基于保幅波动方程的广义高阶屏地震偏移成像方法
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摘要
原始地震数据中饱含丰富的反映相位的走时信息和反映反射率的振幅信息。基于波场延拓理论的波动方程保幅地震偏移成像,是在给出正确构造成像位置的同时也给出真实反射振幅的有效完善。基于全声波方程,利用严格的解耦理论进行单程波动保幅分解,得到一个由波场传播项与振幅补偿项构成的,在走时与振幅上满足全声波方程对应的程函方程与输运方程的保幅单程波动方程;利用摄动理论进行单平方根算子渐进展开,推导出基于保幅波动方程的广义高阶屏地震偏移算子方程。模型测试和实际资料处理表明,该方法不但可以凭借更准确的相位归位和散射能量聚焦提高构造成像精度,而且输出了能更正确反映地下反射属性的能量信息,从而可以为更深层次的勘探开发,提供地球物理技术支撑。
Original seismic data contain rich travel-time information which can reflect phases and amplitude information reflecting frequencies.Waveform equation preserved-amplitude seismic migration imaging based on wave field prolongation theories is an effective improvement which can give true reflection amplitudes as well as the correct locations of structure imaging.This paper,firstly,started from full sound wave equation,and then performed one-way wave preserved-amplitude decomposition according to the strict decoupling theory to got a preserved-amplitude one-way wave equation.This one-way wave equation was formed by wave field propagation items and scattering compensation items.The equation satisfied with eikonal equation and transport equation which corresponded to full sound wave equation on travel time and amplitude.After that this paper derived a generalized high-order screen seismic migration operator equation based on preserved-amplitude wave equation using progressive expansion of single square root operator according to the perturbation theory.Theoretical model testing and real data processing indicated that this method had better imaging precision:It could make scattering energy be focused and migrated to the correct position.At the same time,the imaging gathers had amplitude information which could reflect subsurface reflectivity correctly providing more accurate seismic reflection information for sequent velocity modeling and AVO/AVA seismic attributes analysis.
Original seismic data contain rich travel-time information which can reflect phases and amplitude information reflecting frequencies.Waveform equation preserved-amplitude seismic migration imaging based on wave field prolongation theories is an effective improvement which can give true reflection amplitudes as well as the correct locations of structure imaging.This paper,firstly,started from full sound wave equation,and then performed one-way wave preserved-amplitude decomposition according to the strict decoupling theory to got a preserved-amplitude one-way wave equation.This one-way wave equation was formed by wave field propagation items and scattering compensation items.The equation satisfied with eikonal equation and transport equation which corresponded to full sound wave equation on travel time and amplitude.After that this paper derived a generalized high-order screen seismic migration operator equation based on preserved-amplitude wave equation using progressive expansion of single square root operator according to the perturbation theory.Theoretical model testing and real data processing indicated that this method had better imaging precision:It could make scattering energy be focused and migrated to the correct position.At the same time,the imaging gathers had amplitude information which could reflect subsurface reflectivity correctly providing more accurate seismic reflection information for sequent velocity modeling and AVO/AVA seismic attributes analysis.
引文
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[7]ZHANG YU,ZHANG GuAN-QUAN,BLEISTEINN.Theory of true amplitude one-way wave equa-tions and true amplitude common shot migration[J].Geophysics,2005,70:E1-E10.
[8]崔兴福,张关泉,吴雅丽.三维非均匀介质中真振幅地震偏移算子研究[J].地球物理学报,2004,47(3):509-513.
[9]吕彬,王宇超,李斐.保幅型裂步傅里叶叠前深度偏移方法探讨[J].岩性油气藏,2007,19(3):101-105.
[10]刘定进,印兴耀.傅里叶有限差分法保幅叠前深度偏移方法[J].地球物理学报,2007,50(1):269-277.
[11]ZHANG Y,XU S,ZHANG G Q,BLEISTEIN N.How to obtain true amplitude common-angle gath-ers from one-way wave equation migration[M].Ex-panded Abstracts of 74th SEG Mtg,2004.
[12]刘定进,杨瑞娟,罗申玥,等.稳定的保幅高阶广义屏地震偏移成像方法研究[J].地球物理学报,2012,55(7):2402-2411.
[13]刘定进,周云和,杨瑞娟,等.高精度屏算子地震偏移成像方法研究[J].石油物探,2010,49(6):531-535.
[2]SCHNEIDER W A.Integral formulation for migra-tion in two and three dimension[J].Geophysics,1978,43:49-76.
[3]GAZDAG J.Wave equation with phase-shift meth-od[J].Geophysics,1978,43:1342-1351.
[4]RISTOW D,RüHL T.Fourier finite-difference mi-gration[J].Geophysics,1994,59(12):1882-1893.
[5]张关泉.波动方程的上行波和下行波的耦合方程组[J].应用数学学报,1993,16(2):251-263.
[6]ZHANG YU,ZHANG GUAN-QUAN,BLEISTEINN.True amplitude wave equations migration arisingfrom true amplitude one-way wave equations[J].Inverse Problems,2003,19:1113-1117.
[7]ZHANG YU,ZHANG GuAN-QUAN,BLEISTEINN.Theory of true amplitude one-way wave equa-tions and true amplitude common shot migration[J].Geophysics,2005,70:E1-E10.
[8]崔兴福,张关泉,吴雅丽.三维非均匀介质中真振幅地震偏移算子研究[J].地球物理学报,2004,47(3):509-513.
[9]吕彬,王宇超,李斐.保幅型裂步傅里叶叠前深度偏移方法探讨[J].岩性油气藏,2007,19(3):101-105.
[10]刘定进,印兴耀.傅里叶有限差分法保幅叠前深度偏移方法[J].地球物理学报,2007,50(1):269-277.
[11]ZHANG Y,XU S,ZHANG G Q,BLEISTEIN N.How to obtain true amplitude common-angle gath-ers from one-way wave equation migration[M].Ex-panded Abstracts of 74th SEG Mtg,2004.
[12]刘定进,杨瑞娟,罗申玥,等.稳定的保幅高阶广义屏地震偏移成像方法研究[J].地球物理学报,2012,55(7):2402-2411.
[13]刘定进,周云和,杨瑞娟,等.高精度屏算子地震偏移成像方法研究[J].石油物探,2010,49(6):531-535.
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