用于地震反射数据偏移的反射波方程
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摘要
与地震数据偏移相对应的正演方程是利用线性反演方法开展有效利用地震数据波形信息的偏移方法研究的基础。由于宏观偏移模型下的波动方程不能描述反射波的反射,因此当前反射数据偏移方法缺乏与之相对应的正演方程。为了满足能有效利用波形信息的高精度偏移成像需要,在高频近似条件下,提出了用于反射数据偏移的反射波方程。在给定宏观偏移模型的前提下,从散射理论中的波动方程出发,依据地震波长与地下散射体大小及其物理性质空间变化快慢之间的相对关系,即在高频近似条件下,局部散射体退化为在空间上具有一定延续度的反射体,散射波退化为具有局部平面波特征的反射波,推导出基于物性参数相对变化的反射波方程。针对反射率在地震反射中的广泛应用,定义物性参数相对变化沿入射波传播方向的方向导数为反射体上反射面的反射率,推导出基于反射率变化的反射波方程。根据地下介质的不同,分别给出了宏观偏移模型下基于物性参数相对变化和反射率变化的标量反射波方程、声反射波方程和弹性反射波方程。
The corresponding forward equation of seismic waveform migration is the basis for the study on migration method using waveform information of seismic data by linear inversion.The conventional wave equation for a smooth macro-model cannot describe a wave reflection:the migration method for reflected data has no corresponding forward equation.Herein,we proposed a set of reflection wave equations under high frequency approximation,which can be applied to high-precision migration imaging of waveform information.The relationship between seismic wave wavelength,the size of an inhomogeneous body,and the spatial variability of the body's physical properties,influenced wave scattering under high frequency approximation:the local scatter tends to degenerate into a reflector with a certain lateral continuity,while a scattered wave degenerates into a reflected wave(with the characteristics of a local plane wave).Based on the scattering wave equation,we proposed a reflection wave equation that considers the relative variations in physical parameters in a macro-model framework:reflectivity was considered to be the directional derivative of the relative variation in physical parameters along the propagation direction of the incident wave.Finally,we proposed three reflection wave equations(scalar,acoustic,and elastic) based on the relative physical parameters and reflectivity variations.These equations depend on the subsurface media and have to be considered in the context of a smooth macro-model.
The corresponding forward equation of seismic waveform migration is the basis for the study on migration method using waveform information of seismic data by linear inversion.The conventional wave equation for a smooth macro-model cannot describe a wave reflection:the migration method for reflected data has no corresponding forward equation.Herein,we proposed a set of reflection wave equations under high frequency approximation,which can be applied to high-precision migration imaging of waveform information.The relationship between seismic wave wavelength,the size of an inhomogeneous body,and the spatial variability of the body's physical properties,influenced wave scattering under high frequency approximation:the local scatter tends to degenerate into a reflector with a certain lateral continuity,while a scattered wave degenerates into a reflected wave(with the characteristics of a local plane wave).Based on the scattering wave equation,we proposed a reflection wave equation that considers the relative variations in physical parameters in a macro-model framework:reflectivity was considered to be the directional derivative of the relative variation in physical parameters along the propagation direction of the incident wave.Finally,we proposed three reflection wave equations(scalar,acoustic,and elastic) based on the relative physical parameters and reflectivity variations.These equations depend on the subsurface media and have to be considered in the context of a smooth macro-model.
引文
[1] YILMAZ O.Seismic data analysis[M].Tulsa:Society of Exploration Geophysics,2001:1-2027
[2] CLAERBOUT J.Toward a unified theory of reflector mapping[J].Geophysics,1971,36(3):467-481
[3] CLAERBOUT J.Fundamentals of geophysical data processing[M].New York:McGraw-Hill Book Co.Inc.,1976:1-274
[4] ETGEN J,GRAY S,ZHANG Y.An overview of depth imaging in exploration geophysics[J].Geophysics,2009,74(6):WCA5-WCA17
[5] LEVEILLE J,JONES I,ZHOU Z,et al.Subsalt imaging for exploration,production,and development:a review[J].Geophysics,2011,76(5):WB3-WB20
[6] GRAY S.True-amplitude seismic migration:a comparison of three approaches[J].Geophysics,1997,62(3):926-936
[7] YAO G,JAKUBOWICZ H.Least-squares reverse time migration[J].Expanded Abstracts of 82nd Annual Internat SEG Mtg,2012:https://doi.org/10.1190/segam2012-1425.1
[8] BLEISTEIN N,COHEN J,STOCKWELL J.Mathematics of multidimensional seismic imaging,migration and inversion[M].New York:Springer Verlag,2001:1-510
[9] ROBERSSON J,BEDNAR B,BLANCH J,et al.Introduction to the supplement on seismic modeling with application to acquisition,processing and interpretation[J].Geophysics,2007,72(5):SM1-SM4
[10] TARANTOLA A.Inverse problem theory:Methods for data fitting and model parameterestimation[M].Philadelphia:Society for Industrial and Applied Mathematics,1987:1-358
[11] VIRIEUX J,OPERTO S.An overview of full-waveform inversion in exploration geophysics[J].Geophysics,2009,74(6):WCC1-WCC26
[12] ZHOU H.Fundamental issues in full waveform inversion[J].Expanded Abstracts of 82nd Annual Internat SEG Mtg,2012:1-5
[13] BLEISTEIN N.On the imaging of reflectors in the earth[J].Geophysics,1987,52(7):931-942
[14] BLEISTEIN N,COHEN J,HAGIN F.Computational and asymptotic aspects of velocity inversion[J].Geophysics,1985,50(3):1253-1265
[15] 陈生昌,周华敏.再论地震数据偏移成像[J].地球物理学报,2016,59(2):643-654CHEN S C,ZHOU H M.Re-exploration to migration of seismic data[J].Chinese Journal of Geophysics,2016,59(2):643-654
[16] 陈生昌,周华敏.基于反射波动方程的叠前地震反射数据波阻抗相对变化成像研究[J].石油物探,2017,56(5):651-657CHEN S C,ZHOU H M.A relative impedance variation imaging of pre-stack seismic reflection data based on reflection wave equation[J].Geophysical Prospecting for Petroleum,2017,56(5):651-657
[17] 陈生昌,周华敏.地震数据的反射波动方程最小二乘偏移[J].地球物理学报,2018,61(4):1413-1420CHEN S C,ZHOU H M.Least squares migration of seismic data with reflection wave equation[J].Chinese Journal of Geophysics,2018,61(4):1413-1420
[18] 陈生昌.基于反射波动方程的地震反射数据波形成像[J].石油地球物理勘探,2018,53(3):487-501CHEN S C.Seismic reflection data waveform imaging based on reflection wave equation[J].Oil Geophysical Prospecting,2018,53(3):487-501
[19] 陈生昌.基于地震波方程的地震数据波形偏移与最小二乘波形偏移方法[J].石油物探,2018,57(5):637-646CHEN S C.Waveform migration and least-squares waveform migration of seismic data based on seismic wave equation[J].Geophysical Prospecting for Petroleum,2018,57(5):637-646
[20] AKI K,RICHARDS P.Quantitative seismology[M].2nd ed.Sausalito,California:University Science Books,2002:1-704
[21] GOODMAN J.Introduction to Fourier optics[M].3rd ed.New York:W.H.Freeman and Company,2005:1-491
[22] STOLT R,WEGLEIN B.Seismic imaging and inversion:application of linear inverse theory[M].New York:Cambridge University Press,2012:1-416
[23] SYMES W,KERN M.Inversion of reflection seismograms by differential semblance analysis:algorithm structure and synthetic examples[J].Geophysical Prospecting,1994,42(3):565-614
[24] BLEISTEIN N,ZHANG Y,XU S,et al.Migration/inversion:think image point coordinates,process in acquisition surface coordinates[J].Inverse Problem,2005,21(5):1715-1740
[25] BEKLKIN G,BURRIDGE R.Linearized inverse scattering problems in acoustics and elasticity[J]Wave Motion,1990,12(1):15-52
[2] CLAERBOUT J.Toward a unified theory of reflector mapping[J].Geophysics,1971,36(3):467-481
[3] CLAERBOUT J.Fundamentals of geophysical data processing[M].New York:McGraw-Hill Book Co.Inc.,1976:1-274
[4] ETGEN J,GRAY S,ZHANG Y.An overview of depth imaging in exploration geophysics[J].Geophysics,2009,74(6):WCA5-WCA17
[5] LEVEILLE J,JONES I,ZHOU Z,et al.Subsalt imaging for exploration,production,and development:a review[J].Geophysics,2011,76(5):WB3-WB20
[6] GRAY S.True-amplitude seismic migration:a comparison of three approaches[J].Geophysics,1997,62(3):926-936
[7] YAO G,JAKUBOWICZ H.Least-squares reverse time migration[J].Expanded Abstracts of 82nd Annual Internat SEG Mtg,2012:https://doi.org/10.1190/segam2012-1425.1
[8] BLEISTEIN N,COHEN J,STOCKWELL J.Mathematics of multidimensional seismic imaging,migration and inversion[M].New York:Springer Verlag,2001:1-510
[9] ROBERSSON J,BEDNAR B,BLANCH J,et al.Introduction to the supplement on seismic modeling with application to acquisition,processing and interpretation[J].Geophysics,2007,72(5):SM1-SM4
[10] TARANTOLA A.Inverse problem theory:Methods for data fitting and model parameterestimation[M].Philadelphia:Society for Industrial and Applied Mathematics,1987:1-358
[11] VIRIEUX J,OPERTO S.An overview of full-waveform inversion in exploration geophysics[J].Geophysics,2009,74(6):WCC1-WCC26
[12] ZHOU H.Fundamental issues in full waveform inversion[J].Expanded Abstracts of 82nd Annual Internat SEG Mtg,2012:1-5
[13] BLEISTEIN N.On the imaging of reflectors in the earth[J].Geophysics,1987,52(7):931-942
[14] BLEISTEIN N,COHEN J,HAGIN F.Computational and asymptotic aspects of velocity inversion[J].Geophysics,1985,50(3):1253-1265
[15] 陈生昌,周华敏.再论地震数据偏移成像[J].地球物理学报,2016,59(2):643-654CHEN S C,ZHOU H M.Re-exploration to migration of seismic data[J].Chinese Journal of Geophysics,2016,59(2):643-654
[16] 陈生昌,周华敏.基于反射波动方程的叠前地震反射数据波阻抗相对变化成像研究[J].石油物探,2017,56(5):651-657CHEN S C,ZHOU H M.A relative impedance variation imaging of pre-stack seismic reflection data based on reflection wave equation[J].Geophysical Prospecting for Petroleum,2017,56(5):651-657
[17] 陈生昌,周华敏.地震数据的反射波动方程最小二乘偏移[J].地球物理学报,2018,61(4):1413-1420CHEN S C,ZHOU H M.Least squares migration of seismic data with reflection wave equation[J].Chinese Journal of Geophysics,2018,61(4):1413-1420
[18] 陈生昌.基于反射波动方程的地震反射数据波形成像[J].石油地球物理勘探,2018,53(3):487-501CHEN S C.Seismic reflection data waveform imaging based on reflection wave equation[J].Oil Geophysical Prospecting,2018,53(3):487-501
[19] 陈生昌.基于地震波方程的地震数据波形偏移与最小二乘波形偏移方法[J].石油物探,2018,57(5):637-646CHEN S C.Waveform migration and least-squares waveform migration of seismic data based on seismic wave equation[J].Geophysical Prospecting for Petroleum,2018,57(5):637-646
[20] AKI K,RICHARDS P.Quantitative seismology[M].2nd ed.Sausalito,California:University Science Books,2002:1-704
[21] GOODMAN J.Introduction to Fourier optics[M].3rd ed.New York:W.H.Freeman and Company,2005:1-491
[22] STOLT R,WEGLEIN B.Seismic imaging and inversion:application of linear inverse theory[M].New York:Cambridge University Press,2012:1-416
[23] SYMES W,KERN M.Inversion of reflection seismograms by differential semblance analysis:algorithm structure and synthetic examples[J].Geophysical Prospecting,1994,42(3):565-614
[24] BLEISTEIN N,ZHANG Y,XU S,et al.Migration/inversion:think image point coordinates,process in acquisition surface coordinates[J].Inverse Problem,2005,21(5):1715-1740
[25] BEKLKIN G,BURRIDGE R.Linearized inverse scattering problems in acoustics and elasticity[J]Wave Motion,1990,12(1):15-52