactions on Acoustic, speech and Signal ProcessinR, 1987, 35 (2) : 162-172．
[10] 黄新武.广义拉东变换及其在地震波成像中的应用[D].北京:石油大学,1999．
[11] Hampson D. Inverse velocity stacking for multiple elimination[J]. Journal of the CSEG, 1986, 22 (1) :44-55．
[12] Kabir M M N, Verschuur D J. Parallel computing of the parabolic Radon transform-application for CMP based preprocessing [A]. 63rd SEG meeting,Expanded Abstracts[C].Tulsal: Soc Expl Geophys, 1993． 193-196．
[13] Turner G. Aliasing in the tau-p transform and the removal of spatially aliased coherent noise [J].Geophysics, 1990, 55 (11) : 1496-1503．
[2] 国九英,周兴元,俞寿朋.F-X域等道距道内插[J].石油地球物理勘探,1996,31(1) :28-34．
[3] Darche G. Spatial interpolation using a fast parabolic transform [A]. 60th SEG meeting, Expanded Abstracts [C]. Tulsal: Soc Expl Geophys, 1990． 1647-1650．
[4] Larner K, Gibson B, Rothman D. Trace interpolation and the design of seismic surveys[J]. Geophysics,1981, 46(4) : 407．
[5] Spitz S. Seismic trace interpolation in F-X domain [J]. Geophysics, 1991, 56 (6) : 785-794．
[6] Deregowski S M. What is DMO? [J]. First Break,1986, 4 (1) : 7-24．
[7] Verschuur, D. Surface-related multiple elimination,an inversion approach[D]. Delft: Delft University of Technology, 1991．
[8] Kostov C. Toeplitz structure in slant-stack inversion [A]. 60th SEG meeting, Expanded Abstracts[C].Tulsal: Soc Expl Geophys, 1990． 1618-1621．
[9] Beylkin G. Discrete Radon Transform [J]. IEEE Transactions on Acoustic, speech and Signal ProcessinR, 1987, 35 (2) : 162-172．
[10] 黄新武.广义拉东变换及其在地震波成像中的应用[D].北京:石油大学,1999．
[11] Hampson D. Inverse velocity stacking for multiple elimination[J]. Journal of the CSEG, 1986, 22 (1) :44-55．
[12] Kabir M M N, Verschuur D J. Parallel computing of the parabolic Radon transform-application for CMP based preprocessing [A]. 63rd SEG meeting,Expanded Abstracts[C].Tulsal: Soc Expl Geophys, 1993． 193-196．
[13] Turner G. Aliasing in the tau-p transform and the removal of spatially aliased coherent noise [J].Geophysics, 1990, 55 (11) : 1496-1503．
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