Kirchhoff型高保真反偏移理论
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摘要
为了使Kirchhoff型反偏移的输出结果与数值模拟结果相等,提出了一种旨在消除Kirchhoff型反偏移中所出现的振幅畸变现象的高保真反偏移方法。与常规的Kirchhoff型反偏移不同,高保真反偏移是一种与反射面有关的反射地震成像方法。因此,在高保真反偏移中首先要确定反射面的位置,其次要确定振幅畸变因子的数值,最后要根据在反射点上振幅畸变因子恒等于1这一事实进行振幅畸变校正。在具体实施过程中,为了求出反射点的空间位置和振幅畸变因子的具体数值,采用四重加权叠加法,即在一次反偏移运算中同时采用一个单位加权函数和三个非单位加权函数。其中,非单位加权函数由常规的真振幅加权函数和用于建立Kircohhoff型反偏移算子的全局坐标系中的水平坐标组成。通过在四个反偏移场之间进行比值运算,可以达到提取反射点坐标和振幅畸变因子的目的。一旦得到反射点坐标和振幅畸变因子的具体数值,就可以通过简单的除法消除掉振幅畸变因子对反偏移像场振幅的影响。
For making the output of Kirchhoff-type demigration equal to the output of numerical modeling,we present a demigration method called high fidelity demigration,which is able to eliminate the amplitude distortion effect in Kirchhoff-type demigration.Different from the conventional Kirchhoff-type demigration,the high fidelity demigration is reflector-dependent.As a result,in high fidelity demigration we first need to determine the position of the reflector,then to determine the amplitude distortion factor,and finally to correct the demigration amplitude according to the fact that the amplitude distortion factor in demigration is equal to one at a reflection point.In practical implementation of high fidelity demigration,we use four weighting functions in a single weighted isocheone stack,namely the unit weighting function,the conventional true amplitude weighting function,and the two horizontal coordinates of the global coordinate system that is used for establishing the Kirchhoff-type demigration operator.By performing division operations among the four dimigrated images,we can extract the position of the reflection point and the amplitude distortion factor.Once the position of the reflection point and the amplitude distortion factor are obtained,the amplitude distortion effect in demigration can be corrected by a simple division.
For making the output of Kirchhoff-type demigration equal to the output of numerical modeling,we present a demigration method called high fidelity demigration,which is able to eliminate the amplitude distortion effect in Kirchhoff-type demigration.Different from the conventional Kirchhoff-type demigration,the high fidelity demigration is reflector-dependent.As a result,in high fidelity demigration we first need to determine the position of the reflector,then to determine the amplitude distortion factor,and finally to correct the demigration amplitude according to the fact that the amplitude distortion factor in demigration is equal to one at a reflection point.In practical implementation of high fidelity demigration,we use four weighting functions in a single weighted isocheone stack,namely the unit weighting function,the conventional true amplitude weighting function,and the two horizontal coordinates of the global coordinate system that is used for establishing the Kirchhoff-type demigration operator.By performing division operations among the four dimigrated images,we can extract the position of the reflection point and the amplitude distortion factor.Once the position of the reflection point and the amplitude distortion factor are obtained,the amplitude distortion effect in demigration can be corrected by a simple division.
引文
[1]Hubral P,Schleicher J,Tygel M.A Unified Approach to 3-DSeismic Reflection Imaging;Part I,Basic Concepts[J].Geo-physics,1996,61(3):742-758.
[2]Tygel M,Schleicher J,Hubral P.A Unified Approach to 3-DSeismic Reflection Imaging;Part II,Theory[J].Geophysics,1996,61(3):759-775.
[3]Santos L T,Schleicher J,Tygel M,et al.Seismic Modeling byDemigration[J].Geophysics,2000,65(4):1281-1289.
[4]Deregowski S M,Rocca F.Geometrical Optics and Wave The-ory of Constant Offset Sections in Layered Media[J].Geophysical Prospecting,1981,29(3):374-406.
[5]Tygel M,Schleicher J,Hubral P,et al.2.5-D True-amplitudeKirchhoff Migration to Zero Offset in Laterally Inhomoge-neous Media[J].Geophysics,1998,63(2):557-573.
[6]Whitcombe D N.Fast Model Building Using Demigration andSingle-step Ray Migration[J].Geophysics,1994,59(3):439-449.
[7]Ferber R G.Migration to Multiple Offset and Velocity Analy-sis[J].Geophysical Prospecting,1994,42(2):99-112.
[8]孙建国.论三维等时线叠加反偏移中的有关问题[J].吉林大学学报:地球科学版,2002,32(3):273-278.
[9]孙建国.均匀介质中的F-K反偏移:基本概念、基本公式及其在非均匀介质中的应用[J].吉林大学学报:地球科学版,2008,38(1):135-143.
[10]Sun J G.The Stationary Phase Analysis of the Kirchhoff-typeDemigrated Field[J].Applied Geophysics,2010,7(1):18-30.
[11]Tygel M,Schleicher J,Hubral P,et al.Multiple Weights inDiffraction Stack Migration[J].Geophysics,1993,58(12):1820-1830.
[12]Sun J G.True-amplitude Weight Functions in 3D Limited-ap-erture Migration Revisited[J].Geophysics,2004,69(4):1025-1036.
[13]孙建国.Kirchhoff型真振幅偏移与反偏移[J].勘探地球物理进展,2002,25(6):1-5.
[14]Schleicher J,Tygel M,Hubral P.3-D True-amplitude Finite-offset Migration[J].Geophysics,1993,58(8):1112-1126.
[15]Sun J G.Limited-aperture Migration[J].Geophysics,2000,65(2):584-595.
[16]Bleistein N.On the Imaging of Reflectors in the Earth[J].Geophysics,1987,52(7):931-942.
[2]Tygel M,Schleicher J,Hubral P.A Unified Approach to 3-DSeismic Reflection Imaging;Part II,Theory[J].Geophysics,1996,61(3):759-775.
[3]Santos L T,Schleicher J,Tygel M,et al.Seismic Modeling byDemigration[J].Geophysics,2000,65(4):1281-1289.
[4]Deregowski S M,Rocca F.Geometrical Optics and Wave The-ory of Constant Offset Sections in Layered Media[J].Geophysical Prospecting,1981,29(3):374-406.
[5]Tygel M,Schleicher J,Hubral P,et al.2.5-D True-amplitudeKirchhoff Migration to Zero Offset in Laterally Inhomoge-neous Media[J].Geophysics,1998,63(2):557-573.
[6]Whitcombe D N.Fast Model Building Using Demigration andSingle-step Ray Migration[J].Geophysics,1994,59(3):439-449.
[7]Ferber R G.Migration to Multiple Offset and Velocity Analy-sis[J].Geophysical Prospecting,1994,42(2):99-112.
[8]孙建国.论三维等时线叠加反偏移中的有关问题[J].吉林大学学报:地球科学版,2002,32(3):273-278.
[9]孙建国.均匀介质中的F-K反偏移:基本概念、基本公式及其在非均匀介质中的应用[J].吉林大学学报:地球科学版,2008,38(1):135-143.
[10]Sun J G.The Stationary Phase Analysis of the Kirchhoff-typeDemigrated Field[J].Applied Geophysics,2010,7(1):18-30.
[11]Tygel M,Schleicher J,Hubral P,et al.Multiple Weights inDiffraction Stack Migration[J].Geophysics,1993,58(12):1820-1830.
[12]Sun J G.True-amplitude Weight Functions in 3D Limited-ap-erture Migration Revisited[J].Geophysics,2004,69(4):1025-1036.
[13]孙建国.Kirchhoff型真振幅偏移与反偏移[J].勘探地球物理进展,2002,25(6):1-5.
[14]Schleicher J,Tygel M,Hubral P.3-D True-amplitude Finite-offset Migration[J].Geophysics,1993,58(8):1112-1126.
[15]Sun J G.Limited-aperture Migration[J].Geophysics,2000,65(2):584-595.
[16]Bleistein N.On the Imaging of Reflectors in the Earth[J].Geophysics,1987,52(7):931-942.
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