地震偏移成像广义空间分辨率的定量计算
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摘要
地震分辨率是地震数据处理和偏移成像中的重要问题。从Ricker(1953)开始研究地震分辨率至今已50多年了,但大部分的研究集中在原始地震观测道的垂向分辨率上。近年来开始引进和讨论地震偏移成像空间分辨率的概念。Beylcin(1985)、Wu和Toksoz(1987)、Seggern(1994)、Vermmer(1998)、Chen和Schu-ster(1999)等人做过成像分辨率的研究,但都是定性的实验分析,研究了影响地震成像分辨率的若干因素。我和几位合作者(2002)提出了地震成像分辨率的定量计算公式。本文从理论上完善了地震成像分辨率的分析并进行了一些实验。影响地震成像空间分辨率有8项因素。在三维情况下它们为地震波的频率f、波的传播速度v、炮检距2h、炮检距中点M距坐标原点O的水平距离L、中点M与原点O连接线的方位角α、成像点深度z0、成像分辨率表现方向的水平方向角θ和其与正Z轴的夹角β。每个因素均有不同的作用,其中频率和速度可合并为波长λ。这些因素可分为3种类型:第一种是观测参数,如λ和h;第二种是成像孔径参数,如L和α;第三种为地质参数,如z0、β和θ。为了提高成像分辨率要考虑以下几个重要的成像空间分辨率性质:①成像分辨率随波长的减小而提高;②成像分辨率随成像点的深度增大而降低;③成像孔径内最大炮检距地震道的限定空间分辨力为λ/2;④最大分辨率的地面道位于(Lm,θm)点(Lm=z0tanβ,θm是给定的),为提高成像分辨率,孔径中点应在(Lm,θm),孔径大小由最远道的空间分辨力(λ/2)所限定。本文还讨论了叠前偏移和叠后偏移的空间分辨率。指出振幅保真地震偏移问题应当和高分辨率成像问题同时研究。
Seismic resolution is an important topic in seismic data processing and migration imaging. Seismic resolution has been investigated for more than 50 years since Ricker's paper published (1953), but it is focused only on the vertical resolution of original surveyed seismic traces. In recent years the concept of the spatial resolution of seismic migration imaging is introduced and discussed. Beylkin (1985), Wu and Toksoz (1987), Seggern (1994), Vermmer (1998), Chen (1999) and Schuster (1999), et al, carried out many studies in imaging resolution, which were qualitative, and some factors affecting the seismic imaging resolution were defined. My copartners and I (2002) provided a quantitative equation of seismic imaging resolution. In this paper, I generalized seismic imaging resolution theoretically and showed the results of experiments we made.The spatial imaging resolution are effected by 8 factors in 3D, which are f (wave frequency), v (wave propagation velocity), 2h (geophone offset), L(horizontal range from mid of geophone offset to origin of coordinates), α (azimuth of the line from middle point to origin),z0(depth of imaging point), θ(horizontal azimuth of imaging resolution direction), and β (the angle between θ and positive Z-axis). Each of them plays different role, in which the wavelength (λ) can be derived from the f and v. They can be divided into three types: first is observed parameters, such as λ and h; second is imaging aperture parameters, such as L andα; third is geologic parameters, such as z0 , β and θ. To improve the imaging resolution, the important properties of special imaging resolution below must be considered: ① the imaging resolution comes up while the wave length decreases; ② the imaging resolution comes down while depth of imaging point increases; ③ the limited spatial resolving power of the maximum offset seismic trace in imaging aperture is λ/2; ④ the surface trace of optimum resolution is located at the point (Lm, θm), (Lm=z0tan β, the θm is given). To improve the imaging resolution, the point (Lm, θm) should be defined as center of aperture, the size of aperture depend on the spatial resolving power (λ/2) of farthest trace. The spatial resolution of prestack migration and post-stack migration were discussed also, and presented that the matters of the amplitude fidelity seismic migration and the high resolution imaging should be studied at same time.
Seismic resolution is an important topic in seismic data processing and migration imaging. Seismic resolution has been investigated for more than 50 years since Ricker's paper published (1953), but it is focused only on the vertical resolution of original surveyed seismic traces. In recent years the concept of the spatial resolution of seismic migration imaging is introduced and discussed. Beylkin (1985), Wu and Toksoz (1987), Seggern (1994), Vermmer (1998), Chen (1999) and Schuster (1999), et al, carried out many studies in imaging resolution, which were qualitative, and some factors affecting the seismic imaging resolution were defined. My copartners and I (2002) provided a quantitative equation of seismic imaging resolution. In this paper, I generalized seismic imaging resolution theoretically and showed the results of experiments we made.The spatial imaging resolution are effected by 8 factors in 3D, which are f (wave frequency), v (wave propagation velocity), 2h (geophone offset), L(horizontal range from mid of geophone offset to origin of coordinates), α (azimuth of the line from middle point to origin),z0(depth of imaging point), θ(horizontal azimuth of imaging resolution direction), and β (the angle between θ and positive Z-axis). Each of them plays different role, in which the wavelength (λ) can be derived from the f and v. They can be divided into three types: first is observed parameters, such as λ and h; second is imaging aperture parameters, such as L andα; third is geologic parameters, such as z0 , β and θ. To improve the imaging resolution, the important properties of special imaging resolution below must be considered: ① the imaging resolution comes up while the wave length decreases; ② the imaging resolution comes down while depth of imaging point increases; ③ the limited spatial resolving power of the maximum offset seismic trace in imaging aperture is λ/2; ④ the surface trace of optimum resolution is located at the point (Lm, θm), (Lm=z0tan β, the θm is given). To improve the imaging resolution, the point (Lm, θm) should be defined as center of aperture, the size of aperture depend on the spatial resolving power (λ/2) of farthest trace. The spatial resolution of prestack migration and post-stack migration were discussed also, and presented that the matters of the amplitude fidelity seismic migration and the high resolution imaging should be studied at same time.
引文
[1]Beylkin G,Oristaglio M and Miller D.Spatial resolution of migration algorithms.Proceeding of14th,1985
[2]Chen J and Schuster G T.Resolution limits of migrated images.Geophysics,1999,64(4):1046￣1053
[3]Jnkins P A.Fundamentals of Optics.McGraw Hill,1957
[4]Levin S A.Resolution in seismic imaging:Is it all a matter of perspective?Geophysics,1998,63(3):743￣749
[5]Ricker W.Wavelet contraction,wavelet expansion and control of seismic resolution.Geophysics,1953,18(2):768￣792
[6]Safar M H.On the lateral resolution achieved by Kirchhoff migration.Geophysics,1985,50(4):1091￣1099
[7]Sheriff R E and Geldart L P.Exploration Seismology.Camrage University Press,1982:152￣155
[8]Von Seggern D.Spatial resolution of acoustic imaging with the Born approximation,Geophysics,1991,56
[9]Von Seggern D.Depth-imaging of3-D seismic recording patterns.Geophysics,1994,59(2):564￣576
[10]Vermeer G J O.Factors affecting spatial resolution.The Leading Edge,1998,17(10):1025￣1030
[11]Widess M A.How this is a thin bed?Geophysics,1973,38(4):1176￣1184
[12]Zaitian Ma et al.Quantitative estimation of imaging resolution.SEG72nd annual meeting,Salt city,U S A,2002
[2]Chen J and Schuster G T.Resolution limits of migrated images.Geophysics,1999,64(4):1046￣1053
[3]Jnkins P A.Fundamentals of Optics.McGraw Hill,1957
[4]Levin S A.Resolution in seismic imaging:Is it all a matter of perspective?Geophysics,1998,63(3):743￣749
[5]Ricker W.Wavelet contraction,wavelet expansion and control of seismic resolution.Geophysics,1953,18(2):768￣792
[6]Safar M H.On the lateral resolution achieved by Kirchhoff migration.Geophysics,1985,50(4):1091￣1099
[7]Sheriff R E and Geldart L P.Exploration Seismology.Camrage University Press,1982:152￣155
[8]Von Seggern D.Spatial resolution of acoustic imaging with the Born approximation,Geophysics,1991,56
[9]Von Seggern D.Depth-imaging of3-D seismic recording patterns.Geophysics,1994,59(2):564￣576
[10]Vermeer G J O.Factors affecting spatial resolution.The Leading Edge,1998,17(10):1025￣1030
[11]Widess M A.How this is a thin bed?Geophysics,1973,38(4):1176￣1184
[12]Zaitian Ma et al.Quantitative estimation of imaging resolution.SEG72nd annual meeting,Salt city,U S A,2002
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