孔径角对三维波场外推精度的影响
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摘要
孔径角的选择是影响三维地震波场外推精度和效率的最直接、最关键的因素。本文利用空间频率域的瑞利积分Ⅱ式,对单极源和偶极源的波场外推精度做了理论推导,随后又推出了误差项的解析式。分析表明,振幅误差主要取决于孔径角θ,其他参数如频率f、速度υ、法线距离z等只是有限地影响相位误差。文中通过将外推参考平面网格化,采用离散网格的波函数叠加取代积分求和进行数值模拟计算,验证了解析式的正确性。最后提出高保真(振幅精度≥80％)三维波场外推的最优孔径角选择准则:对于单极源,选择θ>60°;对于偶极源,选择θ≥55°。该准则可用于理论研究,但在处理实际问题时还应做具体分析和综合平衡。
The selection of aperture angle is most direct and key factor for affecting the precision and efficiency of 3D seismic wavefield extrapolation. Using Rayleigh integration formula Ⅱ in space-frequency domain, the paper deduced theoretically the precision of wavefield extrapolation for both single-pole and dipole sources, then deduced the analytic formula of errors. The analysis showed that the errors of amplitude mainly depend on aperture angle θ, the other parameters such as frequency f,velocity υand normal distance z only have limited influence on errors of phase. Numeric modeling by gritting the extrapolated reference plane and replacing integration with stack of wave function at discrete grit,the paper tested the correctness of the analytic formula. Finally, the paper presented the selected criterion of optimal aperture angle with hi-fi 3D wavefield extrapolation (precision of amplitude ≥80%):the angle & is selected as great than 60°for single pole source and the angle θ is selected as great than and equal to 55°for dipole source. This criterion can be used for theoretic study but it must do concrete analysis and synthetic balance when using it to solve the practical problems.
The selection of aperture angle is most direct and key factor for affecting the precision and efficiency of 3D seismic wavefield extrapolation. Using Rayleigh integration formula Ⅱ in space-frequency domain, the paper deduced theoretically the precision of wavefield extrapolation for both single-pole and dipole sources, then deduced the analytic formula of errors. The analysis showed that the errors of amplitude mainly depend on aperture angle θ, the other parameters such as frequency f,velocity υand normal distance z only have limited influence on errors of phase. Numeric modeling by gritting the extrapolated reference plane and replacing integration with stack of wave function at discrete grit,the paper tested the correctness of the analytic formula. Finally, the paper presented the selected criterion of optimal aperture angle with hi-fi 3D wavefield extrapolation (precision of amplitude ≥80%):the angle & is selected as great than 60°for single pole source and the angle θ is selected as great than and equal to 55°for dipole source. This criterion can be used for theoretic study but it must do concrete analysis and synthetic balance when using it to solve the practical problems.
引文
[1]R E谢里夫等编,初英等译.勘探地震学(上册).北京: 石油工业出版社,1999,199-203
[2]Schleicher Jorg等著,沈晓慈等译.偏移和反偏移中的 最优孔径和菲涅耳带.国外油气勘探,1998,10(4):745 -760
[3]Andreas Cordsen等著,俞寿鹏等译.陆上三维地震勘 探的设计与施工.石油地球物理勘探局,1996,53-60
[4]A J别尔克豪特著,马在田等译.地震偏移--波场外 推法声波成像(第五章,第十二章).北京:石油工业出 版社,1983
[5]狄帮让等.三维观测系统优化设计的双聚焦方法.石油 地球物理勘探,2003,38(5):463-469
[6] Volker A W E et al. Analysis and optimization of 3-D seismic acquisition geometries by focal beams. Expanded Abstracts of 70th SEG Mtg,2000
[2]Schleicher Jorg等著,沈晓慈等译.偏移和反偏移中的 最优孔径和菲涅耳带.国外油气勘探,1998,10(4):745 -760
[3]Andreas Cordsen等著,俞寿鹏等译.陆上三维地震勘 探的设计与施工.石油地球物理勘探局,1996,53-60
[4]A J别尔克豪特著,马在田等译.地震偏移--波场外 推法声波成像(第五章,第十二章).北京:石油工业出 版社,1983
[5]狄帮让等.三维观测系统优化设计的双聚焦方法.石油 地球物理勘探,2003,38(5):463-469
[6] Volker A W E et al. Analysis and optimization of 3-D seismic acquisition geometries by focal beams. Expanded Abstracts of 70th SEG Mtg,2000
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